CZECH TECHNICAL UNIVERSITY IN PRAGUE

Faculty of Electrical Engineering — Department of Electromagnetic Field

Phase Shifter Based on Varactor-LoadedTransmission Line

MASTER’S THESIS

Matej Vokac

May 22, 2009

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Declaration of Authorship

I hereby declare that I have written this thesis without any help from othersand without the use of documents and aids other than those stated below,that I have mentioned all used sources and that I have cited them correctlyaccording to established academic citation rules.

Matej VokacMay 22, 2009Prague

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Abstract

The following master’s thesis describes the function principles, design andoptimization of a phase shifter based on a varactor-loaded transmission line.The phase shifter consists of a microstrip transmission line that is periodi-cally loaded with varactor diodes. Since electrical length of such a synthetictransmission line is a function of reverse bias voltage applied to the diodes,the phase of the signal passing through the line can be shifted according tothe control voltage.

In order to simulate the designed phase-shifter circuit accurately, a BB857varactor-diode nonlinear model has been developed based on own measure-ments of the diode. The model is also used to analyze the large-signal be-havior of the resulting circuit. The designed and subsequently fabricatedphase shifter meets the objective of the maximum differential phase shift ofno less than 90 within a one-octave frequency band for the center frequencyof 1 GHz.

Index Terms – Phase shifter, microstrip transmission line, BB857 varactordiode, equivalent circuit, modeling, large-signal behavior

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Abstractin the Czech Language

Nasledujıcı diplomova prace popisuje principy funkce, navrh a optimalizacifazoveho posouvace zalozeneho na vedenı zatızenem varaktory. Tento fazovyposouvac sestava z mikropaskoveho vedenı, ktere je varaktory periodickyzatızene. Jelikoz elektricka delka takto vznikleho syntetickeho vedenı jefunkcı zaporneho predpetı techto kapacitnıch diod, muze byt faze signaluprochazejıcıho vedenım posouvana v zavislosti na rıdicım napetı.

Aby bylo mozne obvod navrzeneho fazoveho posouvace presne simulovat,byl na zaklade vlastnıch merenı varaktoru BB857 vytvoren jeho nelinearnımodel. Tento model je take pouzit k analyze velkosignaloveho chovanı vysled-neho obvodu. Navrzeny a nasledne vyrobeny fazovy posouvac splnuje cıl ma-ximalnıho rozdıloveho fazoveho posuvu o hodnote alespon 90 ve frekvencnımpasmu jedne oktavy pro strednı frekvenci 1 GHz.

Klıcove pojmy – Fazovy posouvac, mikropaskove vedenı, varaktor BB857,nahradnı obvod, modelovanı, velkosignalove chovanı

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Contents

Declaration of Authorship iii

Abstract iv

Abstract in the Czech Language v

Contents vi

List of Symbols viii

List of Figures x

List of Tables xiii

1 Introduction 11.1 Thesis Objectives . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Phase-Shifter Fundamentals . . . . . . . . . . . . . . . . . . . 31.4 Function Principles . . . . . . . . . . . . . . . . . . . . . . . . 41.5 Technologies of Implementation . . . . . . . . . . . . . . . . . 41.6 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Varactor-Loaded Transmission-Line Phase Shifter 52.1 Basic Structure Description . . . . . . . . . . . . . . . . . . . 52.2 Key Transmission-Line Parameters . . . . . . . . . . . . . . . 62.3 Phase Shift Principle . . . . . . . . . . . . . . . . . . . . . . . 82.4 Bragg Frequency . . . . . . . . . . . . . . . . . . . . . . . . . 122.5 Unit-Cell Matrix Description . . . . . . . . . . . . . . . . . . . 172.6 Capacitance Diodes Basics . . . . . . . . . . . . . . . . . . . . 21

3 Phase-Shifter Design and Optimization 243.1 Design Objectives and Constraints . . . . . . . . . . . . . . . 24

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3.2 Design of the Phase Shifter with Ideal Elements . . . . . . . . 283.3 BB857 Varactor-Diode Modeling . . . . . . . . . . . . . . . . . 333.4 Varactor-Diode Measurement and Respective Calibration . . . 403.5 Modeling of the Phase Shifter with Real Elements . . . . . . . 44

4 Phase-Shifter Circuit Fabrication and Measurement 474.1 Circuit Fabrication . . . . . . . . . . . . . . . . . . . . . . . . 474.2 Results of the Small-Signal Measurements . . . . . . . . . . . 484.3 Large-Signal Behavior of the Circuit . . . . . . . . . . . . . . 56

5 Conclusion 58

Acknowledgements 59

Bibliography 60

A Chain to Scattering Matrix Conversion 64

B BB857 Data Sheet 65

C RO4350B Data Sheet 69

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List of Symbols

[A] General chain matrix[Au] Chain matrix of a distributed phase-shifter unit cell[Ag] Chain matrix of a homogenous transmission line section[Avar] Chain matrix of a shunt varactor diode to groundCi Capacitance per unit length of a homogenous transmission lineCj PN junction capacitanceCj0 Zero-bias PN junction capacitanceCL Capacitance per unit length of a synthetic transmission lineCp Varactor-diode package capacitanceCt Equivalent lumped capacitance of a transmission-line sectionCvar Tunable varactor-diode capacitancef Frequencyf0 Center frequency of operationfB Bragg frequencyfmax Maximum frequency of operationfmin Minimum frequency of operationGi Conductance per unit length of a homogenous transmission lineh Height of a microstrip-line substratel Physical length of a transmission linelsp Physical length of varactor-diodes spacingLi Inductance per unit length of a homogenous transmission lineLL Inductance per unit length of a synthetic transmission lineLs Varactor-diode series inductanceLt Equivalent lumped inductance of a transmission-line sectionn PN junction profile exponentN Number of unit cells that make up a distributed phase-shifter circuitRi Resistance per unit length of a homogenous transmission lineRj PN junction resistanceRs Varactor-diode series resistance[S] General scattering matrix[Su] Scattering matrix of a distributed phase-shifter unit cellt Thickness of a microstrip-line metallizationvi Phase velocity on an unloaded transmission linevL Phase velocity on a varactor-loaded transmission lineV Reverse bias voltageV0 PN junction diffusion voltagew Width of a microstrip transmission lineYvar Tunable varactor-diode admittance

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Zi Characteristic impedance of an unloaded transmission lineZin Reference impedance at an input portZout Reference impedance at an output portZL Characteristic impedance of a varactor-loaded transmission lineα Attenuation constantβ Phase constantγ Propagation constant of a homogenous transmission lineδ Loss angleεr Dielectric constantλg Guided wavelength on a transmission lineϕi Electrical length of an unloaded transmission lineϕL Electrical length of a varactor-loaded transmission lineϕsp Electrical length of an unloaded transmission-line section between varac-

tor diodesΦL Maximum differential phase shift of a varactor-loaded transmission-line

phase shifterΦu Maximum differential phase shift of a varactor-loaded transmission-line

phase-shifter unit cellω Angular frequencyωB Bragg angular frequency

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List of Figures

2.1 Varactor-loaded transmission-line circuit . . . . . . . . . . . . 5

2.2 Varactor-loaded transmission-line equivalent circuit . . . . . . 9

2.3 Synthetic transmission line described by voltage-controlled char-acteristic impedance and electrical length . . . . . . . . . . . . 10

2.4 Magnitude of s21 versus frequency f of a distributed phaseshifter with ideal elements for various values of varactor diodescapacitance Cvar . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.5 Magnitude of s21 versus frequency f of a distributed phaseshifter with ideal elements for various values of electrical lengthϕsp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.6 Magnitude of s21 versus frequency f of a distributed phaseshifter with ideal elements for various values of characteristicimpedance Zi . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.7 Varactor-loaded transmission-line unit cell . . . . . . . . . . . 17

2.8 Typical equivalent circuit of packaged capacitance diodes . . . 22

3.1 Minimum number of phase-shifter sections determination . . . 30

3.2 Simulated return loss RL of distributed phase-shifter circuitsversus number of their sections N . . . . . . . . . . . . . . . . 32

3.3 BB857 varactor-diode model . . . . . . . . . . . . . . . . . . . 33

3.4 Phase of s11 versus frequency f of the proposed BB857 varactor-diode model at reverse bias voltage of 1 V, 2 V and 4 V . . . . 36

3.5 Phase of s11 versus frequency f of the proposed BB857 varactor-diode model at reverse bias voltage of 6 V, 8 V and 10 V . . . 37

3.6 Phase of s11 versus frequency f of the proposed BB857 varactor-diode model at reverse bias voltage of 15 V, 20 V and 25 V . . 37

3.7 Magnitude of s11 versus frequency f of the proposed BB857varactor-diode model at reverse bias voltage of 1 V, 2 V and4 V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

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3.8 Magnitude of s11 versus frequency f of the proposed BB857varactor-diode model at reverse bias voltage of 6 V, 8 V and10 V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.9 Magnitude of s11 versus frequency f of the proposed BB857varactor-diode model at reverse bias voltage of 15 V, 20 V and25 V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.10 Designed Line standard no. 1 . . . . . . . . . . . . . . . . . . 41

3.11 Designed Line standard no. 2 . . . . . . . . . . . . . . . . . . 41

3.12 Designed Line standard no. 3 . . . . . . . . . . . . . . . . . . 41

3.13 Designed Line standard no. 4 . . . . . . . . . . . . . . . . . . 41

3.14 Designed Reflect standard . . . . . . . . . . . . . . . . . . . . 42

3.15 Designed Thru standard . . . . . . . . . . . . . . . . . . . . . 42

3.16 Designed circuit for the varactor-diode measurement . . . . . . 42

3.17 Simulated magnitude of s11 versus frequency f of the designedTRL calibration standards . . . . . . . . . . . . . . . . . . . . 43

3.18 Simulated phase of s11 versus frequency f of the designed TRLcalibration standards . . . . . . . . . . . . . . . . . . . . . . . 43

3.19 Simulated magnitude of s21 versus frequency f of the designedTRL calibration standards . . . . . . . . . . . . . . . . . . . . 44

3.20 Simulated phase of s21 versus frequency f of the designed TRLcalibration standards . . . . . . . . . . . . . . . . . . . . . . . 44

3.21 Designed phase-shifter circuit schematic . . . . . . . . . . . . 46

4.1 Designed phase-shifter circuit layout . . . . . . . . . . . . . . 48

4.2 Simulated and measured phase of s21 versus frequency f ofthe designed phase shifter at reverse bias voltage of 5 V, 6 V,7 V and 8 V . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

4.3 Simulated and measured phase of s21 versus frequency f of thedesigned phase shifter at reverse bias voltage of 10 V, 15 V,20 V and 28 V . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

4.4 Simulated and measured magnitude of s11 versus frequency fof the designed phase shifter at reverse bias voltage of 5 V,6 V, 7 V and 8 V . . . . . . . . . . . . . . . . . . . . . . . . . 50

4.5 Simulated and measured magnitude of s11 versus frequency fof the designed phase shifter at reverse bias voltage of 10 V,15 V, 20 V and 28 V . . . . . . . . . . . . . . . . . . . . . . . 51

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4.6 Simulated and measured magnitude of s21 versus frequency fof the designed phase shifter at reverse bias voltage of 5 V,6 V, 7 V and 8 V . . . . . . . . . . . . . . . . . . . . . . . . . 51

4.7 Simulated and measured magnitude of s21 versus frequency fof the designed phase shifter at reverse bias voltage of 10 V,15 V, 20 V and 28 V . . . . . . . . . . . . . . . . . . . . . . . 52

4.8 Simulated and measured magnitude of s21 of the designedphase shifter at reverse bias voltage of 5 V, 6 V, 7 V and 8 Vversus frequency f that goes beyond the maximum frequencyof operation fmax . . . . . . . . . . . . . . . . . . . . . . . . . 52

4.9 Simulated and measured magnitude of s21 of the designedphase shifter at reverse bias voltage of 10 V, 15 V, 20 V and28 V versus frequency f that goes beyond the maximum fre-quency of operation fmax . . . . . . . . . . . . . . . . . . . . . 53

4.10 Simulated and measured phase of s21 versus reverse bias volt-age V of the designed phase shifter at frequency of 0.7 GHz,1.0 GHz, 1.2 GHz and 1.4 GHz . . . . . . . . . . . . . . . . . 53

4.11 Simulated and measured differential phase shift ΦL of the de-signed phase shifter versus reverse bias voltage V at frequencyof 0.7 GHz, 1.0 GHz, 1.2 GHz and 1.4 GHz . . . . . . . . . . . 54

4.12 Simulated and measured magnitude of s11 versus reverse biasvoltage V of the designed phase shifter at frequency of 0.7 GHz,1.0 GHz, 1.2 GHz and 1.4 GHz . . . . . . . . . . . . . . . . . 54

4.13 Simulated and measured magnitude of s21 versus reverse biasvoltage V of the designed phase shifter at frequency of 0.7 GHz,1.0 GHz, 1.2 GHz and 1.4 GHz . . . . . . . . . . . . . . . . . 55

4.14 Output power Pout of simulated and measured first harmon-ics and third-order IM products of the designed phase-shiftercircuit versus input power Pin . . . . . . . . . . . . . . . . . . 57

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List of Tables

2.1 Analytically computed values of fB for different distributedphase-shifter circuits . . . . . . . . . . . . . . . . . . . . . . . 14

2.2 Capacitance diodes equivalent circuit values . . . . . . . . . . 22

2.3 BB857 varactor diode equivalent circuit values . . . . . . . . . 22

3.1 Phase-shifter design objectives . . . . . . . . . . . . . . . . . . 24

3.2 Phase-shifter design constraints . . . . . . . . . . . . . . . . . 28

3.3 Optimal values of the phase-shifter design parameters . . . . . 29

3.4 Simulated characteristics of distributed phase shifters com-posed of N sections . . . . . . . . . . . . . . . . . . . . . . . . 31

3.5 The BB857 chip model data provided by the manufacturer . . 34

3.6 The BB857 parasitics model data provided by the manufacturer 34

3.7 Comparison of the manufacturer’s and the improved BB857chip model data . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.8 Comparison of the manufacturer’s and the improved BB857parasitics model data . . . . . . . . . . . . . . . . . . . . . . . 35

3.9 Maximum absolute deviations in the s11 phase of the improvedBB857 model from the measured data . . . . . . . . . . . . . 36

3.10 Physical characteristics of microstrip transmission lines fabri-cated on RO4350B . . . . . . . . . . . . . . . . . . . . . . . . 45

4.1 Simulated and measured maximum differential phase shift ΦL

of the designed phase shifter at four significant frequencies f . 49

4.2 Simulated and measured minimum return loss RLmin of thedesigned phase shifter at four significant frequencies f . . . . . 55

4.3 Simulated and measured maximum insertion loss ILmax of thedesigned phase shifter at four significant frequencies f . . . . . 55

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4.4 Resulting values of the two-tone third-order output interceptpoint OIP3 and the 1 dB compression point P−1dB of the de-signed phase shifter . . . . . . . . . . . . . . . . . . . . . . . . 57

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Chapter 1

Introduction

1.1 Thesis Objectives

Microwave systems have become an integral part of modern life, particularlyin the field of wireless communications, and have found their applications invarious other spheres of human activity including industry, navigation, radio-location, transportation, medicine, pharmacology and scientific research [1].

A phase shifter is an example of a microwave device that enhances thefeatures of systems operating at microwave frequencies and enables them toprovide the user with new beneficial functions thanks to its ability to adjustthe phase of a passing signal as desired.

The following master’s thesis describes different function principles andtechnologies of implementation of microwave phase-shifter circuits. The ob-jective of this thesis is then to explain the function of a varactor-loadedtransmission-line phase shifter in relation to its physical parameters, spec-ify key variables of the structure and discuss an appropriate choice of theirvalues in order to design and optimize the circuit.

Furthermore, the thesis aims to cover development and fabrication of aparticular phase shifter that operates within a one-octave frequency band forthe center frequency of 1 GHz or higher. A band that spans from 0.7 GHz to1.4 GHz has been chosen for this purpose. The maximum differential phaseshift of the circuit should be no less than 90 within the whole frequency bandand return loss of no less than 10 dB should also be achieved. Moreover, itis desirable that the phase shifter be implemented by simple and inexpensivetechnique.

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Inaccurate circuit-element description or missing element parasitics maylead to imprecise conclusions during microwave systems design and to signif-icant differences between the designed circuit simulations and measurementsof the manufactured circuits. Care must be taken to rely on as precise el-ement models as possible in order to obtain acceptable agreement betweenthe simulated and the measured data.

For the designed phase-shifter circuit to be simulated accurately, a non-linear model of a BB857 varactor diode, manufactured by Infineon Technolo-gies AG, needs to be developed. The model should precisely simulate thereal element within the frequency range of 0.5 GHz through 3 GHz at severalsignificant diode bias voltages with respect to the operating conditions of thephase-shifter circuit, in which the diodes are to be employed. Obviously, thediode package parasitics and the chip bias-dependent character should alsobe taken into account.

Since the function of a varactor-loaded transmission-line phase shifter re-lies on voltage-controlled PN junction capacitance of varactor diodes, precisevaractor-diode modeling is crucial to the phase shifter design. In addition,the nonlinear dependence of the PN junction capacitance on the appliedbias voltage [2] represents the main source of nonlinearity of the circuit andthus the model is also important for the large-signal behavior analysis of thephase-shifter circuit.

1.2 Thesis Outline

Chapter 1 introduces phase shifters as useful components of modern mi-crowave systems, presents the main objectives of the thesis, covers the fun-damentals of the phase-shifter function and explains why accurate elementmodeling is important for the whole system design. It also informs about dif-ferent function principles and technologies of implementation of phase-shiftercircuits intended to operate in microwave frequency bands as well as aboutvarious applications that benefit from the phase-shifter function.

Chapter 2 explores in greater detail the structure, key design parame-ters and the function principle of a varactor-loaded transmission-line phaseshifter. It also explains the phenomenon of the Bragg frequency and formu-lates its restriction on the periodic structure of the distributed phase shiftercircuit. In addition, the basics of capacitance diodes are mentioned in thechapter.

Chapter 3 covers design and optimization of the phase-shifter circuit with

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ideal elements as well as the design objectives and constraints, provides anonlinear equivalent circuit of a BB857 varactor diode and employs the modelin simulations of the phase-shifter circuit with real elements. Accuracy ofboth the model provided by the manufacturer and the resulting improvedmodel is also evaluated.

Chapter 4 provides technical details of the circuit fabrication and presentsresults of small-signal vector measurements of the circuit as well as its mea-sured large-signal behavior. The characteristics obtained from the measure-ments are compared with the simulated data.

Chapter 5 concludes the thesis by summing up and discussing the resultsreached and by proposing additional steps to take in order to further improvethe approach to this topic.

1.3 Phase-Shifter Fundamentals

A phase shifter is a device that adjusts the phase of an input signal accordingto a control signal. This function can be achieved by several principles ofoperation and implemented by different technologies.

This master’s thesis focuses on a phase shifter based on a varactor-loadedtransmission line. The circuit employs voltage-dependent PN junction capac-itance of varactor diodes to alter electrical length of the synthetic transmis-sion line formed by periodical loading of a microstrip transmission line withthe diodes. And because electrical length of such a synthetic transmissionline is a function of reverse bias voltage applied to the diodes, the phase ofthe signal passing through the line can be shifted according to the controlvoltage.

The phase shifter consists of a microstrip transmission line that is period-ically loaded with varactor diodes. Since electrical length of such a synthetictransmission line is a function of reverse bias voltage applied to the diodes,the phase of the signal passing through the line can be shifted according tothe control voltage.

Based on the nature of the control signal, phase shifters can be basicallydivided into two groups—analog and digital phase shifters.

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1.4 Function Principles

There are several means how to achieve the phase-shifting function. Basedon their function principle, phase shifters can be divided into transmission-type loaded-line phase shifters [3], reflective-type phase shifters [4], high-passphase shifters [5], tunable electromagnetic crystal (EMXT) surfaces [6] etc.

For example, reflective-type phase shifters (RTPS) provide better returnloss and larger phase tuning range than, for instance, a transmission-typeloaded-line phase shifter. On the other hand, the RTPS typically take upmore space [4].

1.5 Technologies of Implementation

Phase shifters can be implemented by the microwave monolithic integratedcircuits (MMICs) [8], the pseudomorphic high electron-mobility transistors(pHEMTs) [15], silicon varactor diodes—which is the technology employedin this thesis—, ferroelectric varactors [14], ferrites, micro-electro-mechanicalsystems (MEMS) etc.

For example, the disadvantage of the MMIC technology are the high costsof implementation and technological challenges [8].

1.6 Applications

Various modern electronical and microwave systems benefit from the abilityof phase shifters to adjust the phase of a passing signal as desired, e. g., beamscanning antenna arrays, phase modulators [15], [16], jitter and phase errorcompensation circuits and frequency tunable active microwave filters.

Many radar [10], [11], [8], [6] and wireless communication [9], [10], [6]systems are based on phased-array antennas for achieving electronic beamcontrol and fast beam scanning. Such systems can be used for military, e. g.,early-warning and missile defense systems [10], [8], and commercial appli-cations, e. g., flight control [10], automotive collision-avoidance [9], [10], [8]and cruise-control [8] systems, blind-spot indicators [8], multipoint commu-nications [8], the global positioning system (GPS) [10], compact scanningarrays [8] etc.

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Chapter 2

Varactor-LoadedTransmission-Line Phase Shifter

2.1 Basic Structure Description

A phase shifter that is in the center of attention of this thesis consists of ahigh-impedance transmission line with characteristic impedance Zi periodi-cally loaded with varactor diodes of capacitance Cvar. The spacing betweenthe varactor diodes can be characterized by its physical and electrical length,lsp and ϕsp, respectively. Such a structure along with corresponding param-eters is shown in Fig. 2.1.

Cvar

Zi, φsp

lsp

Zi, φsp Zi, φsp

Cvar Cvar

Fig. 2.1: Varactor-loaded transmission-line circuit

Key parameters of a transmission line and the means how these param-eters are affected by varactor loading need to be explained in order to gainfurther knowledge of the phase shift principle. Before proceeding to the

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phase shifter design itself, theoretical foundations for certain fields of thedesign should also be laid. Namely, the Bragg frequency restriction, the cas-cade structure description and capacitance diodes basics are discussed in thefollowing sections.

2.2 Key Transmission-Line Parameters

Analysis of an elementary transmission-line segment which is excited by aharmonic voltage source of angular frequency ω leads to formula (2.1). Itexpresses propagation constant of a homogenous transmission line γ as fol-lows [20]:

γ =√

(Ri + jωLi) (Gi + jωCi) = α + jβ, (2.1)

where Ri and Gi stand for resistance and conductance per unit length of ahomogenous transmission line, respectively, and Li and Ci are inductance andcapacitance per unit length of a homogenous transmission line, respectively.Factors α = <γ and β = =γ denote attenuation constant and phaseconstant, respectively.

Characteristic impedance of a homogenous transmission line Zi is givenby equation (2.2) derived from the same analysis [20]:

Zi =

√Ri + jωLiGi + jωCi

. (2.2)

Primary transmission-line parameters—Ri, Gi, Li, Ci—dependences on theline characteristic impedance Zi and the propagation constant γ can then bedetermined using formulas (2.1) and (2.2) as:

Ri = <γZi

, (2.3)

Li =1

ω=γZi

, (2.4)

Gi = <

γ

Zi

, (2.5)

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Ci =1

ω=

γ

Zi

, (2.6)

because

γZi = Ri + jωLi, (2.7)

γ

Zi= Gi + jωCi. (2.8)

The speed at which wavefront points of a given phase value propagatedown a transmission line is called phase velocity. Phase velocity on a trans-mission line is expressed [21] by equation (2.9).

vi =ω

β(2.9)

Supposing the considered homogenous transmission line is lossless, i. e. itsresistance Ri and conductance Gi per unit length equal to zero, formulas (2.1)and (2.2) can be simplified to

γ =√jωLijωCi = jω

√LiCi = jβ, (2.10)

Zi =

√LiCi. (2.11)

Based on (2.10), it is evident that a lossless transmission line is charac-terized by the following relations:

α = <γ

= 0, (2.12)

β = =γ

= ω√LiCi. (2.13)

Relations (2.9) and (2.13) further result in the expression of losslesstransmission-line phase velocity:

vi =ω

ω√LiCi

=1√LiCi

. (2.14)

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Dependences of inductance Li and capacitance Ci per unit length on char-acteristic impedance Zi and phase velocity vi can be obtained by modificationof (2.4), (2.6) and (2.9) as follows:

Li =1

ω=γZi

=

Ziviβ=γ

=Ziviβ=jβ

=Ziβ

viβ=Zivi, (2.15)

Ci =1

ω=

γ

Zi

=

1

viβZi=γ

=1

viβZi=jβ

=β

viβZi=

1

Zivi. (2.16)

These dependences are employed in section 2.4 in order to express Braggfrequency fB by means of varactor diode capacitance Cvar, characteristicimpedance of an unloaded transmission line Zi, electrical length of an un-loaded transmission-line section between varactor diodes ϕsp and angularfrequency ω.

2.3 Phase Shift Principle

The goal of this section is to demonstrate that phase difference between a sig-nal at the input port and the same signal at the output port of a transmission-line segment can be altered by variable capacitance by which the transmissionline is loaded. The concept of a distributed phase shifter that uses a tunablesynthetic transmission line to control the phase of the incident signal [3], [22]will be presented.

When a signal propagates down a transmission line, the difference be-tween its respective phases at the input port and at the output port of theline equals to electrical length of the line. Electrical length of a transmissionline ϕi is defined [23] by equation (2.17):

ϕi = 2πl

λg, (2.17)

where l denotes the transmission-line physical length and λg stands for signalwavelength on the transmission line, which is given [23] as follows:

λg =2π

β. (2.18)

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Using relations (2.18) and (2.13), equation (2.17) can be modified toexpress electrical length of a lossless homogenous transmission line by itsprimary parameters, inductance Li and capacitance Ci per unit length:

ϕi = βl = ωl√LiCi = 2πfl

√LiCi. (2.19)

As can be seen in (2.19), the extent to which the phase of a signal is shiftedwhen passing through a lossless homogenous transmission line is proportionalto signal frequency f , physical length of the line l and its inductance Li andcapacitance Ci per unit length.

The distributed phase-shifter circuit, shown in Fig. 2.1, comprises a high-impedance transmission line periodically loaded with varactor diodes of ca-pacitance Cvar while physical spacing between the diodes equals to lsp. Aunit cell can be defined for this periodic structure. It consists of a sectionof the transmission line of length lsp and a shunt variable capacitor Cvar toground.

Each such a transmission-line section can be approximated as lumped in-ductance Lt and capacitance Ct, as shown in the equivalent circuit in Fig. 2.2,where

Lt = Lilsp, (2.20)

Ct = Cilsp. (2.21)

CvarCt

Lt Lt Lt

CvarCt CvarCt

Fig. 2.2: Varactor-loaded transmission-line equivalent circuit

For frequencies f well below the Bragg frequency fB, i. e. f fB, theperiodically loaded line may be treated as a synthetic transmission line [22],depicted in Fig. 2.3, whose capacitance per unit length CL has been increasedfrom the former value of Ci due to the periodic loading with shunt capacitance

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ZL(V), φL(V)

Fig. 2.3: Synthetic transmission line described by voltage-controlled characteristicimpedance and electrical length

Cvar [3]. The inductance per unit length LL for this synthetic line remainsunchanged from that of the original unloaded line, Li. Total inductance LLand capacitance CL per unit length of the designed synthetic transmissionline are then found to be

LL = Li, (2.22)

CL = Ci +Cvarlsp

. (2.23)

Based on relations (2.19), (2.22) and (2.23), the equivalent electricallength ϕL of the varactor-loaded transmission line, which forms the synthetictransmission line, is given as

ϕL = ωl√LLCL = 2πfl

√√√√Li

(Ci +

Cvarlsp

). (2.24)

In equation (2.24), the line inductance Li and line capacitance Ci arenormalized per unit length. In assuming a synthetic transmission line, thediscrete variable capacitance is essentially distributed over the length of thecell [3]. This is why all terms involving Cvar are divided by the spacing be-tween varactor diodes, lsp. This approach breaks down in the vicinity of theBragg frequency where a more exact analysis must recognize the discrete na-ture of the loading [3]. The phenomenon of the Bragg frequency is discussedin section 2.4.

Capacitance Cvar depends on reverse bias voltage applied to correspond-ing varactor diodes [2]. Therefore, electrical length of the designed synthetictransmission line ϕL, which is proportional to Cvar, can be controlled bytuning this voltage as is evident in equation (2.24). This is the phase shift

10

principle employed in a varactor-loaded transmission-line phase shifter thethesis focuses on.

To sum it up, phase difference between a signal at the input port andthe same signal at the output port of a varactor-loaded transmission-linesegment equals to its electrical length ϕL that is voltage-controlled. Thephase of the signal passing through the distributed phase shifter can thus beshifted according to the control voltage.

When varying the varactor diodes capacitance Cvar at any given frequencyf that is well below the Bragg frequency fB, i. e. f fB, the maximumpossible differential phase shift ΦL that can be achieved using a varactor-loaded transmission line of given physical line length l and diodes spacing lspcan be determined, based on (2.24), as follows

ΦL = ∆ϕL = ϕmaxL − ϕminL =

= 2πfl√Li

(√Ci +

Cmaxvar

lsp−

√Ci +

Cminvar

lsp

), (2.25)

where Cmaxvar and Cmin

var indicate the maximum and the minimum capacitanceof the varactor diode, respectively. ϕmaxL and ϕminL mean the maximumand the minimum corresponding equivalent electrical length of the varactor-loaded transmission line, respectively.

Besides its electrical length ϕL, there are other voltage-dependent prop-erties of the varactor-loaded transmission line, such as its characteristicimpedance ZL and phase velocity vL, due to voltage-controlled capacitanceCvar. On the basis of formulas (2.22) and (2.23), expressions (2.11) and (2.14)can be modified accordingly to reflect the line loading:

ZL =

√LLCL

=

√Li

Ci + Cvar

lsp

, (2.26)

vL =1√LLCL

=1√

Li

(Ci + Cvar

lsp

) . (2.27)

11

2.4 Bragg Frequency

This section discusses the phenomenon of the Bragg frequency that affectsthe periodic structure of a distributed phase-shifter circuit and that needs tobe taken into account in the varactor-loaded transmission-line phase-shifterdesign.

A result of creating a periodic structure that is shown in Fig. 2.1 is theexistence of a cutoff frequency, called Bragg frequency fB, near the pointwhere the guided wavelength λg approaches the periodic spacing of the dis-crete components lsp [24].

At the Bragg frequency, the periodic filter structure of the distributedloaded line causes the line impedance ZL to become zero [25] and thus almosttotal reflection occurs [26] so there is no power transfer from one port to theother [25]. For this reason, Bragg frequency has to be considered carefullyto determine the upper operational frequency limit of the circuit [26].

Characteristic impedance ZL of a loaded line that can be approximatedby the lumped-element transmission-line model depicted in Fig. 2.2 is ex-pressed [24], [26] by (2.28) as

ZL =

√Lt

Ct + Cvar·

√1−

(ω

ωB

)2

, (2.28)

where ωB denotes the Bragg angular frequency and is given [24], [26] as

ωB =2√

Lt(Ct + Cvar). (2.29)

By a simple modification of equation (2.29) and by employing relations(2.20) and (2.21), the Bragg frequency fB can be written [3], [27] as follows:

fB =ωB2π

=1

π√Lt(Ct + Cvar)

=1

π√Lilsp(Cilsp + Cvar)

. (2.30)

As can be seen in (2.30), the Bragg frequency fB is inversely proportionalto periodic spacing of the varactor diodes lsp, varactor diode capacitance Cvarand to inductance and capacitance per unit length of an unloaded transmis-sion line Li and Ci, respectively.

12

It is evident from (2.28) that for frequencies well below the Bragg fre-quency, i. e. f fB ∼ ω ωB, expression (2.28) can be simplified to (2.26)using (2.20) and (2.21) as follows:

ZL =

√Lt

Ct + Cvar·

√1−

(ω

ωB

)2ωωB=

√Lt

Ct + Cvar=

=

√Lilsp

Cilsp + Cvar=

√Li

Ci + Cvar

lsp

. (2.31)

On the other hand, when frequency of operation reaches the Bragg fre-quency, i. e. f → fB ∼ ω → ωB, characteristic impedance of a loadedtransmission line ZL approaches zero as is demonstrated in formula (2.32).

ZL =

√Lt

Ct + Cvar·

√1−

(ω

ωB

)2ω→ωB−→ 0 (2.32)

The existence of the Bragg frequency thus imposes certain restrictionson the phase-shifter design. The distributed phase-shifter structure shouldbe optimized to ensure that the Bragg frequency is much higher than thefrequency of operation. Based on (2.30), one way to accomplish this is toreduce the periodic spacing of the varactor diodes lsp.

In order to evaluate the Bragg frequency constraint for the purpose of thephase-shifter design, it is convenient to express Bragg frequency fB by meansof varactor diode capacitance Cvar, characteristic impedance of an unloadedtransmission line Zi, electrical length of an unloaded transmission-line sectionbetween varactor diodes ϕsp and angular frequency ω.

Using equations (2.15), (2.16), (2.9) and (2.19), such a dependence of theBragg frequency fB can be derived from expression (2.30) and is written informula (2.33).

fB =1

π√Lilsp(Cilsp + Cvar)

(2.15), (2.16)=

1

π

√Zilsp

vi

(lsp

Zivi+ Cvar

) (2.9)=

(2.9)=

1

π

√Zilspβ

ω

(lspβ

Ziω+ Cvar

) (2.19)=

1

π

√Ziϕsp

ω

(ϕsp

Ziω+ Cvar

) (2.33)

13

The existence of the Bragg frequency, which is related to the periodicstructure of a distributed phase-shifter circuit, can be proved by a simula-tion in a CAD circuit simulation program. Frequency characteristics of thetransmission scattering coefficient s21 of a phase-shifter circuit with idealelements have been examined in AWR Microwave Office.

The simulated structure is the same as the one depicted in Fig. 3.1 wherefor a basic configuration, number of sections N = 8, varactor diodes ca-pacitance Cvar = 2.3 pF, characteristic impedance Zi = 100 Ω and electricallength ϕsp = 16.8 at f = 1 GHz. Each time, one of these parameters is tunedand its effect on the s21 frequency dependence is observed. The respectivevalue of the Bragg frequency fB can then be determined as a significant fallof the magnitude of s21.

Tab. 2.1: Analytically computed values of fB for different distributed phase-shifter circuits

N = 8, f = 1 GHz, ϕsp = 16.8, Zi = 100 ΩCvar [pF] 1.3 1.8 2.3 2.8 3.3fB [GHz] 3.51 3.09 2.80 2.58 2.40N = 8, f = 1 GHz, Cvar = 2.3 pF, Zi = 100 Ωϕsp [] 12.8 14.8 16.8 18.8 20.8fB [GHz] 3.28 3.02 2.80 2.62 2.47N = 8, f = 1 GHz, Cvar = 2.3 pF, ϕsp = 16.8

Zi [Ω] 60 70 80 90 100fB [GHz] 3.43 3.23 3.07 2.93 2.80

Results of the simulation can be seen in Fig. 2.4 through 2.6 and com-pared with respective theoretical values of fB computed analytically fromrelation (2.33). The computed values are recorded in Tab. 2.1 and indicatevery good agreement with the simulated characteristics. Conclusions aboutthe Bragg frequency phenomenon explored in this section are employed insection 3.1 during the phase-shifter design.

14

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

-80

-70

-60

-50

-40

-30

-20

-10

0

1.3 pF

1.8 pF

2.3 pF

2.8 pF

3.3 pF

f [GHz]

|s21| [dB]

Fig. 2.4: The magnitude of s21 versus frequency f dependence of a distributed phaseshifter with ideal elements for varactor diodes capacitance Cvar of 1.3 pF, 1.8 pF, 2.3 pF,2.8 pF and 3.3 pF where number of sections N = 8, electrical length ϕsp = 16.8 atf = 1 GHz and characteristic impedance Zi = 100 Ω

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

-80

-70

-60

-50

-40

-30

-20

-10

0

12.8°

14.8°

16.8°

18.8°

20.8°

f [GHz]

|s21| [dB]

Fig. 2.5: The magnitude of s21 versus frequency f dependence of a distributed phaseshifter with ideal elements for electrical length ϕsp of 12.8, 14.8, 16.8, 18.8 and 20.8

at f = 1 GHz where number of sections N = 8, varactor diodes capacitance Cvar = 2.3 pFand characteristic impedance Zi = 100 Ω

15

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

-80

-70

-60

-50

-40

-30

-20

-10

0

60 Ω

70 Ω

80 Ω

90 Ω

100 Ω

f [GHz]

|s21| [d

B]

Fig. 2.6: The magnitude of s21 versus frequency f dependence of a distributed phaseshifter with ideal elements for characteristic impedance Zi of 60 Ω, 70 Ω, 80 Ω, 90 Ω and100 Ω where number of sections N = 8, varactor diodes capacitance Cvar = 2.3 pF andelectrical length ϕsp = 16.8 at f = 1 GHz

16

2.5 Unit-Cell Matrix Description

The distributed phase-shifter structure can be described as a cascade of iden-tical two-ports that each corresponds to a varactor-loaded transmission-lineunit cell. Each such a unit cell can be further subdivided into a cascade ofthree elementary two-ports that make up the cell. This reflects the unit-cellconfiguration since it comprises a transmission-line section of length lsp thatis split into two equal parts by a shunt varactor diode to ground of variablecapacitance Cvar, as is depicted in Fig. 2.7.

Cvar

Zi, φsp/2

lsp/2 lsp/2

Zi, φsp/2

Fig. 2.7: Varactor-loaded transmission-line unit cell

With respect to the above mentioned structure, it is desirable to repre-sent each two-port in the cascade by the corresponding chain matrix [28].The resulting chain matrix of the two-port cascade then simply equals to thematrix product of the component chain matrices [29] as is employed in equa-tion (2.37). For the purpose of the distributed phase-shifter design, chainmatrix of the distributed phase-shifter unit cell [Au] will be determined andconverted into the corresponding scattering matrix [Su].

A chain matrix [Ag] of a homogenous transmission-line section of lengthlsp

2is found [30] to be

[Ag] =

[cosh γ lsp

2Zi sinh γ lsp

21Zi

sinh γ lsp

2cosh γ lsp

2

], (2.34)

where Zi stands for characteristic impedance of the unloaded transmissionline and γ denotes propagation constant of the line.

A chain matrix [Avar] of a shunt varactor diode to ground of capacitanceCvar, which loads the line, is given [31] as

17

[Avar] =

[1 0Yvar 1

], (2.35)

where Yvar means tunable varactor-diode admittance for given angular fre-quency ω, which is expressed [32] by formula (2.36).

Yvar = jωCvar (2.36)

A chain matrix [Au] of the distributed phase-shifter unit cell that con-sists of the three elementary two-ports—two homogenous transmission-linesections of length lsp

2and the shunt varactor diode to ground in between—put

in a cascade can then be determined by the matrix product of the respectivechain matrices [29]—[Ag], [Avar] and [Ag]—as

[Au] = [Ag] · [Avar] · [Ag] =

=

[cosh γ lsp

2Zi sinh γ lsp

21Zi

sinh γ lsp

2cosh γ lsp

2

]·[

1 0Yvar 1

]·

·

[cosh γ lsp

2Zi sinh γ lsp

21Zi

sinh γ lsp

2cosh γ lsp

2

]=

[au11 au12

au21 au22

], (2.37)

where

au11 = cos2 ϕsp2− sin2 ϕsp

2+ jYvarZi sin

ϕsp2

cosϕsp2, (2.38)

au12 = −YvarZ2i sin2 ϕsp

2+ 2jZi sin

ϕsp2

cosϕsp2, (2.39)

au21 = Yvar cos2 ϕsp2

+2j

Zicos

ϕsp2

sinϕsp2, (2.40)

au22 = cos2 ϕsp2− sin2 ϕsp

2+ jYvarZi sin

ϕsp2

cosϕsp2. (2.41)

Variable ϕsp, which is present e. g. in equations (2.38)–(2.41), standsfor electrical length of the unloaded transmission-line section between thevaractor diodes.

18

In order to evaluate a contribution of the unit cell to differential phaseshift, return loss and insertion loss of the whole phase-shifter circuit, it is use-ful to convert its chain matrix [Au] into the corresponding scattering matrix[Su] by formulas (A.1)–(A.5) that are recorded in Appendix A.

The resulting scattering matrix of the distributed phase-shifter unit cell[Su] is given by equations (2.42)–(2.52), where Zin and Zout denote referenceimpedance at the input and the output port, respectively.

[Su] =

[su11 su12

su21 su22

](2.42)

su11 =su11a

su11b

(2.43)

su11a = 2ZoutZi cos2 ϕsp2

+ jYvarZoutZ2i cos

ϕsp2

sinϕsp2− ZoutZi+

+ 2jZ2i sin

ϕsp2

cosϕsp2− YvarZ3

i + YvarZ3i cos2 ϕsp

2−

− 2jZ∗inZout cosϕsp2

sinϕsp2− YvarZ∗inZoutZi cos2 ϕsp

2+ Z∗inZi−

− 2Z∗inZi cos2 ϕsp2− jYvarZ∗inZ2

i cosϕsp2

sinϕsp2

(2.44)

su11b = 2jZ2i sin

ϕsp2

cosϕsp2

+ jYvarZinZ2i cos

ϕsp2

sinϕsp2

+

+ jYvarZoutZ2i cos

ϕsp2

sinϕsp2

+ 2jZinZout cosϕsp2

sinϕsp2

+

+ 2ZoutZi cos2 ϕsp2

+ YvarZ∗inZoutZi cos2 ϕsp

2+ 2ZinZi cos2 ϕsp

2−

− ZoutZi − ZinZi + YvarZ3i cos2 ϕsp

2− YvarZ3

i (2.45)

su12 =su12a

su12b

(2.46)

su12a = 2Zi√<Zin<Zout (2.47)

su12b = su11b (2.48)

19

su21 = su12 (2.49)

su22 =su22a

su22b

(2.50)

su22a = −2Z∗outZi cos2 ϕsp2− jYvarZ∗outZ2

i cosϕsp2

sinϕsp2

+ Z∗outZi+

+ 2jZ2i sin

ϕsp2

cosϕsp2− YvarZ3

i + YvarZ3i cos2 ϕsp

2−

− 2jZinZ∗out cos

ϕsp2

sinϕsp2− YvarZinZ∗outZi cos2 ϕsp

2+ ZinZi+

+ 2ZinZi cos2 ϕsp2

+ jYvarZinZ2i cos

ϕsp2

sinϕsp2

(2.51)

su22b = su11b (2.52)

As can be seen in relations (2.42)–(2.52), transmission scattering coeffi-cient of the unit cell su21 is a function of tunable varactor-diode admittanceYvar, which is proportional to varactor diode capacitance Cvar as is obviousfrom (2.36). The transition between two Yvar admittance states thus producesa change in the phase of the transmission scattering coefficient su21 [33].

Therefore, the maximum differential phase shift of the distributed phase-shifter unit cell Φu for given angular frequency ω is determined as

Φu = ∆ arg su21 =∣∣ arg su21

(Cmaxvar

)− arg su21

(Cminvar

)∣∣, (2.53)

where Cmaxvar and Cmin

var indicate the maximum and the minimum capacitanceof the varactor diode, respectively.

When the whole phase-shifter circuit is assembled, i. e. N its unit cells areput in a cascade, the maximum differential phase shift of the varactor-loadedtransmission-line phase shifter ΦL is found to be

ΦL = N · Φu, (2.54)

where the number N is determined during the phase-shifter design in orderto achieve the goal of ΦL by the circuit.

Finally, return loss RLu and insertion loss ILu of the distributed phase-shifter unit cell can be counted by formulas (2.55) and (2.56), respectively,where |su11| and |su21| represent respective magnitudes of su11 and su21.

20

RLu = −20 log |su11| (2.55)

ILu = −20 log |su21| (2.56)

2.6 Capacitance Diodes Basics

The main function of capacitance diodes is to provide variable capacitanceand there are several means how to implement it. These include a PN junc-tion depletion layer, a metal-semiconductor junction or a MIS structure [2].Capacitance diodes are known as varicaps or varactors.

In practice, the PN junction depletion layer capacitance is the most usedcapacitance diode technique. Since the width of a reverse biased PN junctiondepletion layer is voltage dependent and the capacitance of the depletionlayer is inversely proportional to its width, the desired capacitance can thusbe adjusted by an appropriate reverse bias voltage applied to a diode [2].Reverse biased PN junction capacitance is characterized by low temperaturedependence, low noise and by frequency independence reaching as high asthe millimeter-wave bands [2].

The PN junction depletion layer capacitance is referred to as the barriercapacitance. Equation (2.57) shows the dependence of barrier capacitanceCj on reverse bias voltage V applied to the junction [2]:

Cj = Cj0

(1 +

V

V0

)−n, (2.57)

where Cj0 stands for zero-bias PN junction capacitance, V0 is the PN junctiondiffusion voltage and n is the PN junction profile exponent.

The applications of capacitance diodes benefit from the ability to controlthe capacitance by the applied voltage. Capacitance diodes are thereforekey elements to a number of subsystems, namely harmonic signals genera-tors, parametric amplifiers, mixers, detectors, frequency modulators, phaseshifters, tunable resonant circuits with voltage-controlled resonant frequencyetc [2].

A typical equivalent circuit of packaged capacitance diodes is shown inFig. 2.8. It consists of PN junction resistanceRj, PN junction capacitance Cj,series resistance Rs of the semiconductor material and ohmic contacts, series

21

Rs LsRj

Cj

Cp

Fig. 2.8: Typical equivalent circuit of packaged capacitance diodes

inductance Ls of metal contact wires and package capacitance Cp. Tab. 2.2lists typical values of these elements as reported in [2].

The varactor-loaded transmission-line phase shifter is to be implementedusing the BB857 varactor diodes, manufactured by Infineon Technologies AG.Typical values of the BB857 varactor diode chip and the related SCD80 pack-age equivalent circuit elements are recorded in Tab. 2.3 based on data pro-vided by the manufacturer [34]. The manufacturer declares the RF-packageparasitics equivalent circuit to be valid up to 6 GHz [34]. Detailed charac-teristics and parameters of the BB857 varactor diode are recorded in Ap-pendix B [34].

Tab. 2.2: Typical values of the packaged capacitance diode equivalent circuit elements asreported in [2]

Rj 102 Ω–108 Ω PN junction resistanceCj 0.1 pF–1 µF PN junction capacitanceRs 0.1 Ω–10 Ω Series resistanceLs 1 nH–10 nH Series inductanceCp approx. 1 pF Package capacitance

Tab. 2.3: Typical values of the BB857 varactor diode and the related SCD80 packageequivalent circuit elements based on data provided by the manufacturer [34]

Cj 0.52 pF–6.6 pF PN junction capacitanceRs 1.5 Ω Series resistanceLs 0.6 nH Series inductanceCp 90 fF Package capacitance

22

The series resistance Rs is sometimes assumed to be constant with reversebias voltage and frequency in order to simplify use of the model. However,additional losses often result in a significantly higher value for Rs at mi-crowave frequencies. Also, Rs decreases with increasing bias voltage as thewidth of the depletion region around the PN junction increases, reducingthe length of the conductive path through the bulk semiconductor materialsurrounding the junction [37].

23

Chapter 3

Phase-ShifterDesign and Optimization

3.1 Design Objectives and Constraints

This section presents basic objectives of the phase-shifter design as wellas constraints imposed by technological parameters of employed design ele-ments. These constraints and trade-offs are then discussed in order to findoptimal implementation of a varactor-loaded transmission-line phase shifter.

The phase shifter is to be designed to operate within a one-octave fre-quency band whose center frequency is 1 GHz or higher. A band that spansfrom 0.7 GHz to 1.4 GHz has been chosen for this purpose. The maximumdifferential phase shift of the circuit should be no less than 90 within thewhole frequency band and return loss of no less than 10 dB should also beachieved. Moreover, it is desirable that the phase shifter be implemented bysimple and inexpensive technique. These phase-shifter design objectives aresummarized in Tab. 3.1.

Tab. 3.1: Phase-shifter design objectives

Frequency band of operation 0.7 GHz ≤ f ≤ 1.4 GHzMaximum differential phase shift ΦL ≥ 90

Return loss RL ≥ 10 dBImplementation technique simple and inexpensive

Key parameters that the design is based upon comprise tunable varactordiode capacitance Cvar, characteristic impedance of an unloaded transmission

24

line Zi and electrical length of an unloaded transmission-line section betweenvaractor diodes ϕsp, which can be converted to physical length of varactordiodes spacing lsp using relation (2.17). Criteria for an optimal choice of theirvalues are given by the design objectives as well as by the Bragg frequencycondition that is explained in section 2.4.

Since Bragg frequency fB represents a cutoff frequency of the distributedphase-shifter periodic structure, the circuit has to be designed and optimizedcarefully to ensure that the Bragg frequency is much higher than the max-imum frequency of operation fmax. Generally, the operational frequency isapproximately half of the Bragg frequency [26]. This condition can than bewritten as follows:

fB ≥ 2 · fmax. (3.1)

Contribution of the key design parameters to the phase-shifter circuitcharacteristics is discussed below. Also, technological constraints, which limitthe choice of their values, are presented.

Varactor diode capacitance Cvar. As is evident from expression (2.25),the wider the range of achievable varactor diode capacitances Cvar—i. e. the greater the difference between Cmax

var and Cminvar —, the higher

the maximum differential phase shift of a varactor-loaded transmissionline ΦL.

On the other hand, analytical computations based on formulas (2.42)–(2.52) show that high Cvar values lead to high reflections of an incidentsignal and thus to unacceptably low return loss RL. The cause of suchbehavior is partially visible from relation (2.26). Adjusting Cvar tohigh values alters greatly the characteristic impedance of a syntheticline ZL and thus leads to significant impedance mismatch with thephase-shifter input and output port impedance.

Another fact which imposes an upper limit of the varactor diode capac-itances range is the dependence of the Bragg frequency fB on Cvar asexpressed in formula (2.33). The higher the varactor diode capacitanceCvar used, the lower the resulting Bragg frequency fB, as can be seenin Fig. 2.4 and Tab. 2.1.

As far as technological constraints are concerned, the BB857 varactordiodes, manufactured by Infineon Technologies AG, which are to beused for the circuit fabrication, provide the Cvar values that range from0.52 pF to 6.6 pF [34]. Detailed characteristics and parameters of theBB857 varactor diode are recorded in Appendix B [34].

25

Characteristic impedance Zi. If a transmission line is periodically loadedwith varactor diodes, characteristic impedance of the resulting syn-thetic transmission line ZL is proportionally lower in comparison tocharacteristic impedance of the unloaded transmission line Zi as can beseen from equations (2.11) and (2.26). In order to keep the value of ZLin the vicinity of the phase-shifter input and output port impedance andthus to avoid unacceptable impedance mismatch, proportionally highercharacteristic impedance of the unloaded line Zi has to be used [3].

Analytical computations based on formulas (2.42)–(2.52) demonstratethat higher values of Zi allow for wider range of capacitances Cvar tobe employed—and thus providing higher maximum differential phaseshift ΦL as mentioned above—while still keeping the return loss of thecircuit acceptable. It has also been proved by these computations thathigher Zi values provide steeper slope of the s21 phase dependence ontunable capacitance Cvar and thus guarantee higher differential phaseshift ΦL for the same Cvar range.

On the other hand, higher values of Zi reduce the resulting Braggfrequency fB in accordance with equation (2.33), as is demonstrated inFig. 2.6 and Tab. 2.1. In addition, implementation of higher values of Ziby planar technology may be more challenging in terms of fabricationprecision.

The phase shifter is to be implemented in the microstrip transmission-line structure. The microstrip structure will be fabricated on theRO4350B substrate, manufactured by Rogers Corporation. The avail-able technology provides a range of potential Zi values that spans from10 Ω to 100 Ω. Detailed characteristics and parameters of the RO4350Bsubstrate are recorded in Appendix C [35].

w <λg2

(3.2)

Width of a microstrip transmission line w has to be designed in ac-cordance with formula (3.2) to prevent higher-order modes from beinggenerated in the microstrip structure [36]. Taking into account thatZi of a microstrip transmission line is inversely proportional to w [36],condition (3.2) imposes the lower limit of Zi.

Since a guided wavelength on a transmission line λg is inversely propor-tional to frequency f , as can be proven by combining relations (2.18)and (2.13), compliance of w with condition (3.2) should be calculated

26

at f = fmax. In addition, computational software of AWR Corporationrecommends that

w

h≤ 20. (3.3)

Smaller values of the w/h fraction decrease an approximation errorwhen characteristics of a microstrip structure are computed [36]. For amicrostrip structure whose physical parameters are listed in Tab. 3.10,the lower limit of Zi is then, with respect to the above mentioned facts,established as 10 Ω.

Analogically, the maximum value of Zi is limited by the minimum wthat can be fabricated. The available technology provides the minimumvalue of w equal to 0.2 mm. However, a transmission line fabricated atthis limit would likely be inferior in terms of precision of its w param-eter and hence the designed characteristic impedance Zi would not beguaranteed.

For this reason, it seems convenient to increase the minimum permittedvalue of w. Width w of 0.376 mm is sufficiently higher, and for the mi-crostrip structure described in Tab. 3.10, it produces the transmission-line characteristic impedance Zi of 100 Ω, which in turn represents theupper limit of Zi.

Electrical length ϕsp. Electrical length of an unloaded transmission-linesection between varactor diodes ϕsp—convertable to physical length ofvaractor diodes spacing lsp using relation (2.17)—determines densityof the transmission-line loading by varactor diodes. According to for-mula (2.25), smaller values of the varactor diodes spacing lsp lead togreater tunability of the electrical length of a varactor-loaded transmis-sion line ϕL by means of Cvar change and thus to greater achievabledifferential phase shift ΦL. As a result, circuit dimensions can be min-imized.

Moreover, smaller values of lsp or corresponding ϕsp provide better com-pliance with the Bragg frequency constraint written in relation (3.1) ascan be deduced from equation (2.33) and seen in Fig. 2.5 and Tab. 2.1.

On the other hand, when bigger spacing between varactor diodes lsp ischosen, a smaller total number of the diodes has to be employed. Sinceeach varactor diode comprises a certain amount of loss, the configura-tion with fewer diodes results in lower insertion loss IL.

27

As can be seen, the choice of the values that are to be employed in thephase-shifter design is a trade-off between several contradictory constraints.Constraints which are imposed by technological and functional limitationsare summarized in Tab. 3.2.

Tab. 3.2: Technological and functional constraints of the phase-shifter design

Varactor diode capacitance 0.52 pF ≤ Cvar ≤ 6.6 pFCharacteristic impedance of the unloaded trans. line 10 Ω ≤ Zi ≤ 100 ΩBragg frequency fB ≥ 2 · fmax

To sum it up, from the functional point of view and with respect tothe design objectives, it appears convenient to employ as high value of theunloaded-line characteristic impedance Zi as possible to allow wider range ofvariable capacitance Cvar and thus higher achievable differential phase shiftΦL while still maintaining acceptable circuit return loss RL.

Physical spacing of the varactor diodes lsp—or electrical length of theunloaded transmission-line section between varactor diodes ϕsp—needs tobe chosen carefully to balance between insertion loss IL of the circuit andthe Bragg frequency constraint. This constraint can also be better met bylimiting the maximum value of Cvar employed.

3.2 Design of the Phase Shifter

with Ideal Elements

Section 3.1 discussed contribution of the key design parameters to the phase-shifter circuit characteristics trends and presented related technological con-straints. This section aims to determine particular values of the design pa-rameters in order to make up the whole 90 phase-shifter circuit that meetsboth the objectives depicted in Tab. 3.1 and the constraints summarized inTab. 3.2. Ideal elements, namely ideal variable capacitors, ideal transmissionlines and ideal grounds, will be used for the purpose of the design in thissection.

Characteristic impedance Zi. With respect to conclusions of section 3.1,as high value of the unloaded-line characteristic impedance Zi as pos-sible will be employed in the design. This will provide wider range ofvariable capacitance Cvar and steeper slope of the s21 phase dependenceon tunable capacitance Cvar.

28

As a result, higher achievable differential phase shift ΦL will be achievedwhile still maintaining acceptable circuit return loss RL. As is stated insection 3.1, the upper limit of Zi imposed by the available technology is100 Ω. This very value of Zi will therefore be used in the phase-shifterdesign.

Varactor diode capacitance Cvar. In order to avoid unacceptable, i. e.lower than 10 dB, circuit return loss RL, the maximum capacitance ofthe varactor diodes Cmax

var needs to be limited. Another beneficial effectof the lower Cmax

var value is better compliance with the Bragg frequencycondition. These mechanisms are further explained in section 3.1.

Based on circuit simulations, previous theses and the BB857 varactordiode C-V dependence, it seems convenient to choose an empirical valueof 2.3 pF as the maximum capacitance of the varactor diodes Cmax

var . Thelower limit of the varactor diodes capacitance Cvar, i. e. Cmin

var , remainsunchanged and equals to 0.52 pF.

Electrical length ϕsp. When the optimal values of the characteristic impe-dance Zi and the maximum capacitance Cmax

var are chosen, the third keydesign parameter—maximum electrical length of the unloaded trans-mission-line section between varactor diodes ϕmaxsp —can be computedby formulas (2.33) and (3.1) provided that the Bragg frequency condi-tion, expressed in (3.1), has to be met.

For Zi = 100 Ω, Cmaxvar = 2.3 pF and fmax = 1.4 GHz, the resulting

maximum electrical length ϕmaxsp of one phase-shifter section equals to16.8 at the center frequency of operation f = 1 GHz. This upperlimit of ϕsp will be employed in the phase-shifter design. The derivedoptimal values of the phase-shifter design parameters are recapitulatedin Tab. 3.3.

Tab. 3.3: Optimal values of the phase-shifter design parameters

Varactor diode capacitance 0.52 pF ≤ Cvar ≤ 2.3 pFCharacteristic impedance of the unloaded trans. line Zi = 100 ΩElectrical length of one phase-shifter section ϕsp = 16.8

Number of sections N = 8

The last step needed to complete a set of the phase-shifter design param-eters inhere in a determination of the number N of the phase-shifter sectionsor unit cells that are to be put in a cascade. The criterion for such a decision

29

is given by the maximum differential phase shift ΦL that can be achieved bythe whole circuit and that is proportional to N . This mechanism is expressedin equation (2.54).

One of the phase-shifter design objectives, presented in section 3.1, is toguarantee that ΦL will be no less than 90 within the whole frequency bandof operation. Therefore, the number N should be chosen properly to achievethis goal. At the same time, N should be as low as possible to keep theresulting circuit simple, compact and inexpensive.

As is evident from formula (2.53), differential phase shift of the distributedphase-shifter unit cell Φu for given angular frequency ω is accomplished bytuning varactor diode capacitance Cvar. The particular value of Φu can thenbe either analytically computed employing equations (2.42)–(2.52) or deter-mined by simulation in a CAD circuit simulation program.

The latter is used in this thesis. Several phase-shifter circuits with idealelements and incrementing number of identical sections have been examinedin AWR Microwave Office. The goal was to determine the minimum numberof sections N which are necessary to achieve the 90 phase shift in accordancewith relation (2.54).

Cvar

Zi, φsp/2 Zi, φsp/2

Cvar

Zi, φsp/2 Zi, φsp/2

Cvar

Zi, φsp/2 Zi, φsp/2

1 2 N

Fig. 3.1: Minimum number of phase-shifter sections determination

For the purpose of these simulations, each identical phase-shifter sectionhas been assembled from ideal elements whose parameters—Cvar, Zi andϕsp—are summarized in Tab. 3.3. Subsequently, characteristics of a total oftwelve circuits have been examined provided that the N -th circuit consistsof N identical phase-shifter sections. This approach is depicted in Fig. 3.1and results of the simulations are recorded in Tab. 3.4.

As can be deduced from equations (2.53) and (2.54), maximum differen-tial phase shift ΦL corresponds to the difference between arguments of thetransmission scattering coefficient s21 at Cmin

var and Cmaxvar . The varactor diodes

capacitance was therefore tuned within the designed range of the Cminvar and

Cmaxvar values and the respective value of ΦL has been recorded.

30

It is essential that the resulting ΦL of the circuit be examined at theminimum frequency of operation fmin, which represents the worst case, sincemaximum differential phase shift ΦL is proportional to frequency f , as canbe seen in formula (2.25). Data in Tab. 3.4 then show that the minimumnumber of sections N needed to achieve the 90 phase shift is 8 and that forN equal to 1 through 8, the whole range of Cvar presented in Tab. 3.3 has tobe exploited.

Tab. 3.4: Simulated characteristics of distributed phase shifters composed of N sectionswhere ΦL is the maximum differential phase shift at fmin = 0.7 GHz, Cmax

var and Cminvar

indicate the maximum and the minimum employed capacitance of varactor diodes, respec-tively, and RLmin stands for minimum return loss of the circuit

N [-] 1 2 3 4 5 6ΦL [] 11.53 22.78 33.92 45.40 57.80 70.80Cmin

var [pF] 0.52 0.52 0.52 0.52 0.52 0.52Cmax

var [pF] 2.3 2.3 2.3 2.3 2.3 2.3RLmin [dB] > 10 > 10 > 10 > 10 > 10 > 10N [-] 7 8 9 10 11 12ΦL [] 83.80 95.90 90 90 90 90Cmin

var [pF] 0.52 0.52 0.8512 0.8033 0.7055 0.793Cmax

var [pF] 2.3 2.3 2.3 2.234 1.95 1.95RLmin [dB] > 10 > 10 13.35 14.00 14.10 14.35

Besides maximum differential phase shift ΦL, minimum return loss RLminof each of the circuits with different number of sections N can be obtainedfrom the simulations. The return loss was examined within the designedrange of the Cmin

var and Cmaxvar values at three significant frequencies, f =

fmin = 0.7 GHz, f = f0 = 1 GHz and f = fmax = 1.4 GHz.

When the number of sections N increases, the range of Cvar needed toprovide the 90 phase shift can be narrower. As a result, characteristicimpedance of the synthetic transmission line ZL is less altered from the stateof impedance match and the return loss RL is thus higher. This effect isvisible in Tab. 3.4 for N equal to 9 through 12 and the corresponding RLversus N dependence is plotted in Fig. 3.2.

Unlike an ideal variable capacitor, employed so far in this section, a realvaractor diode contains, among others, a nonzero series resistance Rs [2],which contributes to the diode losses and consequently to the overall circuitinsertion loss IL.

Therefore, if every ideal variable capacitor in the simulation schemat-ics is replaced by a varactor-diode equivalent circuit, which is covered in

31

sections 2.6 and 3.3, maximum insertion loss ILmax of a distributed phase-shifter circuit can be obtained for each number of sections N . For example,the simulations show that ILmax equals to 0.83 dB, 1.87 dB and 2.39 dB fortwo, four and six sections, or unit cells, respectively.

0 2 4 6 8 10 12

9

10

11

12

13

14

15

N [-]

RL [dB]

Fig. 3.2: Simulated return loss RL of distributed phase-shifter circuits versus number oftheir sections N

In conclusion, the number N of eight phase-shifter sections has been cho-sen as an optimal value for the phase-shifter design. This value seems justright in order to meet the objective of the 90 phase-shift and to balancebetween the circuit return loss RL on one side and the circuit insertion lossIL, its complexity and dimensions on the other side, all of which being pro-portional to N . This value of N has thus completed the set of the optimalphase-shifter design parameters, written in Tab. 3.3, which lays the founda-tions for further phase-shifter circuit characteristics examination.

This section explored the phase-shifter design employing mainly ideal cir-cuit elements. In order to simulate behavior of the real circuit more precisely,real elements should be taken into account. Section 3.3 presents an equiva-lent circuit of a BB857 varactor diode and via holes positioned between thediode and a ground plane. Section 3.5 covers recomputation of the idealtransmission lines to real microstrip transmission lines including discontinu-ities such as bends and steps in the lines width. Section 4.2 then presentsfinal simulation results based on modeling of the entire phase-shifter circuitschematic with real elements in comparison with the measured data.

32

3.3 BB857 Varactor-Diode Modeling

Inaccurate elements description or missing elements parasitics may lead toimprecise results of microwave systems design because of significant differ-ences between the designed circuit simulations and measurements of the man-ufactured circuits. Care must be taken to rely on as precise element modelsas possible in order to obtain acceptable agreement between simulated andmeasured data.

This section focuses on developing a nonlinear model of a BB857 varactordiode, manufactured by Infineon Technologies AG, that would precisely sim-ulate the real element within the frequency range of 0.5 GHz through 3 GHzfor nine significant diode bias voltages. The diode package parasitics and thechip bias-dependent character are taken into account as well. Moreover, themodel also involves inductive character of via holes positioned between thediode and a ground plane.

The resulting model is then used to enhance the precision of the varactor-loaded transmission-line phase-shifter design, particularly in section 3.5. Andit is partly employed in section 3.2 as well. Since the phase-shifting featurein such a circuit is implemented by a varactor-diode adjustable capacitance,the precise varactor-diode modeling is crucial to the phase shifter designand attention will especially be paid to achieve sufficient agreement betweenmeasured and modeled data in terms of the reflection scattering coefficients11 phase.

Ccv

Cp

Ls2 Ls1 Ls3SDIODE1 2

Fig. 3.3: BB857 varactor-diode model

The manufacturer of the BB857 varactor diodes suggests that the chipitself be simulated by a SPICE diode model and the parasitics, including thepackage parasitics, by reactance elements put around the chip. The entire

33

model schematic is shown in Fig. 3.3. The SPICE parameters of the chip andthe parasitics data provided by the manufacturer are then listed in Tab. 3.5and Tab. 3.6, respectively, accompanied by necessary explanation. Accordingto the manufacturer, the model should be valid up to 6 GHz [34].

In the model displayed in Fig. 3.3, inductances Ls1, Ls2 and Ls3 formoverall series inductance of the diode Ls and capacitance Cp stands for thediode package capacitance. Parallel capacitance Ccv and a very high value forthe bottom built-in voltage are applied for better C-V curve approximationbetween reverse bias voltages of 0.5 V through 28 V [34]. The SPICE diodemodel has been implemented by the SDIODE element in the CAD circuitsimulation program, AWR Microwave Office.

Tab. 3.5: The BB857 chip model data provided by the manufacturer [34]

IS 1.35 fA Reverse saturation currentRS 1.5 Ω Series resistanceNN 1.074 Bottom ideality factorTT 70.0 ns Storage timeCJ0 9.122 pF Zero-voltage bottom junction capacitanceV J 6.223 V Bottom built-in voltageM 2.42 Bottom junction grading coefficientFC 0.5 Bottom depletion capacitance linearization parameterBV 32.0 V Breakdown voltageIBV 5.0 µA Current at breakdown voltageEG 1.16 eV Energy gap at nominal temperatureXTI 3.5 Temperature scaling coefficientCcv 0.27 pF Capacitance for a better C-V curve approximation

Tab. 3.6: The BB857 parasitics model data provided by the manufacturer [34]

Ls1 0.45 nH Series inductance no. 1Ls2 0.15 nH Series inductance no. 2Ls3 0.10 nH Series inductance no. 3Cp 90 fF Package capacitance

In order to employ as precise model of a BB857 varactor diode as possible,this thesis does not rely on the model data provided by the manufacturer.Instead, own measurements of a BB857 varactor diode have been carried outand the manufacturer’s model data have been used as a starting point forthe BB857 model optimization. The BB857 varactor-diode measurement andthe respective calibration is covered in section 3.4.

34

Several parameters of the BB857 equivalent circuit were then optimized inAWR Microwave Office so that the s11 phase characteristics of the model fitthe characteristics of the measured data. The BB857 varactor-diode modelhas thus been improved. The resulting values of the optimized model vari-ables as well as their comparison with the former values, suggested by themanufacturer, are listed in Tab. 3.7 and 3.8.

Tab. 3.7: Comparison of the manufacturer’s and the improved BB857 chip model data

Element Manufacturer’s model Improved modelRS 1.50 Ω 1.58 ΩCJ0 9.122 pF 8.559 pFV J 6.223 V 6.291 VM 2.42 2.40Ccv 0.27 pF 0.27 pF

Tab. 3.8: Comparison of the manufacturer’s and the improved BB857 parasitics modeldata

Element Manufacturer’s model Improved modelLs1 0.45 nH 1.28 nHLs2 0.15 nH 0.13 nHLs3 0.10 nH 0.14 nHCp 0.09 pF 0.22 pF

The agreement between the simulated and measured characteristics ofthe BB857 varactor diode can be verified by plotting frequency dependencesof the s11 phase and magnitude while applying different bias voltages to thediode. These plots are displayed in Fig. 3.4 through 3.9. Accuracy of themodel provided by the manufacturer in comparison with the improved modelcan thus be observed in these figures.

The maximum absolute deviations in the s11 phase of the improved BB857model from the measured data for significant diode bias voltages are pre-sented in Tab. 3.9.

As can be seen in Fig. 3.4 through 3.6, the improved varactor-diode modelprovides excellent agreement between the measured and the simulated phaseof s11 over the frequency range and its phase characteristics are superior tothe ones of the manufacturer’s model. The values of the maximum absolutedeviations in the s11 phase of the improved BB857 model from the measureddata, depicted in Tab. 3.9, are very low.

35

Tab. 3.9: Maximum absolute deviations in the s11 phase of the improved BB857 modelfrom the measured data versus applied reverse bias voltage

Reverse bias Max. negative deviation Max. positive deviationvoltage [V] in the s11 phase [] in the s11 phase []

1 −1.23 0.352 −0.81 1.124 −0.54 1.466 −1.58 0.818 −2.38 2.1110 −1.06 1.1315 −0.68 1.5620 −0.71 1.5425 −1.41 1.11

0.5 1.0 1.5 2.0 2.5 3.0

-200

-150

-100

-50

0

50

100

150

200

Measurement, 1 V

Model, 1 V

Manufacturer, 1 V

Measurement, 2 V

Model, 2 V

Manufacturer, 2 V

Measurement, 4 V

Model, 4 V

Manufacturer, 4 V

f [GHz]

arg

s11 [°]

Fig. 3.4: The phase of s11 versus frequency f dependence of the proposed BB857 varactor-diode model in comparison with the measured characteristics and the model data providedby the manufacturer at reverse bias voltage of 1 V, 2 V and 4 V

On the other hand, the agreement between the measured and the simu-lated magnitude of s11 is worse, as is visible in Fig. 3.7 through 3.9. Thisis due to the fact that the parameters of the BB857 equivalent circuit havebeen optimized to provide the best possible agreement in phase of s11 tothe detriment of the magnitude. This approach corresponds to the primaryapplication for which the varactor diode is employed in the circuit—to shiftthe phase of a signal.

Yet, the agreement in trends of the measured and the simulated frequencycharacteristics of the s11 magnitude is acceptable for the frequency band

36

0.5 1.0 1.5 2.0 2.5 3.0

-200

-150

-100

-50

0

50

100

150

200

Measurement, 6 V

Model, 6 V

Manufacturer, 6 V

Measurement, 8 V

Model, 8 V

Manufacturer, 8 V

Measurement, 10 V

Model, 10 V

Manufacturer, 10 V

f [GHz]

arg s11 [°]

Fig. 3.5: The phase of s11 versus frequency f dependence of the proposed BB857 varactor-diode model in comparison with the measured characteristics and the model data providedby the manufacturer at reverse bias voltage of 6 V, 8 V and 10 V

0.5 1.0 1.5 2.0 2.5 3.0

-120

-100

-80

-60

-40

-20

0

Measurement, 15 V

Model, 15 V

Manufacturer, 15 V

Measurement, 20 V

Model, 20 V

Manufacturer, 20 V

Measurement, 25 V

Model, 25 V

Manufacturer, 25 V

f [GHz]

arg

s11 [

°]

Fig. 3.6: The phase of s11 versus frequency f dependence of the proposed BB857 varactor-diode model in comparison with the measured characteristics and the model data providedby the manufacturer at reverse bias voltage of 15 V, 20 V and 25 V

of 0.7 GHz through 1.4 GHz where the phase shifter operates. Also, thecharacteristics of the improved model are still slightly closer to the measuredcharacteristics of a real BB857 diode than the ones of the manufacturer’smodel. In order to reach better agreement in terms of the s11 magnitude,a more complex equivalent circuit of the varactor diode should likely beemployed.

37

0.5 1.0 1.5 2.0 2.5 3.0

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

Measurement, 1 V

Model, 1 V

Manufacturer, 1 V

Measurement, 2 V

Model, 2 V

Manufacturer, 2 V

Measurement, 4 V

Model, 4 V

Manufacturer, 4 V

f [GHz]

|s11|

[dB

]

Fig. 3.7: The magnitude of s11 versus frequency f dependence of the proposed BB857varactor-diode model in comparison with the measured characteristics and the model dataprovided by the manufacturer at reverse bias voltage of 1 V, 2 V and 4 V

0.5 1.0 1.5 2.0 2.5 3.0

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

Measurement, 6 V

Model, 6 V

Manufacturer, 6 V

Measurement, 8 V

Model, 8 V

Manufacturer, 8 V

Measurement, 10 V

Model, 10 V

Manufacturer, 10 V

f [GHz]

|s11|

[dB

]

Fig. 3.8: The magnitude of s11 versus frequency f dependence of the proposed BB857varactor-diode model in comparison with the measured characteristics and the model dataprovided by the manufacturer at reverse bias voltage of 6 V, 8 V and 10 V

38

0.5 1.0 1.5 2.0 2.5 3.0

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

Measurement, 15 V

Model, 15 V

Manufacturer, 15 V

Measurement, 20 V

Model, 20 V

Manufacturer, 20 V

Measurement, 25 V

Model, 25 V

Manufacturer, 25 V

f [GHz]

|s11|

[dB

]

Fig. 3.9: The magnitude of s11 versus frequency f dependence of the proposed BB857varactor-diode model in comparison with the measured characteristics and the model dataprovided by the manufacturer at reverse bias voltage of 15 V, 20 V and 25 V

39

3.4 Varactor-Diode Measurement and Respec-

tive Calibration

As has been mentioned in section 3.3, own measurements of a BB857 varactordiode have been carried out in order to gain s-parameters of the real element.Besides better control over the measured data and the employed calibrationtechnique, this approach allows to measure the diode in the same circuitconfiguration as in the case of the final phase-shifter circuit.

At the beginning of the vector measurement, an Agilent E8364A vectornetwork analyzer was roughly pre-calibrated by the SOLT calibration tech-nique, i. e. Short, Open, Load and Thru calibration standards were used.Afterwards, raw complex scattering coefficients of TRL calibration standards,i. e. Thru, Reflect and Line, and of the varactor diode itself were measuredup to 3 GHz.

The raw measured data were then numerically calibrated by the TRLcalibration method in the MATLAB environment. As a result, de-embeddeds-parameters of the BB857 varactor diode were obtained of which only an s11

vector was of practical value with respect to the diode one-port configuration.

In order to reduce systematic errors of the measurement to the maximumpossible extent, own set of on-wafer TRL calibration standards has beendeveloped in a microstrip structure and used. The same structure is employedfor the designed phase shifter, i. e. the varactor diode has been measured inthe same configuration as in the case of the phase-shifter circuit.

The dimensions of all the designed TRL calibration standards boardsneeded to be the same since a microwave holder of fixed dimensions had tobe used. Therefore, the Line standard could not be implemented as a straighttransmission line. In order to determine the amount of reflections when ameander line is used, simulations of the EM field have been carried out inAWR EM Sight.

Layouts of the designed TRL calibration standards are depicted in Fig. 3.10through 3.15 and the results of the simulations are plotted in Fig. 3.17through 3.20.

Conclusions published in [38] show that the level of the reflections isacceptable when the meander lines are employed instead of the straight linesand are outweighed by the reduced dimensions of the microstrip structure.The same conclusion has been confirmed by the simulations.

The following from the designed calibration standards have been used forthe purpose of the BB857 varactor-diode measurement calibration: Thru,

40

Reflect, Line no. 1. The layout of the circuit where the varactor diode is tobe placed, is depicted in Fig. 3.16. All the designed circuits consist of 50 Ωmicrostrip transmission lines whose parameters are identical with the onesin Tab. 3.10.

Fig. 3.10: Designed Line standard no. 1

Fig. 3.11: Designed Line standard no. 2

Fig. 3.12: Designed Line standard no. 3

Fig. 3.13: Designed Line standard no. 4

41

Fig. 3.14: Designed Reflect standard

Fig. 3.15: Designed Thru standard

Fig. 3.16: Designed circuit for the varactor-diode measurement

42

0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4

-70

-60

-50

-40

-30

-20

-10

0

Thru

Reflect

Line 1

Line 2

Line 3

Line 4

f [GHz]

|s11|

[dB

]

Fig. 3.17: Simulated magnitude of s11 versus frequency f of the designed TRL calibrationstandards

0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4

-200

-150

-100

-50

0

50

100

150

200

Thru

Reflect

Line 1

Line 2

Line 3

Line 4

f [GHz]

arg s11 [°]

Fig. 3.18: Simulated phase of s11 versus frequency f of the designed TRL calibrationstandards

43

0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4

-0.2

-0.18

-0.16

-0.14

-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0

Thru

Reflect

Line 1

Line 2

Line 3

Line 4

f [GHz]

|s21| [d

B]

Fig. 3.19: Simulated magnitude of s21 versus frequency f of the designed TRL calibrationstandards

0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4

-200

-150

-100

-50

0

50

100

150

200

Thru

Reflect

Line 1

Line 2

Line 3

Line 4

f [GHz]

arg s21 [°]

Fig. 3.20: Simulated phase of s21 versus frequency f of the designed TRL calibrationstandards

3.5 Modeling of the Phase Shifter

with Real Elements

This section covers simulations of the entire phase-shifter circuit schematicwith real elements in AWR Microwave Office. The equivalent circuit of aBB857 varactor diode developed in section 3.3 is employed for this purpose.

44

The model also involves parasitic series inductance of via holes positionedbetween the diode and a ground plane. In addition, the ideal transmissionlines are recomputed to real microstrip transmission lines.

The simulation circuit is based on the determined optimal values of thephase-shifter design parameters written in Tab. 3.3. The phase-shifter circuitconsists of eight (N = 8) identical sections of a microstrip transmission linethat are loaded in the middle with the BB857 varactor-diode model subcircuitand that are put in a cascade. Port 1 of the BB857 varactor-diode modelsubcircuit, shown in Fig. 3.3, is thus connected to the transmission line andport 2 is grounded.

Tab. 3.10: Physical characteristics of microstrip transmission lines fabricated on theRO4350B substrate as reported in [35] or computed in accordance with [36] at frequencyf = 1 GHz

w10 13.16 mm Width of the microstrip transmission line of Zi = 10 Ωw50 1.63 mm Width of the microstrip transmission line of Zi = 50 Ωw100 0.376 mm Width of the microstrip transmission line of Zi = 100 Ωh 0.762 mm Height of the microstrip-line substratet 35 µm Thickness of the microstrip-line metallizationεr 3.66 Dielectric constanttan δ 0.0031 Loss tangent

The determined optimal value of characteristic impedance Zi equals to100 Ω. Therefore, the microstrip transmission-line width have been com-puted to provide this impedance. The values of the microstrip-structurephysical parameters as well as the microstrip transmission-line widths forthree significant characteristic impedances Zi are written in Tab. 3.10. Themicrostrip structure is implemented on the RO4350B substrate, manufac-tured by Rogers Corporation, whose detailed characteristics and parametersare recorded in Appendix C [35].

At frequency f = 1 GHz, the electrical length of the transmission-linesections between varactor diodes ϕsp = 16.8 corresponds to the physicallength of the varactor-diodes spacing lsp = 8.76 mm. And this very value oflsp is used in the phase-shifter circuit schematic.

Based on data in Appendix B, reverse bias voltage V applied to thevaractor diodes should be tuned from 5 V to 28 V in order to exploit the rangeof varactor-diodes capacitance Cvar of 0.52 pF through 2.3 pF, where V = 5 Vcorresponds to Cvar = 2.3 pF and V = 28 V results in Cvar = 0.52 pF.

The designed structure of the phase-shifter circuit can be seen in Fig. 3.21.

45

V

BB857

50 Ω, 72 deg 1 2

3 4 5

6 7 8

Zi, lsp/2 Zi, lsp/2 Zi, lsp/2 Zi, lsp/2

Zi, lsp/2 Zi, lsp/2 Zi, lsp/2 Zi, lsp/2 Zi, lsp/2 Zi, lsp/2

Zi, lsp/2 Zi, lsp/2 Zi, lsp/2 Zi, lsp/2 Zi, lsp/2 Zi, lsp/2

BB857

BB857 BB857 BB857

BB857 BB857 BB857

50 Ω

50 Ω

RF IN

RF OUT

104 nH

Fig. 3.21: Designed phase-shifter circuit schematic

Besides the eight phase-shifter unit cells, the circuit consists of two 50 Ω mi-crostrip transmission-line sections that connect the circuit to its SMA con-nectors, an ideal DC voltage source applying the reverse bias voltage to thevaractor diodes and grounded by an inductor of sufficiently high inductance(104 nH), and a 50 Ω section of an ideal transmission line.

This section of an ideal transmission line compensates the phase differ-ence between the simulated and the measured data due to the fact that theposition of the calibrated reference plane during the measurement was dif-ferent from the phase-shifter circuit input port. The electrical length of thiscompensation section has been determined to be 72 at frequency f = 1 GHz.

The simulations have also involved the influence of discontinuities in themicrostrip structure, namely bends and steps in the lines width, but forsimplicity, these are not depicted in Fig. 3.21.

The simulation results based on modeling of the entire phase-shifter cir-cuit schematic with real elements are presented along with the measuredcharacteristics in section 4.2, in Fig. 4.2 through 4.13.

46

Chapter 4

Phase-Shifter CircuitFabrication and Measurement

4.1 Circuit Fabrication

The designed varactor-loaded transmission-line phase shifter is fabricated onthe RO4350B substrate in the microstrip structure covered in section 3.5.

The layout of the designed phase shifter has been optimized so that theboard with the fabricated circuit fits the horizontal dimensions of the AH101metal box, 67 mm to 46 mm. The existence of the bends in the microstripstructure has thus been outweighed by its more compact footprint. Theresulting layout of the circuit can be seen in Fig 4.1.

After its optimization, the layout was exported from AWR MicrowaveOffice into the Gerber and Excellon data files for the purpose of the copper-layer fabrication using a photoplotter and the control of drilling the via holesthrough the substrate, respectively.

The available technology provides the minimum value of the microstriptransmission-line width w equal to 0.2 mm. However, as has been alreadymentioned in section 3.1, a transmission line fabricated at this limit wouldlikely be inferior in terms of precision of its w parameter and hence thedesigned characteristic impedance Zi would not be guaranteed. A higherminimum value of w has therefore been chosen.

The BB857 varactor diodes have been soldered onto the phase-shiftercircuit board with the cathode connected to the microstrip transmission lineand the anode to a pair of via holes. In order to feed the RF signal intothe phase shifter, SMA connectors have been mounted on the phase-shifter

47

metal box and soldered onto the circuit. An external bias tee has been usedto apply the reverse bias control voltage to the varactor diodes.

Fig. 4.1: Designed phase-shifter circuit layout

4.2 Results of the Small-Signal Measurements

RF measurements using a small signal have been made on an Agilent E8364Avector network analyzer calibrated by SOLT calibration standards. The two-port s-parameters of the fabricated phase-shifter circuit were recorded atfrequencies of 45 MHz through 3 GHz and reverse bias voltages of 1 V through28 V.

The measured characteristics along with the corresponding simulateddata are plotted in Fig. 4.2 through 4.13. Tab. 4.1, 4.2, and 4.3 summarizethe achieved qualities of the designed phase shifter in terms of the maximumdifferential phase shift ΦL, the minimum circuit return loss RLmin and themaximum insertion loss ILmax.

Fig. 4.2 through 4.9 show frequency characteristics of the designed phase-shifter s-parameters, namely phase of s21, magnitude of s11 and magnitudeof s21, which can be used to evaluate the agreement between the simulatedand the measured data.

48

Simulated and measured magnitudes of s21 versus frequency f that goesbeyond the maximum frequency of operation fmax are depicted in Fig. 4.8and 4.9 so that the impact of the Bragg frequency fB on the transmissionscattering coefficient s21 of the phase-shifter circuit can be seen.

Analogically, Fig. 4.10 through 4.13 depict the simulated and the mea-sured s-parameters as functions of applied reverse bias voltage and thus en-able to verify the function and parameters of the designed phase shifter duringits operation at a chosen frequency.

0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4

-200

-150

-100

-50

0

50

100

150

200

Simulated, 5 V

Measured, 5 V

Simulated, 6 V

Measured, 6 V

Simulated, 7 V

Measured, 7 V

Simulated, 8 V

Measured, 8 V

f [GHz]

arg

s21 [°]

Fig. 4.2: Simulated and measured phase of s21 versus frequency f of the designed phaseshifter at reverse bias voltage of 5 V, 6 V, 7 V and 8 V

Tab. 4.1: Simulated and measured maximum differential phase shift ΦL of the designedphase shifter at four significant frequencies f

f [GHz] Simulated ΦL [] Measured ΦL []0.7 106.2 110.11.0 166.1 166.81.2 216.6 212.71.4 293.2 276.7

The primary function of the circuit and the main objective of the design—to provide the maximum differential phase shift ΦL of no less than 90 withinthe whole frequency band—has been successfully met, as is evident fromTab. 4.1 and Fig. 4.11. The fabricated phase shifter provides the maximumdifferential phase shift ΦL of 110.1 at the minimum frequency of operationf = fmin = 0.7 GHz.

49

0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4

-200

-150

-100

-50

0

50

100

150

200

Simulated, 10 V

Measured, 10 V

Simulated, 15 V

Measured, 15 V

Simulated, 20 V

Measured, 20 V

Simulated, 28 V

Measured, 28 V

f [GHz]

arg

s21 [

°]

Fig. 4.3: Simulated and measured phase of s21 versus frequency f of the designed phaseshifter at reverse bias voltage of 10 V, 15 V, 20 V and 28 V

0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4

-50

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

Simulated, 5 V

Measured, 5 V

Simulated, 6 V

Measured, 6 V

Simulated, 7 V

Measured, 7 V

Simulated, 8 V

Measured, 8 V

f [GHz]

|s11| [dB]

Fig. 4.4: Simulated and measured magnitude of s11 versus frequency f of the designedphase shifter at reverse bias voltage of 5 V, 6 V, 7 V and 8 V

Different values of ΦL recorded in Tab. 3.4 for number of sections N = 8and in Tab. 4.1 can be explained by the fact that varactor-diode capacitanceCvar was supposed to be a linear function of applied reverse bias voltage insection 3.2. However, a real varactor-diode capacitance Cvar is a nonlinearfunction of applied reverse bias voltage, based on expression (2.57), and thusthe s21 phase dependence of the phase-shifter circuit versus applied reversebias voltage is nonlinear as well. Therefore, both mentioned simulated valuesof ΦL are slightly different.

50

0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4

-60

-50

-40

-30

-20

-10

0

Simulated, 10 V

Measured, 10 V

Simulated, 15 V

Measured, 15 V

Simulated, 20 V

Measured, 20 V

Simulated, 28 V

Measured, 28 V

f [GHz]

|s11| [dB]

Fig. 4.5: Simulated and measured magnitude of s11 versus frequency f of the designedphase shifter at reverse bias voltage of 10 V, 15 V, 20 V and 28 V

0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4

-5

-4.5

-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

Simulated, 5 V

Measured, 5 V

Simulated, 6 V

Measured, 6 V

Simulated, 7 V

Measured, 7 V

Simulated, 8 V

Measured, 8 V

f [GHz]

|s21| [dB]

Fig. 4.6: Simulated and measured magnitude of s21 versus frequency f of the designedphase shifter at reverse bias voltage of 5 V, 6 V, 7 V and 8 V

Fig. 4.2, 4.3 and 4.10 show excellent agreement between the measured andthe simulated characteristics of the designed phase-shifter circuit in phase ofs21 over the whole range of frequencies and reverse bias voltages, which iscrucial for the successful function of a phase shifter.

Another design objective requires that the minimum circuit return lossRLmin of 10 dB is achieved. As is depicted in Tab. 4.2 and Fig. 4.12, thefabricated phase shifter successfully meets this requirement at the four sig-nificant frequencies f . Even in the worst case, which is visible in Fig. 4.4 at

51

0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

Simulated, 10 V

Measured, 10 V

Simulated, 15 V

Measured, 15 V

Simulated, 20 V

Measured, 20 V

Simulated, 28 V

Measured, 28 V

f [GHz]

|s21| [dB]

Fig. 4.7: Simulated and measured magnitude of s21 versus frequency f of the designedphase shifter at reverse bias voltage of 10 V, 15 V, 20 V and 28 V

0.0 0.5 1.0 1.5 2.0 2.5

-50

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

Simulated, 5 V

Measured, 5 V

Simulated, 6 V

Measured, 6 V

Simulated, 7 V

Measured, 7 V

Simulated, 8 V

Measured, 8 V

f [GHz]

|s21|

[dB

]

Fig. 4.8: Simulated and measured magnitude of s21 of the designed phase shifter at reversebias voltage of 5 V, 6 V, 7 V and 8 V versus frequency f that goes beyond the maximumfrequency of operation fmax in order to depict the impact of the Bragg frequency fB onthe transmission scattering coefficient of the phase-shifter circuit

reverse bias voltage V of 5 V, the limit of 10 dB is exceeded by the fabricatedcircuit by a mere 0.05 dB.

Fig. 4.4 shows very good agreement between the measured and the sim-ulated s11 magnitude of the designed phase shifter over the frequency rangeand at reverse bias voltage of 5 V, 6 V, 7 V and 8 V. Fig. 4.5 depicts thesame dependences at reverse bias voltage of 10 V, 15 V, 20 V and 28 V

52

0.0 0.5 1.0 1.5 2.0 2.5 3.0

-35

-30

-25

-20

-15

-10

-5

0

Simulated, 10 V

Measured, 10 V

Simulated, 15 V

Measured, 15 V

Simulated, 20 V

Measured, 20 V

Simulated, 28 V

Measured, 28 V

f [GHz]

|s21| [dB]

Fig. 4.9: Simulated and measured magnitude of s21 of the designed phase shifter at reversebias voltage of 10 V, 15 V, 20 V and 28 V versus frequency f that goes beyond themaximum frequency of operation fmax in order to depict the impact of the Bragg frequencyfB on the transmission scattering coefficient of the phase-shifter circuit

5 10 15 20 25 30

-200

-150

-100

-50

0

50

100

150

200

Simulated, 0.7 GHz

Measured, 0.7 GHz

Simulated, 1.0 GHz

Measured, 1.0 GHz

Simulated, 1.2 GHz

Measured, 1.2 GHz

Simulated, 1.4 GHz

Measured, 1.4 GHz

V [V]

arg s21 [°]

Fig. 4.10: Simulated and measured phase of s21 versus reverse bias voltage V of thedesigned phase shifter at frequency of 0.7 GHz, 1.0 GHz, 1.2 GHz and 1.4 GHz

where the agreement is worse but still satisfactory. The agreement of the s11

magnitude characteristics plotted in Fig. 4.12 is also satisfactory but withnoticeable difference between the measured and the simulated data.

The difference between the measured and the simulated characteristics atlower values of the s11 magnitude may be explained by reflections of the usedSMA connectors, which may thus mask reflections of the measured circuit

53

5 10 15 20 25 30

0

50

100

150

200

250

300

350

Simulated, 0.7 GHz

Measured, 0.7 GHz

Simulated, 1.0 GHz

Measured, 1.0 GHz

Simulated, 1.2 GHz

Measured, 1.2 GHz

Simulated, 1.4 GHz

Measured, 1.4 GHz

V [V]

Δ a

rg s

21 [°]

Fig. 4.11: Simulated and measured differential phase shift ΦL of the designed phase shifter,which equals to the difference in phase of s21 and is normalized to the s21 phase value at themaximum varactor-diodes capacitance Cmax

var , versus reverse bias voltage V at frequencyof 0.7 GHz, 1.0 GHz, 1.2 GHz and 1.4 GHz

5 10 15 20 25 30

-70

-60

-50

-40

-30

-20

-10

0

Simulated, 0.7 GHz

Measured, 0.7 GHz

Simulated, 1.0 GHz

Measured, 1.0 GHz

Simulated, 1.2 GHz

Measured, 1.2 GHz

Simulated, 1.4 GHz

Measured, 1.4 GHz

V [V]

|s11| [dB]

Fig. 4.12: Simulated and measured magnitude of s11 versus reverse bias voltage V of thedesigned phase shifter at frequency of 0.7 GHz, 1.0 GHz, 1.2 GHz and 1.4 GHz

that are below a certain level.

Values of simulated and measured maximum insertion loss ILmax of thedesigned circuit at four significant frequencies f are recorded in Tab. 4.3 andthe corresponding characteristics are shown in Fig. 4.13. As can be seen, thecircuit insertion loss IL increases with increasing frequency f and decreasingreverse bias voltage V .

54

5 10 15 20 25 30

-5

-4.5

-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

Simulated, 0.7 GHz

Measured, 0.7 GHz

Simulated, 1.0 GHz

Measured, 1.0 GHz

Simulated, 1.2 GHz

Measured, 1.2 GHz

Simulated, 1.4 GHz

Measured, 1.4 GHz

V [V]

|s21| [dB]

Fig. 4.13: Simulated and measured magnitude of s21 versus reverse bias voltage V of thedesigned phase shifter at frequency of 0.7 GHz, 1.0 GHz, 1.2 GHz and 1.4 GHz

Tab. 4.2: Simulated and measured minimum return loss RLmin of the designed phaseshifter at four significant frequencies f

f [GHz] Simulated RLmin [dB] Measured RLmin [dB]0.7 11.0 11.81.0 17.8 18.81.2 8.7 10.11.4 8.9 11.4

Tab. 4.3: Simulated and measured maximum insertion loss ILmax of the designed phaseshifter at four significant frequencies f

f [GHz] Simulated ILmax [dB] Measured ILmax [dB]0.7 0.73 1.181.0 0.81 1.731.2 1.81 3.161.4 2.66 4.47

Based on formula (2.57), varactor-diodes capacitance Cvar increases withdecreasing reverse bias voltage V . And both higher values of varactor-diodescapacitance Cvar and frequency f result in increased varactor-diode admit-tance Yvar, as is evident from equation (2.36). When varactor-diode admit-tance Yvar increases, an amount of an RF current that flows through thediode—and through its series resistance Rs—increases as well. Insertion lossIL of the circuit therefore increases with increasing frequency f and decreas-

55

ing reverse bias voltage V .

Fig. 4.6, 4.7 and 4.13 present acceptable agreement in trends betweenthe measured and the simulated characteristics of the designed phase-shiftercircuit in magnitude of s21 over the range of frequencies and reverse bias volt-ages. However, a more complex model of the varactor diode would probablyneed to be employed in order to simulate the circuit insertion loss IL moreprecisely.

Bragg frequency fB of the designed phase-shifter periodic structure is wellbeyond maximum frequency of operation f = fmax = 1.4 GHz for the wholerange of used reverse bias voltages, as can be seen in Fig. 4.8 and 4.9.

4.3 Large-Signal Behavior of the Circuit

The BB857 varactor-diode nonlinear model has also been exploited to ana-lyze the large-signal behavior of the resulting phase-shifter circuit since thenonlinear dependence of the PN junction capacitance on the applied biasvoltage represents the main source of the circuit nonlinearity.

The two-tone third-order output intercept point OIP3 of the designedphase shifter has been simulated and measured, whereas the 1 dB compres-sion point P−1dB has only been simulated and not measured due to technicallimitations of the available input power level.

Analysis of the large-signal behavior of the designed circuit has beencarried out for tones at f1 = 1.00 GHz and f2 = 1.01 GHz and for reversebias voltage V of 6 V applied to the varactor diodes. AWR Microwave Officehas been used for the simulations.

The two-tone third-order output intercept point OIP3 can be determinedas the y-axis coordinate of an intersection point of tangents to the output-power characteristics of the first-harmonic and the third-order intermodula-tion (IM) products [39]. The 1 dB compression point P−1dB is the y-axis co-ordinate of a point on the first-harmonic output-power characteristic wherethe difference between the compressed output-power characteristic and itstangent equals to 1 dB [39].

The characteristics obtained from the large-signal behavior analysis ofthe circuit are depicted in Fig. 4.14 and the particular resulting values ofOIP3 and P−1dB are recorded in Tab. 4.4. These characteristics provide goodagreement between the measured and simulated behavior of the phase shifter.

56

-5 0 5 10 15 20 25 30 35

-70

-60

-50

-40

-30

-20

-10

0

10

20

30

40

Simulated first harmonics

Simulated third-order IM products

Tangent of simulated first harmonics

Tangent of simulated third-order IM products

Measured first harmonics

Measured third-order IM products

Tangent of measured first harmonics

Tangent of measured third-order IM products

Pin [dBm]

Pout [dBm]

Fig. 4.14: Output power Pout of simulated and measured first harmonics and third-orderIM products of the designed phase-shifter circuit versus input power Pin in order to de-termine the two-tone third-order output intercept point OIP3 and the 1 dB compressionpoint P−1dB

Tab. 4.4: Resulting values of the two-tone third-order output intercept point OIP3 andthe 1 dB compression point P−1dB of the designed phase shifter

Simulated OIP3 [dBm] 28.0Measured OIP3 [dBm] 25.4Simulated P−1dB [dBm] 17.1

57

Chapter 5

Conclusion

The thesis has presented theory behind the function principles of a phaseshifter based on a varactor-loaded transmission line. The function of thephase shifter has been examined in relation to its physical parameters, keyvariables of the structure have been specified and an appropriate choice oftheir values has been discussed in order to design and optimize the phase-shifter circuit.

The main objective of the thesis was to design and fabricate a phase shifterthat operates within a one-octave frequency band for the center frequencyof 1 GHz or higher. The maximum differential phase shift of the circuit wasrequired to be at least 90 within the whole frequency band and its returnloss to be no less than 10 dB.

This objective has been successfully met. The developed phase shifteroperates within the frequency range of 0.7 GHz through 1.4 GHz, providesthe maximum differential phase shift of 110.1 at the minimum frequency ofoperation, the return-loss limit of 10 dB has been exceeded by the fabricatedcircuit by a mere 0.05 dB in the worst case and good agreement between thesimulated and the measured characteristics of the phase-shifter circuit hasbeen obtained. The third-order output intercept point of the phase shifterhas been measured to be 25.4 dBm.

The model of a BB857 varactor diode provided by the manufacturer hasbeen improved based on own measurements of the element for the purposeof the phase-shifter simulations. However, a more complex model of thevaractor diode would probably need to be employed in order to simulate thecircuit insertion loss more precisely.

58

Acknowledgements

First of all, I wish to acknowledge kind support and guidance of my supervi-sor, Ing. Jan Sıstek, Ph.D., that he provided to me during my work on thisthesis as well as highly qualified instruction and suggestions I received fromhim.

I would also like to express my appreciation to prof. Ing. Karel Hoff-mann, CSc. for helpful discussions and assistance in the field of microwavemeasurements.

And last but not least, I wish to thank my parents for their encouragementand loving support not only for the work on this thesis but also throughoutmy whole university studies.

Matej VokacMay 22, 2009Prague

59

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63

Appendix A

Chain to Scattering MatrixConversion

Theory behind conversion of a chain matrix [A] into a scattering matrix [S]is presented in [40] and leads to formulas (A.1)–(A.5), where Zin and Zoutstand for reference impedance at the input and the output port, respectively.

[A] =

[a11 a12

a21 a22

]−→ [S] =

[s11 s12

s21 s22

](A.1)

s11 =a11Zout + a12 − a21Z

∗inZout − a22Z

∗in

a11Zout + a12 + a21ZinZout − a22Zin(A.2)

s12 =det[A] · 2

√<Zin<Zout

a11Zout + a12 + a21ZinZout − a22Zin(A.3)

s21 =2√<Zin<Zout

a11Zout + a12 + a21ZinZout − a22Zin(A.4)

s22 =−a11Z

∗out + a12 − a21ZinZ

∗out − a22Zin

a11Zout + a12 + a21ZinZout − a22Zin(A.5)

64

Appendix B

BB857 Data Sheet

2007-0

4-2

01

BB

837/B

B857...

Silic

on

Tu

nin

g D

iod

e

• F

or

SA

T tuners

• H

igh c

apacitance r

atio

• L

ow

series r

esis

tance

• E

xcelle

nt uniform

ity a

nd m

atc

hin

g d

ue to

"

in-lin

e"

matc

hin

g a

ssem

bly

pro

cedure

• P

b-f

ree (

RoH

S c

om

plia

nt)

package

1)

• Q

ualif

ied a

ccord

ing A

EC

Q101

BB

837

BB

857

12

Typ

eP

ackag

eC

on

fig

ura

tio

nL

S(n

H)

Mark

ing

BB

837

BB

857

SO

D323

SC

D80

sin

gle

sin

gle

1.8

0.6

M OO

Maxim

um

Rati

ng

s a

t T

A =

25°C

, unle

ss o

therw

ise s

pecifie

d

Para

mete

rS

ym

bo

lV

alu

eU

nit

Dio

de r

evers

e v

oltage

VR

30

V

Peak r

evers

e v

oltage

R≥ 5

kΩ

VR

M35

Forw

ard

curr

ent

I F20

mA

Opera

ting tem

pera

ture

range

Top

-55 ... 1

50

°C

Sto

rage tem

pera

ture

Tstg

-55 ... 1

50

1P

b-c

onta

inin

g p

ackage m

ay b

e a

vaila

ble

upon s

pecia

l re

quest

65

20

07

-04

-20

3

BB

837/B

B857...

Dio

de

ca

pa

cit

an

ce

CT =

ƒ (

VR

)

f=

1M

Hz

10

01

01

10

2V

VR

012345678

pF1

0

CT

No

rma

lize

d d

iod

e c

ap

ac

ita

nc

e

C(T

A)/C

(25°C

)=ƒ(T

A);

f =

1M

Hz

-30

-10

10

30

50

70

°C1

00

TA

0.9

75

0.9

8

0.9

85

0.9

9

0.9

951

1.0

05

1.0

1

1.0

15

1.0

2

1.0

25

-

1.0

35

CTA/C25

1V

2V 25

V

28

V

Re

ve

rse

cu

rre

nt

I R =

ƒ (

TA)

VR

= 2

8V

-30

-10

10

30

50

70

°C1

00

TA

01

0

11

0

21

0

31

0

pA

IR

Re

ve

rse

cu

rre

nt

I R =

ƒ(V

R)

TA

= P

ara

me

ter

10

01

01

10

2V

VR

-11

0

01

0

11

0

21

0

31

0

pA

IR

28

°C

60

°C

80

°C

2007-0

4-2

02

BB

837/B

B857...

Ele

ctr

ica

l C

ha

rac

teri

sti

cs

atT

A =

25

°C,

un

less o

the

rwis

e s

pe

cifie

d

Pa

ram

ete

rS

ym

bo

lV

alu

es

Un

it

min

.ty

p.

ma

x.

DC

Ch

ara

cte

ris

tic

s

Re

ve

rse

cu

rre

nt

VR

= 3

0 V

VR

= 3

0 V

, T

A =

85

°C

I R

- -

- -

10

20

0

nA

AC

Ch

ara

cte

ris

tic

s

Dio

de

ca

pa

cita

nce

VR

= 1

V, f

= 1

MH

z

VR

= 2

5 V

, f

= 1

MH

z

VR

= 2

8 V

, f

= 1

MH

z

CT

6 0.5

0.4

5

6.6

0.5

5

0.5

2

7.2

0.6

5

-

pF

Ca

pa

cita

nce

ra

tio

VR

= 1

V, V

R =

25

V, f

= 1

MH

z

CT

1/C

T25

10

.21

2-

-

Ca

pa

cita

nce

ra

tio

VR

= 1

V, V

R =

28

V, f

= 1

MH

z

CT

1/C

T28

9.7

12

.7-

Ca

pa

cita

nce

ma

tch

ing

1)

VR

= 1

V .

.. 2

8V

, f

= 1

MH

z,

7 d

iod

es s

eq

ue

nce

∆C

T/C

T-

-5

%

Se

rie

s r

esis

tan

ce

VR

= 5

V, f

= 4

70

MH

z

r S-

1.5

-Ω

1F

or

deta

ils p

lease r

efe

r to

Applic

ation N

ote

047

66

20

07

-04

-20

5

BB837/BB857...

Da

te C

od

e m

ark

ing

fo

r d

isc

rete

pa

ck

ag

es

wit

h

on

e d

igit

(S

CD

80

, S

C7

9,

SC

75

1) )

CE

S-C

od

e

1)

Ne

w M

ark

ing

La

yo

ut

for

SC

75

, im

ple

me

nte

d a

t O

cto

be

r 2

00

5.

.Mo

nth

20

03

20

04

20

05

20

06

20

07

20

08

20

09

20

10

20

11

20

12

20

13

20

14

01

ap

AP

ap

AP

ap

AP

02

bq

BQ

bq

BQ

bq

BQ

03

cr

CR

cr

CR

cr

CR

04

ds

DS

ds

DS

ds

DS

05

et

ET

et

ET

et

ET

06

fu

FU

fu

FU

fu

FU

07

gv

GV

gv

GV

gv

GV

08

hx

HX

hx

HX

hx

HX

09

jy

JY

jy

JY

jy

JY

10

kz

KZ

kz

KZ

kz

KZ

11

l2

L4

l2

L4

l2

L4

12

n3

N5

n3

N5

n3

N5

20

07

-04

-20

4

BB

837/B

B857...

Packag

e S

CD

80

Pa

ck

ag

e O

utl

ine

Fo

ot

Pri

nt

Ma

rkin

g L

ay

ou

t (E

xa

mp

le)

±0.1 1.7

0.3

12

mark

ing

Cath

ode

0.8

±0.1

10!MAX.

±0.1

0.7

±0.1 1.37!

0.13

±0.0

5

+0.0

5-0

.03

±1.5!

0.2

MA

A ±0.05 0.2

0.350.35

1.45

BA

R63-0

2W

Type c

ode

Cath

ode m

ark

ing

Laser

mark

ing

0.7

20.2

0.9

0.4

8

4

1.45

2.5

Sta

nd

ard

Re

el w

ith 2

mm

Pitc

h

Ca

tho

de

ma

rkin

g

Ca

tho

de

ma

rkin

g

Sta

nd

ard

Pa

ck

ing

Re

el

ø1

80

mm

= 3

.00

0 P

iece

s/R

ee

l

Re

el

ø1

80

mm

= 8

.00

0 P

iece

s/R

ee

l (2

mm

Pit

ch

)

Re

el

ø3

30

mm

= 1

0.0

00

Pie

ce

s/R

ee

l

2005, June

Date

code

67

20

07

-04

-20

7

BB

837/B

B857...

Ed

itio

n 2

00

6-0

2-0

1

Pu

blis

he

d b

y

Infin

eo

n T

ech

no

log

ies A

G

81

72

6 M

ün

ch

en

, G

erm

an

y

© I

nfin

eo

n T

ech

no

log

ies A

G 2

00

7.

All

Rig

hts

Re

se

rve

d.

Att

en

tio

n p

lea

se

!

Th

e in

form

atio

n g

ive

n in

th

is d

oku

me

nt

sh

all

in n

o e

ve

nt

be

re

ga

rde

d a

s a

gu

ara

nte

e

of

co

nd

itio

ns o

r ch

ara

cte

ristics (

“Be

sch

aff

en

he

itsg

ara

ntie

”).

With

re

sp

ect

to a

ny

exa

mp

les o

r h

ints

giv

en

he

rein

, a

ny t

yp

ica

l va

lue

s s

tate

d h

ere

in a

nd

/or

an

y in

form

atio

n

reg

ard

ing

th

e a

pp

lica

tio

n o

f th

e d

evic

e,

Infin

eo

n T

ech

no

log

ies h

ere

by d

iscla

ims a

ny

an

d a

ll w

arr

an

tie

s a

nd

lia

bili

tie

s o

f a

ny k

ind

, in

clu

din

g w

ith

ou

t lim

ita

tio

n w

arr

an

tie

s o

f

no

n-in

frin

ge

me

nt

of

inte

llectu

al p

rop

ert

y r

igh

ts o

f a

ny t

hird

pa

rty.

Info

rma

tio

n

Fo

r fu

rth

er

info

rma

tio

n o

n t

ech

no

log

y,

de

live

ry t

erm

s a

nd

co

nd

itio

ns a

nd

price

s

ple

ase

co

nta

ct

yo

ur

ne

are

st

Infin

eo

n T

ech

no

log

ies O

ffic

e (

ww

w.i

nfi

ne

on

.co

m).

Wa

rnin

gs

Du

e t

o t

ech

nic

al re

qu

ire

me

nts

co

mp

on

en

ts m

ay c

on

tain

da

ng

ero

us s

ub

sta

nce

s.

Fo

r in

form

atio

n o

n t

he

typ

es in

qu

estio

n p

lea

se

co

nta

ct

yo

ur

ne

are

st

Infin

eo

n T

ech

no

log

ies O

ffic

e.

Infin

eo

n T

ech

no

log

ies C

om

po

ne

nts

ma

y o

nly

be

use

d in

life

-su

pp

ort

de

vic

es o

r

syste

ms w

ith

th

e e

xp

ress w

ritt

en

ap

pro

va

l o

f In

fin

eo

n T

ech

no

log

ies,

if a

fa

ilure

of

su

ch

co

mp

on

en

ts c

an

re

aso

na

bly

be

exp

ecte

d t

o c

au

se

th

e f

ailu

re o

f th

at

life

-su

pp

ort

de

vic

e o

r syste

m,

or

to a

ffe

ct

the

sa

fety

or

eff

ective

ne

ss o

f th

at

de

vic

e o

r syste

m.

Life

su

pp

ort

de

vic

es o

r syste

ms a

re in

ten

de

d t

o b

e im

pla

nte

d in

th

e h

um

an

bo

dy,

or

to s

up

po

rt a

nd

/or

ma

inta

in a

nd

su

sta

in a

nd

/or

pro

tect

hu

ma

n life

. If

th

ey f

ail,

it is r

ea

so

na

ble

to

assu

me

th

at

the

he

alth

of

the

use

r o

r o

the

r p

ers

on

s

ma

y b

e e

nd

an

ge

red

.

20

07

-04

-20

6

BB

837/B

B857...

Packag

e S

OD

323

Pa

ck

ag

e O

utl

ine

Fo

ot

Pri

nt

Ma

rkin

g L

ay

ou

t (E

xa

mp

le)

Sta

nd

ard

Pa

ck

ing

Re

el

ø1

80

mm

= 3

.00

0 P

iece

s/R

ee

l

Re

el

ø3

30

mm

= 1

0.0

00

Pie

ce

s/R

ee

l

BA

R63-0

3W

Type c

ode

Cath

ode

mark

ing

Laser

mark

ing

0.8 0.8

0.6

1.7

mark

ing

Cath

ode

±0.2 2.5

0.2

50.3

1

-0.0

5

MA

+0

.1

+0

.2

2

1.2

5-0

.1

+0

.05

-0.2

1.7

0.3

0.1

5-0

.06

+0

.1

0±

0.0

5

+0.2-0.1A

0.9

+0

.2-0

.1

±0.15 0.45

0.2

4

8

2.9

1

2

1.3

5

0.6

5C

ath

ode

mark

ing

68

Appendix C

RO4350B Data Sheet

RO

40

00

® S

erie

s H

igh

Fre

qu

en

cy C

irc

uit M

ate

ria

ls a

re g

lass

rein

forc

ed

hyd

roc

arb

on

/ce

ram

ic la

min

ate

s (N

ot

PTF

E)

de

sig

ne

d f

or

pe

rfo

rma

nc

e s

en

sitiv

e,

hig

h v

olu

me

co

mm

erc

ial

ap

plic

atio

ns.

RO

40

00

lam

ina

tes

are

de

sig

ne

d t

o o

ffe

r su

pe

rio

r h

igh

fre

qu

en

cy p

erf

orm

an

ce

an

d lo

w c

ost

circ

uit f

ab

ric

atio

n.

Th

e

resu

lt is

a lo

w lo

ss m

ate

ria

l wh

ich

ca

n b

e f

ab

ric

ate

d u

sin

g

sta

nd

ard

ep

oxy

/gla

ss (

FR

4)

pro

ce

sse

s o

ffe

red

at

co

mp

etitiv

e

pric

es.

The

se

lec

tio

n o

f la

min

ate

s ty

pic

ally

av

aila

ble

to

de

sig

ne

rs is

sig

niÞ

ca

ntly r

ed

uc

ed

on

ce

op

era

tio

na

l fre

qu

en

cie

s in

cre

ase

to 5

00

MH

z a

nd

ab

ov

e.

RO

40

00

ma

teria

l po

sse

sse

s th

e

pro

pe

rtie

s n

ee

de

d b

y d

esi

gn

ers

of

RF m

icro

wa

ve

circ

uits

an

d

allo

ws

for

rep

ea

tab

le d

esi

gn

of Þ lte

rs,

ma

tch

ing

ne

two

rks

an

d c

on

tro

lled

imp

ed

an

ce

tra

nsm

issi

on

lin

es.

Lo

w d

iele

ctr

ic

loss

allo

ws

RO

40

00

se

rie

s m

ate

ria

l to

be

use

d in

ma

ny

ap

plic

atio

ns

wh

ere

hig

he

r o

pe

ratin

g f

req

ue

nc

ies

limit t

he

use

of

co

nv

en

tio

na

l circ

uit b

oa

rd la

min

ate

s. T

he

te

mp

era

ture

co

efÞ

cie

nt

of

die

lec

tric

co

nst

an

t is

am

on

g t

he

low

est

of

an

y

circ

uit b

oa

rd m

ate

ria

l (C

ha

rt 1

), a

nd

th

e d

iele

ctr

ic c

on

sta

nt

is

sta

ble

ov

er

a b

roa

d f

req

ue

nc

y r

an

ge

(C

ha

rt 2

). T

his

ma

ke

s it

an

ide

al s

ub

stra

te f

or

bro

ad

ba

nd

ap

plic

atio

ns.

RO

40

00

ma

teria

l’s

the

rma

l co

efÞ

cie

nt

of

exp

an

sio

n (

CTE

)

pro

vid

es

sev

era

l ke

y b

en

eÞ ts

to

th

e c

irc

uit d

esi

gn

er.

Th

e

exp

an

sio

n c

oe

fÞ c

ien

t o

f R

O4

00

0 m

ate

ria

l is

sim

ilar

to t

ha

t

of

co

pp

er

wh

ich

allo

ws

the

ma

teria

l to

exh

ibit e

xce

llen

t

dim

en

sio

na

l sta

bili

ty,

a p

rop

ert

y n

ee

de

d f

or

mix

ed

die

lec

tric

mu

ltila

ye

r b

oa

rds

co

nst

ruc

tio

ns.

Th

e lo

w Z

-axi

s C

TE o

f R

O4

00

0

lam

ina

tes

pro

vid

es

relia

ble

pla

ted

th

rou

gh

-ho

le q

ua

lity,

ev

en

in s

ev

ere

th

erm

al s

ho

ck a

pp

lica

tio

ns.

RO

40

00

se

rie

s m

ate

ria

l

ha

s a

Tg

of

>2

80

°C (

53

6°F

) so

its

exp

an

sio

n c

ha

rac

terist

ics

rem

ain

sta

ble

ov

er

the

en

tire

ra

ng

e o

f c

irc

uit p

roc

ess

ing

tem

pe

ratu

res.

RO

40

00

se

rie

s la

min

ate

s c

an

ea

sily

be

fa

bric

ate

d in

to p

rin

ted

circ

uit b

oa

rds

usi

ng

sta

nd

ard

FR

4 c

irc

uit b

oa

rd p

roc

ess

ing

tec

hn

iqu

es.

Un

like

PTF

E b

ase

d h

igh

pe

rfo

rma

nc

e m

ate

ria

ls,

RO

40

00

se

rie

s la

min

ate

s d

o n

ot

req

uire

sp

ec

ializ

ed

via

pre

pa

ratio

n p

roc

ess

es

suc

h a

s so

diu

m e

tch

. Th

is m

ate

ria

l is

a

rig

id,

the

rmo

set

lam

ina

te t

ha

t is

ca

pa

ble

of

be

ing

pro

ce

sse

d

by a

uto

ma

ted

ha

nd

ling

syst

em

s a

nd

sc

rub

bin

g e

qu

ipm

en

t

use

d f

or

co

pp

er

surf

ac

e p

rep

ara

tio

n.

Da

ta S

he

et

RO

4000

® S

erie

s H

igh

Fre

qu

en

cy

Circ

uit M

ate

ria

ls

Fe

atu

res:

•

No

t-P

TFE

•

Exc

elle

nt

hig

h f

req

ue

nc

y p

erf

orm

an

ce

du

e t

o

low

die

lec

tric

to

lera

nc

e a

nd

loss

•

Sta

ble

ele

ctr

ica

l pro

pe

rtie

s v

ers

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RO

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69

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nd

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lth

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Ro

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me

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esi

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co

mb

ina

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ss f

or

use

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er

the

en

tire

life

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en

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rod

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nd

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RO

40

03

C:

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08

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2 (

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05

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06

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20

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0.0

32

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13

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), 0

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1.5

24

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RO

43

50

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04

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01

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), 0

.00

66

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3 (

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20

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0.0

30

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62

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24

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12

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5 X

45

7 m

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0 X

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91

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m)

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24

m X

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00

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size

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rge

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24

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2 o

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in

form

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on

tain

ed

in t

his

fa

bric

atio

n g

uid

e is

inte

nd

ed

to

ass

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u in

de

sig

nin

g w

ith

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ge

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uit m

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ria

ls a

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pre

pre

g.

It is

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t

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nd

ed

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d d

oe

s n

ot

cre

ate

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lied

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ty o

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erc

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ty o

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ess

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rtic

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r

pu

rpo

se o

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at

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re

sults

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wn

on

th

is f

ab

ric

atio

n g

uid

e w

ill b

e a

ch

iev

ed

by a

use

r fo

r a

pa

rtic

ula

r p

urp

ose

. Th

e u

ser

is r

esp

on

sib

le f

or

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term

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g t

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og

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uit m

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nd

pre

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or

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00

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RO

40

03

RO

43

50

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Ch

art

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40

00

Se

rie

s M

ate

ria

ls

Die

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tric

Co

nsta

nt

vs.

Te

mp

era

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art

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40

00

Se

rie

s M

ate

ria

ls

Die

lec

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Co

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nt

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qu

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art

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nse

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Fre

qu

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70

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form

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n c

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tain

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in t

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fa

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atio

n g

uid

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nd

ed

to

ass

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de

sig

nin

g w

ith

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ge

rs’

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uit m

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ria

ls a

nd

pre

pre

g.

It is

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t

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nd

ed

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d d

oe

s n

ot

cre

ate

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an

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xp

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lied

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g a

ny w

arr

an

ty o

f m

erc

ha

nta

bili

ty o

r Þ tn

ess

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r a

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rtic

ula

r

pu

rpo

se o

r th

at

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re

sults

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wn

on

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is f

ab

ric

atio

n g

uid

e w

ill b

e a

ch

iev

ed

by a

use

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r a

pa

rtic

ula

r p

urp

ose

. Th

e u

ser

is r

esp

on

sib

le f

or

de

term

inin

g t

he

su

ita

bili

ty o

f R

og

ers

’ c

irc

uit m

ate

ria

ls a

nd

pre

pre

g f

or

ea

ch

ap

plic

atio

n.

DR

ILLIN

G C

ON

DIT

ION

S:

Su

rfa

ce

sp

ee

ds

gre

ate

r th

an

50

0 S

FM

an

d c

hip

loa

ds

less

th

an

0.0

02

” (

0.0

5m

m)

sho

uld

be

av

oid

ed

, w

he

ne

ve

r

po

ssib

le.

R

ec

om

me

nd

ed

Ra

ng

es:

Su

rfa

ce

Sp

ee

d:

30

0 -

50

0 S

FM

(9

0 t

o 1

50

m/m

m)

C

hip

Lo

ad

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02

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0.0

04

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0 m

m/r

ev

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R

etr

ac

t R

ate

: 5

00

- 1

00

0 IP

M 5

00

IP

M (

12

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/min

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r to

ol l

ess

th

an

0.0

13

5"

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43

mm

),1

00

0 IP

M (

25

.4 m

/min

) fo

r a

ll o

the

rs.

To

ol T

yp

e:

Sta

nd

ard

Ca

rbid

e

To

ol l

ife

:

20

00

-30

00

hits

Ho

le q

ua

lity s

ho

uld

be

use

d t

o d

ete

rmin

e t

he

eff

ec

tiv

e t

oo

l life

ra

the

r th

an

to

ol w

ea

r. T

he

RO

40

03

™ m

ate

ria

l will

yie

ld g

oo

d h

ole

qu

alit

y w

he

n d

rille

d w

ith

bits

wh

ich

are

co

nsi

de

red

wo

rn b

y e

po

xy/g

lass

sta

nd

ard

s. U

nlik

e e

p-

oxy/g

lass

, R

O4

00

3 m

ate

ria

l ho

le r

ou

gh

ne

ss d

oe

s n

ot

inc

rea

se s

ign

iÞ c

an

tly w

ith

to

ol w

ea

r. T

yp

ica

l va

lue

s ra

ng

e

fro

m 8

-25

um

re

ga

rdle

ss o

f h

it c

ou

nt

(ev

alu

ate

d u

p t

o 8

00

0 h

its)

. Th

e r

ou

gh

ne

ss is

dire

ctly r

ela

ted

to

th

e c

era

mic

Þ lle

r si

ze a

nd

pro

vid

es

top

og

rap

hy t

ha

t is

be

neÞ c

ial f

or

ho

le-w

all

ad

he

sio

n.

Drilli

ng

co

nd

itio

ns

use

d f

or

ep

oxy/

gla

ss b

oa

rds

ha

ve

be

en

fo

un

d t

o y

ield

go

od

ho

le q

ua

lity w

ith

hit c

ou

nts

in e

xc

ess

of

20

00

.

CA

LC

ULA

TIN

G S

PIN

DLE S

PEED

AN

D IN

FEED

:

1

2 x

[Su

rfa

ce

Sp

ee

d (

SFM

)]

Sp

ind

le S

pe

ed

(R

PM

)

=

!

x

[To

ol D

iam

. (i

n.)

]

Fe

ed

Ra

te (

IPM

) =

[S

pin

dle

Sp

ee

d (

RP

M)]

x [

Ch

ip L

oa

d (

in/r

ev

.)]

Exa

mp

le:

D

esi

red

Su

rfa

ce

Sp

ee

d:

40

0 S

FM

D

esi

red

Ch

ip L

oa

d:

0

.00

3”(0

.08

mm

)/re

v.

To

ol D

iam

ete

r:

0

.02

95

”(0

.75

mm

)

12

x [

40

0]

Sp

ind

le S

pe

ed

=

=

5

1,8

00

RP

M

3.1

4

x

[0.0

29

5]

In

fee

d R

ate

=

[5

1,8

00

] x

[0

.00

3]

=

15

5 IP

M

The

in

form

atio

n c

on

tain

ed

in t

his

fa

bric

atio

n g

uid

e is

inte

nd

ed

to

ass

ist

yo

u in

de

sig

nin

g w

ith

Ro

ge

rs’

circ

uit m

ate

ria

ls a

nd

pre

pre

g.

It is

no

t in

ten

de

d t

o a

nd

do

es

no

t c

rea

te a

ny w

arr

an

tie

s, e

xpre

ss o

r im

plie

d,

inc

lud

ing

an

y w

arr

an

ty o

f m

erc

ha

nta

bili

ty o

r Þ tn

ess

fo

r a

pa

rtic

ula

r p

urp

ose

or

tha

t th

e r

esu

lts

sho

wn

on

th

is f

ab

ric

atio

n g

uid

e w

ill b

e a

ch

iev

ed

by a

use

r fo

r a

pa

rtic

ula

r p

urp

ose

. Th

e u

ser

is r

esp

on

sib

le f

or

de

term

inin

g t

he

su

ita

bili

ty o

f R

og

ers

’ c

irc

uit m

ate

ria

ls a

nd

pre

pre

g f

or

ea

ch

ap

plic

atio

n.

Fa

bri

ca

tio

n G

uid

elin

es f

or

RO

40

00

® S

eri

es H

igh

Fre

qu

en

cy

Cir

cu

it M

ate

ria

ls

RO

40

00

® H

igh

Fre

qu

en

cy C

irc

uit M

ate

ria

ls w

ere

de

ve

lop

ed

to

pro

vid

e h

igh

fre

qu

en

cy p

erf

orm

an

ce

co

mp

ara

-

ble

to

wo

ve

n g

lass

PTF

E s

ub

stra

tes

with

th

e e

ase

of

fab

ric

atio

n a

sso

cia

ted

with

ep

oxy

/gla

ss la

min

ate

s. R

O4

00

0

ma

teria

l is

a g

lass

re

info

rce

d h

yd

roc

arb

on

/ce

ram

ic Þ ll

ed

th

erm

ose

t m

ate

ria

l with

a v

ery

hig

h g

lass

tra

nsi

tio

n

tem

pe

ratu

re (

Tg >

28

0°C

). U

nlik

e P

TFE b

ase

d m

icro

wa

ve

ma

teria

ls,

no

sp

ec

ial t

hro

ug

h-h

ole

tre

atm

en

ts o

r h

an

-

dlin

g p

roc

ed

ure

s a

re r

eq

uire

d.

The

refo

re,

RO

40

00

ma

teria

l circ

uit p

roc

ess

ing

an

d a

sse

mb

ly c

ost

s a

re c

om

pa

-

rab

le t

o e

po

xy/g

lass

lam

ina

tes.

So

me

ba

sic

gu

ide

line

s fo

r p

roc

ess

ing

do

ub

le s

ide

d R

O4

00

0 p

an

els

are

pro

vid

ed

be

low

. In

ge

ne

ral,

pro

ce

ss p

a-

ram

ete

rs a

nd

pro

ce

du

res

use

d f

or

ep

oxy

/gla

ss b

oa

rds

ca

n b

e u

sed

to

pro

ce

ss R

O4

00

0 b

oa

rds.

DR

ILLI

NG

:

EN

TR

Y/EX

IT M

ATER

IAL:

En

try a

nd

exi

t m

ate

ria

ls s

ho

uld

be

ß a

t a

nd

rig

id t

o m

inim

ize

co

pp

er

bu

rrs.

Re

co

mm

en

de

d e

ntr

y m

ate

ria

ls in

-

clu

de

alu

min

um

an

d r

igid

co

mp

osi

te b

oa

rd (

0.0

10

” t

o 0

.02

5” (

0.2

54

0.6

35

mm

)).

Mo

st c

on

ve

ntio

na

l exi

t m

ate

ria

ls

with

or

with

ou

t a

lum

inu

m c

lad

din

g a

re s

uita

ble

.

MA

XIM

UM

STA

CK

HEIG

HT:

The

th

ickn

ess

of

ma

teria

l be

ing

drille

d s

ho

uld

no

t b

e g

rea

ter

tha

n 7

0%

of

the

ß u

te le

ng

th.

This

inc

lud

es

the

th

ick-

ne

ss o

f e

ntr

y m

ate

ria

l an

d p

en

etr

atio

n in

to t

he

ba

cke

r m

ate

ria

l.

Fo

r e

xam

ple

:

Flu

te L

en

gth

: 0

.30

0” (

7.6

2m

m)

En

try M

ate

ria

l: 0

.01

5” (

0.3

81

mm

)

Ba

cke

r P

en

etr

atio

n:

0.0

30

” (

0.7

62

mm

)

Ma

teria

l Th

ickn

ess

: 0

.02

0” (

0.5

08

mm

) (0

.02

3”(0

.58

4m

m)

with

1 o

z C

u o

n 2

sid

es)

Ma

xim

um

Sta

ck

=

0

.70

x 0

.30

0”(7

.62

mm

) =

0

.21

0” (

5.3

3m

m)

(av

aila

ble

ß u

te le

ng

th)

He

igh

t

-0.0

15

” (

0.3

81

mm

) (e

ntr

y)

-0.0

30

” (

0.7

62

mm

) (b

ac

ke

r p

en

etr

atio

n)

0.1

65

”(4

.19

mm

) (

av

aila

ble

fo

r P

CB

s)

Ma

xim

um

0

.16

5” (

4.1

9m

m)

(av

aila

ble

fo

r P

CB

s)

Bo

ard

s p

er

=

=

7.2

= 7

b

oa

rds/

sta

ck

Sta

ck

0

.02

3” (

0.5

8m

m)

(th

ickn

ess

pe

r b

oa

rd)

(ro

un

d d

ow

n)

71

The

in

form

atio

n c

on

tain

ed

in t

his

fa

bric

atio

n g

uid

e is

inte

nd

ed

to

ass

ist

yo

u in

de

sig

nin

g w

ith

Ro

ge

rs’

circ

uit m

ate

ria

ls a

nd

pre

pre

g.

It is

no

t

inte

nd

ed

to

an

d d

oe

s n

ot

cre

ate

an

y w

arr

an

tie

s, e

xp

ress

or

imp

lied

, in

clu

din

g a

ny w

arr

an

ty o

f m

erc

ha

nta

bili

ty o

r Þ tn

ess

fo

r a

pa

rtic

ula

r

pu

rpo

se o

r th

at

the

re

sults

sho

wn

on

th

is f

ab

ric

atio

n g

uid

e w

ill b

e a

ch

iev

ed

by a

use

r fo

r a

pa

rtic

ula

r p

urp

ose

. Th

e u

ser

is r

esp

on

sib

le f

or

de

term

inin

g t

he

su

ita

bili

ty o

f R

og

ers

’ c

irc

uit m

ate

ria

ls a

nd

pre

pre

g f

or

ea

ch

ap

plic

atio

n.

HA

SL a

nd

REFLO

W:

RO

40

00

ma

teria

l ba

kin

g r

eq

uire

me

nts

are

co

mp

ara

ble

to

ep

oxy/g

lass

. In

ge

ne

ral,

fac

ilitie

s w

hic

h d

o n

ot

ba

ke

ep

oxy/g

lass

bo

ard

s w

ill n

ot

ne

ed

to

ba

ke

RO

40

00

bo

ard

s. F

or

fac

ilitie

s th

at

do

ba

ke

ep

oxy/g

lass

as

pa

rt o

f th

eir

no

rma

l pro

ce

ss,

we

re

co

mm

en

d a

t 1

-2 h

ou

r b

ake

at

25

0oF-3

00

oF (

12

1oC

-14

9oC

).

Wa

rnin

g: R

O4003 d

oe

s n

ot

co

nta

in Þ re

re

tard

an

t(s)

. W

e u

nd

ers

tan

d b

oa

rds

tra

pp

ed

in a

n in

fra

red

(IR

) u

nit o

r

run

at

ve

ry s

low

co

nv

eyo

r sp

ee

ds

ca

n r

ea

ch

te

mp

era

ture

s w

ell

in e

xc

ess

of

70

0°F

(3

71

°C).

RO

40

03

ma

y b

eg

in

to b

urn

at

the

se h

igh

te

mp

era

ture

s. F

ac

ilitie

s w

hic

h s

till

use

IR

reß o

w u

nits

or

oth

er

eq

uip

me

nt

wh

ich

ca

n r

ea

ch

the

se h

igh

te

mp

era

ture

s sh

ou

ld t

ake

th

e n

ec

ess

ary

pre

ca

utio

ns

to a

ssu

re t

ha

t th

ere

are

no

ha

zard

s.

SH

ELF L

IFE:

Ro

ge

rs' H

igh

Fre

qu

en

cy la

min

ate

s c

an

be

sto

red

ind

eÞ n

ite

ly u

nd

er

am

bie

nt

roo

m t

em

pe

ratu

res

(55

-85

°F,

13

-

30

°C)

an

d h

um

idity le

ve

ls.

At

roo

m t

em

pe

ratu

re,

the

die

lec

tric

ma

teria

ls a

re in

ert

to

hig

h h

um

idity.

Ho

we

ve

r,

me

tal c

lad

din

gs

suc

h a

s c

op

pe

r c

an

be

oxid

ize

d d

urin

g e

xp

osu

re t

o h

igh

hu

mid

ity.

Sta

nd

ard

PW

B p

re-e

xp

o-

sure

cle

an

ing

pro

ce

du

res

ca

n r

ea

dily

re

mo

ve

tra

ce

s o

f c

orr

osi

on

fro

m p

rop

erly s

tore

d m

ate

ria

ls.

RO

UTIN

G:

RO

40

00

ma

teria

l ca

n b

e m

ac

hin

ed

usi

ng

ca

rbid

e t

oo

ls a

nd

co

nd

itio

ns

typ

ica

lly u

sed

fo

r e

po

xy/g

lass

. C

op

pe

r

foil

sho

uld

be

etc

he

d a

wa

y f

rom

th

e r

ou

tin

g c

ha

nn

els

to

pre

ve

nt

bu

rrin

g.

MA

XIM

UM

STA

CK

HEIG

HT:

The

ma

xim

um

sta

ck h

eig

ht

sho

uld

be

ba

sed

on

70

% o

f th

e a

ctu

al ß

ute

len

gth

to

allo

w f

or

de

bris

rem

ov

al.

Exa

mp

le:

Flu

te L

en

gth

:

0

.30

0” x

0.7

0 =

0

.21

0”(5

.33

mm

)

Ba

cke

r P

en

etr

atio

n:

–

0.0

30

”(0

.76

2m

m)

Ma

x.

Sta

ck H

eig

ht:

0

.18

0”(4

.57

2m

m)

TOO

L TY

PE:

Ca

rbid

e m

ultiß

ute

d s

pira

l ch

ip b

rea

ke

rs o

r d

iam

on

d c

ut

rou

ter

bits.

RO

UTI

NG

CO

ND

ITIO

NS:

Su

rfa

ce

sp

ee

ds

be

low

50

0 S

FM

sh

ou

ld b

e u

sed

wh

en

ev

er

po

ssib

le t

o m

axim

ize

to

ol l

ife

. T

oo

l life

is g

en

era

lly

gre

ate

r th

an

50

lin

ea

r fe

et

wh

en

ro

utin

g t

he

ma

xim

um

allo

wa

ble

sta

ck h

eig

ht.

C

hip

Lo

ad

:

0.0

01

0-0

.00

15

”(0

.02

54

-0.0

38

1m

m)/

rev

Su

rfa

ce

Sp

ee

d:

3

00

- S

FM

The

in

form

atio

n c

on

tain

ed

in t

his

fa

bric

atio

n g

uid

e is

inte

nd

ed

to

ass

ist

yo

u in

de

sig

nin

g w

ith

Ro

ge

rs’

circ

uit m

ate

ria

ls a

nd

pre

pre

g.

It is

no

t

inte

nd

ed

to

an

d d

oe

s n

ot

cre

ate

an

y w

arr

an

tie

s, e

xp

ress

or

imp

lied

, in

clu

din

g a

ny w

arr

an

ty o

f m

erc

ha

nta

bili

ty o

r Þ tn

ess

fo

r a

pa

rtic

ula

r

pu

rpo

se o

r th

at

the

re

sults

sho

wn

on

th

is f

ab

ric

atio

n g

uid

e w

ill b

e a

ch

iev

ed

by a

use

r fo

r a

pa

rtic

ula

r p

urp

ose

. Th

e u

ser

is r

esp

on

sib

le f

or

de

term

inin

g t

he

su

ita

bili

ty o

f R

og

ers

’ c

irc

uit m

ate

ria

ls a

nd

pre

pre

g f

or

ea

ch

ap

plic

atio

n.

QU

ICK

REFER

EN

CE T

AB

LE:

Too

l D

iam

ete

r

Sp

ind

le S

pe

ed

(k

RPM

)

Infe

ed

Ra

te (

IPM

)

0.0

10

0” (

0.2

54

mm

)*

9

5.5

1

90

0.0

13

5” (

0.3

43

mm

)*

7

0.7

1

41

0.0

16

0” (

0.4

06

mm

)*

9

5.5

1

90

0.0

19

7” (

0.5

00

mm

)*

7

7.6

1

90

0.0

25

6” (

0.6

50

mm

)

60

.0

18

0

0.0

25

8” (

0.6

55

mm

)

6

0.0

1

80

0.0

29

5” (

0.7

49

mm

)

5

1.8

1

55

0.0

35

4” (

0.8

99

mm

)

4

3.2

1

30

0.0

39

4” (

1.0

01

mm

)

3

8.8

1

16

0.0

45

3” (

1.1

51

mm

)

3

3.7

1

01

0.0

49

2” (

1.2

57

mm

)

31

.1

93

0.0

53

1” (

1.3

49

mm

)

28

.8

8

6

0.0

62

5” (

1.5

88

mm

)

24

.5

74

0.0

92

5” (

2.3

50

mm

)

16

.5

50

0.1

25

0” (

3.1

75

mm

)

15

.0

45

*

Co

nd

itio

ns

sta

ted

are

ta

pe

red

fro

m 2

00

SFM

an

d 0

.00

2 c

hip

lo

ad

up

to

40

0 S

FM

an

d 0

.00

3"

ch

ip.

DEB

UR

RIN

G:

RO

40

00

ma

teria

l ca

n b

e d

eb

urr

ed

usi

ng

co

nv

en

tio

na

l nylo

n b

rush

sc

rub

be

rs.

CO

PPER

PLA

TIN

G:

No

sp

ec

ial t

rea

tme

nts

are

re

qu

ire

d p

rio

r to

ele

ctr

ole

ss c

op

pe

r p

latin

g.

Bo

ard

sh

ou

ld b

e p

roc

ess

ed

usi

ng

co

n-

ve

ntio

na

l ep

oxy/g

lass

pro

ce

du

res.

De

sme

ar

of

drille

d h

ole

s is

no

t ty

pic

ally

re

qu

ire

d,

as

the

hig

h T

g (

28

0°C

+

[53

6°F

]) r

esi

n s

yst

em

is n

ot

pro

ne

to

sm

ea

rin

g d

urin

g d

rill.

Re

sin

ca

n b

e r

em

ov

ed

usi

ng

a s

tan

da

rd C

F4

/O2

pla

sma

cyc

le o

r a

do

ub

le p

ass

th

rou

gh

an

alk

alin

e p

erm

an

ga

na

te p

roc

ess

sh

ou

ld s

me

ar

resu

lt f

rom

ag

gre

ssiv

e

drilli

ng

pra

ctic

es.

IMA

GIN

G/E

TCH

ING

:

Pa

ne

l su

rfa

ce

s m

ay b

e m

ec

ha

nic

ally

an

d/o

r c

he

mic

ally

pre

pa

red

fo

r p

ho

tore

sist

. Sta

nd

ard

aq

ue

ou

s o

r se

mi-

aq

ue

ou

s p

ho

tore

sist

s a

re r

ec

om

me

nd

ed

. A

ny o

f th

e c

om

me

rcia

lly a

va

ilab

le c

op

pe

r e

tch

an

ts c

an

be

use

d.

SO

LDER

MA

SK

:

An

y s

cre

en

ab

le o

r p

ho

toim

ag

ea

ble

so

lde

r m

ask

s ty

pic

ally

use

d o

n e

po

xy/g

lass

lam

ina

tes

bo

nd

ve

ry w

ell

to t

he

surf

ac

e o

f R

O4

00

3.

Me

ch

an

ica

l sc

rub

bin

g o

f th

e e

xp

ose

d d

iele

ctr

ic s

urf

ac

e p

rio

r to

so

lde

r m

ask

ap

plic

atio

n

sho

uld

be

av

oid

ed

as

an

"a

s e

tch

ed

" su

rfa

ce

pro

vid

es

for

op

tim

um

bo

nd

ing

.

72

The

in

form

at io

n in

th

is d

ata

sh

ee

t is

in

ten

de

d t

o a

ssis

t y

ou

in

de

sig

nin

g w

ith

Ro

ge

rs’

cir

cu

it m

ate

ria

l la

min

ate

s.

It is

no

t in

ten

de

d t

o a

nd

do

es

no

t c

rea

te a

ny

wa

rra

ntie

s e

xp

ress

or

imp

lie

d,

inc

lud

ing

an

y w

arr

an

ty o

f m

erc

ha

nta

bility

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ess

fo

r a

pa

rtic

ula

r p

urp

ose

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tha

t th

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lts

sho

wn

on

th

is d

ata

sh

ee

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ill b

e a

ch

iev

ed

by

a u

ser

for

a p

art

icu

lar

pu

rpo

se.

Th

e u

ser

sho

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term

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th

e s

uita

bility

of

Ro

ge

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cir

cu

it

ma

teri

al la

min

ate

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r e

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h a

pp

lic

atio

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lon

ge

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xp

osu

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an

ox

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iro

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en

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ay

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use

ch

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ge

s to

th

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ic p

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ert

ies

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dro

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ase

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ate

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rate

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pe

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rob

lem

s a

re e

xtr

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ely

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re,

Ro

ge

rs r

ec

om

me

nd

s th

at

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cu

sto

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lua

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ate

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nd

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sig

n c

om

bin

atio

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o d

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e Þ t

ne

ss f

or

use

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er

the

en

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life

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en

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t.

The

se c

om

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ec

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m t

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Un

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ac

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xp

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Ad

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D

ive

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on

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o U

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law

pro

hib

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TMM

, R

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f R

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The

wo

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tte

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ith

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ge

rs.

an

d t

he

Ro

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ma

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Ro

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orp

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© 1

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Prin

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CP

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lic

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n #

92

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CO

NTA

CT

INFO

RM

ATI

ON

:

USA

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Ad

va

nc

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Circ

uit M

ate

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ls,

ISO

90

02

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17

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56

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lgiu

m:

Ro

ge

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en

t Te

l: +

32

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35

36

11

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x:

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2-9

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53

65

8

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pa

n:

R

og

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pa

n In

c.

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81

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1

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65

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Wo

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Cla

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ea

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in R

og

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on

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glo

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mm

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ica

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c

om

mu

nic

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infr

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pu

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n t

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as

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glo

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ac

h t

o m

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om

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s.

Ro

ge

rs o

pe

rate

s fa

cili

tie

s in

th

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nite

d S

tate

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uro

pe

an

d A

sia

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e w

orld

ru

ns

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tte

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ith

Ro

ge

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QU

ICK

REFER

EN

CE T

AB

LE:

To

ol D

iam

ete

r

Sp

ind

le S

pe

ed

Late

ral Fe

ed

Ra

te

1

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4

0 k

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0 k

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73