microwave lab manual

ECE402 – Microwave Engineering Lab

School of Electronics Engineering

Microwave Lab Manual Winter Semester

2012 -13

VIT U N I V E R S I T Y

(Estd. u/s 3 of UGC Act 1956)

List of MW Lab experiments

• Gunn Diode Oscillator

• Directional Coupler & Circulator

• Waveguide Tee Junctions

• Magic Tee

• Measurement of impedance of a device (Antenna)

• Measurement of Antenna Radiation Pattern

• MIC Power Dividers

• Two Port Networks

• Wilkinson Power Divider ( Equal & Unequal )

• Branch Line Coupler

• 180o Hybrid Coupler

• LPF – Richard’s Transformation Method

• LPF – Stepped Impedance Method

Gunn Diode Objectives: To study Gunn diode as a microwave source and hence to study

1. I-V characteristics 2. Power – Bias voltage characteristics 3. Power – Frequency characteristics

Equipment & Components required : Gunn Oscillator Gunn power supply PIN modulator Isolator Variable attenuator Detector mount VSWR meter Cables Theory : The Gunn diode is a very useful microwave source and is widely used. The Gunn oscillator

is based on negative differential conductivity effect in bulk semiconductors such as GaAs. From

the DC V-I characteristics, we will see that the Gunn diode has a negative differential resistance

region. In GaAs, electrons can exist in a high-mass low velocity state as well as their normal low-

mass high-velocity state and they can be forced into the high-mass state by a steady electric field of

sufficient strength. In this state they form domains which cross the field at a constant rate causing

current to flow as a series of pulses. This is the Gunn effect and one form of diode which makes use

of it consists of an epitaxial layer of n-type GaAs grown on a GaAs substrate. A potential of a few

volts applied between ohmic contacts to the n-layer and substrate produces the electric field which

causes clusters. The frequency of the current pulses so generated depends on the transit time

through the n-layer and hence on its thickness. If the diode is mounted in a suitably tuned cavity

resonator, the current pulses cause oscillation by shock excitation and r.f. power up to 1 W at

frequencies between 10 and 30 GHz is obtainable.

Block diagram:

Gunn power supply

Gunn Oscillator

PIN Modulator Isolator Variable

Attenudator Detector Mount

VSWR Meter

Expt. No. : Date :

Figure (1)

Procedure: 1. Set the components as shown in figure 1.

2. Set the micrometer of Gunn Oscillator for required frequency of operation (9 GHz).

3. Change the Gunn bias voltage in steps of 0.5 V and measure the Gunn diode current

through the digital panel meter.

4. Plot the voltage & current readings on a graph.

5. Measure the threshold voltage (Vo) which corresponds to maximum current.

6. Set Gunn biasing just above Vo and note down corresponding power.

7. Change the Gunn bias voltage in steps of 0.5 V and measure the power VSWR meter.

8. Plot power – bias voltage characteristics.

9. Set Gunn biasing for maximum power output and note down this power.

10. Move micrometer screw in steps of 0.5 mm and note down corresponding power till the

screw reaches one extreme.

11. Plot power – frequency characteristics.

Sample Observations:

Bias voltage = 4 V Frequency = 10 GHz

Bias Voltage

(V) Current (mA) Power (dB)

1 0.176 -70

2 0.306 -70

3 0.362 -46

3.28 0.367 -44

4 0.198 -40

5 0.147 -47

6 0.301 -58

7 0.298 -58

8 0.296 -58

9 0.294 -58

10 0.293 -58

Frequency

(GHz) Power (dB)

9 -58

9.2 -62

9.4 -58

9.6 -44

10 -40

10.4 -33

10.6 -38

11 -32

11.4 -36.5

11.75 -39

12.4 -46

Model graph:

0 2 4 6 8 10

0.15

0.20

0.25

0.30

0.35

0.40

Cur

rent

(mA

)

Voltage (V)

I-V characteristics Practical Observations: Bias voltage = Frequency =

Bias Voltage

(V) Current (mA) Power (dB)

Frequency

(GHz) Power (dB)

Conclusions:

Expt. No. : Date :

Directional Coupler Objective: To study the function of a directional coupler by measuring the following parameters.

4. Insertion loss 5. Coupling coefficient 6. Directivity 7. Isolation

Equipment & Components required : Reflex Klystron Reflex Klystron power supply Isolator Directional coupler Detector mount VSWR meter Matched termination Slotted section with detector Cables & stands Theory : A directional coupler is a four port wave guide junction as shown in figure 1. Directional

couplers are used to divide signals from a single channel into multiple channels in both small signal

and large signal applications. Also directional couplers are used to sample propagating microwave

energy for the purpose of monitoring or measuring. It consists of a primary wave guide called main

arm (1 & 2 ports) and a secondary wave guide called auxiliary arm ( 3 & 4 ports).

The operation of a directional coupler can be illustrated with the help of figure 1. If power

fed at port 1 is coupled to port 3 (coupled port) with the coupling factor while the remainder of the

in put power is delivered fed to port 2 (through port). In an ideal directional coupler, no power is

delivered to port 4 (Isolated port). The following quantities are generally used to characterize

directional coupler

Insertion loss = 1

2

10 log PP

dB

Coupling coefficient = 1

3

10 log PP

dB

Directivity = 3

4

10 log PP

dB

Isolation = 1

4

10 log PP

dB

Isolated Coupled

Input Through

34

21

Figure (1) Block diagram:

Klystron power supply

Klysron Oscillator

Isolator Slotted Section

Main arm Matched termination

Detector VSWR Meter

Auxiliary arm

Figure (2)

Procedure:

1. Set the components as shown in figure 2 without directional coupler.

2. Energise the microwave source for particular frequency of operation.

3. Set any reference level of power on VSWR meter with the help of gain control knob of

VSWR meter, and note down the reading (P1 in dB).

4. Insert the directional coupler as shown in figure 2 with detector to the auxiliary port 3

and matched termination to port 2, without changing the position of gain control knob of

VSWR meter.

5. Note down the reading of VSWR meter with the help of range-dB switch if required (P3

in dB).

6. Calculate coupling coefficient C = P1 – P3 (dB).

7. Now carefully disconnect the detector from the auxiliary port 3 and matched termination

from port 2 without disturbing the set-up.

8. Connect the matched termination to the auxiliary port 3 and detector to port 2 and

measure the reading on VSWR meter (P2 in dB).

9. Compute insertion loss I.L. = P1 – P2 (dB).

10. Connect the directional coupler in the reverse direction, i.e. port 2 to slotted section side,

matched termination to port 1 and detector mount to port 3 without disturbing the

position of the gain control knob of VSWR meter.

11. Note down the reading on VSWR meter (P4 in dB ).

12. Compute Isolation = P1 – P4 (dB) and Directivity = P3 – P4 (dB).


I/P port

P1(dB)

O/P port

P2(dB)

Coupled

port P3(dB)

Isolated

port P4(dB) I.L. (dB) C.C. (dB)

Directivity

(dB)

Isolation

(dB)

-20 -21 -30 -60 1 10 30 40

Practical Observations:

I/P port

P1(dB)

O/P port

P2(dB)

Coupled

port P3(dB)

Isolated

port P4(dB) I.L. (dB) C.C. (dB)

Directivity

(dB)

Isolation

(dB)

Conclusions:

Expt. No. : Date :

Circulator Objective: To study the function of a 3-port circulator by measuring the following parameters.

1. Insertion loss 2. Isolation

Equipment & Components required : Reflex Klystron Reflex Klystron power supply Isolator Circulator Detector mount VSWR meter Matched termination Slotted section with detector Cables & stands Theory :

A circulator is a non reciprocal device with ports arranged in such a way that power

entering at a port is coupled to an adjacent port but not coupled to the other ports. Based on the

direction of the energy propagation to the adjacent ports we have clockwise and anti-clockwise

circulators. Circulators can have any number of ports. Wave propagation in a 3-port clockwise

circulator is shown in figure 1. The following quantities are generally used to characterize

circulator

Insertion loss = 1

2

10 log PP

dB

Isolation = 1

3

10 log PP

dB

Port 2

Port 1

Port 3

Figure (1) Block diagram:


Klysron Oscillator


Circulator Matched termination

Detector VSWR Meter

Figure (2)

Procedure:

1. Set the components as shown in figure 2 without circulator.




4. Insert the circulator as shown in figure 2 with detector to adjacent port 2 and matched

termination to port 3, without changing the position of gain control knob of VSWR

meter.


in dB).

6. Calculate insertion loss I.L. = P1 – P2 (dB).

7. Now carefully disconnect the detector from port 2 and matched termination from port 3

without disturbing the set-up.

8. Connect the matched termination to port 2 and detector to port 3 and measure the

reading on VSWR meter (P3 in dB).

9. Compute Isolation. = P1 – P3 (dB).

10. Repeat the experiment for other ports similar way.


I/P port

power(dB)

O/P port

power(dB)

Isolated port

power(dB) I.L. (dB)

Isolation

(dB)

P1= -20 P2=-20.5 P3=-60 0.5 40

P2= -20 P3=-20.8 P1=-62 0.8 42

P3= -20 P1=-20.9 P2=-61 0.9 41


I/P port

power(dB)

O/P port

power(dB)

Isolated port

power(dB) I.L. (dB)

Isolation

(dB)

Conclusions:

Waveguide Tee junctions

Expt. No. : Date :

Objectives: 1. To study the function of a E-plane and H-plane Tee 2. To determine scattering parameters of a E-plane and H-plane Tee

Equipment & Components required : Reflex Klystron Reflex Klystron power supply Isolator E or H-plane Tee Detector mount VSWR meter Matched termination Slotted section with detector Cables & stands Theory : A waveguide T-junction is a simple three port network that can be used for power

division or combining. These junctions are not matched perfectly at all ports. Waveguide tees may

be consists of E-plane tee, H-plane Tee or Magic Tee.

E-plane Tee :

An E-pane tee is a waveguide in which the axis of its side arm is parallel to the E filed of

the main guide as shown in figure 1. If the collinear arms are symmetric about the side arm, there

are two different transmission characteristics. E-plane tee can be perfectly matched with the aid of

screw tuners or capacitive or inductive windows at the junction, the diagonal elements of the S-

matrix S11, S22, S33 are zero because there is no reflection. When the waves are fed into side arm

(port 3), the waves appearing at port 1 and port 2 of the collinear arm will be in opposite phase and

in the same magnitude as shown in figure 2.

Figure 1 Figure 2

H-plane Tee : An H-plane tee is a waveguide tee in which the axis of its side arm(port 3) is

shunting the E-field or parallel to the H filed of the main arm as shown in figure 3. If two input

waves are fed at port 1 and port 2 in same phase, the output wave at port 3 will be additive and in

phase. On the other hand, if the input is fed into port 3, the wave will split equally into port 1 and

port 2 in phase and in the same magnitude.

Figure 3

Block diagram:


Klysron Oscillator


Tee junction Matched termination

Detector VSWR Meter

Figure (4)

Procedure:

1. Set the components as shown in figure 4 without Tee junction.

2. Energize the microwave source for particular frequency of operation.



4. Insert the Tee junction as shown in figure 4 with detector to port 2 and matched

termination to port 1, without changing the position of gain control knob of VSWR

meter.


in dB).





8. Repeat the experiment by keeping port 2 and port 3 as input ports.

9. Scattering parameters of the Tee junction are calculated as follows

Port 1 as input port then, 221

1

PSP

= ; 331

1

PSP

=

Port 2 as input port then 112

2

PSP

= ; 332

2

PSP

=


3

PSP

= ; 223

3

PSP

=


I/P port

power(dB)

O/P port 1

power(dB)

O/P port 2

power(dB)

P3= -20 P1=-25.5 P2=-25.4

P2= -20 P3=-22.6 P1=-29

P1= -20 P2=-22.6 P3=-29

Practical Observations: I/P port

power(dB)

O/P port 1

power(dB)

O/P port 2

power(dB)

Conclusions:

Expt. No. : Date :

Magic Tee Objective: To study the function of a Magic Tee by measuring Isolation. Equipment & Components required : Reflex Klystron Reflex Klystron power supply Isolator Magic Tee Detector mount VSWR meter Matched termination Slotted section with detector Cables & stands Theory : A magic tee is a combination of E-plane and H-plane tee, shown in figure 1. The magic

tee is commonly used for mixing, duplexing and impedance measurements. The magic tee has

several characteristics.

1. If two waves of equal magnitude and the same phase are fed into port 1 and port 2, the

output will be zero at port 3 and additive at port 4.

2. If a wave is fed into port 4 (the H arm) , it will be divided equally between port 1 and port 2

of the collinear arms and will not appear at port 3 (the E arm).

3. If a wave is fed into port 3 (the E arm), it will produce output of equal magnitude and

opposite phase at port 1 and port 2. The output at port 4 is zero. That is S34=S43=0.

4. If a wave is fed into one of the collinear arms at port 1 or port2 , it will not appear in the

other collinear arm at port 2 or port 1 because the E arm causes a phase delay while H arm

causes a phase advance. That is S12=S21=0.

Therefore the S matrix of a magic tee can be expressed as

13 14

23 24

31 32

41 42

0 00 0

0 00 0

S SS S

SS SS S

⎛ ⎞⎜ ⎟⎜ ⎟ =⎜ ⎟⎜ ⎟⎝ ⎠

Figure (1)

Block diagram:

Figure (2)


Klysron Oscillator


Magic Tee Matched termination

VSWR Meter

Detector Mount

Matched termination

Procedure:

1. Set the components as shown in figure 2 without magic tee



VSWR meter, and note down the reading (Pin in dB).

4. Insert the Tee junction as shown in figure 2 with detector to port 3 and matched

termination to port 1 and port 2, without changing the position of gain control knob of

VSWR meter.


in dB).

6. Repeat the experiment by keeping port 1, Port 2 and port 3 as input ports.


I/P port power(dB) O/P port power(dB)

E-arm

P3= -20

P1 = -25.5

P2 = -25.4

P4 = - 65

H-arm

P4= -20

P1 = -26.1

P2 = -25.7

P3 = -68


I/P port power(dB) O/P port power(dB)

E-arm

H-arm

Conclusions:

Expt. No. : Date :

Measurement of Unknown Impedance Objectives: To measure the impedance of an Unknown load. Equipment & Components required : Reflex Klystron Reflex Klystron power supply Isolator Directional coupler Detector mount VSWR meter Matched termination Slotted section with detector Cables & stands Short plate Unknown load Theory :

The impedance at any point on a transmission line can be written in the form (R + jX).

For comparison VSWR can be calculated as

1 | |1 | |

VSWR + Γ =

− Γ

11

ref L oL L

inc L o

V Z Z VSWRV Z Z VSWR

− −Γ = ; Γ = ; Γ =

+ +

Z0 = Characteristics impedance of waveguide at operating frequency.

ZL is the load impedance.

The unknown device is connected to the slotted line and the position of the minima is

determined. The unknown device is replaced by movable short to the slotted line. Two successive

minima positions are noted. The twice the difference between minima position will be guided

wavelength. One of the minima is used as reference for Impedance measurement. Find the

difference of reference minima and minima position obtained from unknown load. Let it be d.

Take a Smith Chart towards load side at a distance equal to d/λg. Join the centre with this point.

Find the point where it cut the drawn circle. The co-ordinates of this point will show the

normalized impedance of load.

Block diagram:


Klysron Oscillator


Main arm Matched termination

Detector VSWR Meter/CRO

Auxiliary arm

Procedure:

1. Set the components as shown in figure with a matched load.


3. Keep the Controls knobs of klystron power supply (SKPS-610) as below:-

i) Beam voltage Switch- ‘OFF’

ii) Beam voltage control knob- Fully anticlockwise

iii) Repeller voltage control knob- Fully clockwise

iv) Mod Switch- AM

v) AM Amplitude- Around fully clockwise

vi) AM Frequency knob- Around mid position.

4. Switch ‘ON’ the klystron power supply, VSWR meter and cooling fan.

5. Switch ‘ON’ the Beam voltage Switch and set and rotated the beam voltage knob

clockwise slowly up to 270 volt meter reading and observe beam current position, “The

beam current should not increase more than 30 mA”.

6. Adjust the repeller voltage knob to get some deflection in VSWR meter.

7. Maximize the deflection with AM amplitude and frequency control knob of power supply.

8. Tune the repeller voltage knob for maximum deflection.

9. Now connect a movable short at the slotted line.

10. Move the probe along the Slotted line. Note the two successive minima positions; let it be

as d1 and d2. Hence λg = 2(d1- d2).

11. One of the minima is used as reference for Impedance measurement. Let it be DR.

12. The unknown device is connected to the slotted line and the position of minima is

determined. Let it be DU. Measure VSWR S0.

13. Find d = (DR - DU). Calculate:- d / λg

Impedance measurement using Smitch Chart:

Take a Smith Chart, taking ‘(1,0)’ as centre, draw a circle of radius equal to VSWR S0.

Fix the voltage minimum point at the extreme left of the horizontal axis of the smith chart. Mark a

point on circumference on VSWR circle towards load side at a distance equal to d / λg. Join the centre

with this point. Find the point where it cut the drawn circle. The co-ordinates of this point will show

the normalized Impedance of load. Multiply with the wave impedance of the waveguide at the

operating frequency.

Impedance measurement using Calculation:

min

min

L

11

2

2where ;

distance between two minima of short circuit & unknown load

The load impedance is then 1Z1

g

i

o

VSWRVSWR

l

l

e

Z

θ

θ π β

πβλ

− | Γ | =

+

= +

=

=

Γ =| Γ |

+ Γ⎛ ⎞= ⎜ ⎟− Γ⎝ ⎠


Unknown Impedance

Ref Min Position

(Cm) (DR)

Guided Wave

length (without Sample)

λg = 2*(d1- d2) Cm

Minima with the sample (Cm) (DU)

VSWR with the

Sample (S0)

d =(DR- DU)

d -- λg

Calculated Impedance

1 2 3

4 Conclusions:

Expt. No. : Date :

Measurement of Radiation Pattern Objective: 1. To measure the E plane and H plane radiation pattern of a pyramidal horn antenna. 2. To compute the 3 dB beam width and directivity of horn antenna. Equipment & Components required : Reflex Klystron Reflex Klystron power supply Isolator Waveguide twist Detector mount VSWR meter Matched termination Pyramidal horn antennas Theory : The radiation pattern of an antenna is a plot of field strength of the power intensity as a

function of the aspect angle at a constant distance from the radiating antenna. It is a 3D plot of the

radiation properties far from the source such as the radiation intensity, power density, directivity

and polarization of an antenna as a function of the spatial coordinates which are described in terms

of spherical coordinates. An antenna pattern consists of several lobes, the main lobe, side lobes,

and the back lobe. The major power is concentrated in the main lobe and it is required to keep the

power in the side lobes and back lobe as low as possible.

Usually the radiation pattern is shown in principal planes of interest. Further, for linearly

polarized antennas, patterns may be plotted in E – plane or H – plane. E- plane is defined as the

plane passing through the antenna in the direction of beam maximum and parallel to the far field E

– vector. One defines the H – plane similarly. It is quire common to plot the pattern by normalizing

the field values with respect to the field strength in the direction of maximum radiation.

The radiation pattern of typical microwave antennas consists of a main lobe and a few

minor or side-lobes. Beam-width of an antenna is defined as the angular separation between 3 dB

points with respect to the maximum field strength. Side lobes represent a loss and leakage of

information in the transmit mode. In the receive mode, sidelobes may cause an uncertainty in

determining the angle of arrival of a signal. However, sidelobes are very sensitive to the

surroundings in which the radiation pattern is measured.

The wavefronts in the vicinity of an antenna have a small radius or curvature but after

traveling some distance the radius of curvature increases to such an extent as to make the wave

front practically a plane wave. A receiving antenna is considered to be in the far-field of the test

antenna if the wavefront across it is practically plane. Most measurements are carried out in the far

field region since; otherwise, when the receiving antenna is kept in the region of curved wavefornt,

there will be a phase difference across the receiving aperture. It can be shown that the phase

variation over the receiving aperture is less than one sixteenth of a wavelength if it is at a distance

R from the transmitting antenna, where

In which D = largest dimension of the larger of the receiver and transmitter antennas.

A horn antenna is a flared out waveguide at the end. If the flaring is done along both the

walls of the rectangular wave guide, then the pyramidal horn is obtained. Horn antennas are

extensively used at microwave frequencies. Theoretically the 3 dB beam width of the pyramidal

horn antenna is

0

0

53 where ' ' is the narrower dimension of the waveguide

80 where ' ' is the broader dimension of the waveguide

E

H

bb

aa

λθ

λθ

=

=

The directivity D can be calculated using the following approximate formula

32400 32400 or ( ) 10log

E H E H

D D dBθ θ θ θ

⎛ ⎞= = ⎜ ⎟

⎝ ⎠

Block diagram:

Procedure:

1. Set up the apparatus as shown in Figure. Again the antenna for maximum meter reading and mark this position of the receiver antenna as 0°. Use square- wave modulation if necessary, and tune the detector. Take care to kept the distance between the antennas sufficiently large so that they are in the far-field zone. 2. Rotate the receiving horn clockwise, in steps of 100, to cover the main lobe and atleast the first

sidelobe( till 900) . At each position, note the reading on the VSWR meter in dB scale. 3. Return to the position 0° and repeat the measurements by rotating the antenna in steps of 100 in the

anticlockwise direction till -900 . At each position, note the reading on the VSWR meter in dB scale.

4. Plot the radiation pattern in the above manner for both E- and H-plane. Determine the beam width and level of the first side lobe with respect to the main lobe.

5. Calculate the directivity and compare the result with the theoretical value. E - plane : H – plane :

Conclusions:

Out put power ( VSWR meter reading ) Angular

Position Clockwise Anti

clockwise

Out put power ( VSWR meter reading ) Angular

Position Clockwise Anti

clockwise

MIC Power Dividers

Objective : To measure the power division, isolation and return loss characteristics of Wilkinson power dividers and branch line coupler . Equipment & Components required :

Signal source Attenuator VSWR meter

Frequency meter Power divider Directional coupler, Detector Matched load Theory: The Wilkinson power divider is generally designed using microstrip lines as shown in

figure 2 and can be made with any number of ports with equal or unequal power divisions.

Wilkinson power divider has many advantages over other power dividers and has the following

properties

Expt. No. : Date :

1. Matched at all ports.

2. Large isolation between output ports

3. Reciprocal

4. Lossless when output ports are matched

The S-matrix of a 3-port Wilkinson power divider is given by

02 2

[ ] 0 02

0 02

j j

jS

j

− −⎛ ⎞⎜ ⎟⎜ ⎟

−⎜ ⎟= ⎜ ⎟⎜ ⎟

−⎜ ⎟⎜ ⎟⎝ ⎠

Theory : Branch line couplers are 3 dB directional couplers with a 900 phase difference in the

outputs of the through and coupled ports. This type of hybrid is often made in microstrip line form

as shown in figure 2. It is also known as Quadrature hybrid or 900 hybrid couplers. With all the

ports matched, power entering port 1 is eventually divided between ports 2 and 3 with a 900 phase

shift between these outputs. No power is coupled to port 4. Branch line coupler has a high degree

of symmetry, as any port can be used as the input port. The output ports will always be on the

opposite of the junction from the input port and the isolated port will be the remaining port on the

same side as the input port. The S-matrix will have the following form

Figure 1

0 1 00 0 11[ ]

1 0 020 1 0

jj

Sj

j

⎛ ⎞⎜ ⎟− ⎜ ⎟=⎜ ⎟⎜ ⎟⎝ ⎠

Attenuator (Optional)

Wilkinson power divider

Matched termination

Detector VSWR Meter

Microwave Source

Procedure: 1. Set the components as shown in figure 4 without Wilkinson power divider.




4. Insert the Wilkinson power divider as shown in figure 4 with detector to port 2 and

matched termination to port 1, without changing the position of gain control knob of

VSWR meter.


in dB).





8. Repeat the experiment by keeping port 2 and port 3 as input ports.

9. Scattering parameters of the Tee junction are calculated as follows

Port 1 as input port then, 221

1

PSP

= ; 331

1

PSP

=


2

PSP

= ; 332

2

PSP

=


3

PSP

= ; 223

3

PSP

=

10. Perform the experiment in a similar way using branch line coupler


I/P port

power(dB)

O/P port 1

power(dB)

O/P port 2

power(dB)

P3= -40 P1=-43 P2=-43

P2= -40 P3=-43 P1=-43

P1= -40 P2=-43 P3=-43

Practical Observations: (Wilkinson power divider) Practical Observations: (Branch Line Coupler)

Conclusions :

I/P port

power(dB)

O/P port 1

power(dB)

O/P port 2

power(dB)

I/P port

power(dB)

O/P port 1

power(dB)

O/P port 2

power(dB)

O/P port 3

power(dB)

Two Port Networks

Objective: To study the performance of different two port networks by determining their scattering parameters. Equipment required : AWR Microwave Office software Specifications : Characteristic impedance Z0 = Operating frequency f = Substrate thickness H = Metal thickness T = Dielectric constant εr = Loss tangent L = Theory : Microstrip lines: The simple microstrip line uses a single strip conductor on the dielectric that

rests on a single ground plane. Generally the ground plane made up of with good conductor like

silver or copper and the material used for the dielectric is Teflon or Aluminum or Silicon, etc.. It is

possible to use several independent strips with the same ground planes and dielectric. Microstrip

lines use quasi TEM mode of propagation. The ground plane of the microstrip line must be wide

compared with the top conductor, so it appears like a nearly infinite wide ground plane with only

very small electric field fringes at its edges. The characteristic impedance of a microstrip line

depends on the strip line width, thickness, the distance between microstrip line and ground plane

and the dielectric constant of the dielectric material.

Figure 1

Expt. No. : Date :

Design Equations: The effective dielectric constant is calculated by:

⎟⎠⎞

⎜⎝⎛+

−+

+=

WH

rre

1212

12

1 εεε

2

0

0

0

82

44 212 0.611 ln(2 1 ln( 1) 0.39

2

1 1 0.110.2360 2 1

3772

2

A

A

rr

r r

r r

r r

r

g

eeW forZ narrowstrip

H B B B

ZA

B forwidestripZ

l l

εε

π ε ε

ε εε ε

πε

φ πβ φ ββ λ

⎧ ⎫⎪ ⎪−⎪ ⎪= >⎨ ⎬⎡ ⎤⎧ ⎫−⎪ ⎪− − − + − + −⎨ ⎬⎢ ⎥⎪ ⎪⎩ ⎭⎣ ⎦⎩ ⎭

⎛ ⎞+ −= + +⎜ ⎟+ ⎝ ⎠

=

= = =

−

2gl

φλπ

=

W= Width of the microstrip line, l = Length of transmission line, H = Thickness of the substrate, A,B constants, Φ = Phase shift, λg=Guide wavelength.

Sample Observations: The behaviour of a two port network when matched with 50 ohm at both

input and output ports for a typical microstrip line with the following specifications is shown

below.

Z0 = 50 Ω, f = 3 GHz , H = 1.6 mm, T = 0.036 mm, εr = 4.4 , L = 0.001

Model graph: Practical Observations:

1 2 3 4 5Frequency (GHz)

Graph 1

-150

-100

-50

0

DB(|S(1,1)|)TWO PORT NETWORKDB(|S(2,1)|)TWO PORT NETWORK

6

Frequency S11 S12 S21 S22

Conclusions:

Wilkinson Power Divider

Objectives:

Expt. No. : Date :

1. To design and simulation of a Wilknson power divider for equal and unequal power divisions.

2. To determine the scattering parameters of Wilkinson power divider. Equipment required : AWR Microwave Office software Specifications : Characteristic impedance Z0 = Operating frequency f = Substrate thickness H = Metal thickness T = Dielectric constant εr = Loss tangent L = Figure (1) Theory: The Wilkinson power divider is generally designed using microstrip lines as shown in

figure 2 and can be made with any number of ports with equal or unequal power divisions.

Wilkinson power divider has many advantages over other power dividers and has the following

properties

5. Matched at all ports.

6. Large isolation between output ports

7. Reciprocal

8. Lossless when output ports are matched

The S-matrix of a 3-port Wilkinson power divider is given by

02 2

[ ] 0 02

0 02

j j

jS

j

− −⎛ ⎞⎜ ⎟⎜ ⎟

−⎜ ⎟= ⎜ ⎟⎜ ⎟

−⎜ ⎟⎜ ⎟⎝ ⎠

Figure (2)

Design Equations:

KZRKZR

KKZR

kKZKZZ

KKZZ

PPKionRatioPowerdivis

/

)1(

)1(

1

03

02

0

20

20302

3

2

003

2

32

==

+=

+==

+=

==

Sample Observations: For equal power division, sample results of a Wilkinson power divider

shown below


Model graph:


1 2 3 4 5 6Frequency (GHz)

S parameters

-80

-60

-40

-20

0

DB(|S(1,1)|)Wilknson dividerDB(|S(2,1)|)Wilknson dividerDB(|S(3,1)|)Wilknson dividerDB(|S(3,2)|)Wilknson divider


Conclusions:

Branch Line Coupler

Objectives:

Expt. No. : Date :

3. To design and simulation of a branch line coupler. 4. To determine the scattering parameters of branch line coupler.

Equipment required : AWR Microwave Office software Specifications : Characteristic impedance Z0 = Operating frequency f = Substrate thickness H = Dielectric constant εr = Loss tangent L = Figure (1)

Theory : Branch line couplers are 3 dB directional couplers with a 900 phase difference in the

outputs of the through and coupled ports. This type of hybrid is often made in microstrip line form

as shown in figure 2. It is also known as Quadrature hybrid or 900 hybrid couplers. With all the

ports matched, power entering port 1 is eventually divided between ports 2 and 3 with a 900 phase

shift between these outputs. No power is coupled to port 4. Branch line coupler has a high degree

of symmetry, as any port can be used as the input port. The output ports will always be on the

opposite of the junction from the input port and the isolated port will be the remaining port on the

same side as the input port. The S-matrix will have the following form

0 1 00 0 11[ ]

1 0 020 1 0

jj

Sj

j

⎛ ⎞⎜ ⎟− ⎜ ⎟=⎜ ⎟⎜ ⎟⎝ ⎠

Figure (2)



Model graph:


S parameters

-60

-50

-40

-30

-20

-10

0

DB(|S(1,1)|)Branch line coupler






Conclusions:

1800 Hybrid Coupler

Objectives:

Expt. No. : Date :

5. To design and simulation of 1800 hybrid coupler. 6. To determine the scattering parameters of 1800 hybrid coupler.

Equipment required : AWR Microwave Office software Specifications : Characteristic impedance Z0 = Operating frequency f = Substrate thickness H = Dielectric constant εr = Loss tangent L = Figure (1) Theory : The 1800 hybrid junction is a four port network with a 1800 phase shift between the two

output ports. It can also be operated so that the outputs are in phase. With reference to the hybrid

coupler shown in figure 2, a signal applied to port 1 will be evenly split into two in-phase

components at ports 2 and 3, and port 4 will be isolated. If the input is applied to port 4, it will be

equallysplit into two compoents with a 1800 phase difference at ports 2 and 3, andport 1 will be

isolated. When operated as a combiner with input signals applied at ports 2 and 3, sum of the

inputs will be formed at port 1, while the difference will be formed at port 4. The 180 hybrid can be

fabricated in several forms. The ring hybrid or rat-race shown in figure 2 can be easily constructed

in microstrip form shown in figure 2. The scattering matrix for the ideal 3 dB 1800 hybrid thus has

the following form

0 1 1 01 0 0 1

[ ]1 0 0 120 1 1 0

jS

⎛ ⎞⎜ ⎟−− ⎜ ⎟=⎜ ⎟⎜ ⎟

−⎝ ⎠

Figure (2)



Model graph:


S parameters

-80

-60

-40

-20

0

DB(|S(1,1)|)180 Hybrid coupler






Conclusions:

LPF – Richard’s Transformation Method Objectives: To design and simulation of low pass filter using Richard’s transformation method with parallel stubs. Equipment required : AWR Microwave Office software Filer specifications :

Filter type - Butterworth (or) Chebyshev Cutoff frequency(fc) - Insertion loss & - Frequency (w) - Ripple factor (δ) - Microstrip specifications :

Characteristic impedance Z0 = Operating frequency f = Substrate thickness H = Dielectric constant εr = Loss tangent L = Figure (1) Theory :

A microwave filter is a two port network used to control the frequency response at a certain

point in a microwave system by providing transmission at frequencies within the passband of the

filter and attenuation in the stopband of the filter. Most microwave filter design is done based on

the insertion loss method. The perfect filter would have zero insertion loss in the passband, infinite

attenuation in the stopband and a linear phase response in the pass band. Filter design at

microwave frequencies using lumped elements arise two problems. First, lumped elements such as

inductors and capacitors are generally available only for a limited range of values and are difficult

to implement at microwave frequencies, but must be approximated with distributed components. In

addition, at microwave frequencies the distance between filter components is not negligible.

Expt. No. : Date :

Richard’s transformation is used to convert lumped elements to transmission line sections,

while Kuroda’s identities can be used to separate filter elements by using transmission line

sections. Because such additional transmission line sections do not affect the filter response, this

type of filter design is called redundant filter synthesis. The Richard’s transformation is given by

Tan lβΩ =

By this equation, the inductors and capacitors of a lumped element filter design can be

replaced with short circuited and open circuited stubs as shown in figure 2, where the length of

each stub is λ/8 at cutoff frequency ωc. Three element filter design using parallel stubs in

microstrip form is shown in figure 3.

Figure 2 Figure 3

Design equations: (a) Maximally flat (or) Butterworth type:

Order of the filter: ( )

⎥⎥⎦

⎤

⎢⎢⎣

⎡+⎟⎟

⎠

⎞⎜⎜⎝

⎛

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛−

=

δ1010

1010

loglog2

110log

c

L

ww

N

L (in dB) is Insertion loss at w. δ is ripple factor.

Table of Element values for maximally flat LPF prototype (g0=1, gN+1=1)Order C1 L2 C3 L4 C5 L6 C7 L8 C9 L10

1 2.000 2 1.41421 1.41421 3 1.00000 2.00000 1.00000 4 0.76357 1.84776 1.84776 0.76537 5 0.61803 1.61803 2.00000 1.61803 0.61803 6 0.51764 1.41421 1.93185 1.93185 1.41421 0.51764 7 0.44504 1.24698 1.80194 2.00000 1.80194 1.24698 0.44504 8 0.39018 1.11114 1.66294 1.96157 1.96157 1.66294 1.11114 0.39018 9 0.34730 1.00000 1.53209 1.87938 2.00000 1.87938 1.53209 1.00000 0.34730 10 0.31287 0.90798 1.41421 1.78201 1.97538 1.97538 1.78201 1.41421 0.90798 0.31287 L1 C2 L3 C4 L5 C6 L7 C8 L9 C10

(b) Equal-ripple type:

Order of the filter

⎟⎟⎠

⎞⎜⎜⎝

⎛

⎥⎥⎦

⎤

⎢⎢⎣

⎡

−

−

=−

×

×−

c

G

L

ww

Mr

1

1.0

1.01

cosh

110110cosh

L (in dB) is the insertion loss at w. Gr is ripple amplitude in dB

Normalized Chebyshev element values, 0.01 dB ripple

Order C1 L2 C3 L4 C5 L6 C7 L8 C9

2 0.4489 0.4078 0.9085 3 0.6292 0.9703 0.6292 4 0.7129 1.2004 1.3213 0.6476 0.9085 5 0.7653 1.3049 1.5773 1.3049 0.7563 6 .07814 1.3600 1.6897 1.5350 1.4970 0.7098 0.9085 7 0.7970 1.3924 1.7481 1.6331 1.7481 1.3924 .07970 8 0.8073 1.4131 1.7824 1.6833 1.8529 1.6193 1.5555 0.7334 0.9085 9 0.8145 1.4271 1.8044 1.7125 1.9058 1.7125 1.8044 1.4271 0.8145

L1 C2 L3 C4 L5 C6 L7 C8 L9



2 0.8431 0.6220 .07378 3 1.0316 1.1474 1.0316 4 1.1088 1.3062 1.7704 0.8181 0.7378 5 1.1468 1.3712 1.9750 1.3712 1.1468 6 1.1681 1.4040 2.0562 1.5171 1.9029 0.8618 .07378 7 1.1812 1.4228 2.0967 1.5374 2.0967 1.4228 1.1812 8 1.1898 1.4346 2.1199 1.6010 2.1700 1.5641 1.9445 0.8778 0.7378 9 1.1957 1.4426 2.1346 1.6167 2.2054 1.6167 2.1346 1.4426 1.1957

L1 C2 L3 C4 L5 C6 L7 C8 L9



2 1.0379 .06746 0.6499 3 1.2276 1.1525 1.2276 4 1.3029 1.2844 1.9762 0.8468 0.6499 5 1.3395 1.3370 2.1661 1.3370 1.3395 6 1.3598 1.3632 2.2395 1.4556 2.0974 0.8838 0.6499 7 1.3723 1.3782 2.2757 1.5002 2.2757 1.3782 1.3723 8 1.3804 1.3876 2.2964 1.5218 2.3414 1.4925 2.1349 0.8972 0.6499 9 1.3861 1.3939 2.3094 1.5340 2.3728 1.5340 2.3094 1.3939 1.3861

L1 C2 L3 C4 L5 C6 L7 C8 L9



2 1.4029 0.7071 0.5040 3 1.5963 1.0967 1.5963 4 1.6704 1.1926 2.3662 0.8419 .05040 5 1.7058 1.2296 2.5409 1.2296 1.7058 6 1.7254 1.2478 2.6064 1.3136 2.4759 0.8696 0.5040 7 1.7373 1.2582 2.6383 1.3443 2.6383 1.2582 1.7373 8 1.7451 1.2647 2.6565 1.3590 2.6965 1.3389 2.5093 0.8795 0.5040 9 1.7505 1.2690 2.6678 1.3673 2.7240 1.3673 2.6678 1.2690 1.7505

L1 C2 L3 C4 L5 C6 L7 C8 L9

Sample Observations: Specifications for a maximally flat low pass filter are

Cut off frequency is 1.5 GHz; insertion loss at 2.5 GHz is 10 dB .

With the given specifications, number of elements required is 3.

Z0 = 50 Ω, f = 1.5 GHz , H = 1.6 mm, T = 0.036 mm, εr = 4.4 , L = 0.001

Model graph:


0 1 2Frequency (GHz)

S parameters

-150

-100

-50

0

DB(|S(1,1)|)LPF RICHARDSDB(|S(2,1)|)LPF RICHARDS

3

Frequency S11 S21

Conclusions:

LPF – Stepped Impedance Method Objectives: To design and simulation of low pass filter using Stepped Impedance method. . Equipment required : AWR Microwave Office software Filer specifications :

Filter type - Butterworth (or) Chebyshev Cutoff frequency(fc) - Insertion loss & - Frequency (w) - Ripple factor (δ) - Microstrip specifications :

Characteristic impedance Z0 = Operating frequency f = Substrate thickness H = Dielectric constant εr = Loss tangent L = Figure (1) Theory :

A microwave filter is a two port network used to control the frequency response at a certain

point in a microwave system by providing transmission at frequencies within the passband of the

filter and attenuation in the stopband of the filter. Most microwave filter design is done based on

the insertion loss method. The perfect filter would have zero insertion loss in the passband, infinite

attenuation in the stopband and a linear phase response in the pass band. Filter design at

microwave frequencies using lumped elements arise two problems. First, lumped elements such as

inductors and capacitors are generally available only for a limited range of values and are difficult

to implement at microwave frequencies, but must be approximated with distributed components. In

addition, at microwave frequencies the distance between filter components is not negligible.

Expt. No. : Date :

One easy way to implement low pass filter in microstrip form is to use alternating sections

of very high and very low characteristic impedance lines. Such filters are usually referred to as

stepped impedance or hi-Z, low-Z filters. These filters are popular because they are easier to design

ad take up less space than a similar low pass filter using stubs. Because of the approximations

involved, however, their electrical performance is not as good, so the use of such filters is usually

limited to applications where a sharp cutoff is not required.

By using this method, the series inductors of a low pass prototype can be replaced with high

impedance line section (Z0=Zh) and the shunt capacitors can be replaced with low impedance line

sections (Z0=Zl). Stepped impedance filter implementation and its microstrip form is shown in

figure 2. With these approximations the electrical lengths of the inductor and capacitor sections are

calculated as follows

Inductor hZ

LRl 0=β and Capacitor

0RCZ

l l=β

R0 is the filter impedance; L, C are element values from the table.

Figure 2

Design equations: (a) Maximally flat (or) Butterworth type:

Order of the filter: ( )

⎥⎥⎦

⎤

⎢⎢⎣

⎡+⎟⎟

⎠

⎞⎜⎜⎝

⎛

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛−

=

δ1010

1010

loglog2

110log

c

L

ww

N

L (in dB) is Insertion loss at w. δ is ripple factor.

Table of Element values for maximally flat LPF prototype (g0=1, gN+1=1)Order C1 L2 C3 L4 C5 L6 C7 L8 C9 L10

1 2.000 2 1.41421 1.41421 3 1.00000 2.00000 1.00000 4 0.76357 1.84776 1.84776 0.76537 5 0.61803 1.61803 2.00000 1.61803 0.61803 6 0.51764 1.41421 1.93185 1.93185 1.41421 0.51764 7 0.44504 1.24698 1.80194 2.00000 1.80194 1.24698 0.44504 8 0.39018 1.11114 1.66294 1.96157 1.96157 1.66294 1.11114 0.39018 9 0.34730 1.00000 1.53209 1.87938 2.00000 1.87938 1.53209 1.00000 0.34730 10 0.31287 0.90798 1.41421 1.78201 1.97538 1.97538 1.78201 1.41421 0.90798 0.31287 L1 C2 L3 C4 L5 C6 L7 C8 L9 C10

(b) Equal-ripple type:

Order of the filter

⎟⎟⎠

⎞⎜⎜⎝

⎛

⎥⎥⎦

⎤

⎢⎢⎣

⎡

−

−

=−

×

×−

c

G

L

ww

Mr

1

1.0

1.01

cosh

110110cosh

L (in dB) is the insertion loss at w. Gr is ripple amplitude in dB



2 0.4489 0.4078 0.9085 3 0.6292 0.9703 0.6292 4 0.7129 1.2004 1.3213 0.6476 0.9085 5 0.7653 1.3049 1.5773 1.3049 0.7563 6 .07814 1.3600 1.6897 1.5350 1.4970 0.7098 0.9085 7 0.7970 1.3924 1.7481 1.6331 1.7481 1.3924 .07970

8 0.8073 1.4131 1.7824 1.6833 1.8529 1.6193 1.5555 0.7334 0.9085 9 0.8145 1.4271 1.8044 1.7125 1.9058 1.7125 1.8044 1.4271 0.8145

L1 C2 L3 C4 L5 C6 L7 C8 L9



2 0.8431 0.6220 .07378 3 1.0316 1.1474 1.0316 4 1.1088 1.3062 1.7704 0.8181 0.7378 5 1.1468 1.3712 1.9750 1.3712 1.1468 6 1.1681 1.4040 2.0562 1.5171 1.9029 0.8618 .07378 7 1.1812 1.4228 2.0967 1.5374 2.0967 1.4228 1.1812 8 1.1898 1.4346 2.1199 1.6010 2.1700 1.5641 1.9445 0.8778 0.7378 9 1.1957 1.4426 2.1346 1.6167 2.2054 1.6167 2.1346 1.4426 1.1957

L1 C2 L3 C4 L5 C6 L7 C8 L9



2 1.0379 .06746 0.6499 3 1.2276 1.1525 1.2276 4 1.3029 1.2844 1.9762 0.8468 0.6499 5 1.3395 1.3370 2.1661 1.3370 1.3395 6 1.3598 1.3632 2.2395 1.4556 2.0974 0.8838 0.6499 7 1.3723 1.3782 2.2757 1.5002 2.2757 1.3782 1.3723 8 1.3804 1.3876 2.2964 1.5218 2.3414 1.4925 2.1349 0.8972 0.6499 9 1.3861 1.3939 2.3094 1.5340 2.3728 1.5340 2.3094 1.3939 1.3861

L1 C2 L3 C4 L5 C6 L7 C8 L9



2 1.4029 0.7071 0.5040 3 1.5963 1.0967 1.5963 4 1.6704 1.1926 2.3662 0.8419 .05040 5 1.7058 1.2296 2.5409 1.2296 1.7058 6 1.7254 1.2478 2.6064 1.3136 2.4759 0.8696 0.5040 7 1.7373 1.2582 2.6383 1.3443 2.6383 1.2582 1.7373 8 1.7451 1.2647 2.6565 1.3590 2.6965 1.3389 2.5093 0.8795 0.5040 9 1.7505 1.2690 2.6678 1.3673 2.7240 1.3673 2.6678 1.2690 1.7505

L1 C2 L3 C4 L5 C6 L7 C8 L9

Sample Observations: Specifications for a maximally flat low pass filter are

Cut off frequency is 2.5 GHz; insertion loss at 4 GHz is 20 dB, highest practical line impedance is

120 Ω and the lowest is 20 Ω .

With the given specifications, number of elements required is 6.


Model graph:


S parameters

-40

-30

-20

-10

0

DB(|S(1,1)|)LPF STEPPED IMPEDANCEDB(|S(2,1)|)LPF STEPPED IMPEDANCE


Frequency S11 S21

Conclusions:

microwave lab manual

Documents

gain control

repeller voltage

branch line

gunn bias

lumped elements

branch line

wilkinson

klystron power