m.sc. in electronics engineering · 2017-10-10 · ¾ thanks to engg. victor of general...

JALL i

NOVEL COMPACT MICROSTRIP

BANDSTOP FILTERS AT MICROWAVE FREQUENCIES

By

ENG.TEJINDER KAUR

A DISSERTATION SUBMITTED TO PROGRAM IN ELECTRONICS DEPARTMENT IN PARTIAL

FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF

M.SC. IN ELECTRONICS ENGINEERING

At the

NATIONAL INSTITUTE FOR ASTROPHYSICS, OPTICS AND ELECTRONICS

TONANTZINTLA, PUEBLA

JULY 2007

Advisors:

DR. ALONSO CORONA CHAVEZ (GTM) DR. IGNACIO ENRIQUE ZALDIVAR HUERTA (INAOE)

©INAOE 2007

TONANTZINTLA, PUEBLA.

ALL RIGTHS RESERVED THE AUTOR HEREBY GRANTS TO INAOE PERMISSION TO REPRODUCE AND TO

DISTRIBUYE COPIES OF THIS THESIS DOCUMENT IN WHOLE OR IN PART .

i

Microwave Filters are essential components in the communications industry and are

fundamental elements in wireless and satellite technology. The need of filters has

become more apparent as spectrum crowding increases with the development of new

systems. In this thesis, novel compact microstrip resonators and bandstop filters

configuration have been proposed for narrow band applications such as, wireless

communication and satellite systems at 1.5 GHz and 10 GHz.

At 1.5 GHz, several novel microstrip resonators have been proposed and at this

frequency successfully obtained the ultra compact size of the resonator from

conventional resonator. At this frequency, Chebyshev bandstop filters have been

designed using proposed resonators and experimentally measured. The first filter

consists of a 3 pole Chebyshev bandstop filter at 1.5 GHz using T-shape straight

resonators. The second type of structure is 3 poles Chebyshev bandstop filter using ultra

compact meandered T-shape resonators.

Also at 1.5GHz a novel Trisection bandstop filter with an extra transmission zero have

been proposed with narrow bandwidth, this work is unique as this topic is not known to

have been presented anywhere else in the review literature.

At 10 GHz novel compact high-Q (quality factor) microstrip resonators have been

explored with application such as wireless and satellite communication. These

resonators use micromachining technology to remove selective parts of the substrate to

increase the quality factor and hence filter performance. Also, miniaturization techniques

were applied to decrease the overall resonator size. The full design procedure and

simulation results are presented of several resonators and Chebyshev filter, along with

experimental results of fabricated resonators on HR-Si.

ii

Los filtros de microondas son dispositivos de suma importancia en la industria de las

telecomunicaciones. La necesidad de filtros ha llegado a ser más aparente como

espectro que llena los aumentos con el desarrollo de nuevos sistemas. En este trabajo

de tesis, se presenta el diseño y fabricación de filtros de banda angosta utilizando

estructuras de microcinta con aplicaciones a 1.5 GHz y 10 GHz. Los filtros aquí

presentados tienen aplicaciones potenciales en los sistemas de comunicación

inalámbrica y satelital.

Para una frecuencia de 1.5 GHz se han propuesto varios resonadores de tipo

microcinta. En esta frecuencia se obtuvo con éxito un tamaño ultra compacto de un

resonador convencional. Asimismo se diseñan y fabrican dos filtros rechaza-banda de

banda angosta tipo Chebyshev de tres polos utilizando estructuras del tipo microcinta.

El primer filtro se diseña y fabrica en base a resonadores en forma de T. El segundo

filtro se diseña y fabrica mediante la utilización de resonadores en forma serpenteada.

Se presenta también el diseño de un filtro tipo Triplet rechaza-banda de banda angosta,

el cual es un diseño único en su tipo y no reportado aún en la literatura.

Finalmente, se describe de manera detallada el diseño y fabricación de un filtro

rechaza-banda del tipo Chebyshev con un alto factor de calidad (Q) para la frecuencia

de 10 GHz. Esta estructura se fabrica en un substrato de silicio de alta resistividad (HR-

Si), y mediante el uso de técnicas de micro-maquinado se realiza un proceso selectivo

de grabado del substrato lo cual permite incrementar el factor de calidad así como

mejorar los parámetros del filtro.

iii

This thesis work has been done in two year course of master’s in Electronics. I would

like to thank my parents, Sqn. Ld. (Retd.) Mr. B.S Kataria and Mrs. Mohinder Kaur,

my brother Mr. Karanveer Singh and sisters and my jijus; Mrs. Narinder Kaur, Mrs.

Parminder Kaur, Miss Harpreet Kaur, Mr. Ranjit Singh and Mr. Ranjeet Singh, for

there complete support during this period of my study. I am grateful to my Assessor Dr.

Alonso Corona Chávez for his supervision and for his full support during master’s

course, which result in finishing this incredible thesis work in time. I am also thankful to

my Co-Assessor Dr. Ignacio Enrique Zaldivar Huerta for his help and assist in this

work. I want to thank to the Ministry of Foreign Affairs of Mexico and INAOE for

sponsoring my master’s course.

Special gratitude for following persons who helped me a lot during these two years of

master’s course:

The team of Microelectronics and MEMS laboratory of INAOE to support in

fabricating proposed device and Mechanical department (INAOE) for their help.

Thanks to my professor Dr. Ignacio Llamas for his help and support Thanks to Engg. Victor of General Administration Department of Computers who

helped me in maintaining my computer. Special thank to my very special friend David Chillon (bachas) for his help and

full support during hard and good time and also in translating resume into

Spanish.

iv

ABSTRACT (ENGLISH AND SPANISH)……………………………………………………i-ii

ACKNOWLEDGMENT…………………………………………………………………………iii

PREFACE…………………………………………………………………………………….… ix

CHAPTER 1: BASIC MICROWAVE THEORY

1.1 INTRODUCTION ............................................................................................ 1

1.2 TRANSMISSION LINE THEORY............................................................4

1.2.1 TRANSMISSION LINE EQUATIONS…………………………………....4

1.2.2 TYPES OF TRANSMISSION LINES……………………..……………. 8

1.2.3 MICROSTRIP LINE………………........................................................9

1.2.4 COPLANAR WAVEGUIDE…………………………………………..…13

1.3 THE SCATTERING PARAMETERS (S-PARAMETER)........................ .14

1.4 VECTOR NETWORK ANALYZER (VNA)……………………..……..….19

REFERENCES………………………………….……..……………………………20 CHAPTER 2: THEORY OF MICROWAVE FILTER DESIGN

2.1 BASIC INTRODUCTION TO MICROWAVE RESONATORS………..…….....22

2.1.1 BASIC PROPERTIES OF SERIES RLC RESONANT CIRCUIT…….24

2.1.2 BASIC PROPERTIES OF PARALLEL RLC RESONANT CIRCUIT...26

2.1.3 QUALITY FACTOR (Q)………….......................................................28

2.2 GENERAL FILTER DESIGN...................................................................…...31

v

2.2.1 TRANSFER FUNCTIONS…………………………………………….….31

2.2.2 LOWPASS PROTOTYPE FILTERS AND ELEMENTS……………….36

2.2.3 FREQUENCY AND ELEMENTS TRANSFORMATION….................38

2.2.4 IMMITTANCE INVERTERS………………………………….................43

REFERENCES…………….………….…………………………….………………........ 47 CHAPTER 3: LITERATURE REVIEW OF MICROWAVE FILTERS

3.1 MICROMACHINED MICROWAVE FILTERS...................... ………..…….....50

3.1.1 MEMBRAN SUPPORTED FILTERS……………...…………………….50

3.2 BANDSTOP FILTERS……………...................................................................54

3.2.1 L-RESONATOR BANDSTOP FILTER…...………………………….….55

3.2.2 MICROMACHINED BANDSTOP FILTER………………………..…….57

3.2.3 HIGH Tc SUPERCONDUCTING BANDSTOP FILTER

FOR RADIO ASTRONOMY FRONT ENDS…….………………………59

3.2.4 A SUPERCONDUCTING MICROSTRIP BANDSTOP

FILTERS FOR AN L-BAND RADIO TELESCOP RECEIVER............61

3.3 QUASI ELLIPTIC FILTERS.............…............................................................63

3.3.1 HIGH PERFORMANCE HTS PESUDO-ELLIPTIC

BANDSTOP FILTER........................................................…………....63 REFERENCES…………...……………………………………….………………66

CHAPTER 4: DESIGNING OF RESONATORS AND 3-POLE CHEBYSHEV BANDSTOP FILTERS AT1.5 GHz AND10 GHz

4.1 ELECTROMAGNETIC (EM) SIMULATOR ................................................... 70

4.2 MICROSTRIP RESONATORS AT 1.5GHz....................................................71

vi

4.2.1 MICROSTRIP RESONATOR (λ/2) ……………………………………..71

4.2.2 INTERDIGITAL T-SHAPE STRAIGHT RESONATOR ……….….….74

4.2.3 NOVEL ULTRA COMPACT INTERDIGITAL

MEANDERED RESONATOR …………………………….………...……75 4.3 3-POLE CHEBYSHEV BANDSTOP FILTER ON DUROID SUBSTRATE AT

1.5GHz................................................……………………………………….....79

4.3.1 3-POLE CHEBYSHEV BANDSTOP FILTER USING INTERDIGITAL T-SHAPE STRAIGHT RESONATORS…………….…………….…….80

4.3.2 3-POLE CHEBYSHEV BANDSTOP FILTER USING ULTRA

COMAPCT INTERDIGITAL MEANDERED RESONATORS ..…….86 4.4 MICROSTRIP RESONATORS AT 10 5GHz.......................................................90

4.4.1 MICROSTRIP CONVENTIONAL λ/2 ..RESONATOR.……..….……92

4.4.2. MICROSTRIP PATCH RESONATORS………………...……….…….94 4.4.3 MICROSTRIP PATCH RESONATORS WITH AIR WINDOW.….. .…96

4.5 3 POLE CHEBYSHEV BANDSTOP FILTER ON HR-SI SUBSTRATE AT 10 GHz……………………………………………………………………………101 4.6 DESIGNING OF COPLANAR WAVEGUIDE (50Ω) ………...……….….……….105

REFERENCES………….……………………………………….… ……………...………..109 CHAPTER 5: DESIGNING OF TRIPLET BANDSTOP FILTER AT 1.5GHz

5.1 FILTERS WITH SINGLE PAIR OF TRANSMISSION ZERO (QUASI ELLIPTIC RESPONSE)………………………………………...……………..112

5.1.1 APPROXIMATION SYNTHESIS PROCESS OF QUASI- ELLIPTIC…………………………………………………………..…..113

5.2 TRISECTION FILTERS………………………………….………………………….116

5.2.1 MICROSTRIP TRISECTION FILTERS……………………………….118 5.3 DESIGNING PROCEDURE OF NOVEL TRISECTION BANDSTOP FILTER AT

1.5 GHz………………………………………………………………………………..119

vii

REFERENCES…………………………..……………...…………………………………..140 CHAPTER 6: FABRICATION PROCESS OF MICROMACHINED FILTERS

6.1 MASK……………………………………………………..……………………………141 6.2 TYPES OF ETCHING TECHNIQUES……………………………………………..145

6.2.1 CAVITY DIMENSIO…………………………...………………………..147

6.3 FABRICATION PROCESS………………………………………………………….148

6.3.1 EXPERIMENT- I: LITHOGRAPHIC PROCESS USING SiO2 LAYER ON SILICON AS SUPPORTIVE LAYER…………………………….150

6.3.2 EXPERIMENT-II: LITHOGRAPHIC PROCESS USING SiO2, SILICON

NITRIDE(SiH4+NH3)ON SILICON AS SUPPORTIVE SUBSTRATE………………...…………………………..159

REFERENCES……………………………………………………….…………..…………..166

CHAPTER 7: EXPERIMENTAL RESULTS

7.1 EXPERIMENTAL RESULTS OF CHEBYSHEV BANDSTOP FILTERS AT 1.5 GHz…………………………………………………………….……………167

7.1.1 3 POLE CHEBYSHEV BANDSTOP FILTER AT1.5GHz USING INTERDIGITAL T-SHAPE STRAIGHT RESONATORS ON DUROID SUBSTRATE………………………………………………………….…168

7.1.2 3 POLE CHEBYSHEV BANDSTOP FILTER USING ULTRA COMPACT INTERDIGITAL MEANDERED RESONATORS AT 1.5GHz…..….173

7.2 TRIPSECTION BANDSTOP FILTER WITH AN EXTRA TRANSMISSION ZERO

USING ULTRA COMPACTINTERDIGITAL MEANDERED RESONATORS

AT 1.5GHz…………………………………………………………………………….178

7.3 INTERDIGITAL T- SHAPE PATCH RESONATOR ON SILICON SUBSTRATE AT 10GHZ …………………………………………….………………………………….183

viii

CHAPTER 8: CONCLUSION AND FUTURE WORK

8.1 CONCLUSION……………………………………………………………….…………186 8.2 FUTURE WORK ……………………………………………………….…..………….189 APPENDIX-I…………………………………………………………………..……………….190 APPENDIX-II……………………………………………………………………..……………192 LIST OF FIGURES……………………………………………………………………………194 LIST OF TABLES…………………………………………………………………...…..…..203 PUBLICATIONS………………………………………………………………………………205

ix

Filters are essential components in the communications industry and are

fundamental elements in wireless and satellite technology. There is constant

need for microwave filters with higher selectivity and lower losses filters in

communication systems as spectrum crowding increases with the development

of new systems. Further, subsystems miniaturization may require high

performance filters to occupy the same packages as high frequency integrated

circuits or least employ packages that are similar and handled the same way in

production. Microwave and millimeter-wave circuits as well as modules are

based on planar technologies using microstrip lines, coplanar waveguide or finite

ground coplanar waveguides since they provide compact, light weight and low

loss solutions, and are combined using wide variety of interconnects such as via

holes, and air bridges. Silicon micromachining technology has been used to build

low-loss lumped elements, filters, resonators and couplers. Currently, Radio

Frequency Micro Electronics Mechanical System (RF-MEMS) has been an

attractive field for both science research and industry due to its promising

application in future civil and military wireless communication and remote

controlling and sensing systems. RF-MEMS implicates that the devices and

structures realized via microsystem technologies, or RF-MEMS are technology

used for fabrication of miniaturized RF and Microwave device.

Bandstop filters are used to reject unwanted frequencies; the Chebyshev

bandstop filters proposed in this thesis have applications in radio astronomy,

satellite communications, mobile base stations as multiplexers and diplexer to

separate transmitted and received signals, front-end filters that protect receivers

from adjacent channel interference and output filters that limit the bandwidth of

transmitter noise.

x

Filters can be configured as Chebyshev, Butterworth, Quasi-Elliptic, cascaded

quadruplets, Trisection with extra transmission zero. In the literature, extensive

work has been found on Bandstop filters with Chebyshev and Quasi-Elliptic

configuration but no work was found on Trisection Bandstop filters; which makes

the proposal of a novel configuration of Bandstop Trisection filter with extra

transmission zero in this thesis highly valuable and propositive. For applications

where very steep cutoffs are needed on only one side of the reject band,

Trisection Bandstop filters are ideal candidates as they required only three

resonators, for such response. As apposed to Quasi-Elliptic filter which would

require many poles to obtain the higher selectivity needed. To have both sides

with high selectivity, two Trisection bandstop filters can be cascaded.

Applications for Trisection filters can be found in Multiplexers to separate

transmitted signals from received signals at mobile base station, satellite

communication systems and radio telescope.

At millimeter wave frequencies, membrane support high filters play an important

role in high performance systems. At higher frequencies (above 30GHz) the size

of the filters reduces due to which it becomes feasible to support thin silicon

membranes (1-2µm thick). But at lower frequencies (< 30GHz) the size of the

filters would be too large and becomes mechanically impossible to support them

on silicon membranes. Thus, in this thesis a novel way to achieve high Q filters

and mechanical strength is proposed by partially removing selective parts of the

silicon substrate. This work is novel as there is no work found in literature review

with selective removal of substrate to increase Q and also to obtain compact

structure of the resonator.

In this thesis work on novel designs of microstrip resonators and bandstop filters

at L and X band are shown. It includes all experimental and simulation results

and also the complete fabrication process of the filter at X band using

xi

Micromachining technology. At L band the central frequency selected is 1.5 GHz

and at X band is 10GHz. This thesis is divided into nine chapters:

First chapter presents the basic review of microwave theory, its applications and

microwave engineering.

Second chapter, explains general designing theory of microwave filters which

are going to be used in designing of proposed filters in chapter 4 and 5.

Third chapter presents literature review of the work done related to microwave

filters using different technologies of fabrication.

Fourth chapter describes the designing procedure of novel resonators and

Chebyshev bandstop filters at 1.5GHz and 10GHz along with the simulation

results. At 10GHz compact resonators with selective removal of the silicon

substrate using micromachining technology are proposed.

Chapter fifth shows the designing of advanced filter topologies using trisections

with a single transmission zero.

Chapter sixth presents the detailed micromachining fabrication procedure for

the device at 10GHz,

Chapter seventh gives experimental results of all the proposed filters at 1.5GHz

and resonator at 10GHz.

Chapter eight illustrates the conclusion of all the experimental and simulation

results obtained. And gives details related to the work proposed for future.

CHAPTER 1: BASIC MICROWAVE THEORY 1

1.1 INTRODUCTION In this chapter, brief description of basic microwave theory is presented. The

main objective of this introduction is to revise the basic aspects of microwave

applications, microwave engineering, transmission line theory and the

important parameter (S-Parameter) to measure the performance of the

resonators and filters in terms of Q value and bandwidth.

The range of the electromagnetic spectrum from 300 MHz to 300 GHz is

commonly referred to as the microwave range. Microwave signals with

wavelength of millimeters are called millimeter waves.

The RF/ Microwave have applications in following areas:

Communication

Radar

Navigation

Radio astronomy

Sensing

Medical instrumentation

To recall the spectrum of microwave signals and its applications, Figure 1.1

presents the electromagnetic spectrum with some applications.


Figure 1.1: Electromagnetic Spectrum (Taken from © 2005 SURA www.sura.org Copyrighted

images used with permission. Rev2C 6-June-2005)

The standard radar frequency letter-band nomenclature according to IEEE

Standard 521-1984 is shown in table1.1. From this table its clear which range

of frequency belongs to which respective band. Microwave technology has

been used extensively by the broadcast and cable television industries, as

well as in other telecommunications applications, since the early 1950’s.

http://www.sura.org/


Band

Designator

Frequency

(GHz)

Wavelength

in Free Space

(cm)

L band 1 to 2 30.0 to 15.0

S band 2 to 4 15 to 7.5

C band 4 to 8 7.5 to 3.8

X band 8 to 12 3.8 to 2.5

Ku band 12 to 18 2.5 to 1.7

K band 18 to 27 1.7 to 1.1

Ka band 27 to 40 1.1 to 0.75

V band 40 to 75 0.75 to 0.40

W band 75 to 110 0.40 to 0.27

AM Broadcast

Band

535-1605

kHz

Shortwave

radio

3-30MHz

FM Broadcast

band

88-108MHz

VHF TV (2-4) 54-72 MHz

UHF TV (5-6) 76-88MHz

UHF TV (7-

13)

174-216

MHz

UHF TV (14-

83)

470-

890MHz

Microwave

ovens

2.45GHz

(a) Standard Radar Frequency Letter-Band

Nomenclature (IEEE Standard 521-1984)

(b) Typical Frequencies

Table 1.1: (a) Standard Radar Frequency Letter-Band Nomenclature (IEEE Standard 521-

1984), (b) Typical Frequencies

For applications with wavelengths from 1m to 1mm, low frequency circuit

analysis techniques can not be used and for that transmission-line theory is

used. In transmission-line theory, the voltage and current along a

transmission line can vary in magnitude and phase as a function of position

which is discussed in next section.


1.2 TRANSMISSION LINE THEORY

The uniform two-conductor transmission line is an essential element in the

realization of many transmission line circuits. In transmission-line theory, the

voltage and current along a transmission line can vary in magnitude and

phase as a function of position. Many different types of microwave

transmission lines have been developed over the years. In an evolutionary

sequence from rigid rectangular and circular waveguide, to flexible coaxial

cable, to planar stripline to microstrip line, microwave transmission lines have

been reduced in size and complexity.

1.2.1 TRANSMISSION LINE EQUATIONS

A transmission line can be approximated by a distributed-parameter network

with the circuit parameters distributed throughout the line, transmission line

always have at least two conductors. The current flowing in the two-wire line

and the potential difference between the two conductors is function of

distance z and time t. Figure 1.2(a) shows the voltage and current definition

of transmission line of short length Δ z and the effect of a short length of the

line Δ z is depicted in Figure 1.2(b).

The series impedance and shunt admittance per unit length of this line are

given by equation (1-1) and (1-2), respectively.

LjRZ ω+= (1-1)

CjGY ω+= (1-2)

Where,


♦ R is the resistance in both conductors per unit length in Ω /m

♦ L is the inductance in both conductors per unit length in H/m

♦ G is the conductance of the dielectric media per unit length in S/m

♦ C is the capacitance between the conductors per unit length F/m

(a) Voltage and current definition (b) Lumped element equivalent circuit

Figure 1.2: Voltage and current definition and Equivalent circuit of an element of a

transmission line with a length of Δ z (a) Voltage and current definition, (b) Lumped element

equivalent circuit.

The potential drop across a section of line of length Δ z is given by equation

(1-3):

zz ILjR

dzdV )( ω+−= (1-3)

The current across the same section is given in equation (1-4):

zz VCjG

dzdI )( ω+−= (1-4)


The negative signs in equations (1-4) signify that both the voltage and current

on the line decrease with increasing z [1].

The propagation constant of the line is given by equation (1-5)

ZY=γ (1-5)

Equation (1-5) is usually written in terms of its real and imaginary parts as:

( )( )CjGLjRj ωωβαγ ++=+= (1-6)

Where, α = attenuation constant of the line per unit length (Nepers /meter)

β = phase constant per unit length (radians / meter)

At very high frequency or for transmission lines with very small losses:

Rlj >>ω (1-7)

GCj <<ω (1-8)

And α and β approximated by:

0=α (1-9)

LCωβ = (1-10)


From linear combination of forward and backward traveling waves as shown

in Figure 1.3, the wave equation is given by equation (1-11) and (1-12)

describing Vz and Iz

zzz BeAeV γγ += − (1-11)

( )zz

oz BeAe

ZI γγ −= −1 (1-12)

Where, Z o = Characteristic impedance of the line:

YZZ o = (1-13)

If equation (1-7) and (1-8) satisfies, then characteristic impedance is given by

equation (1-14) [3]:

CLZ o = (1-14)


Figure 1.3: Diagram of transmission line with load showing incident, reflected-transmitted

waves.

1.2.2 TYPES OF TRANSMISSION LINES

Many different types of microwave transmission lines have been developed

over the years. In an evolutionary sequence from rigid rectangular and

circular waveguide, to flexible coaxial cable, to planar stripline to microstrip

line, microwave transmission lines have been reduced in size and complexity.

The microstrip transmission line is the technology employed in the current

hyperthermia applicator studied.

Types of transmission lines are shown in Figure 1-4. Parallel plate, Coaxial

and Strip lines are examples of homogeneous dielectric and have pure TEM

mode and microstrip line is example of inhomogeneous dielectric Quasi-TEM

mode.


Figure 1-4: Types of Transmission Lines

1.2.3 MICROSTRIP LINE

Some relations specific to microstrip will now be discussed here. Microstrip

line is one of the trendiest planar transmission lines, the main advantages of

microstrip lines are:

♦ It can be fabricated by photolithographic process

♦ It is easily integrated with other passive and active microwave devices.


(a) The general geometry of a Microstrip line.

(b) Electric and magnetic field lines

Figure 1-5: (a) the general geometry of a Microstrip line, (b) Electric and magnetic field lines

The geometry of a typical microstrip line can be seen in Figure 1-5(a). A

conductor of width (W) with thickness (t) is printed on a thin, grounded

dielectric substrate of thickness d and relative permittivity (εr); the field lines

are shown in Figure 1-5(b).


CHARACTERISTICS OF MICROSTRIP

a) DC as well as AC signals may be transmitted.

b) Active devices, diodes and transistors may readily be incorporated (shunt

connections are also quite easily made).

c) In –circuit characterization of devices is straightforward to implement.

d) Line wavelength is reduced considerably from its free space value,

because of the substrates high εr. Hence, distributed component

dimensions are relatively small.

e) The structure is quite rugged and can withstand moderately high voltages

and power level.

Microstrip involves an abrupt dielectric interface between the substrate and

the air above it. Any transmission line that is filled with a uniform dielectric can

support a single, well- defined mode of propagation, at least over a specified

range of frequency (TEM for coaxial lines, TE for waveguides, etc.)

Transmission lines that do not have such a uniform dielectric filling cannot

support a single mode of propagation; microstrip is within this category.

Although this is true the bulk of energy is transmitted along microstrip with a

field distribution which is quite closely resembles TEM; it is usually referred to

as Quasi-TEM [4]. i.e., the speed of light (c) is different in air and dielectric the

boundary-value conditions at the air-dielectric interface can not be met with a

pure TEM wave and the exact fields constitute a hybrid TM-TE wave.

Because the dielectric substrate is electrically very thin ( )λ<<d , for this

application, the fields are quasi-TEM. Because the fields are quasi-TEM,

good approximations for the phase velocity, propagation constant and

characteristic impedance can be obtained from the static solution.


The phase velocity in microstrip line is given by equation (1-15):

r

cvε

= (1-15)

And the propagation constant is given by equation (1-16):

eooreok εεμμωεβ == (1-16)

Where, eε is the effective dielectric constant and is given by:

⎟⎟⎠

⎞⎜⎜⎝

⎛+

−+

+=

Wdrr

e /1211

21

21 εε

ε (1-17)

The effective dielectric constant eε is the dielectric constant of an equivalent

homogenous medium that replaces the air and dielectric layers.

The characteristic impedance of a microstrip line can be calculated using

equation (1-18), when width W and substrate thickness d are known

( )[ ] ⎪⎪⎭

⎪⎪⎬

⎫

≥

≤

⎪⎪⎩

⎪⎪⎨

⎧

+++

⎟⎠⎞

⎜⎝⎛ +

=

1/

1/

444.1/ln667.0393.1/120

48ln60

dforW

dforW

dWdW

dW

Wd

Z

e

ro

επ

ε (1-18)

If all microstrip based circuits consisted of a proper width straight feed line

terminating in a load, there would not be much need to worry about

compensating for discontinuities. Even in this ideal case, the transition from


microwave source to microstrip line and from the microstrip to load can be the

source of large reflections. Typical microstrip discontinuities are junctions,

bends, step changes in width and the coaxial cable to microstrip junction. If

these discontinuities are not compensated, they introduce parasitic reactance

that can lead to phase and amplitude errors, input and output mismatch, and

possibly spurious coupling. The strength of a particular discontinuity is

frequency dependent, where the higher the frequency, the larger is the

discontinuity [1].

1.2.4 COPLANAR WAVEGUIDE

Coplanar waveguide can be thought of as slotline with third conductor

centered in the slot region. Coplanar waveguide consists of a centre strip with

two ground planes located parallel to and in the plane of the strip. Figure 1-

6(a) depicts the schematic diagram of this transmission line (coplanar

waveguide) and Figure 1-6(b) shows the electric and magnetic fields in the

quasi- static situation.

Because of the presence of additional conductor, this type of structures can

support even or odd quasi-TEM modes, depending on whether the E-fields in

the two slots are in the opposite direction, or the same direction. Coplanar

waveguide is particularly useful for fabricating active circuitry, due to the

presence of the center conductor and close proximity of ground planes [3].


(a) Schematic diagram of coplanar waveguide

(b) Field patterns in coplanar waveguide

Figure 1-6: (a) Schematic diagram of coplanar waveguide, (b) Field patterns in coplanar

waveguide

1.3 THE SCATTERING PARAMETERS (S-PARAMETER)

S-parameters are important in microwave design because they are easier to

measure and to work at high frequencies than other kinds of two port

parameters. They are conceptually simple, analytically convenient and

capable of providing detailed insight into a measurement and modeling

problem. However, it must be kept in mind that, like all other two port


parameters, S-parameters are linear by default i.e., they represent the linear

behavior of the two ports [1].The following signal flow graph in two port

network in Figure 1.7, gives the situation for the S-parameter interpretation in

voltages.

Figure 1.7: Signal flow graph in two port network

Looking at the S-parameter coefficients individually from Figure 1.7, we have:

021_

1__

1

111 === a

VV

abS

porttowards

portatreflected

(1-19a)

021_

2__

1

221 === a

VV

abS

porttowards

portatreflected

(1-19b)

012_

1__

2

112 === a

VV

abS

porttowards

portatreflected

(1-19c)


012_

2__

2

222 === a

VV

abS

porttowards

portatreflected

(1-19d)

Where, the wave variables , and , are recognized as normalized

versions of forward and backward traveling waves and Z

1a 1b 2a 2b

0 is the input

impedance.

The S11 and S22 are also called the reflection coefficients, whereas S12 and

S21 the transmission coefficients. These are the parameters directly

measurable at microwave frequencies.

an = 0 implies a perfect impedance match (no reflection from terminal

impedance) at port n. These definitions can be expressed in term of a matrix

as:

⎥⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡=⎥

⎦

⎤⎢⎣

⎡

2

1

22

12

21

11

2

1

aa

SS

SS

bb

(1-20)

Where the matrix containing the S parameters is referred to as the

scattering matrix or S- matrix.

The S parameters are in general complex, and it is convenient to express

them in amplitude and phase, i. e,

mnjmnmn eSS Φ= (1-21)

Their amplitude is given in decibels (dB), which are defined as:

mnSlog20 dB m, n = 1, 2 (1-22)


Where, the logarithm operation is base 10. For characterizations, two

parameters are important:

LA = - mnSlog20 dB m, n = 1,2(m n) (1-23) ≠

LR = - mnSlog20 dB m=n = 1,2 (1-24)

Where, LA = Insertion loss between ports n and m.

LR = Return loss at ports n.

Instead of using the return loss, the voltage standing wave ration (VSWR)

may be used. The VSWR is defined as:

nn

nn

SS

VSWR−

+=

11

(1-25)

Whenever a signal is transmitted through a frequency – selective network

such as a filter, some delay is introduced into the output signal in relation to

the input signal. There are other two parameters that play role in

characterizing filter performance related to this delay.

1) PHASE DELAY: ω

τ 21Φ=p sec (1-26)

2) GROUP DELAY: ω

τd

dd

21Φ= sec (1-27)

♦ PHASE DELAY: the time delay for steady sinusoidal signal and is not

necessarily the true signal delay because a steady sinusoidal signal


does not carry information; and is sometimes also called as Carrier

delay.

♦ GROUP DELAY: This represents the true signal (baseband signal)

delay, and is also referred to as Envelop delay.

In network analysis or synthesis, the reflection parameter S11 is expressed in

terms of terminal impedance Z01 and called as Input Impedance (Z in ), which

is the impedance looking into port1 and is given by equation (1-28).

1

11 I

VZ in = (1-28)

Where, Zin1 is the input impedance looking into port1.

S11 is given in equation (1-29):

011

01111 ZZ

ZZS

in

in

+−

= (1-29)

Similarly S22 is given by equation (1-30):

022

02222 ZZ

ZZS

in

in

+−

= (1-30)

2

22 I

VZ in = (1-31)


Where, Zin2 is the input impedance looking into port2 of the network. Equation

(1-30) and (1-31) indicate the impedance matching of the network with

respect to its terminal impedance.

The properties of reciprocal and symmetrical network are:

♦ For reciprocal networks: S12=S21

♦ If the network is symmetrical: S11= S22

Hence, the symmetrical network is also reciprocal. For a lossless passive

network the transmitting power and the reflected power must equal to the

total incident power. The mathematical statements of this power conversion

condition are given in equation (1-32):

1

1

1

1

212

212

22221212

211

221

11112121

=+

=+

=+

=+

∗∗

∗∗

SS

SSSS

SS

SSSS

(1-32)

1.4 VECTOR NETWORK ANALYZER (VNA) A vector network analyzer (VNA) is an instrument which measures the

complex transmission and reflection characteristics of two-port devices in the

frequency domain by sampling the incident signal, separating the transmitted

and reflected waves, and then performing ratios that are directly related to the

reflection and transmission coefficients of the two-port. Frequency is swept to

rapidly obtain amplitude and phase information over a band of frequencies of

interest [6].


VNA Antrisu (Wiltron model 360B Network Analyzer) as shown in Figure 1.8

was utilized to measure experimental response of proposed filters in terms of

S-parameters directly in our work.

Figure 1.8: Vector Network Analyzer Antrisu (model 360B Network Analyzer)

REFERENCES

[1] David M. Pozar, “Microwave Engineering second edition”, John Wiley

& Sons, Inc. © 1998.

[2] Danny Banks “Introduction to Microengineering MEMS Micromachines

MST”© DBanks1999. [email protected], 5 June 1999.


[3] J.Helszain, “Microwave Engineering Passive, Active and Non-

Reciprocal Circuits.” ©1992 McGraw- Hill Book Company.

[4] T.C Edwards, M.B.Steer “Foundations of Interconnect and Microstrip

Design”, third edition, © 2000 John Wiley & Sons.Ltd.

[5] Franz Sischka, “Characterization handbook” 1SBASIC1.doc,

18.03.2002.

[6] Handbook of VNA Antrisu (model 360B Network Analyzer).

CHAPTER 2: THEORY OF MICROWAVE FILTER DESIGN 22

INTRODUCTION

This chapter presents the necessary theory to design resonators and

Chebyshev bandstop filters. This theory is going to be used in chapter 4 for

the design procedure of Chebyshev bandstop filters at 1.5 and 10 GHz.

Typical frequency response of microwave filters includes low-pass, high-pass,

bandpass, and bandstop characteristics; applications can be found virtually in

any type of microwave communication, radar, or test and measurement

system. Most microwave filter design is done with sophisticated

computer-aided design (CAD) packages based such as the Advanced Design

Systems (ADS), Microsoft office (AWR simulator), HFSS etc.

2. 1 BASIC INTRODUCTION TO MICROWAVE RESONATORS

Microwave resonators are used in a variety of applications like filters,

oscillators, frequency meters and tuned amplifiers. Resonators are key

elements in the realization of filters and oscillators, as their quality factor (Q)

determines the insertion loss and phase noise, respectively.


♦ Resonator is an electrical circuit that combines capacitance and

inductance in such a way that a periodic electric oscillation will reach

maximum amplitude.

Figure 2.1: LC circuit diagram

An LC circuit shown in Figure 2.1 consists of an inductor (L), and a capacitor

(C). When connected together, an electrical current can alternate between

them at an angular frequency. Angular frequency is shown in equation (2-1):

LC1

0 =ω (2-1)

Where, L is the inductance in henries, and C is the capacitance in farads. The

angular frequency has units of radians per second.

LC circuits are key components in many applications such as oscillators,

filters, tuners and frequency mixers. An LC circuit is an idealized model since

it assumes there is no dissipation of energy due to resistance.

Resonance effect: The LC circuit does not, by itself, resonate. The LC

circuit must be driven. The frequency at which the equality holds for

the particular circuit is called the resonant frequency.


The resonant frequency of the LC circuit (in radians per second) is given by

equation (2-2):

LCf

ππω

21

2== (2-2)

Near resonance, microwave resonators can usually be modeled by either a

series or parallel RLC lumped-elements equivalent circuit.

2.1.1 BASIC PROPERTIES OF SERIES RLC RESONANT CIRCUIT

A series RLC lumped resonant circuit is shown in Figure 2.2(a). Here R, L

and C are in series in an ac circuit. Inductive reactance (ZL) increases as

frequency increases while capacitive reactance (ZC) decreases with increase

in frequency. Figure 2.2(b), presents the input impedance magnitude versus

frequency [1].

(a)

(b)

Figure 2.2: Series RLC resonator and its response, (a) Series RLC circuit, (b) the input

impedance magnitude versus frequency.


At a particular frequency, these two reactances are equal in magnitude but

opposite in phase. The frequency at which this happens is the resonant

frequency for the given circuit resonant frequency for the given circuit.

The input impedance of series RLC resonant circuit, power dissipation by

resistor, average magnetic energy stored in inductor and average electric

energy stored in the capacitor are presented in table – 2.1 .

INPUT IMPEDANCE

POWER

DISSIPATED

BY RESISTOR

(R)

AVERAGE

MAGNETIC ENERGY

STORED IN THE

INDUCTOR (L)

AVERAGE ELECTRIC

ENERGY STORED IN THE CAPACITOR (C)

RIPloss2

21

=

LIWm2

41

=

CICVW ce 2

22 141

41

ω==

Vc = The voltage across the

capacitor.

CjLjRZin ω

ω 1−+=

Table 2.1: Formulas of Series RLC resonant circuit

At resonance, the input impedance is given by equation (2-3):

RI

PZ loss

in ==

2

2 (2-3)

This is purely real impedance. Hence, at resonance frequency ZL= ZC and

when the average stored magnetic and electric energies are equal, em WW =

implies that the resonant frequency 0ω , is defined as equation (2-4) [1].


LC1

0 =ω LC

fπ2

1= (2-4)

Where, f = Resonant frequency.

In a series ac circuit, ZC leads by 90 degrees while ZL lags by 90. Therefore

they both cancel each other out. Only opposition to current is coil resistance.

Hence in series resonance, at resonant frequency, current is maximum.

In summary:

1. At resonance, current is maximum. Circuit impedance is minimum. In

this state circuit is called acceptor circuit. 2. Below resonance frequency, ZL < ZC. Hence circuit is capacitive.

3. Above resonance frequency, ZL > ZC. Hence circuit is inductive.

2.1.2 BASIC PROPERTIES OF PARALLEL RLC RESONANT CIRCUIT

The parallel RLC circuit, shown in Figure 2.3(a), is dual of the series RLC

circuit and Figure 2.3(b) presents the input impedance magnitude versus

frequency graph.

(a)

(b)

Figure 2.3: Parallel RLC resonators and its response, (a) Parallel RLC circuit, (b) the input impedance magnitude versus frequency.


The input impedance of parallel RLC resonant circuit, power dissipation by

resistor, average magnetic energy stored in inductor and average electric

energy stored in the capacitor are presented in table – 2.2.

Here, a coil (L) and capacitor (C) are connected in parallel with an ac power

supply and R is the internal resistance of the coil. When ZL equals ZC, the

reactive branch currents are equal and opposite. Hence, they cancel each

other to give minimum current in the main line. Since total current is minimum,

in this state the total impedance is maximum. At resonance, resonant

frequency is similar to equation (2-4) [1].

input impedance power

dissipated by

resistor

(R)

average magnetic energy stored in

the inductor (L)

average electric energy stored in the capacitor

(C)

LIW Lm2

41

=

LVWm 2

2 141

ω=

CVWe2

41

=

R

VPloss

2

21

=11 −

⎟⎠⎞

⎜⎝⎛ −+=

CjLjRZin ω

ω

Table 2.2: Formulas of Parallel RLC resonant circuit

At resonance any reactive branch, current is not minimum, but each is given

separately by dividing source voltage (V) by reactance (Z). Hence, I = V / Z,

as per Ohm’s Law. In summary:

1. At resonance, line current is minimum. Total impedance is maximum.

In this state circuit is called rejecter circuit. 2. Below resonance frequency, circuit is inductive.


3. Above resonance frequency, circuit is capacitive.

2.1.3 QUALITY FACTOR (Q)

Q-factor is an important parameter of resonant circuit, which is defined as:

⎟⎠⎞

⎜⎝⎛

=

secondlossenergy

stored)energy (averageωQ (2-5)

The Q - factor compares the frequency at which a system oscillates to the

rate at which it dissipates its energy. It is particularly useful in determining the

qualitative behavior of a system. A higher Q indicates a lower rate of energy

dissipation relative to the oscillation frequency. The Quality factor of the

series tuned circuit is calculated as the ratio of the resonance frequency to

the bandwidth (in Hz) is given by equation (2-6):

0f

fΔ

ffQ s Δ

= 0 (2-6)

When the system is driven by a sinusoidal drive, its resonant behavior

depends strongly on Q. Resonant systems respond to frequencies close to

their natural frequency much more strongly than they respond to other

frequencies. A system with a high Q resonates with greater amplitude (at the

resonant frequency) than one with a low Q factor, and its response falls off


more rapidly as the frequency moves away from resonance. Thus, a radio

receiver with a high Q would be more difficult to tune with the necessary

precision, but would do a better job of filtering out signals from other stations

that lay nearby on the spectrum. The width of the resonance is given by

equation (2-7). Figure 2.4 illustrates the transfer characteristic of resonator

circuit to obtain bandwidth and Q-factor [2].

Qf

f 0=Δ (2-7)

Where, is the resonant frequency, 0f fΔ represent the bandwidth, is the width

of the range of frequencies for which the energy is at least half its peak

value.

Figure 2.4: Transfer characteristic of resonant circuit.


LOADED AND UNLOADED Q

The Q defined in the preceding section is a characteristic of resonant circuit

itself, in the absence of any loading effects caused by external circuitry, called

the unloaded Q.

In practice, a resonant circuit is invariably coupled to other circuitry, which will

always have the effect of lowering the overall, or loaded Q (QL), of the circuit.

If the resonator is a series RLC circuit Figure 2.2(a), the load resistor RL adds

in series with R, the effective resistance is given by (R+RL). If the resonator is

a parallel RLC circuit, Figure 2.3(a), the load resistor RL combines in parallel

with R, the effective resistance becomes [RRL / R+RL)].

Hence, the external Quality factor (Qe) is defined as:

⎪⎪⎩

⎪⎪⎨

⎧

=circuits parallelFor

circuits seriesFor

0

0

LRR

L

QL

Le

ω

ω

(2-8)

The loaded Q is expressed as:

QQQ eL

111+= (2-9)


2.2 GENERAL FILTER DESIGN

The main objective of this section is to describe about the basic concepts and

theories that form the foundation for the design of general RF/ microwave

filters and it also present equations and tables for obtaining elements values

of Chebyshev lowpass prototype filters which will be used in chapter 4 to

design Chebyshev bandstop filter.

FILTER: A passive filter is a device consisting of inductors and

capacitors arranged in a particular configuration (topology), so that a

group of specified frequencies is allowed to pass with little attenuation

while undesired frequencies are attenuated.

2.2.1 TRANSFER FUNCTIONS

The transfer function of two port filter network is a mathematical description of

network response characteristics, S21.

For lossless passive filter network transfer function is given as:

( ) ( )Ω+=Ω 22

221 1

1

nFjS

ε (2-10)

Where, ε is ripple constant, ( )ΩnF represents a filtering or characteristic

function and Ω is a frequency variable (rad / sec)

Ω represent a radian frequency variable of a lowpass prototype filter that has

a cut-off frequency at Ω = Ωc for Ωc = 1 (rad/ s).

The insertion loss response of the filter for equation (2-10) is computed by

equation (2-11).


( )( )

dBjS

L A 221

1log10Ω

=Ω (2-11)

Since 12

212

11 =+ SS for lossless, passive two-port network, the return loss

response of the filter is obtained by equation (2-12) [3]:

( ) ( )[ ]dBjSLR2

211log10 Ω−=Ω (2-12)

1. BUTTERWORTH (MAXIMALLY FLAT) RESPONSE

The amplitude–squared transfer function for Butterworth filters that have an

insertion loss LAr= 3.01dB at cut-off frequency Ωc = 1 (rad / s) is given by:

( ) njS 22

21 11Ω+

=Ω (2-13)

Where, n is the degree or the order of filter, which corresponds to the number

of reactive elements required in the lowpass prototype filter. This type of

response is also referred to as maximally flat because its amplitude-squared

transfer function defined in equation (2-13) has the maximum number of

(2n-1) zero derivatives at Ω = 0. Therefore, the maximally flat approximation

to the ideal lowpass filter in the passband is best at Ω = 0, but deteriorates as

Ω approaches the cutoff frequency Ωc. Figure 2.5, shows a typical maximally

flat response. The transfer function constructed from equation (2-13) is [3].


( )( )∏

=

−= n

iipp

pS

1

211

(2-14)

Figure 2.5: Butterworth (maximally flat) lowpass response

2. CHEBYSHEV LOWPASS FILTER

The Chebyshev filter response (Figure 2.6) exhibits the equal–ripple

passband (LAr) and maximally flat stopband with cut-off frequency

Ωc = 1 (rad / s).The amplitude–squared transfer function for this type of

response is presented in equation (2-15):

( ) ( )Ω+=Ω 22

221 1

1

nTjS

ε (2-15)


110 10 −=ArL

ε (2-16)

Were, ε is ripple constant is related to given passband ripple LAr in dB and

represent Chebyshev functions of first kind of order n. ( )ΩnT

Figure 2.6: Chebyshev lowpass response

3. ELLIPTIC FUNCTION RESPONSE

The response that is equal-ripple in both the passband and stopband is the

elliptic function response, as illustrated in Figure 2.7.

The transfer function for this type of response is:

( ) ( )Ω+=Ω 22

221 1

1

nFjS

ε (2-17)


With

( )

( )

( )( )

( ) ( )

⎪⎪⎪⎪⎪⎪

⎩

⎪⎪⎪⎪⎪⎪

⎨

⎧

≥

⎟⎠⎞

⎜⎝⎛

Ω−ΩΩ

Ω−ΩΩ

⎟⎠⎞

⎜⎝⎛

Ω−ΩΩ

Ω−Ω

=Ω

∏

∏

∏

∏

−

=

−

=

=

=

oddnforN

evennforM

F

n

i i

s

n

ii

n

i i

s

n

ii

n

32

1

122

2

21

1

22

2

122

2

2

1

22

(2-18)

Where, and ( )10 <Ω<Ω ii 1>Ω s represent some critical frequencies; M and

N are constants. Fn (Ω) will oscillate between 1± for 1≤Ω , and

( ) 11 =±=ΩnF [3].

Figure 2.7: Elliptic function lowpass response.


2.2.2 LOWPASS PROTOTYPE FILTERS AND ELEMENTS

Lowpass prototype filter is in general defined as the lowpass filter whose

element values are normalized to make the source resistance or conductance

equal to one denoted by =1, cut-off angular frequency (Ω0g c) =1 rad/s.

Figure 2.8 demonstrate two possible forms of n pole lowpass prototype for

realizing an all-pole filter response, including Chebyshev, Butterworth.

In Figure 2.8, for i = 1 to n represent either the inductance of series

inductor or the capacitance of shunt capacitor; n = number of reactive

elements. If is shunt capacitance or series inductance, then,

0g

1g 0g = shunt

capacitance or the series inductance.

Similarly series inductance becomes the load resistance or the load

conductance. Unless otherwise specifies these values are supposed to be

the inductance in henries, capacitance in farads, resistance in ohms and

conductance in mhos. This type of lowpass filter serves as prototype for

designing many practical filters with frequency and element transformation

[3].

1+ng

0g


Figure 2.8: Lowpass prototype filters for all- pole filters with ladder (a) A ladder

network structure, (b) its dual.

CHEBYSHEV LOWPASS PROTOTYPE FILTERS For Chebyshev prototype filters having the transfer function given in equation

(2-15) with passband ripples LAr a cut-off frequency (Ωc) =1 and the elements

values for two port networks shown in Figure 2.8 the g values can be

computed with formula given in reference [3]. Table-2.3 presents elements

values for Chebyshev lowpass prototype filters ( =1, Ω0g c = 1) for passband

ripples LAr = 0.04321 dB which will be used in this thesis work to design


3 pole Chebyshev filter and a triplet bandstop filter with an extra transmission

zero [3].

n

1g 2g 3g 4g 5g 6g 7g 8g 9g 10g

1 0.2 1

2 0.6648 0.5445 1.2210

3 0.8516 1.1032 0.8516 1

4 0.9314 1.2920 1.5775 0.7628 1.2210

5 0.9714 1.3721 1.8014 1.3721 0.9714 1

6 0.9940 1.4131 1.8933 1.5506 1.7253 0.8141 1.2210

7 1.0080 1.4368 1.9398 1.6220 1.9398 1.43680 0.8330 1.2210

8 1.0171 1.4518 1.9667 1.6574 2.0237 1.6107 1.7726 0.8330 1.2210

9 1.0235 1.4619 1.9837 1.6778 2.0649 1.6778 1.9837 1.4619 1.0235 1

Table 2.3: Elements values for Chebyshev lowpass filters (g0=1, Ωc = 1) for passband

ripples LAr = 0.04321 dB (taken from [3])

2.2.3 FREQUENCY AND ELEMENTS TRANSFORMATION In this section, we describe the procedure to design bandstop filter from

lowpass prototype filter, by means of frequency mapping, impedance scaling,

lowpass transformation and bandstop transformation.

1. FREQUENCY TRANSFORMATION To obtain characteristics and element values for practical filter based on the

lowpass prototype, which have a normalized source resistance / conductance

0g = 1 and cut-off frequency Ωc = 1, we have to apply frequency and element

transformations.


Frequency transformation or frequency mapping is required to map a

response of Chebyshev response in lowpass prototype frequency domain (Ω)

to that in frequency domain (ω) in which a practical filter response such as

lowpass, highpass, bandpass and bandstop are expressed. The frequency

transformation will have effect on all the reactive elements accordingly, but no

effect on the resistive elements [3].

In addition to frequency transformation mapping, impedance scaling

(equation 2-19) is also required to accomplish the elements transformation.

Impedance scaling will remove the 0g = 1 normalization and adjust the filter

to work for any value of the source impedance denoted by , impedance

scaling factor (

0Z

0γ ).

⎪⎪⎩

⎪⎪⎨

⎧

=e.conductanc thebeing gfor

.resistance thebeing gfor

00

0

00

0

0

YggZ

γ (2-19)

Where, 0

01

ZY = is the source admittance. In principle, applying the

impedance scaling upon filter network like in equation (2-20) has no effect on

the response shape [3].

0

0

γ

γCC

LL

→

→

0

0

γ

γ

GG

RR

→

→

(2-20)


2. LOWPASS TRANSFORMATION

The frequency transformation from lowpass prototype to practical lowpass

filter having cut-off frequency cω in the angular frequency axis ω is given by

equation (2-21).To obtain element transformation apply equation (2-21)

together with the impedance scaling (equation 2-22) [3].

ωω ⎟⎟

⎠

⎞⎜⎜⎝

⎛ Ω=Ω

c

c (2-21)

ecapacitanc thengrepresenti gfor

inductance thengrepresenti gfor

0

0

γω

γω

gC

gL

c

c

c

c

⎟⎟⎠

⎞⎜⎜⎝

⎛ Ω=

⎟⎟⎠

⎞⎜⎜⎝

⎛ Ω=

(2-22)

3. BANDSTOP TRANSFORMATION The frequency transformation from Chebyshev lowpass prototype to

Chebyshev bandstop is achieved by the frequency mapping given by

equations (2-23):

⎟⎟⎠

⎞⎜⎜⎝

⎛−

Ω=Ω

0

0

ωω

ωω

FBWc (2-23a)

Where, 210 ωωω = and fractional bandwidth (FBW) is given by equation (2-23b).


0

12

ωωω −

=FBW (2-23b)

Where, 12 ωω − is bandwidth.

The elements for LC resonators transformed to bandstop filter are shown in

Figure (2.10). For representing the inductance is given by equation (2-24a)

and for representing the capacitance is given by equation (2-24b):

g

g

gFBW

L

gFBWC

cp

cp

00

00

11

γω

γω

⎟⎟⎠

⎞⎜⎜⎝

⎛ Ω=

⎟⎟⎠

⎞⎜⎜⎝

⎛Ω

=

(2-24a)

00

0

0

1

γω

γω

gFBWC

gFBWL

cs

cs

⎟⎟⎠

⎞⎜⎜⎝

⎛ Ω=

⎟⎟⎠

⎞⎜⎜⎝

⎛Ω

=

(2-24b)

Basic element representation of equation (2-24) is shown in Figure 2.9(a)

Lowpass prototype to 3-pole bandstop transformation is shown in Figure

2.9(b) [3].


(a)

(b)

Figure 2.9: Lowpass prototype to 3 pole bandstop transformation (a) basic element

transformation, (b) a practical bandstop filter based on the transformation.


2.2.4 IMMITTANCE INVERTERS An inverter has a phase shift of or an odd multiple thereof. Immittance

inverters are either impedance or admittance inverters.

090±

IMPEDANCE INVERTER: A two-port network that has unique property at all

frequencies. If it’s terminated in impedance on one port, the impedance

seen looking in at the other port is where, K is real and is characteristic

impedance of the inverter. Impedance inverters also have a phase shift of

± 90 degrees pr and odd multiple thereof. If is inductive / conductive,

will become conductive / inductive, Impedance inverters are also known as K-

inverters.

2Z

1Z

2Z 1Z

2

2

1 ZKZ = (2-25)

ADMITTANCE INVERTER: In two port network, if admittance is

connected at one port, the admittance , seen looking in the other port is

where J is real and is called characteristic admittance of the inverter.

Admittance inverters also have a phase shift of ± 90 degrees pr and odd

multiple thereof and also known as J- inverters.

2Y

1Y

2

2

1 YJY = (2-26)

In this thesis we implemented admittance inverter to design Quasi-elliptic

bandstop filter from Chebyshev lowpass prototype filter:

By network analysis it can be seen that a series inductance with an inverter

on each side looks like shunt capacitance from its exterior terminals, as

inductance in Figure 2.10 (a). Likewise, a shunt capacitance with an inverter

on each side looks like a series inductance from its external terminals, as

demonstrated in Figure 2.10 (b) [4].


Figure 2.10: (a) Immittance inverter used to convert a shunt capacitance into as

equivalent circuit with series inductance. (b) Immittance inverter used to convert a series inductance into as equivalent circuit with shunt capacitance.

Inverters have the ability to shift impedance or admittance levels depending

on the choice of K or J parameters. Making use of these properties enables to

convert a filter circuit to an equivalent form that would be more convenient for

implementation with microwave structure. Using this technique we convert the

common lowpass prototype structure into the bandpass filter or bandstop filter

[3].

1. PRACTICAL REALIZATION OF IMMITTANCE INVERTERS

Another type of practical immittance inverter is a circuit mixed with lumped

and transmission line elements which are used in this thesis to design

Trisection (Triplet) bandstop filter at 1.5 GHz as shown in Figure 2.11.


` Figure 2.11: Immittance inverts comprised of lumped and transmission line element.

Where, are the characteristics impedance and admittance of line, and θ

denotes the total electrical length of the line. In practice, the line of positive or

negative electrical length can be added to or subtracted from adjacent lines of

the same characteristic impedance [1].

0Y

For the admittance inverter equation (2.27 a) applies:

L

in YJY

2

= (2-27a)

For the line equation (2.27 b) applies: 090


0YJ = (2-27b)

For lumped element implementation, the values, J, B, θ are calculated from

equation (2-28):

2tan0θYJ = (2-28a)

2

01 ⎟

⎠⎞⎜

⎝⎛−

=

YJ

JB (2-28b)

0

1 2tanYB−−=θ (2-28c)

CONCLUSION

In this chapter, types of resonators and some of the important parameters

that count up for designing of filter have been presented. The main objective

of presenting the general designing of filter is to describe about the basic

concepts and theories that form the foundation for the design of general RF/

microwave filters. The chapter also presents equations and tables for

obtaining elements values of Chebyshev lowpass prototype filters which will

be used in chapter 4 to design Chebyshev bandstop filter.


REFERENCES

[1] David M. Pozar, “Microwave Engineering second edition”, John Wiley

& Sons, Inc. ©1998

[2] Héctor J. De Los Santos,”RF MEMS for Wireless Communication

Systems” © 2002 Héctor J. De Los Santos, MEMS Series.

[3] Jia-Sheng Hong and M.J.Lancaster, “Microstrip Filters for

RF/Microwave Applications”, © 2001 by Wiley Series in Microwave and

Optical engineering.

[4] Sonnet® User Manual Release 7.0 volume

CHAPTER 3: LITERATURE REVIEW OF MICROWAVE FILTERS

48

INTRODUCTION

Microwave and millimeter-wave communication systems are expanding

rapidly as they offer many advantages over conventional wireless links. They

allow the use of very wideband radio links suitable for inter satellite and

personal communications. Filters play important roles in many

RF / microwave applications. They are used to separate or combine different

frequencies. The electromagnetic spectrum is limited and has to be shared.

Filters are used to select or confine the RF / microwave signals within

assigned spectral limits.

Emerging applications such as Wireless communication continues to

challenge RF/Microwave filters with ever more stringent requirements:

1. High performance

2. Smaller size

3. Lighter weight

4. Lower cost.


49

Depending on the requirements and specifications, RF / Microwave filters

may be designed as lumped element or distributed elements circuits [1].

At microwave frequency a lot of work has been done on bandpass filters

(Chebyshev, Butterworth, quasi elliptic etc) [2, 6] but very little work has been

done on Chebyshev bandstop filters, and bandstop filters with transmission

zero such as Quasi elliptic, Quadruplet and Triplets.

In this chapter, literature reviews of microwave filters including

micromachined filters are presented. The objective is to shown different

microwave filters, designed by using different technologies. In this chapter,

work related to bandstop filters will be presented due to two main reasons:

firstly, as there is very little work done in area of Bandstop filters at microwave

frequencies and secondly, this thesis work is based on novel bandstop filters.

The purpose of presenting the state of art of membrane support filters using

micromachining techniques is because in this thesis a novel configuration of

resonators with selective removal of substrate is proposed using

micromachining technology at X- band (chapter 4).

Finally, quasi-elliptic bandstop filter review will be presented in this chapter as

this relates to the novel work on Trisection (Triplets) bandstop filters with

extra transmission zero presented in chapter 5.

This chapter is divided in to three sub-sections, section (3.1) present some of

the work done on micromachined microwave filters. Section (3.2) shows

bandstop filters with different technologies. Section (3.3) present microwave

quasi elliptic bandstop filter.


50

3.1 MICROMACHINED MIRCOWAVE FILTERS

In this section a review of micromachined filters is presented, with the

objective of showing different micromachined microwave filters designed by

different technologies.

3.1.1 MEMBRANE SUPPORT FILTERS

Membrane supported striplines [7] and microstrips [8], [9] have become a way

of producing high performance millimeter wave circuits. High performance

planar micromachined filters at 37 and 60 GHz are presented in [9], the filters

consist of a 3.5% fractional bandwidth two pole Chebyshev filter with

transmission zeros at 37 GHz, which had a 2.3 dB port to port insertion loss.

The layout of an 8% fractional bandwidth quasi elliptic filter at 60 GHz

exhibiting an insertion loss 1.5 dB which is shown in Figure 3.1. A 2.7% and

4.3% fractional bandwidth four and five pole Chebyshev filters at 60 GHz,

which had an insertion loss of 2.8 and 3.4 dB respectively demonstrated in

Figure 3.2.


51

Figure 3.1: Layout of the 4 pole membrane quasi elliptic filter L1=820, L2=2180,

L3=645, L4=300, L5=675, w=500, G1=15, G2=200, G3=175, G4=625 (Dimensions

in microns), taken from [10]

All measurements of the filters presented in [9], include the losses of the

coplanar to microstrip transitions. These resonators are known to have Q’s in

the range of 400 to 500 at millimeter waves, from 30 GHz to 60 GHz. The

measured response of the 8% fractional bandwidth filter is presented in

Figure 3.2, the conductor width used is 500 µm and the ground to conductor

spacing is 250 µm, a single resonator exhibits a Q of 454 and the

metallization used is 1 µm of evaporated gold. The shielding is made using

via groves surrounding the filter. The insertion loss is 1.5 dB including the

transition and the whole filter is smaller than 4mm x 6mm.

A planar diplexer integrated on a single silicon substrate is presented in [7],

the diplexer channels have a Chebyshev response and have a 5% and 6.5%

relative bandwidth at 28 and 31 GHz, respectively. The layout of the diplexer


52

is shown in Figure 3.3, and consists of two capacitively coupled bandpass

filters with one port shared between the filters.

Figure 3.2: Measured response of the 4 pole membrane quasi elliptic filter, taken from [9]

The receive band filter is designed using a four pole Chebyshev prototype

with a centre frequency of 28 GHz, a relative bandwidth of 5.5%, and a ripple

of 0.1 dB. The transmit band filter is a three pole Chebyshev filter with a

centre frequency of 31.75 GHz, and a relative bandwidth of 5.5%, and a

ripple of 0.1 dB. The author claims that, bent diplexer structure has a better

performance than one having straight sections, because it helps to disturb

any possible parasitic modes of the micromachined structure.


53

Figure 3.3: Layout of the K-band diplexer, taken from [10]

The resonators used in the diplexer consist of 800 micrometers wide lines

with a ground plane height of 250 micrometers, and a shielding cavity height

of 800 µm. The distance from the edge of the conductors to the sidewalls of

the micromachined channel is 700 micrometers. The conductors are 2 µm

thick electroplated gold. A half wavelength resonator constructed of this

geometry has an unloaded quality factor of 460 at 29 GHz. The filter

response of the diplexer is shown in Figure 3.7.The diplexer outer dimensions

are 1.5cm x 1.6cm x 1.4mm thick. The insertion loss is 1.4 dB for the 28 GHz

band and 0.9 dB for the 31 GHz band, including all transition effects. The

measured isolation is better than –35 dB across the receive band, and better

than –50 dB in the transmit band.


54

Figure 3.4: Response of the K band diplexer, taken from [10]

3.2 BANDSTOP FILTERS In this section, the review of bandstop filters with the objective of showing

different bandstop microwave filters designed using different technologies is

presented. Very few papers have been found on bandstop filter design and

they all are presented in this section of literature review.


55

3.2.1 L - RESONATOR BANDSTOP FILTER The L-resonator bandstop filter configuration provides increased options in

the design of narrow bandstop filters using TEM transmission-line elements.

A design procedure is presented for narrow bandstop filters using TEM

transmission line L resonators in [11], which are intermediate of the gap and

parallel-coupled resonators. In this configuration, parallel coupling occurs

over a portion of the resonator length, with the remaining resonator length

forming a stub. The grounded end of the resonator may be in either the

coupled or stub portion of the resonator.

Figure 3.5: Bandstop filter with shunt-connected L resonators, taken from [11].

Figure 3.6, shows a five-resonator filter in another configuration which is also

suitable for narrow bandstop applications. Each resonator has a parallel-line

coupling with an electrical length of less than λ/4 at resonance, a shunt stub,

and an uncoupled portion of the through line to provide additional electrical

length between resonators as required. The stub portion of the resonator

(because of the shape),is called an “L-resonator”. Coupled and stub line

lengths can be arbitrarily chosen with some limitations, and can vary between


56

resonators. The theoretical response is shown in Figure (3.7) and is close to

that of the highpass prototype.

Figure 3.6: Bandstop filter with shunt-connected L resonators, taken from [11]

Figure 3.7: Theoretical loss and return loss of degree 5 elliptic-function

L-resonator bandstop filter, taken from [11].


57

3.2.2 MICROMACHINED BANDSTOP FILTER Membrane supported microstrip structures are formed by removing the silicon

substrate and suspending a microstrip line on a thin (1.4 μm) dielectric

membrane [12]. A ground plane is formed by another micromachined

substrate and attached to the top of the circuit. The bottom is also shielded

with a third substrate shown in Figure 3.8. These resonators show large

improvements in quality factor over conventional techniques, and more

importantly, allow for planar integration in complex systems. Resonators were

fabricated in suspended microstrip at 29, 37, and 62 GHz with quality factors

of over 450 with very close agreement between simulated and measured

results. For this structure, dielectric loss was eliminated with the air dielectric, the

radiation loss is minimized by shielding the structure on all sides using thick

via grooves to limit substrate modes, and ohmic loss is greatly reduced by

allowing for very wide transverse microstrip geometries. Micromachining

techniques are used to produce a micro packaged, air dielectric line with wide

transverse dimensions resulting in high-Q resonators at millimeter-wave

frequencies. The micromachined suspended microstrip transmission line is

based a three wafer process (Figure 3.8).

For the circuit wafer, a stress compensated 1.4μm membrane layer consisting

of SiO2 / Si3N4 / SiO2 (7000°A / 4000°A / 3000°A) is deposited on a high

resistivity 525 μm thick silicon substrate using thermal oxidation and low

pressure chemical vapor deposition. This process deposits the thin film on

both sides of the silicon wafer allowing for a membrane on the top side of the

wafer and a good etch mask for the silicon removal on the back side.

Complete dimensions and thickness are described in [12]. A single resonator

fabricated at 29GHz in a bandstop configuration (Figure 3.19). The measured


58

loaded Q was 190 with a coupling -4.6 dB giving an extracted unloaded Q of

460 at 28.7 GHz.

Figure 3.8: transverse section of the microstrip structure, taken from [12]

(a) Bottom view (b) Top view

Figure 3.9: Circuit wafer of 29 GHz microstrip resonator in bandstop configuration (a) Bottom view, (b) Top view, taken from [12].


59

Figure 3.10: Measured S11 of bandstop resonator including effects of transition, taken from [12].

3.2.3 HIGH TC SUPERCONDUCTING CPW BANDSTOP

FILTERS FOR RADIO ASTRONOMY FRONT ENDS

A superconducting coplanar waveguide (CPW) bandstop filter consisting of 8

coupled line sections at a center frequency of 1.53 GHz is shown in Figure

(3.14) [13]. A packaged 94.7% bandwidth low pass; Chebyshev design

yielded a filter with a center frequency of 1.58 GHz, less than 1.2 dB insertion

loss in the passband and better than 28 dB rejection at 20 Kelvin.

At a center frequency of 1.56 GHz 8 coupled lines constitute a 7 pole filter

having an insertion loss of less than 1.2 dB and a skirt selectivity of 1.53 with

band rejection better than 28 dB. The radio telescope receivers are already


60

cooled to 20 Kelvin to reduce the noise in the semiconductor electronics, high

Tc; materials are very attractive for this application.

Figure 3.11: The bandstop filter specification taken from [13]

Other work on high Tc bandstop filters have been reported by [14] who used a

6 bank optically switchable bandstop filter and Lancaster et al. [15] who

employed a lumped element approach. Figure 3.12 illustrate measurement

results, which show the reduced band rejection and the extra ripple near the

stopband. A band rejection of -28 dB is less than the desired - 40 dB due to

direct and parallel plate coupling from input to output.


61

Figure 3.12: Measurement of the bandstop filter, taken from [13]

3.2.4 A SUPERCONDUCTING MICROSTRIP BANDSTOP FILTER FOR AN L-BAND RADIO TELESCOPE RECEIVER

A seven-pole High Temperature Superconducting (HTS) microstrip bandstop

filter at L band Chebyshev bandstop filter shown in Figure 3.13(b) is

fabricated on a 2” LaAlO3 substrate to eliminate the strong interference at

1394MHz [16]. The filter has application in a radio astronomy receiver. The

zig-zag loop resonator and the zig-zag phase line are developed to reduce

the parasitic effect of the direct resonator-to-resonator coupling. The designed resonator has a large loop at the middle of the line, and the

lines are then folded inward in a zig-zag shape Figure 3.13 (a). On a 0.508

mm thick LaAlO3 substrate (relative dielectric constant =23.6), the overall size

of the zig-zag loop resonator is 6.92mm wide and 2.32mm long. The HTS line


62

width of the resonator is 0.2mm. The radiation from one resonator to the

others is reduced because the electric current at any two symmetrical

positions with regard to the centre of the resonator flows in opposite

directions. Both the strong electric field at the open ends and the strong

magnetic field at the middle of the resonator are reduced by the opposite

current flow in the inward zig-zag lines, allowing resonators to be placed in a

relative small area without substantial unwanted coupling .Figure 3.13(b)

shows the whole phase through line was folded to 4-leg zigzag line. All seven

resonators are implemented on 2” wafer [16]. The simulation results are also

shown in Figure 3.14. The measured centre frequency is 1394.02MHz.

(a)

(b) Figure 3.13: (a) Coupling structure between the resonator and 50-.microstrip line on a

0.508 mm-thick LaAlO3 substrate, (b) Layout of the 7-pole microstrip HTS bandstop filter on 0.508mm-thick LaAlO3 (44mm×26mm), taken from [16].


63

Figure 3.14: Measured (thick solid line S21 (dB); thick dash line S11 (dB)) and

simulated (thin solid line S21 (dB); thin dash line S11 (dB)) performance of the seven-pole HTS microstrip bandstop filter, taken from [16].

3.3 QUASI ELLIPTIC FILTERS

3.3.1 HIGH PERFORMANCE HTS PSEUDO-ELLIPTIC BAND-STOP FILTERS

Elliptic function band-stop filters play an important role in cellular front end

filtering. The filter shown in Figure 3.15 is 6th order pseudo-elliptic band-stop

design, the design techniques described can be extended to any order band-

stop filter and a large range of frequencies [17]. Design is an approximate

elliptic filter that shares the key properties of an elliptic function filter.

According to author, this pseudo-elliptic band-stop filter is of a form that is

easily realized in microstrip form. In both the elliptic and Chebyshev filters, the

reactance slope parameter of the resonators generally varies from one


64

resonator to the next. By constraining the optimization [17] complete lumped

element represent the filter shown in Figure 3.15.

A plot of the filter performance is seen in Figure 3.16 (including approximately

12 dB of gain). This filter was used to notch out the AMPS A prime frequency

band (845 MHz - 856.5 MHz) from the full AMPS B band (835 MHz - 849

MHz). This filter was designed as a 6th order band-stop.

The filter’s passband was 800 MHz to 900 MHz, and the measured rejection

on this design rejection was achieved while maintaining a pass band insertion

loss of less than 1 dB. The pass band return loss was measured to be >20

dB. The filter was cascaded with a low noise amplifier and the response is

shown in Figure 3.17.

Figure 3.15: Complete Band-stop Filter Assembly, taken from [17]


65

Figure 3.16: S-parameter plot of B band-stop filter (includes 12 dB LNA gain), taken

from [17].

Figure 3.17: S-parameter plot of AMPS-B micro enclosure, take from [17]


66

CONCLUSION In this chapter, the literature reviews relevant to the thesis was presented.

Firstly, the state of art of membrane support filters was exhibited, which is

related to the work of chapter 4. Secondly, the work published on advance

bandstop filter configurations was reported, which sets the basis of the work

of chapter 5.

REFERENCES

[1] Jia-Sheng Hong and M.J. Lancaster,”Microstrip Filters for RF/

Microwave Applications”©2001 by John Wiley & Sons, Inc.

[2] Jen-Tsai Kuo, Member, Ming-Jyh Maa, and Ping-Han Lu “A Microstrip

Elliptic Function Filter with Compact Miniaturized Hairpin Resonators”,

IEEE microwave and guided wave letters, Vol.10, No.3,March 2000.

[3] J.-T. Kuo and E. Shih, “Wideband bandpass filter design with three-line

microstrip structures” IEE Proc-Microw. Antennas Prop. , Vol. 149, No.

516, October/ December 2002

[4] Jen-Tsai Kuo,Tsung-Hsun Yeh, and Chun-Cheng Yeh “Design of

Microstrip Bandpass Filters With a Dual-Passband Response”, IEEE

transactions on microwave theory and techniques, Vol. 53, NO. 4, April

2005.

[5] G. L. Hey-Shipton, N. 0. Fenzi, K. F. Raihn, “HTS Diplexer & Low

Noise Amplifier RF Module,” 1997 IEEE MTT-S International

Microwave Symposium Digest, pp. 295-298.


67

[6] E. R. Soares, K. F. Raihn, A. A. Davis, R. L. Alvarez, P. J. Marozick, G.

L. Hey-Shipton, “HTS AMPS-A and AMPS-B Filters for Cellular

Receive Base Stations,” April 1998.

[7] Lee Harle and Linda P.B. Katehi, “A Vertically Integrated

micromachined Filter“, IEEE transactions on microwave theory and

techniques, Vol. 50, NO. 9, September 2002.

[8] Chen-Yu Chi and Gabriel Rebeiz, “Conductor loss limited stripline

resonator and filters”, IEEE transactions on microwave theory and

techniques, Vol 44, No 4, April 1996.

[9] Pierre Blondy, Andrew R. Brown, Dominique Cross and Gabriel M.

Rebeiz, “Low loss micromachined filters for millimeter wave

communication systems”, IEEE transactions on microwave theory and

techniques, Vol 46, No 12, December 1998.

[10] Andrew R. Brown and Gabriel M. Rebeiz, “A high performance

integrated K-band diplexer”, IEEE transactions on microwave theory

and techniques, Vol 47, No 8, August 1999.

[11] H. Clark Bell, “L-Resonator Bandstop Filters”, IEEE Transactions on

Microwave Theory and Techniques, Vol. 44, No. 12, December 1996.

[12] Andrew R. Brown, Pierre Blondy, and Gabriel M. Rebeiz “Microwave

and Millimeter-wave High-Q Micromachined Resonators” published in

the international journal of RF and Microwave Computer-Aided

Engineering, 1999, page 1.

[13] S. Wallage, J. b. Tauritz , G. H. Tan , P. Hadley and J. E. Mooij “High

Tc superconducting CPW bandstop filters for radio astronomy front


68

ends”, IEEE Transactions on applied superconductivity, Vol. 7, No. 2,

JUNE 1997.

[14] N.O. Fenzi, K.F. Raihn, G.V. Negrete, E.R. Soares, and G.L.Matthaei,

“An Optically Switched Bank of HTS Bandstop Filters,” In 1994 IEEE

MTT-S International Microwave Sympo sium Digest [12], pp. 195-198.

[15] M. J. Lancaster, J. C. Li, A. Porch, and N. G. Chew, “High

Temperature Superconducting Lumped Element Resonator,”

Electronic Letters, vol. 29, no. 19, pp. 1728-1729, Sept. 1993.

[16] Guoyong Zhang, Michael J. Lancaster, Frederick Huang, and Neil

Roddis “A Superconducting Microstrip Bandstop Filter for an L-Band

Radio Telescope Receiver” published in IEEE.

[17] Edward R. Soares “Design and Construction of High Performance HTS

Pseudo-Elliptic Bandstop Filters”, 1999 IEEE MlT-S Digest.

CHAPTER 4: DESIGNING OF RESONATORS AND 3 POLE CHEBYSHEV BANDSTOP FILTERS AT 1.5 GHz AND 10 GHz

69

INTRODUCTION

In this chapter, designing of novel structures of resonators and 3 pole

Chebyshev bandstop filters at 1.5GHz and at 10GHz are presented along

with there respective simulation response. Design of resonators starts with

conventional (λ/2) resonator which are miniaturized with the addition of

capacitive patch. At 1.5GHz this patch was modified into an interdigital

structure (interdigital T-shape straight resonator) to enhance the coupling to

the transmission line. Further more, these novel compact resonators were

used to design Chebyshev bandstop filters at 1.5GHz and 10GHz central

frequencies. All proposed resonators and filters were designed using

microstrip technology (for microstrip see chapter 1).

This chapter is divided into five sections. Section 4.1, gives a general

description about EM simulator [1] used for designing. Section 4.2, consists of

designing of λ/2 resonator, Interdigital T-shape straight resonator, and ultra


70

compact interdigital meandered resonator. Section 4.3, describes about the

two different designs of compact 3 pole Chebyshev bandstop filter at 1.5GHz

and its respective simulation response. Section 4.4, consists of the designing

procedure and simulation results of λ/2 resonator, patch resonator, and novel

compact patch resonators with selective removal of substrate at 10GHz.

Section 4.5, presents a 3 pole Chebyshev bandstop filter at 10GHz.

Section 4.6 describes, about λ/2 coplanar waveguide used to connect the X-

band devices to the probe station for measurement.

4.1 ELECTROMAGNETIC (EM) SIMULATOR

Electromagnetic simulator is a CAD tool used to obtain S parameters for all

the components to be modeled over the ranges of designable parameters

and frequencies for which these models are expected to be used.

Electromagnetic (EM) simulation solves the Maxwell equations with the

boundary conditions imposed upon the RF/Microwave structure to be

modeled. Most commercially available EM simulators use numerical methods

to obtain the solution. One principle error, which is common to all the

numerical methods, is due to the finite cell or mesh sizes. These EM

simulators divide a RF/microwave filter structure into subsections or cells with

2D or 3D meshing, and then solve Maxwell’s equations upon these cells.

Larger cells yields faster simulations, but at the expense of larger errors.

Errors are diminished by using smaller cells, but at the cost of longer

simulation times. The errors in the filter simulation are due to mesh sizes

errors. This can be done by repeating the EM simulation using different mesh

sizes and comparing the results, which is known as a convergence analysis

[2-3]. The most common EM techniques used by modern simulators are:

Method of Moments, Finite Element Method [9-11].The packages used for the


71

realization of this thesis is [1], which use the Method of Moments to solve the

electromagnetic structures.

4.2 MICROSTRIP RESONATORS AT 1.5GHz

In this section, the designing procedure of λ/2 resonator, Interdigital T-shape

straight resonator, novel ultra compact interdigital meandered resonators are

presented.

4.2.1 MICROSTRIP RESONATORS (λ/2)

To design the microstrip resonator at 1.5 GHz, duroid [table 4.1] substrate

and copper as conductor were selected. The designing parameters used for

microstrip resonators and filters at 1.5GHz are specified in table 4.1 and 4.2.

substrate

Thickness

(mm)

Relative

Permittivity (εr)

Dielectric tangent

loss (tan δ)

(Duroid RT/6010LM) 0.64 10.8 0.0023

Table 4.1: Specifications of substrate to design resonators at 1.5GHz [5]

Metal

Thickness (mm)

R dc (Ω/sq)

Skin effect

Copper 0.017 0.001021 2.618e-7

Table 4.2: Specifications of Copper to design resonators at 1.5GHz [7]

Initially, the length of microstrip resonator (λ/2) was calculated with respect to

central frequency and relative permittivity of the substrate using formula (4-1).


72

rofc

ελ = (4-1)

Where, λ is the wavelength (mm).

fo is the central frequency (1.5 GHz)

c is speed of light (3 x 108 m/sec).

εr is the relative permittivity of the substrate.

The wavelength of λ= 60.8mm and resonator (λ/2) = 30.4mm were obtained

using (4-1). The width of the resonator was chosen to be 0.6mm equivalent to

50Ω transmission line calculated using [12].

In order to calculate the unloaded Q of the resonator (described in chapter 2),

the resonators were weakly coupled to the input and output transmission lines

of 50Ω (0.1mm spacing between transmission line and resonator) as shown

in Figure 4.1. De-embedded [1] lines were used as feeds to remove the port

discontinuity and transmission line effects from the analysis results.

Figure 4.1: Microstrip resonator λ/2 on Duroid substrate at 1.5GHz.


73

The simulation response of this resonator using copper is shown in

Figure 4.2. The Q-value of resonator with copper is 108 (with lossless

metal = 462) at central frequency of 1.5GHz. This Q is calculated with

equation (4-2) (explained in chapter 2).

BWfQ 0= (4-2)

1.42 1.44 1.46 1.48 1.50 1.52 1.54 1.56 1.58-50

-45

-40

-35

-30

-25

Δf = 0.0139 GHz

Mag

nitu

de (d

B)

Frequency (GHz)

S12

QU= 108Δf

Simulation result of λ/2 resonator on duroid substrate at 1.5GHz

fo=1.5GHz

Figure 4.2: S12 Response of microstrip resonator (λ/2) at 1.5 GHz.


74

4.2.2 INTERDIGITAL T-SHAPE STRAIGHT RESONATOR

T-shape straight resonator is presented in Figure 4.3. For narrow bandwidth

filters, strong coupling is required between the resonators and the

transmission lines. Hence, this structure presents enhanced coupling having

an interdigital capacitor to couple to the main transmission line. It was

observed that with the addition of interdigital fingers, the overall length of the

resonator was reduced to 27.6mm. But due to the dissipation at the edges of

the patch the Q value decreases.

Figure 4.3: Interdigital T-shape straight resonator on Duroid using Copper at

1.5GHz.


75

Figure 4.4, presents the Q value simulation results obtained for weakly

coupled T-shape resonator with transmission line. With copper the Q-value is

107 and with lossless metal, it is 378 at central frequency of 1.5 GHz.

1.40 1.45 1.50 1.55 1.60-50

-45

-40

-35

-30

-25

Δ f

Mag

nitu

de (d

B)

Frequency (GHz)

S12

QU= 107fo=1.5 GHz

Simulation result of interdigital T-shape resonator on duroid substrate with copper

Δ f = 0.014 GHz

Figure 4.4: S12 Response of Interdigital T-shape straight resonator (λ/2) on Duroid

using Copper at 1.5GHz.

4.2.3 NOVEL ULTRA COMPACT INTERDIGITAL MEANDERED

RESONATOR

Figure 4.5, shows the dimensional details of an ultra compact interdigital

meandered resonator. Its total length is 12.4mm, which is three times smaller

than conventional one (Figure 4.3). This miniaturization achieved by


76

meandering the T-shape straight resonator presented previously. The

meander line is 4.4mm long and width is 0.6mm.

Figure 4.5: Proposed novel ultra compact interdigital meandered resonator on

Duroid using Copper at 1.5 GHz.


77

1.3 1.4 1.5 1.6 1.7

-55

-50

-45

-40

-35

-30

-25

-20M

agni

tude

(dB

)

Frequency (GHz)

S12

Simulation results of Novel ultra compact interdigital meandered resonator on Duroid substrate at 1.5GHz

QU= 100fo =1.5 GHzΔ f = 0.015

Δ f

Figure 4.6: S12 response of novel ultra compact interdigital meandered resonator

on Duroid using Copper at 1.5GHz.

The simulation result of this resonator is shown in Figure 4.6, using copper.

The Q-value with lossless metal obtained was 375 and with copper were 100

at central frequency 1.5 GHz. The Q value is expected to decrease due to the

meandering of lines, as corner edges make the current peak so higher losses

are present, and also radiation losses increases. Figure 4.7, shows the

comparison of proposed resonators at 1.5GHz in terms of size, it’s clearly

visible that the ultra compact meandered resonator is very compact.


78

Figure 4.7: Comparison of proposed resonators with respect to size


79

Table 4.3 presents a summary of the obtained Q-values with copper and

lossless metal.

METAL TYPES of RESONATOR Q-VALUE ( unloaded)

Lossless Conventional (λ/2) 462

Interdigital T-shape straight resonator 378

Ultra compact interdigital meandered resonator

375

Copper Conventional (λ/2) 108

Interdigital T-shape straight resonator 107

Ultra compact interdigital meandered resonator

100

Table 4.3: Summary of Q-value obtained with Copper and lossless metals on Duroid

(εr= 10.8, thickness (t) = 0.64mm and tan δ = 0.0023) for all types of resonators

proposed at 1.5 GHz.

4.3 3 POLE CHEBYSHEV BANDSTOP FILTER ON DUROID

SUBSTRATE AT 1.5 GHz

In this section, the designing procedure of 3 pole Chebyshev bandstop filter is

presented. The main theory of band reject filters was presented in chapter 2.

Two filters are designed; the first one use the T-shape straight resonator

described in section 4.2.2 and other one uses the ultra-compact meandered

resonator described in section 4.2.3.


80

4.3.1 3-POLE CHEBYSHEV BANDSTOP FILTER USING

INTERDIGITAL T-SHAPE STRAIGHT RESONATOR

Bandstop filters consist of serially coupled resonators to a transmission line.

Each resonator absorbs energy at a certain frequency and hence the

transmitted power from input and output is equivalent to the power that was

not trapped in the resonators. This turns out to be a bandreject filter

characteristic. The resonators can be electromagnetically coupled to the main

transmission line, or can be directly connected to it. A general bandstop filter

is shown in Figure 4.8 each resonator is coupled to the transmission line with

interdigital capacitors. The distance between adjacent resonators is λ/4.

To design the 3 pole Chebyshev bandstop filter shown in Figure 4.8, a

bandwidth (BW) of 10% was chosen. Initially the reactance slope parameters

were calculated using following gi values of Chebyshev lowpass prototype:

The element values of the chosen Chebyshev lowpass prototype for Ωc=1

are [4]:

Passband equal-ripple (LAr) = 0.04321dB

g0 = g4= 1, g1= g3= 0.8516 and g2= 1.1032

FBWgg

ZZ

Zxci

o

o

uoi Ω⎟⎟

⎠

⎞⎜⎜⎝

⎛=

2

i= 1, 2, 3 (4-3)

Where, is reactance slope parameter, Zix o is terminal impedance (50 ohms)

and Zu is the characteristic impedance.


81

Figure 4.8: Three pole Chebyshev bandstop filter T-shape straight resonator on

Duroid at 1.5 GHz using copper.

The calculated normalized reactance slope parameter values are in (4-4).

74.11

9

74.11

3

2

1

=

=

=

o

o

o

ZxZxZx

(4-4)

To obtain similar normalized reactance slope parameter values of (4-4) in EM

simulator, the length of the interdigital capacitor (Li) was varied and coupling

gap (Cg) was kept fixed to 0.4mm, as shown in Figure 4.9.


82

(a)

(b)

Figure 4.9: (a) Structure to obtain x1/ Zo and x3 / Zo value of Normalized reactance slope parameter in EM simulator by varying Li, (b) Structure to obtain x2 / Zo

value of Normalized reactance slope parameter in EM simulator by varying Li.


83

dB

o

dB

o

o

i

ff

Zx

33 22 Δ=

Δ=

ωω

(4-5)

The different values of normalized slope parameter with respect to variable

length (Li) of the capacitor are shown in Figure 4.10. The different values of

capacitor length with the respective normalized slope parameter for first and

second resonators at 1.5 GHz are shown in Figure (4.10(a.b)). The desired

lengths of the capacitor (Li) were determined to be L1 = L3 =7.6 mm and

L2 = 6.9mm.

7.0 7.2 7.4 7.6 7.8 8.0 8.2 8.4 8.6 8.8 9.06

8

10

12

14

16

Xi /

Zo

Length of capacitance (mm)

11.7

Normalized reactance slope parameter against length of capacitor

Figure 4.10: (a) Normalized reactance slope parameters obtained by varying

(Li) capacitance by for 1st and 3rd resonators.


84

6.2 6.4 6.6 6.8 7.0 7.2

6

8

10

12

14X

i / Z

o

Length of capacitor (mm)

9

Normalized reactance slope parameter against length of capacitor

(b)

Figure 4.10: Illustrate the extracted normalized reactance slope parameter against

variable lengths (Li) of capacitor (a) Normalized reactance slope parameters obtained by varying (Li) capacitor by for 1st and 3rd resonators, (b) Normalized reactance slope parameters obtained by varying (Li) capacitance by for 2nd resonators.

Figure 4.11, shows the detail dimension used to design interdigital T-shape

3-pole Chebyshev bandstop filter at 1.5GHz and Figure 4.12, presents its

simulation results. From this graph it is seen that the bandwidth was 9.9%,

the return losses were -2.7dB and the insertion losses were below -20dB at

the centre frequency.


85

Figure 4.11: Detail dimension of 3 pole Chebyshev bandstop filter using T-shape straight resonators at 1.5 GHz


86

1.3 1.4 1.5 1.6 1.7-35

-30

-25

-20

-15

-10

-5

0M

agni

tude

(dB)

Frequency (GHz)

S11_simulated S12_simulated

BW=9.9%fo= 1.49GHz

3 pole Chebyshev bandstop filter

Figure 4.12: Simulation response of 3 pole Chebyshev bandstop filter using interdigital

T-shape straight resonators using copper at 1.5GHz.

4.3.2 3 POLE CHEBYSHEV BANDSTOP FILTER USING ULTRA

COMPACT INTERDIGITAL MEANDERED RESONATOR AT

1.5 GHz

In this section, the designing of a 3pole Chebyshev bandstop filter using ultra

compact interdigital meandered resonator is described. The design procedure

is similar to the one described in section 4.3.1, the only changed is the type of

resonator and length of the interdigital capacitance used to calculate

reactance slop parameter. Figure 4.13, shows the layout of the filter using

ultra compact meandered resonators. The advantage of this filter is its


87

compact size (39.2mm x 13mm) as compared to the bandstop filter proposed

in section 4.31 (41mm x 28.2mm). The values of normalized reactance slope

parameters described in previous section were used to design this filter.

Figure 4.13: The 3 pole compact Chebyshev bandstop filter using ultra compact

interdigital meandered resonators at 1.5 GHz.

The required length of the capacitor with respect to the required normalized

slope parameter is L1= 6.1mm for the first and third resonators; and for

second resonator the length of the capacitor L2= 6.5mm. Figure 4.14 shows

the detail dimensions of the capacitor.


88

Figure 4.14: Structure to calculate reactance slope parameter by varying length of

interdigital capacitor (Li).

Figure 4.15 (a) is photograph of the fabricated microstrip 3 pole Chebyshev

bandstop filter using ultra compact interdigital meandered resonators and

Figure 4.15 (b) shows the simulation response of this filter. The bandwidth

obtained by simulation was 8.6% with central frequency 1.506 GHz. Insertion

losses were below -20dB and return loss -2.7 dB at the centre frequency.


89

4.15: (a) Photograph of the fabricated microstrip 3 pole Chebyshev bandstop filter

using compact interdigital meandered line resonator.


90

1 .3 1 .4 1 .5 1 .6 1 .7-30

-25

-20

-15

-10

-5

0M

agni

tude

(dB)

F re qu en cy (G H z)

S 1 1 S 1 2

B W = 8 .6 %fo = 1 .5G H z

S im u la tion re su lt o f C om ap ct 3 p o le C he bysh ev b an ds to p filte r

(b)

Figure 4.15: (a) Photograph of the fabricated microstrip 3 pole Chebyshev

bandstop filter using compact interdigital meandered line resonator, (b) The simulation response of microstrip 3 pole Chebyshev bandstop filter using compact interdigital meandered line resonator at 1.5GHz.

4.4 MICROSTRIP RESONATORS AT 10GHz

In this section the designing of resonator at 10 GHz is described, which

follows the same procedure designed as mentioned in section 4.1 of this

chapter. The main idea of the resonators presented in this section is the

removal of silicon substrate beneath selective parts of the resonator using

micromachining technology to increase Q value. This proposal is very unique


91

as there is no literature found related to selective removal of substrate. This

proposal is very beneficial at lower end of the millimeter spectrum, since high

Q values are obtained with enough mechanical strength to support the

structure, something that could not be achieved by traditional membrane

support structures (chapter 2).

There are three types of resonators proposed to design filters at 10GHz, they

are:

(λ/2) resonator on silicon substrate.

Patch resonator on silicon substrate.

Patch resonator on silicon substrate with air window beneath the patch.

Patch resonator on silicon substrate with air window beneath the strip.

At 10GHz all proposed resonators and filter are fabricated on HR-Si using

Aluminum as conductor. Silicon substrate was used due to following

advantages.

Silicon is a mature technology

It has an excellent planarity for the flip chip and bounding technologies.

It is good thermal conductor.

Multi interconnect metal layer are easily achieved devices that can not

be realized on wafer can be realized on other material and then flip

chip can be attached.

Micromachining technology works on Silicon.

Integrability with active circuits.


92

4.4.1. MICROSTRIP CONVENTIONAL RESONATORS (λ/2)

To design the microstrip resonator at 10 GHz we selected N type high

resistivity (HR) silicon substrate of resistivity 2000 Ω cm with 400 15µm

thickness, its orientation is <100>. Aluminum of resistivity 2.2µΩ-cm was

used as conductor. For comparison purpose, the resonators were simulated

with Aluminum and Silver. The design parameters are specified in tables 4.4

and 4.5.The cross section view of a microstrip circuit is shown in Figure 4.16.

It can be seen that SiO

±

2 layer was used to electrically isolate the HR-Si and

the metal to decrease the substrate losses [13]. The figure also shows the

grounded coplanar waveguide used to connect the device to a probe station.

Figure 4.16: Cross section view of microstrip

Layer Thickness (mm)

Relative Permittivity (εr)

Dielectric tangent loss (tan δ)

SiO2 0.0015 3.9 0.007

Substrate

(Silicon -HR )

0.4 11.9 0.01

Table 4.4: Specifications of substrate to design microstrip resonators at 10GHz [6, 7].


93

Metal Thickness (µm) R dc ⎟⎟

⎠

⎞⎜⎜⎝

⎛tσ

1

(Ω/sq)

Skin effect

( )⎟⎟⎠

⎞⎜⎜⎝

⎛

σπμ

Aluminum 2 0.13440 3.25e-7

Silver 2 8.104 x 10 -3 2.53 e-7

Table 4.5: Specifications of Copper and Silver metals to design microstrip

resonators at 10GHz [7].

The length of the microstrip resonator (λ/2) (shown in Figure 4.17) was

calculated with respect to central frequency and relative permittivity of the

substrate using formula (4-1). The wavelength λ = 8.7mm was obtained;

hence the resonator length (λ/2) is 4.35mm. By using full EM simulator [1] the

resonator length (λ/2) is optimized to 5mm, using a line width of 0.4mm. This

resonator was weakly coupled to the feed lines in order to obtain the

unloaded Q-factor. The response of this resonator (λ/2) is shown in Figure

4.18 giving a simulated Q is 43 using equation (4-2).

Figure 4.17: conventional resonator at 10GHz on HR-Si substrate using Aluminum.


94

9.8 10.0 10.2 10.4 10.6 10.8-36

-34

-32

-30

-28

-26

-24

-22

-20M

agni

tude

(dB

)

Frequency (GHz)

S12_simulated

Δ f

fo=10.26GHz

Δ f=0.235QU= 43

S12 response of Conventional (λ/2) resonator on HR-Si at 10GHz

Figure 4.18: S12 Response of microstrip resonator (λ/2) at 10 GHz.

4.4.2. MICROSTRIP PATCH RESONATORS

In order to reduce the length of the resonator an extra capacitive patch was

added to it, hence increasing the capacitance to ground and thus reducing

the total length. The final layout of this resonator is shown in Figure 4.19(a).

As it can be seen, the overall length was decreased from 5mm (conventional

resonator) to 4.4mm. Figure 4.19(b) represents the simulation results of the

weakly coupled resonator. The obtained Qu is 40.


95

(a)

9.9 10.0 10.1 10.2 10 .3 10 .4 10.5-29

-28

-27

-26

-25

-24

-23

-22

-21

-20

Δ f

Mag

nitu

de (d

B)

F requency (G H z)

S12_sim ula ted

fo = 10.2G H z

Δ f3dB = 0.255

Q U = 40

S12 Sim ulation response of Patch resonator on H R-Si at 10G H z

(b) Figure 4.19: (a) Layout of patch resonator on HR-Si substrate, (b) S12 Simulation

results of patch resonator representing at 10 GHz.


96

4.4.3. MICROSTRIP PATCH RESONATORS WITH AIR WINDOWS

In this section, the approach to increase the Q-value of the resonator is

proposed by removing selective parts of the substrate beneath the resonator

using micromachining technology. Here two different patch resonators with

higher Q-value are proposed using micromachining technology.

The first proposed patch resonator with selective removal of silicon beneath

the patch is illustrated in Figure 4.20 and the second, resonator with air

window beneath the strip is shown in Figure 4.21. The patch resonator with

Silicon removal underneath the patch has a total length of 5.61mm

(Figure 4.20a). The simulation results of the weakly coupled resonator are

shown in Figure 4.20(b), the unloaded Qu is 114 using Aluminum.

Figure 4.20: (a)(i): Cross section view of Patch resonator having Air window

underneath the Patch


97

Figure 4.20: (ii): (a)

9.5 10.0 10.5 11.0-45

-40

-35

-30

-25

-20

Mag

nitu

de (d

B)

Frequency (GHz)

S12_ simulated

S12 Simulation Response of Silicon with air window beneath Patch of resonator using Aluminum

fo = 10.25 GHz

QU = 114

(b)

Figure 4.20: (a): (i) Cross section view of Patch resonator having Air window

underneath the Patch, (ii) 3-D view of Patch resonator on Silicon having Air window underneath the Patch (using Coventor), (b): S12 simulation result of patch resonator with high Q on air window beneath the patch on HR-silicon substrate at 10GHZ using Aluminum.


98

The second proposed patch resonator with removal of silicon beneath the

strip, has a total length of 6.32mm is shown in Figure 4.21a. The simulation

results of the weakly coupled resonator are shown in Figure 4.21b, the

unloaded Qu is 171 using Aluminum.

Figure 4.21: (a) (i): cross section view of patch resonator with selective removal of

substrate beneath the strip of resonator,

Figure 4.21: (a) (ii): 3-D view of Patch resonator on Silicon having Air window beneath

the strip (using Coventor),


99

9.5 10.0 10.5 11.0-50

-45

-40

-35

-30

-25

-20M

agni

tude

(dB

)

Frequency (Ghz)

S12_ simulated

S12 Simulation response of patch resonator with air window betneath strip using Aluminum metal

fo= 10.3 GHz

QU = 171

(b)

Figure 4.21: (a): (i): cross section view of patch resonator with selective removal of substrate beneath the strip of resonator,

(ii): 3-D view of Patch resonator on Silicon having Air window beneath the strip (using Coventor),

(b): S12 simulation result of patch resonator with high Q on air window beneath the patch on HR-silicon substrate using Aluminum metal.

The choice of the resonator should depend on the type of application

requirements or upon the size and performance. The performance of these

two higher Q resonators is better than the conventional resonator presented

in section 4.4.1 which had a Qu is 43.


100

Table 4.6 represents comparison of Q-values obtained when Aluminum was

used as conductor and when Silver was used as conductor. From table 4.6

the Silver metal gives better Q values as compared to Aluminum. With Silver

the Q value obtained for a conventional resonator is 46(with aluminum 43).

For the patch resonator on HR-silicon substrate is the Q is 49 (40 with

aluminum). With air window beneath the strip of patch resonator the Q valued

raised to 229 by using Silver metal (compared to 171 with Aluminum). For the

fabrication Aluminum was selected as conductor for fabrication as it is

compatible with CMOS processes used in the Microelectronics Laboratory at

INAOE.

229 Patch resonator Silicon with air window beneath

strip

117 Patch resonator Silicon with air window

underneath patch

49 Patch resonator Silicon

46 resonator Silicon Silver

171 Patch resonator Silicon with air window beneath

strip

114 Patch resonator Silicon with air window

underneath patch

40 Patch resonator Silicon

43 resonator Silicon Aluminum

Q-VALUE (unloaded)

RESONATOR TYPE SUBSTRATE METAL

λ/2

λ/2

Table-4.6: Comparison of Q-value of resonators proposed obtained with

Aluminum and Silver metal at 10GHz.


101

4.5 3 POLE CHEBYSHEV BANDSTOP FILTER ON

HR-SILICON SUBSTRATE AT 10 GHz

In this section, design of compact 3 pole Chebyshev bandstop filter using

patch resonator is presented. The designing method is similar as described in

section 4.3.1. The chosen substrate was HR-Si (εr = 11.9 and thickness 0 0.4

μm) without any removal of Si and the resonator is shown in section 4.4.2.

The conductor used is Aluminum. The filter layout is shown in Figure 4.22.

Figure 4.22: Three pole Chebyshev bandstop filter using patch resonator at 10 GHz

using Aluminum as metal.


102

The designing parameters used to calculate normalized reactance

slope parameter were:

Bandwidth (BW) = = 10%

Fractional bandwidth (FBW) = 0.1

The element values of the chosen Chebyshev lowpass prototype

for Ωc=1 are [4]:

Passband equal-ripple (LAr) = 0.04321dB

g0 = g4= 1, g1= g3= 0.8516 and g2= 1.1032

Equation (4-3), was used to calculate normalized reactance slope

parameters [4]. The 50 Ω main line has a width of 0.4mm (Figure 4.20). By

following the procedure already described in section 4.3.1, the gaps between

the 50 Ω line and the resonator were changed and simulated using [1] in

order to obtain the different reactance slope parameters. The normalized

reactance slope parameter is then extracted according to equation (4-5).

Figure 4.23, presents the structure to obtain normalized reactance slope

parameter in EM simulator by varying lengths (Li) of the capacitor coupled to

the patch resonator, keeping coupling fixed to 0.04mm between patch and

capacitor and also between resonator and transmission line. Its simulation

response is shown in Figure 4.24. The desired length of the capacitors are

L1 = L3 =1.07 mm and L2 = 0.53mm.


103

(a)

(b)

Figure 4.23: Structure to calculate normalized reactance slope parameter by varying

length of capacitor (Li).


104

(a)

(b)

Figure 4.24: Extracted normalized reactance slope parameter against variable lengths (Li) of extra capacitance coupled to the patch resonator, (a): The reactance slope parameter by the extra capacitance introduced to patch of the resonator, (b): The reactance slope parameters obtained by varying extra capacitance length introduced towards strip of patch resonator.


105

Figure 4.25, shows the simulation response of microstrip Chebyshev

bandstop filter on silicon substrate at 10GHz (Figure 4.22). As it can be seen

the bandwidth is 0.9GHz (9%) and the return loss is -1.5 dB throughout the

band and the insertion loss at center frequency is about -15dB.

8.0 8.5 9.0 9.5 10.0 10.5 11.0

-25

-20

-15

-10

-5

0

Mag

nitu

de (d

B0

F requency (G H z)

S11_sim ula ted S12_sim ula ted

fo

f0= 9 .72 G H zBW =0.9G hz

3 pole Chebyshev bandstop filter at 10GHz on silicon using Alum inum

Figure 4.25: Simulation response of microstrip Chebyshev bandstop filter on silicon

substrate at 10GHz using Aluminum.

4.6 DESIGNING OF COPLANAR WAVEGUIDE (50Ω)

In this section, coplanar waveguide designing and simulation is presented. A

conventional grounded CPW consist of dielectric substrate with conductors on

the top surface and bottom surface as shown in Figure 4.26(a). The CPW


106

used in this work is necessary for probe station measurements. The CPW to

microstrip transition was optimized by adjusting L1, L2, L3, L4 and G1, G2,

G3, G4. Figure 4.26(b), shows the simulation response of final structure

obtained with L1=0.45mm, L2=0.4mm, L3=2.6mm, L4=4.9mm and width

G1=0.04mm, G2= 0.07mm, G3=0.1mm and G4=0.2mm at the central

frequency (10GHz).

(a)


107

(b)

Figure 4.26: Proposed CPW to microstrip transition (a) Proposed CPW structure, (b) Transition frequency response.

Initially, all the steps were simulated separately for 50 Ω and after that all

were combined into one structure and input and output port impedance was

obtained to be 50 Ω. Small step were used in this CPW structure to maintain

the characteristic of lump elements through out the transmission line. The

return loss (S11) response is -23dB. Two via holes were micromachined on

each ground surface to connect bottom and top ground planes. The size of

via holes was 500 µm x 500 µm. The fabrication process is shown in

chapter 6.


108

CONCLUSION

In this chapter, the design of novel resonators and Chebyshev bandstop

filters along with there respective simulation results have been presented.

The objective of designing resonators was to obtain compact size as well as

high Q value.

At 1.5GHz, three novel structures of resonators are presented and were

compared in terms of Q values and size to achieve the goal of compactness

and high Q. The first is conventional resonator (37mm) with copper Qu is 108

(lossless metal=462). Second is T-shape straight resonator (27.6mm)

structure which is 9.4mm smaller than conventional and its Q value with

copper is Qu is 107 (lossless metal=378), and the third is Ultra compact

interdigital meandered resonator (12.4mm), which is three times smaller than

the conventional resonator (37mm). The Q value with copper is Qu is100

(lossless metal=375).

At 1.5GHz, two 3 pole Chebyshev bandstop filters with 10% bandwidth have

been designed using the pervious resonators with good simulation responses.

At 10GHz, novel patch resonators layout have been proposed with selective

air windows beneath the patch and underneath the strip of the resonator

using micromachining technology. The total length of the conventional

resonator was 5mm with Qu is 43 and the patch resonators length was 4.4mm

with Qu is 40. The Q value obtained with patch resonator having air window

beneath the patch was Qu is 114 and with patch resonator having air window

underneath the strip is Qu is 171. Hence, by comparing the Q values it is clear

that we successfully increased the Q values from 40 (patch resonator) to

114(air window beneath patch) and 171(air window beneath strip). This


109

proposal is another special achievement in this thesis work as there is no

literature found on selective removal of substrate at lower frequency to obtain

higher Q values.

A Chebyshev bandstop filter is proposed using patch resonator on HR-Si at

10GHz with good simulation response.

REFERENCES

[1] “Sonnet 7.0b”, ©1989, 1991, 1993, 1995-2001 Sonnet Software, Inc.

[2] Jia-Sheng Hong and M.J.Lancaster, “Investigation of microstrip

pseudo-interdigital bandpass filters using a full-wave electromagnetic

simulator”, International Journal of Microwave and Millimeter-Wave

computer-Aided engineering, 7, 3, May 1997, 231-240.

[3] J.C.Rautio and G.Mattaei, “Tracking error sources in HTS filters

simulations”. Microwave & RF, 37, Dec,. 1998, 119-130




[5] Data sheet, www.Rogerscorporation.com

[6] http://www.rfcafe.com/references/electrical/dielectric_constants_streng

ths.htm.

[7] Brain C.Wadell, “Transmission Line Design handbook”, © 1991 Artech

house, Inc.

http://www.rogerscorporation.com/

http://www.rfcafe.com/references/electrical/dielectric_constants_strengths.htm

http://www.rfcafe.com/references/electrical/dielectric_constants_strengths.htm


110

[9] R.F. Harringdon, Field Communication by Moments Methods,

Macmillian, New York, 1968.

[10] J.C.Rautio and R.F Harrington,”An electromagnetic time-harmonic

analysis of arbitarary microstrip circuits”. IEEE Trans., MTT-35,

Aug.1987, 726-730.

[11] M.Koshiba, K.Hatata, and M.Suzuki, “Finite-element formulation in

terms of the electric-filed vector for electromagnetic waveguide

problems”, IEEE Trans.MTT-33, Oct.1985, 900-905.

[12] Paolo Delmastro “TRANSLIN software”, Artech house.

[13] J.A.Reynoso-Hernández, Raúl Rancel-Rojo, M.Aceves, I. Zaldivar,

L.E. Sánchez, and M.Herrera “ Influence of the SRO as passivation

Layer on the Microwave attenuation Losses of the CPWs Fabricated

on HR-Si”, IEEE microwave and wireless components

letter ,Vol.13,No.12,Dec.2003.

CHAPTER 5: DESIGNING OF TRIPLET BANDSTOP FILTERS AT 1.5 GHz

111

INTRODUCTION

There has been an increasing demand for advance RF /microwave filters

other than conventional Chebyshev filters in order to meet stringent

requirement from RF/microwave systems, particularly from wireless

communications systems. In this chapter, the designing of advanced filter

topologies using trisections with single transmission zero is proposed which

gives higher selectivity at one side of the band. If double side selectivity is

required then two Trisection filters can be cascaded. In practice single side

selectivity is used in Diplexer designs where, Transmission and Receive

signals have to separate at mobile base stations, Satellite systems, etc.

No other work has been published (to the author’s knowledge) on Triplet

bandstop filters which makes this work highly valuable and propositive. The

principle of operation of these filters is based on the cross coupling of

non-adjacent resonators. In this chapter, the full designing procedure will be

explained and simulation results of the proposed structure are presented.


112

This chapter is divided into three subsections, section 5.1, presents theory of

selective filters with transmission zeroes (Quasi-elliptic response), Section 5.2,

gives information about the working of Trisection filters with the help of

bandpass filter structures, section 5.3, describes about the designing

procedure of Triplet bandstop filter at 1.5 GHz based on optimization method.

5.1 FILTERS WITH SINGLE PAIR OF TRANSMISSION ZERO (QUASI ELLIPTIC RESPONSE)

The filter having only one pair of transmission zeroes at finite frequencies

gives much improved skirt selectivity, making it a viable intermediate between

the Chebyshev and elliptic function filters (Figure 5.1). The transfer function of

this type of filter is:

( ) ( )Ω+=Ω

nFS 22

221 1

1ε

(5-1)

110

1

10 −

=− RL

ε (5-2)

( ) ( ) ( )⎭⎬⎫

⎩⎨⎧

⎟⎟⎠

⎞⎜⎜⎝

⎛Ω+Ω+ΩΩ

+⎟⎟⎠

⎞⎜⎜⎝

⎛Ω−Ω−ΩΩ

+Ω−=Ω −−−

a

a

a

an nF

1cosh

1coshcosh2cosh 111


113

Figure 5.1: Comparison of frequency of the Chebyshev filter and the design filters with

single pair of attenuation poles at finite frequency (n=6)

Where Ω is the frequency variable that is normalized to the passband cut-off

frequency of the lowpass prototype filter, ε is ripple constant to a given return

loss 11log20 SLR = in dB, and n is the degree of the filter. The closer the

attenuation poles to the cutoff frequency (Ω=1), the shaper the filter skirt will

be and higher will be the selectivity.

5.1.1 APPROXIMATION SYNTHESIS PROCESS OF QUASI ELLIPTIC

The transmission zeroes of this type of filter may be realized by cross

coupling the pair of non adjacent resonators of the standard Chebyshev filter

the approximate synthesis method based on a lowpass prototype filter is

shown in Figure 5.2 [1], where the rectangular box represents ideal

admittance inverters with characteristic admittance J. The approximate

synthesis starts with the element values for Chebyshev filter using (5-1, 5-2).


114

γ

πng 2

sin21 = (5-1)

( ) ( )

( ) ( ) 2/,,.....2,11sin

232sin

212sin4

221 nmmi

ni

ni

ni

gg ii ==−

+

−−

=− πγ

π

(5-2)

Where,

⎟⎠⎞

⎜⎝⎛= −

εγ 1sinh1sinh 1

n (5-3)

( ) ( )

0

11

1

22

=

=

++=

−m

m

JS

J

VSWRpassbandtheS εε

(5-4)

In order to introduce transmission zero at aΩ±=Ω the required

value of Jm-1 is given by equation (5-5):

( ) 2'2

'

1

mma

mm

JgJJ−Ω

−=− (5-5)


115

Figure 5.2: Standard Chebyshev filter the approximate synthesis method based on a lowpass prototype filter

Introduction of Jm-1 mismatches the filter, and to maintain the required return

loss at midband it is necessary to change the value of Jm slightly according to

the formula given by equation (5-6).

1

'

1 ++=

mm

mm

JJJ

J (5-6)

Where, is interpreted as the updated J'mJ m. Equation (5-6) and (5-5) are

solved iteratively with the initial values of Jm and Jm-1 given in equation (5-2).

No other elements of Chebyshev filter are changed.

The method is simple, however quite useful in many cases for the design of selective

filters. It suffers from inaccuracy, and even can fail for very high selective filters that

require moving the attenuation poles closer to the cut-off frequencies of the passband.

This implies the use of more accurate synthesis procedure. Alternatively, one can use

a set of more accurate design tabulated data [1]. For less selective filters that require a

larger Ωa, the element values can be obtained using above approximation synthesis

procedure.


116

5.2 TRISECTION FILTERS In this section the importance of working with Trisection filters is explained. As

there is no pervious report on Triple Bandstop, we are presenting the theory

available on bandpass Triplets. Trisection filter is basic unit for construction of

higher-degree cascaded trisection (CT) filters. To understand how it works

lets take case of the narrow-band, an equivalent circuit of Figure 5.3 (a) can

represent a trisection filter. The coupling between adjacent resonators are

indicated by the coupling coefficient M12 and M23 and the cross coupling is

denoted by M13. Qe1 and Qe3 are the external quality factors denoting the

input and output couplings.

Note: the resonators are not necessary synchronously tuned for trisection

filter and therefore each resonator resonates at different frequencies.

iiCL1 =ωoi=2πfoi is the resonator angular frequency of the resonator i for i=1,

2 and 3. To have asymmetric response of frequency trisection filters, the

physical configuration of the filter can be kept symmetric. Therefore, let

M12=M23, Qe1=Qe3 and ωo1=ωo3.

Figure 5.3: (a) Equivalent circuit of a trisection bandpass filters.


117

Figure 5.3: (b) Associated lowpass prototype filter.

TRISECTION FILTER

CHEBYSHEV

TRANSMISSION ZERO

(c)

Figure 5.3: (a) Equivalent circuit of a trisection bandpass filter, (b) Associated lowpass prototype filter, (c) the comparison between ideal Chebyshev filter and Trisection filter

response.

The above coupled resonator circuit may be transferred to lowpass prototype

filter as shown in Figure 5.3(b). Each of the rectangular boxes represents a


118

frequency invariant immittance inverter, with J the characteristic admittance of

the inverter, here J12=J23=1 of the inverters along the main path of the filter.

The bypass inverter with a characteristic admittance J13 accounts for cross

coupling gi and Bi (i=1, 2, 3) denote the capacitance and the frequency

invariant susceptance of the lowpass prototype filter, respectively. g0 and g4

are the resistive terminations. With symmetric two-port circuit of Figure 5.3(b),

g0=g4, g1=g3 and B1=B3. Also g0=g4=1 be the normalized termination. The

scattering parameters of the symmetric circuit may be expressed in terms of

even and odd mode parameters of one-port circuit formed by inserting an

open or short circuited plan along its symmetric plan [1]. Figure 5.3 (c),

shows the comparison between Ideal Chebyshev filter and Trisection filter

response. The transmission zero makes very selective cut off at one side as

shown in figure 5.3(c), which makes the use of Trisection filters advantageous

for certain applications. If double side selectivity as required then two

Trisection filters could be cascaded.

5.2.1 MICROSTRIP TRISECTION FILTERS Microstrip trisection filters with different resonator shapes, such as open-loop

resonator and triangular patch resonator, can produce asymmetric frequency

responses with an attenuation pole of finite frequency on either side of the

passband.

When all the designing parameters are know gi, Jnm, Qe, Mmn, fo for the cross-

coupled resonator filter using formula given in [1], we can obtain an image

frequency response of the filter with finite frequency attenuation pole moved

to the low side of the passband.This kind of design parameters have dual

usage, and one may take the advantage of this to design the filter with the

image frequency response also. Having obtained the required design


119

parameters for bandpass filter, the physical dimensions of the microstrip

trisection filter can be determined using full EM simulator to extract the

coupling and external quality factor.

5.3 DESIGNING PROCEDURE OF NOVEL TRISECTION

BANDSTOP FILTER AT 1.5 GHz

In this section, the design procedure of Trisection filters is presented.

Photograph of proposed triplet filter is shown in Figure 5.4. The design

parameters for the filters are:

Bandwidth = 4.5%

Fractional bandwidth = 0.1

Central frequency = 1.5GHz

To design this filter the substrate was duroid [table 5-1] and copper was

chosen as conductor [table 5-2]. The substrate and metal specification used

in this work are given in table-5.1 and table-5.2.

Substrate Thickness (mm)

Relative Permittivity (εr)

Dielectric tangent loss (tan δ)

Substrate

(Duroid RT/6010LM)

0.64 10.8 0.0023

Table 5.1: Specifications of substrate to design microstrip resonators at 1.5GHz [5]

Metal Thickness

(mm) R dc

(Ω/sq) Skin effect

Copper 0.017 0.001021 2.618e-7

Table-5.2: Specifications of copper to design microstrip resonators at 1.5GHz [7]


120

Figure 5.4: Photograph of proposed novel Trisection Bandstop filter at 1.5GHz.

The design procedure steps are shown in Figure 5.5.

Figure 5.5: The steps follow to design Trisection filter.


121

STEP1: Initially, the 3 pole Chebyshev bandstop filter with lumped

elements was designed using the procedure shown in chapter 4, as shown in

Figure 5.6.

The designing parameters to calculate normalized reactance slope

parameter were:

Bandwidth = 4.5%

Fractional bandwidth = 0.1

The element values of the chosen lowpass prototype for Ωc=1 are [4]:

For a Chebyshev filter with passband equal-ripple (LAr) = 0.04321dB

g0 = g4= 1, g1= g3= 0.8516 and g2= 1.1032

Equation (5-7) was used calculate reactance slope parameter [1].

FBWg

gZZ

Zxci

o

o

uoi Ω⎟⎟

⎠

⎞⎜⎜⎝

⎛=

2

i= 1, 2, 3 (5-7)

Where, is reactance slope parameter, Zix 0 is terminal impedance (50 ohms)

and Zu is the characteristic impedance. Consider = in equation (5-7)

which is to normalized impedance to calculate slope parameter.

uZ oZ

From equation (5-7) we obtained reactance slope parameter values given in

equation (5-8) for each resonator to be coupled to the main transmission line.


122

74.11

9

74.11

3

2

1

=

=

=

o

o

o

ZxZxZx

(5-8)

At first instance, the coupling was achieved with lumped capacitances as it is

shown on Figure 5.6.

CAP

C=ID=

C1 pFC1

CAP

C=ID=

C2 pFC2

CAP

C=ID=

C1 pFC3

TLIN

F0=EL=Z0=ID=

1.5 GHz270 DegZ12 OhmTL1

TLIN

F0=EL=Z0=ID=


TLOC

F0=EL=Z0=ID=

1.5 GHzEL1 Deg50 OhmTL4

TLOC

F0=EL=Z0=ID=


TLOC

F0=EL=Z0=ID=


PORT

Z=P=

50 Ohm1

PORT

Z=P=

50 Ohm2

Z12=50

C2=0.6

C1=0.5

EL2=155

EL1=159

Figure 5.6: Chebyshev bandstop filter using lump elements.


123

STEP 2: After designing Chebyshev bandstop filter using lumped

elements, cross coupling was done between non-adjacent resonators with

50Ω transmission line having 90 degrees electrical length as shown in Figure

5.7 and its response is presented in Figure 5.7(b). As it can be seen, the

response does not give the desired response, hence, optimization using AWR

[2] optimizer was done to obtain exact values of the capacitance and

transmission line dimensions as presented in step 3.The optimization goals

are shown in Figure 5.7 (c).

CAP

C=ID=

C1 pFC1

CAP

C=ID=

C2 pFC2

CAP

C=ID=

C1 pFC3

TLIN

F0=EL=Z0=ID=


TLIN

F0=EL=Z0=ID=


TLIN

F0=EL=Z0=ID=


TLOC

F0=EL=Z0=ID=

1.5 GHz158 Deg50 OhmTL4

TLOC

F0=EL=Z0=ID=


TLOC

F0=EL=Z0=ID=


PORT

Z=P=

50 Ohm1

PORT

Z=P=

50 Ohm2

Z13=50

C2=0.5

C1=0.5

Z12=50

Figure 5.7: (a) Cross-coupling of non-adjacent resonators of Chebyshev bandstop

filter with 50Ω transmission line of 90 degrees electrical length.


124

Figure 5.7: (b) Response of initial trisection filter


125

Figure 5.7 :(c) Optimization goals to obtain required response.


filter with 50Ω transmission line of 90 degrees electrical length, (b) Response of initial trisection filter, (c) Optimization goals to obtain required response.

STEP 3: In this step the 50Ω transmission line cross-coupled to the

non- adjacent resonators was optimized to obtain improved response of the

Trisection bandstop filter with extra transmission zero. The optimized

Trisection filter is shown in Figure 5.8(a) and its optimized response is

presented in Figure 5.8(b). Here extra transmission zero response is clearly

visible towards higher frequency. The asynchronicity of the filter is clearly

seen as resonators 1 and 3 resonate at 1.49GHz where as resonator 2

resonate at 1.5GHz.


126

CAP

C=ID=

C1 pFC1

CAP

C=ID=

C2 pFC2

CAP

C=ID=

C1 pFC3

TLIN

F0=EL=Z0=ID=


TLIN

F0=EL=Z0=ID=


TLIN

F0=EL=Z0=ID=


TLOC

F0=EL=Z0=ID=


TLOC

F0=EL=Z0=ID=


TLOC

F0=EL=Z0=ID=


PORT

Z=P=

50 Ohm1

PORT

Z=P=

50 Ohm2

C1=0.95C2=1

Z12=50

Z13=200

Figure 5.8: (a) Cross-coupling of non-adjacent resonators of Trisection bandstop filter with 200Ω transmission line.


127

(b)

Figure 5.8: (a) Cross-coupling of non-adjacent resonators of Trisection bandstop filter

with 200Ω transmission line of 90 degrees electrical length, (b) Response of Trisection filter with lump elements.

STEP 4: The optimized lumped elements Trisection filters presented in

step 3 were replaced with layout structures. The resonator used to design

Trisection bandstop filter is ultra compact interdigital meandered resonators

(described in chapter 4). For Trisection filter, asymmetry tuning was required

as stated earlier, here the two different frequencies chosen was1.5GHz for

the first and third resonators and 1.49GHz was chosen for second resonator.

Hence, with respect to these two resonating frequencies, the slope

parameters were implemented using method described below.


128

The normalized reactance slope parameter 11.7 was chosen with respect to

the central frequency 1.5GHz of the resonator and normalized reactance

slope parameter 9 was selected for 1.49 GHz central frequency resonator.

Hence, Figure 5.9 gives the graph of normalized reactance slope parameter

of 1.5 GHz and 1.49 GHz and the typical response and extracted normalized

reactance slope parameters. The desired coupling (Li) are: L1 = L3 =6.3mm for

resonator first and third with central frequency 1.5GHz and L2 = 6.8mm length

of capacitor introduced to the second resonator with central frequency

1.49GHz.

6.0 6.2 6.4 6.6 6.8 7.0 7.2

4

6

8

10

12

14

16

18

Xi/Z

o


reactance slope parameter _Lossles

reactance slope parameter_copper

Normalized reactance slope parameter at 1.5GHz

11.6

Figure5.9: (a) The reactance slope parameter by varying the length of interdigital

capacitance at 1.5GHz,


129

6.0 6.2 6.4 6.6 6.8 7.0 7.2

4

6

8

10

12

14

16

18

Normalized reactance slope parameter at 1.49 GHz


Xi/Z

o reactance slope

parameter _Lossles

reactance slope parameter_copper

8.8

(b)

Figure5.9: (a) the reactance slope parameter by varying the length (Li) of interdigital capacitance at 1.5GHz, (b) The reactance slope parameters obtained by varying interdigital capacitance length (Li) at 1.49 GHz.

Figure 5.10 (a), shows the initial circuit of Trisection Bandstop filter replaced

with sub-circuits of original resonators and with interdigital capacitor with

transmission lines, its simulation response is presented in Figure 5.10(b). The

central frequency obtained was 1.5 GHz the transmission zero was obtained

at 1.49 GHz with return loss of -1.13dB and insertion loss of -15.6 dB at

central frequency, the drawback was the coupling transmission line between

resonator 1 and 3 was of impedance 200 Ω, which was not possible to

fabricate as the line would be extremely thin.


130

Figure 5.10: (a) The initial circuit of Trisection bandstop filter replaced with sub-circuits of original resonators and transmission line inverter.


131

(b)

Figure 5.10: (a) The initial circuit with transmission line inverter, (b) Response of filter with interdigital capacitor equivalent to transmission line of 200 Ω.

STEP 5: To over come the problem of 200 Ω transmission line,

transmission line inverter was implemented and the transmission line was

obtained in the form of interdigital capacitor of 0.95pF which was connected

to transmission line of electrical length 151.1 degrees at the left side and 11.5

degrees at the right side of interdigital capacitor. The calculation to obtain the

capacitive value of the inverter was done using formula given in [3]. The

circuit was optimized again to central frequency 1.5GHz with extra

transmission zero. Figure 5.11 (a), presents the steps and formulas used to

convert the 200Ω transmission line into 50Ω transmission line with a capacitor

[3]. The final circuit with transmission line inverter is shown in Figure 5.11(b),

and the circuit with interdigital capacitor, which is equivalent to the


132

transmission line 200 Ω is shown in Figure 5.11 (c) and its response is

present in Figure 5.11 (d).

Figure 5.11 (a) Steps and formulas used to convert transmission line of 200 Ω to

50 Ω transmission line using Admittance.


133

TLIN

F0=EL=Z0=ID=

1.5 GHzTheta/2 DegImp OhmTL2

TLIN

F0=EL=Z0=ID=

1.5 GHz(Theta/2)-140 DegImp OhmTL3

MSUB

Name=ErNom=

Tand=Rho=

T=H=

Er=

SUB1 2.2 0 1 0.017 mm0.64 mm10.8

CAP

C=ID=

0.96 pFC1 PORT

Z=P=

50 Ohm1

PORT

Z=P=

50 Ohm2

Theta=303

Imp=50

Figure 5.11: (b) The final circuit with transmission line inverter


134

Figure 5.11: (c) The circuit with interdigital capacitor, which is equivalent to the transmission line 200 Ω


135

(d)

Figure 5.11: (a) Steps and formulas used to convert transmission line of 200 Ω to 50 Ω transmission line using Admittance, (b) The final circuit with transmission line inverter, (c) the circuit with interdigital capacitor, which is equivalent to the transmission line 200 Ω, (d) Response of filter with interdigital capacitor equivalent to transmission line of 200 Ω.

The practical structure of interdigital capacitor of 0.95pF which is connected

to the transmission line of electrical length 200 degrees (41.4mm) with

impedance 48Ω on both sides to obtain transmission zero response is shown

in Figure 5.12(a). The total length is 31.6mm, the length of each capacitor

finger is 30.8mm, and the gap between each capacitive finger is 0.4mm. The

electrical length of transmission line used to couple resonator 1 with

resonator 2 is 190 degrees (39.6mm) with impedance of 48Ω. Practical


136

structure of Trisection bandstop filter is shown in Figure 5.12 (b), its

simulation response is present in Figure 5.12 (c).

Figure 5.12(a): The interdigital capacitor which is connected to the transmission line.


137

Figure 5.12(b): Dimensional detail of Photograph of proposed novel Trisection

bandstop filter at 1.5GHz.


138

.71.4 1.5 1.6 1

-35

-30

-25

-20

-15

-10

-5

0

Mag

nitu

de (d

B)

Frequency (GHz)

S11 S12

fo= 1.5GHzBW=3.3%Return loss= -1.9dBinsertion loss= -15.7dB

(c) Simulation response of Triplet bandstop filter with extra transmission zero.

Figure 5.12: (a): The interdigital capacitor which is connected to the transmission line, (b): The practical structure of Triplet bandstop filter at 1.5GHz, (c): Simulation results of Triplet bandstop filter with extra transmission zero.

The transmission lines are meandered to miniaturize the length of the

transmission line as shown in Figure 5.12(b). The lengths of the transmission

line used here to couple resonators are as follows in terms of electrical length:

1) To connect resonator 1 to resonator 2 the transmission line electrical

length is 190o and impedance is 50 Ω.

2) To connect resonator 2 to resonator 3 the transmission line electrical

length is 190o and impedance is 50 Ω.


139

3) To connect resonator 3 to one end of interdigital capacitor, the

transmission line electrical length is 200o and impedance is 50 Ω.

4) To connect resonator 1 to the interdigital capacitor the transmission

line electrical length is 200o and impedance is 50 Ω.

From simulation response shown in Figure 5.12(c) the central frequency

obtained was 1.57GHz and the bandwidth obtain was3.3%, transmission zero

was obtained on the higher frequency side. The experimental results of this

filter are presented in chapter 7.

CONCLUSION

In this chapter, the design procedure of Trisection filter has been presented.

The designing of a Novel Trisection bandstop filter with 4.5% bandwidth at

1.5 GHz has been proposed in this chapter using ultra compact T-shape

meandered resonator of 12.4mm x 10.6mm along with the simulation results.

The total size of Trisection bandstop filter is 72mm x 34mm. For Trisection

filters the asymmetric tuning of resonators was required to resonate each

resonator at different frequencies. To design triplet filter with extra

transmission zero, non-adjacent resonators were coupled directly with

interdigital capacitor, which is equivalent to transmission line of electrical

length 90o with the impedance of 200Ω. The bandwidth obtained by

simulation was 3.3% and central frequency 1.505 GHz. The experimental

results are presented in chapter 7.

Trisection filters very important and advantageous as these filter topology is

based on three resonators which make it compact. If double side selectivity is

required then two Trisection filters can be cascaded. In practice single side

selectivity is used in diplexer design.


140

REFERENCES




[2] Microwave office” Advancing the wireless revolution (AWR)” software

[3] Brain C.Wadell, “Transmission Line Design handbook”, © 1991 Artech

house, Inc.

[4] “Sonnet 7.0b”, ©1989, 1991, 1993, 1995-2001 Sonnet Software, Inc.

CHAPTER 6: FABRICATION PROCESS

141

INTRODUCTION

The main objective of this chapter is to describe the fabrication process for

the resonator and filter on high resistivity silicon (HR-Si) substrate at 10 GHz.

In first section, we depict about the mask to define the structure for resonator

and Chebyshev filter. In second section, we illustrate micromaching

techniques to etch the silicon (HR-Si). In last section; we give details of the

fabrication process.

6.1 MASK The design of photolithography mask for micromachining is generally

straightforward. Normally, designs incorporate relative large structures

(1-10 μm +) compared to the sub-micron structures that are now incorporated

into advanced Very Large Scale Integrated (VLSI) technologies. All that is

required is some suitable CAD (computer aided design) software, and a

platform to run it on. The basic CAD software required to design mask is a

"layout editor" (L-Edit). This enables to place different polygons onto different

layers, each layer being a mask design for a particular step in the fabrication


142

process, assemble these into "structures" (or "cells") which can be placed

adjacent to one another on the final design, and export the design file in a

suitable format [1].

Two masks where made using L-Edit [1]. The first one is of patch resonator at

10 GHz shown in Figure 6.1 and the second one is of 3-pole Chebyshev filter

at 10GHz illustrated in Figure 6.2. The Figure 6.1 (a) represent mask of metal

layer for resonator structure and coplanar waveguide (CPW) and 6.1(b)

corresponds to bottom layer of cavities designed for CPW. Figure 6.2 (a)

correspond to metallic layer for Chebyshev filter and CPW and Figure 6.2(b)

corresponds to bottom layer of cavities designed for CPW.


143

(a) Top layer mask for metal

(b) Bottom layer cavity mask

Figure 6.1: Mask of single Resonator on Silicon substrate at 10 GHz, (a) top metal layer mask, (b) bottom layer cavity mask. (Scale corresponds to 1λ = 1 μm).


144

(a) Top layer mask for metal

(b) Bottom cavity layer mask

Figure 6.2: Mask of Chebyshev band stop filter on Silicon substrate at 10 GHz (a) top metal layer mask, (b) bottom cavity layer mask. (Scale corresponds to 1λ = 1 μm).


145

6.2 TYPES OF ETCHING TECHNIQUES

In this section we describe about types of etching technique to obtain cavity.

There are two types of etching process:

1) WET ETCHING 2) DRY ETCHING

Wet etching was the technique we used in our work to fabricate filter

coupled with CPW.

Wet etching is the removal of material by immersing the wafer in a

liquid bath of the chemical etchant. Wet etchants fall into two broad

categories; isotropic etchants and anisotropic etchants.

♦ Isotropic etchants: These etchants attacks the material being etched

at the same rate in all directions. Figure 6.3 presents isotropic etching.

These etchant are available for oxide, nitride, aluminum, polysilicon,

gold, and silicon. Since isotropic etchants attack the material at the

same rate in all directions, they remove material horizontally under the

etch mask (undercutting) at the same rate as they etch through the

material.

Figure 6.3: Isotropic Etching


146

♦ Anisotropic etchants: These etchants attack the silicon wafer at

different rates in different directions, and so there is more control of the

shapes produced.

Some etchants attack silicon at different rates depending on the

concentration of the impurities in the silicon (concentration dependent

etching). Anisotropic etchants are available which etch different crystal planes

in silicon at different rates. The most popular anisotropic etchant is

potassium hydroxide (KOH) [2].

The simplest structures that can be formed using KOH to etch a silicon wafer

with the most common crystal orientation <100> are shown in figure 6.4.

These are V shaped groves, or pits with right angled corners and sloping side

walls. Using wafers with different crystal orientations can produce grooves or

pits with vertical walls.

Both oxide and nitride etch slowly in KOH. Oxide can be used as an etch

mask for short periods in the KOH etch bath (i.e. for shallow grooves), for

long periods, nitride is a better etch mask as it etches more slowly in the

KOH.

Figure 6.4: Grooving by KOH etchant.


147

Dry etching is also known as ion etching .The most common

micromachining applications is reactive ion etching (RIE). Ions are

accelerated towards the material to be etched, and the etching

reaction is enhanced in the direction of travel of the ion. RIE is an

anisotropic etching technique. Deep trenches and pits (up to ten or a

few tens of microns) of arbitrary shape and with vertical walls can be

etched in a variety of materials including silicon, oxide and nitride. The

etching rate is lower than wet etching rate. Dry etching is recognized

as practical alternative to wet etching.

For the proper flow of aluminum through cavities, it is necessary to have

smooth slope at the edges. Hence, wet etching process was selected for this

work.

The following section (6.3) presents the mathematical calculation that was

used to obtain the base of pyramidal cavity structure with respect to the upper

dimension of cavity and thickness of substrate [2] (Figure 6.5).

6.2.1 CAVITY DIMENSION

Figure 6.5 shows the shape of a cavity etched in Silicon using wet etching

process to obtain the base dimension (X) of pyramidal cavity with respect to

the dimension of top layer cavity and thickness of substrate, equation (6-1) is

used [2].

yhx +×⎟⎠⎞

⎜⎝⎛

×= 2

7.54tan (6-1)

Where, h = Thickness of substrate (μm)

x = Length of the edge.


148

y = Upper dimension of pyramid

Values used to obtain via hole was, y = 500 μm, from equation (6-1) the

dimension obtained for the base (x) of pyramidal cavity was 1066 x 1066 μm

(a) top view of via (b) Cross- section view of wafer to calculation of dimensions for via

Figure 6.5: Dimensions obtained for base of pyramidal via.

6.3 FABRICATION PROCESS

In this section, we describe the complete lithographic process using

micromaching technique with the help of two experiments done to machine

via holes to ground of our CPW (Figure 6.5). Figure 6.6 shows the structure

used for Experiment-I and Figure 6.7 structure was used for Experiment-II.


149

Figure 6.6: Experiment-I SiO2 as protective layer on silicon.

Figure 6.7: Experiment-II SiO2 and Silicon Nitride (Si3N4) as protective layer on silicon.

N-type high resistivity silicon (HR-Si) as substrate reduces the DC leakage

current between the signal and ground conductors of CPWs, and for

minimizing the attenuation loss [3].

The characteristics of the substrate used to fabricate our device are:

Substrate type = N type Silicon (HR-Si)

Resistivity = greater than 2000 Ω-cm


150

Thickness = µm 15400 ±

Orientation = <100>

The thickness for conductors (aluminum) proposed for our work is 2 µm.

6.3.1 EXPERIMENT- I: LITHOGRAPHIC PROCESS USING SiO2 LAYER

ON SILICON AS SUPPORTIVE LAYER.

In this section, the experimental steps of fabrication process to via through a

substrate of thickness 400 µm are described.

STEP 1 : CLEANING PROCESS OF WAFER

Contaminants present on the surface of silicon wafers at the start of

processing, or accumulated during processing, have to be removed at

specific processing steps in order to obtain high performance and high

reliability semiconductor devices, and to prevent contamination of process

equipment, especially the high temperature oxidation, diffusion, and

deposition tubes. The RCA (Radio Corporation of America) is the industry

standard cleaning process for removing contaminants from wafers.

The RCA cleaning procedure has three major steps used sequentially:

I. RCA-I (Organic Clean): Removal of insoluble organic

contaminants with a ration of 5:1:1 (H2O: H2O2: NH4OH)

solution.

II. RCA-II (Oxide Strip): Removal of a thin silicon dioxide layer

where metallic contaminants may accumulated as a result of

RCA-I, using a (diluted H2 O: HF) solution.


151

III. RCA-III (Ionic Clean): Removal of ionic and heavy metal

atomic contaminants using a solution of ratio 6:1:1 ( H2O: H2O2:

HCl).

In this step of cleaning of wafer we followed only two steps of RCA (I and

II).

STEP 2 : OXIDATION PROCESS

SiO2 on wafer was used as a protective layer on both sides of wafer as shown

in Figure (6.8a). The deposition of silicon oxide was done under following

conditions:

Technique = Thermal oxidation

Thickness of SiO2 = 1.5 µm (measured)

Temperature = 1200oC

Total time = 4 ½ hrs.

Thermal oxidation is a way to produce a thin layer of oxide (usually silicon

dioxide) on the surface of a wafer (semiconductor). The technique forces an

oxidizing agent to diffuse into the wafer at high temperature and react with it.

Thermal oxidation of silicon is usually performed at a temperature between

800 and 1200 oC. It may use either water vapor (steam) or molecular oxygen

as the oxidant. The reaction is:

22 SiOOSi →+

The expected thickness of SiO2 was 1.5 μm and the measured thickness was

1.5 μm, measured by the use of an alpha-stepper.


152

STEP 3 : PHOTOLITHOGRAPHY PROCESS

Photolithography is a process used in microfabrication to selectively remove

parts of a thin film (or the bulk of substrate). It uses light to transfer a

geometric pattern from a photomask to a light-sensitive chemical (photoresist)

on the substrate. A series of chemical treatments then engraves the exposure

pattern into the material underneath the photoresist. This process is used

because it affords exact control over the shape and size of the objects it

creates, and because it can create patterns over an entire surface

simultaneously. Its disadvantages are that it requires a flat substrate to start

with, it is not very effective at creating shapes that are not flat, and it can

require extremely clean operating conditions

In this step, the wafer was coated on both sides with a photoresistive polymer

which is sensitive to ultra-violet (UV) light called as photoresist.

The wafer is covered with photoresist (“PR”) by spin coating. A viscous, liquid

solution of photoresist is dispensed onto the wafer, and the wafer is spun

rapidly to produce a uniformly thick layer. The spin coating typically runs at 20

to 80 Hz for 30 to 60 seconds, and produces a layer between 2.5 and 0.5 μm

thick. The photoresist- coated wafer is then “soft baked” or “prebaked” to drive

off excess solvent, typically at 60 to 100 oC for 5 to 30 minutes.

This process shown in Figure (6.8b) was done under following specific

conditions:

Type of photoresist = photoresist (+)

Spinning Rotation = 3000 rpm for 30 sec.

Temperature = 85 oC for 17 mints.


153

Positive Photoresist, the most common type, becomes less chemically robust

when exposed; negative photoresist becomes more robust. This chemical

change allows some of the photoresist to be removed by a special solution,

called "developer" by analogy with photographic developer. A post-exposure

bake is performed before developing, typically to help reduce standing wave

phenomena caused by the destructive and constructive interference patterns

of the incident light [5].

STEP 4: EXPOSURE AND DEVELOPING

After prebaking, the photoresist is exposed to a pattern of intense light (UV)

shown in Figure 6.8 (c). Ultraviolet light was then passed through the mask

onto the photoresist for 9 seconds.

The resulting wafer is then “hard baked”, typically at 120 to 180 oC for 20 to

30 minutes. The hard bake solidifies the remaining photoresist, to make a

more durable protecting layer in future ion implantation, wet chemical etching.

STEP 5 : PHOTORESIST DEVELOPING PROCESS

In the etching step, a liquid ("wet") chemical agent removes the uppermost

layer of the wafer in areas that are not protected by photoresist shown in

Figure 6.8(d).

Semiconductor fabrication prefers dry etchants, because they do not undercut

the photoresist as much. However, this same property makes wet etchants

indispensable for microelectromechanical systems; where suspended

structures must be "released" from the underlying layer by a strongly

undercutting etch.


154

STEP 6: PHOTORESIST REMOVAL

After a photoresist is no longer needed, it must be removed from the

substrate. This usually requires a liquid “resist stripper”, which chemically

alters the resist so that it no longer adheres to the substrate.

STEP 7 : SiO2 ETCHING PROCESS

In this process Silicon oxide was etched with respect to the pattern on the

photoresist positive layer. An etching solution was used to remove the oxide

where it was exposed through the openings in the photoresist and obtain

structure as shown in Figure 6.8 (e1), Figure 6.8(e2). Specifications of this

step are:

Etching Solution= H2O + NH4F + HF (7:1)

Chemical etching duration =3mint

Boiler Temperature =32 oC

After this step, the wafer was ready for complete etching of silicon completely

to obtain via holes to ground.

STEP 8 : Si ETCHING PROCESS

In this step the silicon was completely etched to obtain the via holes of CPW

using wet etching technique under following specific conditions:

Wet Etching Solution= KOH

Etching duration =10 -30 mints.

Boiler Temperature =80 oC


155

The wet etching process was done from bottom side toward the top side; this

step was repeated until the silicon gets completely etched. This process goes

for 24 hours as a resulting in the structure as shown in Figures 6.8(f1), Figure

6.8(f2).

STEP 9 : METALLIZATION PROCESS

Deposition of aluminum metal was done by evaporation technique in which

the vapor source is heated; the vapor pressure of the evaporant (metal to be

evaporated) becomes substantial. Hence, atoms are sent out into the vacuum

chamber, some of which reach the substrate to form a metal film. This step

was done under following conditions:

Technique= Evaporation Technique

Thickness = 2µm both sides of wafer

Time taken for deposition of Al = 2 hrs

The ideal case of this process is shown in figure 6.8(g); the flow of metal was

done from bottom side of wafer toward the top side to make proper flow of

aluminum. The thickness of aluminum was measured to be 2 µm with the

help of alpha stepper which is similar to the expected thickness.

STEP 10 : LITHOGRAPHY, MASKING, PHOTORESIST

DEVELOPING AND REMOVAL OF PHOTORESIST PROCESS

These processes and condition are exactly similar from step 3 till step 6. The

photoresist process under metallization is shown in Figure 6.8(h). The

masking process is shown in Figure (6.8i) and photoresist developing process

is shown in Figure 6.8(j).


156

STEP 11 : METAL ETCHING OF ALUMINUM

The aluminum metal was etched by the use of Al etch (phosphoric acid,

acetic acid, nitric acid) solution. Figure (6.8k) shows the metal etching

process and Figure (6.8l) corresponds to the finally fabricated device.

Table-6.1 shows the dimensions of cavity proposed and measured after

fabrication. As it can be seen, the final dimension is very close to the desired

ones.

Structure Thickness of metal (µm)

Base of pyramidal cavity (µm)

Top of pyramidal cavity (µm)

CAVITY IN CPW 2 1066 x 1066 500 x 500 Proposed Dimensions

2 1050 x 1050 550 x 550 Dimensions measured after

fabrication

Table- 6.1: Results of measurement of dimension of cavity in CPW on HR-Si using experiment – I

(a) OXIDATION PROCESS

(b) PHOTORESIST (+) PROCESS


157

(c) MASKING PROCESS

(d) DEVELOPING PROCESS

(e1) SiO2 ETCHING PROCESS

(f1) SILICON ETCHING PROCESS

(e2) : SiO2 ETCHING

( f2) : SILICON ETCHED WAFER


158

(g) METALLIZATION PROCESS

(h) PHOTORESIS (+) PROCESS

(i) MASKING PROCESS

(j) DEVELOPING PROCESS


159

(k) METAL ETCHING PROCESS

(l) FINAL DEVICE

Figure 6.8: STEPS OF FABRICATION PROCESS FOR EXPERIMENT- I

6.3.2 EXPERIMENT-II: LITHOGRAPHIC PROCESS USING SiO2,

SILICON NITRIDE (SiH4+NH3) ON SILICON AS SUPPORTIVE

SUBSTRATE.

In this experiment we followed similar lithographic process steps as

mentioned in experiment-I. To protect the silicon surface, silicon nitride over

SiO2 layer was used which results in reducing silicon etching time. In the

pervious experiment we obtained irregular, rough surface and the flow of

aluminum was not fine through the whole cavity due to lengthy Silicon etching

process of. To improve these effects experiments-II was performed.

STEP 1 : OXIDATION PROCESS

The procedure of this step is exactly similar to the step2 of experiment-1

under following conditions [refer Figure 6.9(a)].

Deposition technique = Thermal oxidation


160

Thickness of SiO2 = 0.2 μm

Temperature = 1200oC

Time = 20 mints.

STEP 2 : DEPOSITION OF SILICON NITRIDE

Deposition of silicon nitride over silicon oxide was done to act as extra

protective layer for silicon surface under following conditions [refer Figure

6.9(b)]:

Technique = Low Pressure Chemical Vapor Deposition (LPCVD)

Thickness of Si3N4 = 0.66 μm

Temperature = 755 oC

Pressure applied = 2.332 torrs

Time = 27 mints.

STEP 3 : PHOTOLITHOGRAPHY AND MASKING PROCESS

The lithographic process is similar to step 3 till step 4 of experiment-I with

similar conditions [refer Figures 6.9 (c), Figures 6.9 (d)].

STEP 4 : DEVELOPING AND PHOTORESIS REMOVAL

PROCESS

This process is similar to step 5 and step 6mentioned in experiment-I with

similar conditions of temperature and time [refer Figure (6.9e)].


161

STEP 5 : SILICON NITRIDE ETCHING PROCESS

In this step removal of silicon nitride was done using Reactive ion etching

(RIE) etching technique. In RIE, Ions are accelerated towards the material to

be etched, and the etching reaction is enhanced in the direction of travel of

the ion. RIE is an anisotropic etching technique. Deep trenches and pits (up

to ten or a few tens of microns) of arbitrary shape and with vertical walls can

be etched in a variety of materials including silicon, oxide and nitride. The

etching rate is lower than the wet etching rate.

Specific conditions for RIE process [refer Figure 6.9(f)] are:

Etching technique = RIE

Power applied = 200 Watts

Pressure applied = 300 m torrs

Gases passed = CF4 & Freon

Time = 5 mints.

STEP 6 : SILICON OXIDE ETCHING PROCESS

This process is exactly similar to step 7 of experiment-I [refer Figure 6.9(g)]

under following conditions:

Etching solution = HF+H2O+NH4F

Temperature = 32 oC

Time = 3 mints.


162

STEP 7 : WET ETCHING FOR SILICON ETCHING PROCESS

In this process, similar etching technique was used as mentioned in step 8 of

experiment-I with following etchant and conditions:

Etching agent = KOH

Temperature = 80 oC

Total time for process = 4 hrs

This step was repeated until silicon was completely etched [refer Figure

6.8(f)].

STEP 8: METELLIZATION AND METAL ETCHING PROCESS

Metallization process and metal etching was done in experiment-II following

similar steps and condition from (step 9) till (step 11) of experiment-I, [see

Figures 6.9 (g) till 6.9(l)].

Table-6.2, present the measurement of the dimensions of proposed cavity

and measured dimensions after fabrication. As it can be seen, the final

dimensions are very similar to the theoretical ones.

Structure Thickness of metal (µm)

Base of pyramidal cavity (µm)

Top of pyramidal cavity (µm)

Cavity in CPW 2 1066 x 1066 500 x 500 Proposed

dimensions

2 1050 x 1050 550 x 550

Dimensions

after

measured

fabrication

Table-6.2: Measured and proposed dimensions of cavity using experiment-II


163


164

Figure 6.9: FABRICATION PROCESS OF EXPERIMENT- II

Figure 6.10, shows photos obtained from Scanning electronic microscope

(SEM) viewing the edges and slope obtained after wet etching of silicon and

the flow of aluminum through cavity and on the surface.

Figure 6.10 :(a) SEM microscope and display

Figure 6.10 :(b) View of Coplanar waveguide with cavity in SEM


165

Figure 6.10: ( c) View of cavity edge

Figure 6.10 : (d) View of flow of Aluminum at the edges and on surface

Figure 6.10 Photos from SEM (a) SEM and display of device , (b) View of Coplanar waveguide with cavity in SEM, ( c) View of cavity edge, (d) View of flow of Aluminum at the edges and on surface.

CONCLUSION

Two different experiments to fabricate resonator and Chebyshev filter at

10 GHz using bulk micromachining technique to obtain cavities for CPW have

been described in this chapter. Very rough and irregular surface of Silicon

was obtained with first experiments due to longer process of etching SiO2 and

Silicon which result in imperfect flow of Aluminum through cavities which lead

to poor continuity between upper and bottom layer of Aluminum, which

effected experimental results.

To improve surface of silicon after etching process we introduced Silicon

nitride layer over SiO2 as protective layer in experiment-II. In this experiment

all the fabrication procedures were similar to the ones as followed in

experiment-I. Etching of Silicon Nitride was performed with a RIE process.


166

Here it was observed that, a smoother surface of Si was obtained as compare

to experiment –I. Also the process of etching of silicon oxide, silicon nitride

and silicon takes less time as compare to the experiments -I process.

REFERENCES

[1] “L-Edit version 12.2 user guide”.

[2] Danny Banks “Introduction to Microengineering MEMS Micromachines

MST”, © D Banks 1999. All rights [email protected]

5 June 1999.

[3] J.A.Reynoso-Hernández, Raúl Rancel-Rojo, M.Aceves, I. Zaldivar,

L.E. Sánchez, and M.Herrera “ Influence of the SRO as passivation

Layer on the Microwave attenuation Losses of the CPWs Fabricated

on HR-Si”, IEEE microwave and wireless components letter

,Vol.13,No.12,Dec.2003.

[4] http://en.wikipedia.org/wiki/Thermal_oxidation.

[5] http://en.wikipedia.org/wiki/Photolithography

mailto:[email protected]

http://en.wikipedia.org/wiki/Photolithography


167

INTRODUCTION

In this chapter the experimental results are presented. The comparisons of

experimental and simulated results are done to know the performance of

proposed filters.

This chapter is divided into three subsections; first section 7.1 describes the

experimental results of Chebyshev bandstop filters at 1.5 GHz, second

section 7.2, presents the experimental results of Triple bandstop filter with an

extra transmission zero, and the last section 7.3, and shows the experimental

results obtained for patch resonator on silicon substrate at 10 GHz.

7.1 EXPERIMENTAL RESULTS OF CHEBYSHEV BANDSTOP

FILTERS AT 1.5 GHz

In this thesis work two different structure of Chebyshev bandstop filter have

been proposed at 1.5GHz. In this section the experimental results obtain by

Chebyshev bandstop filters are presented. Experimental and simulated

results have been compared throughout to know the actual performance and

effect of the proposed device.


168

7.1.1 3 POLE CHEBYSHEV BANDSTOP FILTER AT 1.5GHZ

USING T-SHAPE STRAIGHT RESONATORS ON

DUROID SUBSTRATE

3-pole Chebyshev bandstop filter using T-shape straight resonators response

was tested using a Vector Network Analyzer Antrisu (model 360B Network

Analyzer), with VF 1M-KM S/N 3113 cables (coaxial). The measurement set

up for testing is shown in Figure 7.1(a). The testing device, 3-pole Chebyshev

bandstop filter using T-shape interdigital resonators is shown in Figure 7.1(b).

Figure 7.1 (a) VNA (model 360B Network Analyzer) and cables are VF 1M-KM S/N 3113


169

(b)

Figure 7.1: (a) shows the set up to measure this filter with the help of VNA, (b) the device for test. Figure 7.2, shows the experimental results of the filter. Figure 7.2(a), presents

the experimental S11 and S12 response of filter before tuning. The center

frequency was measured was 1.414 GHz. The insertion loss was about

-53dB and the return losses was -2.3dB throughout the band. The bandwidth

measured was 10%. Figure 7.2(b), shows the S11 experimental and simulated

response of the filter after tuning and Figure 7.2(c), illustrate S12 experimental

and simulated response after tuning. With simulation the central frequency

was 1.496GHz and bandwidth obtained was 9.9%.The insertion losses

obtained with simulation was -30.3dB. The return losses of simulated result

were -2.4dB. The tuning was performed to the filter by inserting small

substrate bits of duroid on the filter. After tuning, the central frequency was

1.38GHz and bandwidth was 11%. The insertion loss was improved by -22dB

and the return loss lower than 1dB. The over all frequency shift obtained was


170

0.1GHz. The simulated and experimental results show overall good

agreement.

1.0 1.1 1.2 1.3 1.4 1.5 1.6-60

-55

-50

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

Mag

nitu

de (d

B)

Frequency (GHz)

S11_m easured S12_m easured

EXPERIMENTAL RESULT BEFORE TUNING

BW = 0.16GHzfo=1.41 GHz

Figure 7.2 (a) The response of filter without tuning obtained bandwidth 10%


171

1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7-35

-30

-25

-20

-15

-10

-5

0

Mag

nitu

de(d

B)

Frequency(GHz)

S11_experimental S11_simulated

Figure 7.2 (b) S11 simulated and experimental results after tuning.


172

1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7

-35

-30

-25

-20

-15

-10

-5

0

Mag

nitu

de(d

B)

Frequency(GHz)


Δf

(c) S12 simulated and experimental results after tuning

Figure 7.2: Results of 3 pole Chebyshev bandstop filter using T-shape straight resonators, (a) The response of filter without tuning, (b) S11 simulation and electrical response after tuning, (c) S12 simulation and electrical response after tuning.


173

7.1.2 3 POLE CHEBYSHEV BANDSTOP FILTER USING

ULTRA COMPACT MEANDERED RESONATORS AT

1.5GHz

Figure 7.3(a), shows the photo of Chebyshev bandstop filter using ultra

compact meandered resonators. Figure 7.3 (b), presents the response of filter

before tuning. The center frequency was measured to 1.424GHz. The

insertion losses were about -15.7dB and the return loss was -2.4dB

throughout the band. The bandwidth measured experimentally was 10%.

Figure 7.3 (c), shows the S11 experimental and simulated response of the

filter after tuning and Figure 7.3 (d), illustrate S12 experimental and simulated

response after tuning. With simulation the central frequency was 1.506GHz

and bandwidth obtained was 8.6%.The insertion loss obtained with simulated

response was -23.5dB. The return loss of simulated result was -2.7dB. The

tuning was performed to the filter response by inserting small substrate bits of

duroid on the filter. After tuning, the central frequency was 1.417GHz and

bandwidth was 9.8%.The insertion loss was improved by -25.2dB and the

return loss was -3dB. The overall frequency shift obtained was 0.09GHz. The

simulated and experimental results show overall good agreement.


174

Figure 7.3 (a) The 3 pole Chebyshev bandstop filter using ultra compact T-shape

meandered resonator


175

1.0 1.1 1.2 1.3 1.4 1.5 1.6-30

-25

-20

-15

-10

-5

0

EXPERIMENTAL RESULT WITHOUT TUNING

Mag

nitu

de (d

B)

Frequency (GHz)

S11_measured S12_measured

fo =1.428 GHz

BW=10%

Figure 7.3 (b) Experimental response of filter without tuning


176

1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7-30

-25

-20

-15

-10

-5

0

Mag

nitu

de (d

B)

Frequency (GHz)


S11 SIMULATION AND EXPERIMENTAL RESULTS AFTER TUNING

Return loss_experimental=-2.7dBReturn loss_simulated ==2.7dB

Figure 7.3 (c) S11 simulation and experimental results of filter after tuning.


177

1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7

-25

-20

-15

-10

-5

0

Mag

nitu

de (d

B)

Frequency (GHz)

S12_experimental S12_simulation

fo_experimental =1.417GHzfo_simulation=1.506GhzBW 3db_experimental=9.8%Bw3db_simulation=8.6%

S12 SIMULATION AND EXPERIMENTAL RESULTS AFTER TUNING

(d) S12 simulation and experimental results of filter after tuning

Figure 7.3: Results of 3 pole Chebyshev bandstop filter using interdigital T-shape

meandered resonators, (a) The response of filter without tuning, (b) S11 simulation and electrical response after tuning, (c) S12 simulation and electrical response after tuning.


178

7.2 TRIPSECTION BANDSTOP FILTER WITH AN EXTRA

TRANSMISSION ZERO USING ULTRA COMPACT

INTERDIGITAL MEANDERED RESONATORS AT 1.5GHz

The set up to test this filter is similar to the one presented in Figure 7.1.

Figure 7.4, shows the experimental results of the filter. Figure 7.4(a), presents

the photo of Triplet bandstop filter using ultra compact interdigital meandered

resonators. Figure 7.4(b), presents the response of filter before tuning. The

center frequency measured was 1.406 GHz. The insertion losses at the

center frequency were about -18.1dB and the return loss was –2.6dB

throughout the band. The bandwidth obtained was 4%. Figure 7.4(c), shows

the S11 experimental and simulated response of the filter after tuning and

Figure 7.4(d), illustrate S12 experimental and simulated response after tuning.

With simulation the central frequency was 1.505 GHz and bandwidth obtained

was 3.3%.The insertion loss obtained with simulated response was -15.7dB.

The return loss of simulated result was -0.95dB. The tuning was performed to

the filter response by inserting small substrate bits of duroid on the filter. After

tuning, the central frequency was 1.403GHz and bandwidth was 4.5%. The

insertion loss was improved by –16.4dB and the return loss was -2.7dB.

Successfully obtained transmission zero towards lower frequency with

experimental response. Overall, simulation and experimental results was a

good agreement.


179

Figure 7.4: (a) Trisection bandstop filter with an extra transmission zero using ultra compact interdigital meandered resonators to test.


180

1.3 1.4 1.5 1.6

-25

-20

-15

-10

-5

0

f0=1.46GHzBW =4%

EXPERIMENTAL RESULTS OF TRIPLE BANDSTOP FILTER WITHOUT TUNING

Mag

nitu

de (d

B)

Frequency (GHz)

S11_measured S12_measured

fo

Figure 7.4: (b) The experimental response of Trisection bandstop filter without tuning.


181

1.35 1.40 1.45 1.50 1.55 1.60-35

-30

-25

-20

-15

-10

-5

0

Mag

nitu

de (d

B)

Frequency (GHz)

S11_simulated S11_experimental

Figure 7.4: (c) S11 simulation and experimental results of filter after tuning


182

1.35 1.40 1.45 1.50 1.55 1.60

-30

-25

-20

-15

-10

-5

0

Mag

nitu

de (d

B)

Frequency(GHz)


Δf = 0.1GHz

(d): S12 simulation and experimental results of filter after tuning

Figure 7.4: Results of Trisection bandstop filter using ultra compact T-shape

meandered resonators, (a) photograph of device to be test ,(b) The response of filter without tuning, (c) S11 simulation and electrical response after tuning, (d) S12 simulation and electrical response after tuning.


183

7.3 INTERDIGITAL T- SHAPE PATCH RESONATOR ON SILICON SUBSTRATE AT 10GHZ

The set up to test this resonator at 10GHz is shown in Figure 7.5, where input

and output ports of the device is coplanar waveguide. One end of the probe is

connected to the coplanar and other to the VNA.

Figure 7.6, shows the experimental and simulated result for the weakly

coupled resonator. The experimental Q value was 26 whereas the simulated

Q value was 40.

For the simulation the following parameters were used:

Metal: Aluminum

Thickness: 2 μm

Tan δ: 0.01

Conductivity of HR-Si: 0.05 (S/cm)

Metal Conductivity: 0.13440(Ω/sq)

Figure 7.5: The set up to test resonator at 10GHz.on silicon substrate.


184

The difference in Q value from the experimental (26) to the simulation (40) is

small. This small difference is thought to be due to surface roughness,

manufacturing tolerance and em radiation not considered in the simulation.

Factors which affects the experimental results:

Some of them are:

1) Rough surface of substrate due to not proper fabrication process due

to long process of etching for larger size via holes in CPW connected

to resonator at both ends.

2) The resistivity of the substrate was not according to the simulation

values used.

3) There are radiation losses due to higher frequency.

4) Non uniform distribution of metal on the surface of silicon.

The central frequency obtained from experimental result was 9.9GHz and

with simulation it was 10.2GHz. There was a frequency shift of 0.3GHz. For

comparison purposes both the experimental and simulated graphs were

shifted to same frequency (Figure 7.6).


185

9.0 9.2 9.4 9.6 9.8 10.0 10.2 10.4

-32

-30

-28

-26

-24

-22

-20

Δ f

Mag

nitu

de (d

B)

Frequency (GHz)


Δ f = 0.3GHzfo_simulated=10.2GHzfo_experimental =9.9GHz

EXPERIMENTAL AND SIMULATION RESPONSE OF PATCH RESONATOR AT 10GHz

Figure 7.6: S12 experimental and simulation results of patch resonator on HR-Si

substrate using Aluminum at 10GHz.

CHAPTER 8: CONCLUSION AND FURURE WORK

186

8.1 CONCLUSION

In this thesis work novel compact bandstop filters topologies at L and X band

have been presented. Full design procedure along with simulation and

experimental results with fabrication methods were described. All the filters

find applications in satellite communications, mobile communications and

radioastronomy.

At 1.5GHz two novel resonators have been proposed on duroid substrate of

relative permittivity (10.8) and thickness 0.64mm using copper as conductor

of thickness 0.017mm (chapter 4). The first one is conventional λ/2 resonator;

with simulated Q-value were 108. The length of this resonator was 37mm and

0.6mm width. Second resonator is T-shape straight resonator, which is

27.6mm in length. This reduction of size by the addition of extra capacitance

to ground. The simulated Q-value obtained from this resonator was 107. The

third resonator proposed at 1.5 GHz is an ultra compact meandered

resonator. This resonator is three times smaller that conventional


187

λ/2 resonator; its length is 12.4mm. The Q value of this resonator is 100,

which is very close to the Q value of the conventional resonator.

Using these latter two resonators at 1.5GHz, a Chebyshev bandstop filter with

3 poles has been designed (chapter 4). The total length of this filter is 41mm

x 38.6mm (4.1cm x 2.9cm). The bandwidth obtained by simulation was 9.9%

with central frequency 1.495GHz. The experimental response after tuning

filter gives a bandwidth of 11% with central frequency 1.38GHz. The

frequency shift between simulations and experiment was only 0.1GHz which

is thought to be due to manufacturing tolerances. Overall, the simulation and

experimental results were very similar.

A second Chebyshev bandstop filter with 3 pole has been designed using

meandered resonators of length 12.4mm x 10.6mm (chapter 4). The total

length of this filter is 39.2mm x 13mm. The bandwidth obtained by simulation

was 8.6% with central frequency 1.506GHz and return loss -2.6dB at the

centre frequency. The bandwidth obtained with experimental result was 9.8%

with central frequency 1.417GHz with return loss -3dB at the centre

frequency. The frequency shift was 0.09GHz. With these results it can be said

that there is good agreement between simulated and experimental results.

At 1.5 GHz, a Novel Trisection bandstop filter with 4.5% bandwidth has been

shown using T-shape meandered resonator of (12.4mm x 10.6mm)

(chapter 5). The total size of Trisection bandstop filter is 72mm x 34mm

(7.2cm x 3.4cm). For this Trisection bandstop filter, as extra cross coupling

between the first and the third resonator is included, this gives the needed

transmission zero of the response. In the experimental results, the

transmission zero of the characteristic triplet response is clearly seen. The


188

bandwidth obtained by simulation was 3.3% and central frequency 1.505

GHz. The experimental results gave bandwidth of 4.5% with central frequency

of 1.403GHz and the return loss was -2.7 at central frequency. The frequency

shift obtained between simulation and experiment was 0.1 GHz. Also, good

agreement was found between simulation and experimental results.

Finally, at 10GHz three compact resonators on HR-Si substrate have been

proposed (chapter 4). The thickness of the substrate is 400µm with resistivity

2000 Ωcm. A 2 µm aluminum layer was taken as conductor. The first

resonator at 10GHz adds a capacitive patch (1.8mm x 1.7mm) to a

conventional λ/2 resonator, achieving size miniaturization. The length of the

strip is 2.6mm and its width is 0.4mm. With simulation the obtained unloaded

Q-value was 40 at a central frequency of 10.2 GHz. The experimental results

of this resonator gave a Q value of 26 with central frequency of 9.9 GHz. The

small difference between the measured and simulated values is thought to be

due to conductor roughness plus the radiation losses not taken into account

in simulator.

At 10GHz, two patch resonators with selective removal of substrate to

increase Q value have been proposed and it has been proven that by

removing selective parts of the silicon using micromaching techniques higher

Q values are achieved. The Q value obtained with patch resonator having air

window beneath the patch is 114 (using Aluminum as conductor). The Q

value, obtained with second proposed micromachined patch resonator with

air window beneath the strip was 171 when Aluminum was used as

conductor. The Q value increased from 40 (patch resonator on silicon

substrate) to 114 and 171 with resonator with selective removal of substrate.

It was also proven that if silver was used as conductor, the Q values would


189

improve to 117 (Si removed underneath the patch) and 229 (Si removal

underneath the strip).

At 10GHz, Chebyshev band stop filter using patch resonators on silicon

substrate was designed (chapter 4). With simulation response the bandwidth

obtained was 9% and insertion losses -15dB dB and return losses through

out band was -1.5 dB.

8.2 FUTURE WORK Firstly, the fabrication of Chebyshev bandstop filter using patch resonator at

10GHz on HR-Si is proposed.

Secondly, the fabrication of patch resonators at 10GHz with improved Q by

removal of selective part of the substrate using micromaching is left as future

work. The fabrication procedure is described in Appendix-I.

Thirdly, the fabrication of Chebyshev bandstop filter (chapter 4) on Silicon

substrate at 10GHz using fabrication steps presented in chapter 6 is

proposed.

Fourthly, the designing and fabrication of Chebyshev bandstop and Triplet

filters with improved Q by selective removal of substrate is proposed for future

work.

APPENDIX-I

190

PROPOSED FABRICATION PROCESS TO OBTAIN AIR WINDOW

BENEATH PATCH AND STRIP OF THE RESONATOR AT 10GHZ FOR

FUTURE WORK

Fabrication of pact resonator on HR-Si with selective removal of substrate

follows similar lithographic process till masking step as mentioned in

chapter 6.

For the step to obtain via holes and completely removal of selective part of

silicon substrate, use SiO2 and Nitro as a protective layer on silicon and KOH

as the etching agent to achieve smooth surface and less time of etching

silicon. For this follow similar steps of the fabrication till Silicon etching as

presented in chapter 6. Subsequently, a mask is placed on the air window

section before metallization and then Aluminum metal layers is deposited

from top to bottom, allowing the connection between top metal layer and

bottom metal layer through via shown in Figure-I (a). The mask prevents the

Al to be deposited over the air window. Afterward the resonator / filter

structures are patterned using UV photolithography as shown in Figures-I (b)

and (c). Finally the mask is removed by Lift Off process and additional wafer

with 2 µm aluminum layer could be bonded to the ground plane as shown in

Figure-I(e).

APPENDIX-I

191

(a) Metallization

(c) Developing process

(b) Photoresist (+) and masking

(d) Metal etching process

(e) LIFT OFF process and adding additional wafer with metal both side

Figure-I: Fabrication process for future work.

APPENDIX-II

192

A.1 PHYSICAL CONSTANTS

Speed of light in vacuum

Permittivity of vacuum

Permeability of vacuum

Impedance of free space

Bolzmann´s constant

Charge of electron

Electron rest mass

C = 2.99792458 x 108m/s

εo = 8.85418782 x 10-12 ≈ (1/36π ) x 10-9 F/m

μo = 4π x 10-7 H/m

ηo = 376.7303 ≈ 120 π Ω

k =1.3806 x 10-23 J/K

e = 1.602177 x 10-19 C

m = 9.10938 x 10-31 kg

A.2 CONDUCTIVITY OF METALS AT 25o C (298 K)

MATERIAL

CONDUCTIVITY

σ (S/m)

MATERIAL

CONDUCTIVITY

σ (S/m)

Silver

Copper

Gold

Aluminum

6.18 x 107

5.84 x 107

4.43 x 107

3.69 x 107

Zinc

Nickel

Platinum

Chromium

1.66 x 107

1.40 x 107

0.97 x 107

0.79 x 107

APPENDIX-II

193

A.3 ELECTRICAL RESISTIVITY ρ IN 10-8 Ω m OF METALS*

T/K

ALUMINUM

COPPER

GOLD

SILVER

40

60

100

200

273

300

400

0.0181

0.0959

0.442

1.587

2.417

2.733

3.87

0.0239

0.0971

0.348

1.046

1.543

1.725

2.402

0.141

0.308

0.650

1.462

2.051

2.271

3.107

0.0539

0.162

0.418

1.029

1.467

1.629

2.241

* Conductivity σ= 1/ ρ

A.4 PROPERTIES OF DIELECTRIC SUBSTRATES

MATERIAL

RELATIVE

DIELECTRIC

CONSTANT AT

10GHz

LOSS

TANGENT

AT 10GHz

THERMAL

CONDUCTIVITY

(W/m K)

Aluminum

Fused quartz

Polystyrene

Beryllium oxide

GaAs

Si

RT/duroid 5880

RT/duroid 6002

RT/duroid 6006

RT/duroid 6010

9.7

3.8

2.53

6.6

12.9

11.7

2.20 ± 0.015

2.94 ± 0.04

6.15 ± 0.15

10.8 ± 0.25

0.0002

0.0001

0.00047

0.0001

0.0016

0.005

0.0009

0.0012

0.0019

0.0023

30

1

0.15

250

30

90

0.26

0.44

0.48

0.41

194

Figure 1.1: Electromagnetic Spectrum (Taken from © 2005 SURA www.sura.org

Copyrighted images used with permission. Rev2C

6-June-2005)……………………….…………………………………..………2

Figure 1.2: Voltage and current definition and Equivalent circuit of an element of a

transmission line with a length of Δ z (a) Voltage and current definition,

(b)Lumped element equivalent circuit……………………………….…….5

Figure 1.3: Diagram of transmission line with load showing incident, reflected-

transmitted wave……………...……………………………………..…………8

Figure 1-4: Types of Transmission Lines-……………………….……………………….9

Figure 1-5: (a) the general geometry of a Microstrip line, (b) Electric and magnetic

field lines………………………………………………………............………10

Figure 1-6: (a) Schematic diagram of coplanar waveguide, (b) Field patterns in

coplanar waveguide ……………………………………………...…………..14

Figure 1.7 Signal flow graph in two port network…………………………………….15

Figure 1.8: Vector Network Analyzer Antrisu (model 360B Network Analyzer)……..20

Figure 2.1: LC circuit diagram………………………………………..………………….23

Figure 2.2: Series RLC resonator and its response, (a) Series RLC circuit, (b) the

input impedance magnitude versus frequency………………………….....24

http://www.sura.org/

195

Figure 2.3: Parallel RLC resonators and its response, (a) Parallel RLC circuit,

(b) the input impedance magnitude versus frequency…………………….26

Figure 2.4: Transfer characteristic of resonant circuit………………………………….29

Figure 2.5: Butterworth (maximally flat) lowpass response……………………………33

Figure 2.6: Chebyshev lowpass response…………………...………………………….34

Figure 2.7: Elliptic function lowpass response…………………………...……………..35

Figure 2.8: Lowpass prototype filters for all- pole filters with ladder (a) A ladder

network structure, (b) its dual……………………..…………………………37

Figure 2.9: Lowpass prototype to 3 pole bandstop transformation (a) basic element

transformation, (b) a practical bandstop filter based on the

transformation……………………………………………………………..….42

Figure 2.10: (a) Immittance inverter used to convert a shunt capacitance into as

equivalent circuit with series inductance. (b) Immittance inverter used to

convert a series inductance into as equivalent circuit with shunt

capacitance……………………………………………………………………44

Figure 2.11: Immittance inverts comprised of lumped and transmission line

element………………………………………………………………………...45

Figure 3.1: Layout of the 4 pole membrane quasi elliptic filter L1=820, L2=2180,

L3=645, L4=300, L5=675, w=500, G1=15, G2=200, G3=175, G4=625

(Dimensions in microns), taken from [10]……………………………...…..51

196

Figure 3.2: Measured response of the 4 pole membrane quasi elliptic filter,

taken from [9]……………...…………..……………………………………..52

Figure 3.3: Layout of the K-band diplexer, taken from [10]………..…..………………53

Figure 3.4: Response of the K band diplexer, taken from [10]……….……….………54

Figure 3.5: Bandstop filter with shunt-connected L resonators, taken from [11].…..55

Figure 3.6: Bandstop filter with shunt-connected L resonators, taken from [11]…...56

Figure 3.7: Theoretical loss and return loss of degree 5 elliptic-function

L-resonator bandstop filter, taken from [11]……………………………….56

Figure 3.8: Transverse section of the microstrip structure, taken from [12]……....…58

Figure 3.9: Circuit wafer of 29 GHz microstrip resonator in bandstop configuration

(a) Bottom view, (b) Top view, taken from [12]……………………. ….……58

Figure 3.10: Measured S11 of bandstop resonator including effects of transition,

taken from [12]…….…………………………………………………………..59

Figure 3.11: The bandstop filter specification taken from [13]………….……...……..60 Figure 3.12: Measurement of the bandstop filter, taken from [13]………...…………61

Figure 3.13: (a) Coupling structure between the resonator and 50Ω microstrip line

on a 0.508 mm-thick LaAlO3 substrate, (b) Layout of the 7-pole microstrip

HTS bandstop filter on 0.508mm-thick LaAlO3 (44mm×26mm),

taken from[16]……………………..………………………….……………….62

Figure 3.14: Measured (thick solid line S21 (dB); thick dash line S11 (dB)) and

simulated (thin solid line S21 (dB); thin dash line S11 (dB) performance of

the seven-pole HTS microstrip bandstop filter, taken from [16]......……..63

197

Figure 3.15: Complete Band-stop Filter Assembly, taken from [17]….………………64

Figure 3.16: S-parameter plot of B band-stop filter (includes 12 dB LNA gain), taken

from [17]……………………………………..………….……………….…….65

Figure 3.17: S-parameter plot of AMPS-B micro enclosure, take from [17]….…..….65

Figure 4.1: Microstrip resonator λ/2 on Duroid substrate at 1.5GHz…………………72

Figure 4.2: S12 Response of microstrip resonator (λ/2) at 1.5 GHz………………….73

Figure 4.3: Interdigital T-shape straight resonator on Duroid using Copper at

1.5GH………………………………………………………………………......74

Figure 4.4: S12 Response of Interdigital T-shape straight resonator (λ/2) on Duroid

using Copper at 1.5GHz………………….…………………………………..75

Figure 4.5: Proposed novel ultra compact interdigital meandered resonator on Duroid

using Copper at 1.5 GHz……………………………………………………..76

Figure 4.6: S12 response of novel ultra compact interdigital meandered resonator on

Duroid using Copper at 1.5GHz……………………………..………………77

Figure 4.7: Comparison of proposed resonators with respect to size…...……..….…80

Figure 4.8: Three pole Chebyshev bandstop filter T-shape straight resonator on

Duroid at 1.5 GHz using copper………………………………………..……81

Figure 4.9: (a) Structure to obtain x1/ Zo and x3 / Zo value of Normalized reactance

slope parameter in EM simulator by varying Li, (b) Structure to obtain

x2 / Zo value of Normalized reactance slope parameter in EM simulator

by varying Li……………………………………………………………….82

198

Figure 4.10: Illustrate the extracted normalized reactance slope parameter against

variable lengths (Li) of capacitor (a) Normalized reactance slope

parameters obtained by varying (Li) capacitor by for 1st and 3rd

resonators, (b) Normalized reactance slope parameters obtained by

varying (Li) capacitance by for 2nd resonators……………….…………83-84

Figure 4.11: Detail dimension of 3 pole Chebyshev bandstop filter using T-shape

straight resonators at 1.5 GHz……………...…………….…..85

Figure 4.12: Simulation response of 3 pole Chebyshev bandstop filter using

interdigital T-shape straight resonators using copper at 1.5Hz…...…..86

Figure 4.13: The 3 pole compact Chebyshev bandstop filter using ultra compact

interdigital meandered resonators at 1.5 GHz…………………………..87

Figure 4.14: Structure to calculate reactance slope parameter by varying length of

interdigital capacitor (Li)…………....…...……..…………………………..88

Figure 4.15: (a) Photograph of the fabricated microstrip 3 pole Chebyshev bandstop

filter using compact interdigital meandered line resonator, (b) The

simulation response of microstrip 3 pole Chebyshev bandstop filter

using compact interdigital meandered line resonator at

1.5GHz………………………...………………………………..……..89-90

Figure 4.16: Cross section view of microstrip ………………………….………………92

Figure 4.17: conventional resonator at 10GHz on HR-Si substrate using

Aluminum…………………………………………………………………….93

Figure 4.18: S12 Response of microstrip resonator (λ/2) at 10 GHz…………………94

Figure 4.19: (a) Layout of patch resonator on HR-Si substrate, (b) S12 Simulation

results of patch resonator representing at 10 GHz………..………………95

199

Figure 4.20: (a): (i) Cross section view of Patch resonator having Air window

underneath the Patch, (ii) 3-D view of Patch resonator on Silicon having

Air window underneath the Patch (using Coventor), (b): S12 simulation

result of patch resonator with high Q on air window beneath the patch on

HR-silicon substrate at 10GHZ using Aluminum………….………...…96-97

Figure 4.21: (a)(i): cross section view of patch resonator with selective removal of

substrate beneath the strip of resonator, (ii): 3-D view of Patch

resonator on Silicon having Air window beneath the strip (using

Coventor), (b): S12 simulation result of patch resonator with high Q on

air window beneath the patch on HR-silicon substrate using Aluminum

metal………………………………………………….……….……..…..98-99

Figure 4.22: Three pole Chebyshev bandstop filter using patch resonator at 10 GHz

using Aluminum as metal…………….…………………………………..101

Figure 4.23: Structure to calculate normalized reactance slope parameter by varying

length of capacitor (Li)…………… ……………….………..……………103

Figure 4.24:Extracted normalized reactance slope parameter against variable

lengths (Li) of extra capacitance coupled to the patch resonator, (a):

The reactance slope parameter by the extra capacitance introduced to

patch of the resonator, (b): The reactance slope parameters obtained

by varying extra capacitance length introduced towards strip of patch

resonator…………………………………………………………………..104

Figure 4.25: Simulation response of microstrip Chebyshev bandstop filter on silicon

substrate at 10GHz using Aluminum……………….………………….105

Figure 4.26: Proposed CPW to microstrip transition (a) Proposed CPW structure,

(b) Transition frequency response……………………………..106-107

200

Figure 5.1: Comparison of frequency of the Chebyshev filter and the design filters

with single pair of attenuation poles at finite frequency (n=6)……….113

Figure 5.2: Standard Chebyshev filter the approximate synthesis method based on a

lowpass prototype filter…………………………………………………….115

Figure 5.3: (a) Equivalent circuit of a trisection bandpass filter, (b) Associated

lowpass prototype filter, (c) the comparison between ideal Chebyshev

filter and Trisection filter response…………………….…………...116-117

Figure 5.4: Photograph of proposed novel Trisection Bandstop filter at

1.5GHz……………………………………………….………….……………120

Figure 5.5: The steps follow to design Trisection filter……………………….………120

Figure 5.6: Chebyshev bandstop filter using lump elements………………….…….122


filter with 50Ω transmission line of 90 degrees electrical length, (b)

Response of initial trisection filter, (c) Optimization goals to obtain

required response.………………………………………………...123-125

Figure 5.8: (a) Cross-coupling of non-adjacent resonators of Trisection bandstop

filter with 200Ω transmission line of 90 degrees electrical length, (b)

Response of Trisection filter with lump elements………………......126-127

Figure 5.9: (a) the reactance slope parameter by varying the length (Li) of interdigital

capacitance at 1.5GHz, (b) The reactance slope parameters obtained by

varying interdigital capacitance length (Li) at 1.49

GHz…………………………………………………………………..….128-129

201

Figure 5.10: (a) The initial circuit with transmission line inverter, (b) Response of filter

with interdigital capacitor equivalent to transmission

line of 200 Ω……………………………………………………………130-131

Figure 5.11: (a) Steps and formulas used to convert transmission line of 200 Ω to 50

Ω transmission line using Admittance, (b) The final circuit with

transmission line inverter, (c) the circuit with interdigital capacitor, which is

equivalent to the transmission line 200 Ω, (d) Response of filter with

interdigital capacitor equivalent to transmission

line of 200 Ω……………………………………………………..…..…132-135

Figure 5.12: (a): The interdigital capacitor which is connected to the transmission line,

(b): The practical structure of Triplet bandstop filter at 1.5GHz,

(c):Simulation results of Triplet bandstop filter with extra transmission

zero………………………………………………………………….….136-138

Figure 6.1: Mask of single Resonator on Silicon substrate at 10 GHz, top metal layer

mask, (b) bottom layer cavity mask.

(Scale corresponds to 1λ =1 µm)………………………….………………143

Figure 6.2: Mask of Chebyshev band stop filter on Silicon substrate at 10 GHz (a)

top metal layer mask, (b) bottom cavity layer mask.

(Scale corresponds to 1λ =1 µm)……………………………………..…...144

Figure 6.3: Isotropic Etching………………………………………………………..…..145

Figure 6.4: Grooving by KOH etchant…………………………,……………….……..146

Figure 6.5: Dimensions obtained for base of pyramidal via………………………..148

Figure 6.6: Experiment-I SiO2 as protective layer on silicon……..…………………149

Figure 6.7: Experiment-II SiO2 and Silicon Nitride (Si3N4) as protective layer on

silicon…………………………………………………………………………149

202

Figure 6.8: Steps of fabrication process for experiment- I…………….………156-159

Figure 6.9: Fabrication process of experiment- II…………..…………………..163-164

Figure 6.10 Photos from SEM (a) SEM and display of device, View of Coplanar

waveguide with cavity in SEM, ( c) View of cavity edge, (d) View of flow

of Aluminum at the edges and on surface………………………..164-165

Figure 7.1: (a) shows the set up to measure this filter with the help of VNA,

(b) the device for test…………………………………….………….168-169

Figure 7.2: Results of 3 pole Chebyshev bandstop filter using interdigital

T-shape straight resonators, (a) The response of filter without tuning,

(b) S11 simulation and electrical response after tuning,

(c) S12 simulation and electrical response after tuning………….170-172

Figure 7.3: Results of 3 pole Chebyshev bandstop filter using interdigital T-shape

meandered resonators, (a) The response of filter without tuning, (b) S11

simulation and electrical response after tuning, (c) S12 simulation and

electrical response after tuning…………………………………….…174-177

Figure 7.4: Results of Trisection bandstop filter using ultra compact interdigital

meandered resonators, (a) photograph of device to be test ,(b) The

response of filter without tuning, (c) S11 simulation and electrical

response after tuning, (d) S12 simulation and electrical response after

tuning………………………………………...……………………...…..179-183

Figure 7.5: The set up to test resonator at 10GHz.on silicon substrat……………..183

Figure 7.6: S12 experimental and simulation results of patch resonator

on HR-Si substrate using Aluminum at 10GHz. ………..………………185

Figure 9.1: Fabrication process for future work………………………………………191

203

Table I: (a) Standard Radar Frequency Letter-Band Nomenclature (IEEE Standard

521-1984), (b) Typical Frequencies………………………………………………3

Table 2.1: Formulas of Series RLC resonant circuit……………….....………….……25

Table 2.2: Formulas of Parallel RLC resonant circuit…………………....……..……..27

Table 2.3: Elements values for Chebyshev lowpass filters (g0=1, Ωc = 1) for

passband ripples LAr = 0.04321 dB (taken from [3])……………..……..…38

Table 4.1: Specifications of substrate to design resonators at 1.5GHz [5]………..71

Table 4.2: Specifications of Copper to design resonators at 1.5GHz [7]……….…71

Table 4.3: Summary of Q-value obtained with Copper and lossless metals on

Duroid (εr= 10.8, thickness (t) = 0.64mm and tan δ = 0.0023) for all

types of resonators proposed at 1.5 GHz. ……….………………..……79

Table 4.4: Specifications of substrate to design microstrip resonators at

10GHz [6, 7]…………………………………………………….………….92

Table 4.5: Specifications of Copper and Silver metals to design microstrip

resonators at 10GHz [7]………………………………………….………..93

Table-4.6: Comparison of Q-value of resonators proposed obtained with Aluminum

and Silver metal at 10GHz………………..…………….…………..……100

204

Table 5.1: Specifications of substrate to design microstrip resonators at

1.5GHz [5]………………………… …………………….…………..……119

Table-5.2: Specifications of copper to design microstrip resonators at

1.5GHz [7]………………. …………………………………….……..……119

Table- 6.1: Results of measurement of dimension of cavity in CPW on HR-Si using

experiment – I……………..…………………………………..…………..156

Table-6.2: Measured and proposed dimensions of cavity using experiment-II…162

205

Kataria Tejinder Kaur, Corona Chávez Alonso, Llamas-Garro Ignacio, “Novel Trisection bandstop filter ”, IEE Electronics Letter (under preparation).

Kataria Tejinder Kaur, Alonso Corona-Chavez , Ignacio Zaldivar-Huerta,

Ignacio Llamas-Garro, “Micromachined Compact High-Q Microstrip Resonators Using Selective Substrate Removal for Wireless Communication Systems at 10 GHz”, accepted in IEEE XVII International

Conference on Electronics Communication and Computers, Conielecomp

2007 , Mexico.

Kataria Tejinder Kaur, Corona-Chávez Alonso, Zaldivar-Huerta Ignacio,

Llamas-Garro Ignacio, “Compact High-Q Microstrip Resonator for

Wireless Communication Systems Using Micromachined Technology at 10 GHz”, Séptimo Encuentro de Investigación INAOE, 8-9 November 2006,

México.

Kataria Tejinder Kaur, Corona Chávez Alonso, Zaldivar-Huerta Ignacio,

Llamas-Garro Ignacio, “Compact High-Q Resonators For Wireless

Communication Systems Using Micromachining Technology at 10 GHz”, XXVI Congreso Nacional de la Sociedad Mexicana de Ciencia y

Tecnología de Superficies y Materiales, 25-29 de Septiembre 2006, Puebla,

México, pp 203.

INVITED TALK

Invited talk on “HIGH SPEED FUTURE RF-MEMS FILTERS” Congreso de

Electronica I Telecommunicacion I Sistema, IEEE, at Veracruz, Mexico.

14th Nov.2006.

m.sc. in electronics engineering · 2017-10-10 · ¾ thanks to engg. victor of general...

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