ECE2708 Microwave Engineering Lab Joournal

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MAHARASHTRA (AUM)
AMITY SCHOOL OF
ENGINEERING AND TECHNOLOGY (ASET)
Dept. of Electronics and Communication Engineering (ECE)
Laboratory Journal
COURSE: ECE2708 Microwave Engineering Lab

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CERTIFICATE
AMITY UNIVERSITY MAHARASHTRA
Established vide Maharashtra Act No. 13 of 2014, of Government of Maharashtra, and
recognized under Section 2(f) of UGC Act 1956
This is to certify that Mr. Rishabh Gogna Enrollment No. A70472117001
of Class B.Tech (ECE-3C), Semester VII has satisfactorily completed the
practical course prescribed by Amity University Maharashtra during the
academic year 2020-2021 .
Sign of Faculty I/C
Name:
Sign of Faculty I/C
Name:
Sign of Dept. Coordinator
Name:
Department Seal

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INDEX
Name of Student: Rishabh Gogna
Enrolment No: A70472117001
Course Code and Name: Microwave Engineering Lab/ ECE2708
Name of Course Instructor: Mr. Chaitanya Mahamuni
Sr.
No
TITLE PAGE
NO
DATE OF
EXPERIMENT
DATE OF
CORRECTION
GRADE SIGN
1 To study microwave components. 4 15/01/2021
2 To study the RF behaviour of
Carbon Composition Resistor.
6 29/01/2021
3 To study the behaviour of Metal
Film Resistor.
9 29/01/2021
4 To study the RF behaviour of an
Inductor.
12 05/02/2021
5 To study the RF behaviour of a
Capacitor.
15 05/02/2021
6 To study Smith Chart as a tool for RF
and Microwave Circuit Analysis and
plot it in MATLAB.
18 19/02/2021
7 To design a Rectangular Cavity
Resonator for given resonant
frequency.
21 05/03/2021
8 To plot impedances on a Smith
Chart.
23 12/03/2021
9 To plot E-H field in a Rectangular
Waveguide in dominant mode.
26 16/04/2021
10 To study Microwave Test Bench
and measurement of wavelength,
frequency, power and VSWR
34 24/04/2021
Overall Grade and Remarks:
Name and Sign of Faculty:

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EXPERIMENT 1
Introduction to Microwave components
AIM: To study microwave components.
REQUIREMENTS: Flanges, Twisted wave guide, wave guide tees, Directional Coupler,
Attenuator, Isolators, Circulators, Matched terminator, Slide screw tuner, Slotted Section,
Tunable probe, Horn antennas, Movable Short, Detector mount.
THEORY: A pipe with any sort of cross- section that could be used as a wave guide or
system of conductors for carrying electromagnetic wave is called a wave guide in which the
waves are truly guided.
(1) FLANGES: Flanges are used to couple sections of wave guide components. These flanges
are designed to have not only mechanical strength but also desirable electric characteristics.
(2) TWISTED WAVEGUIDE: If a change in polarization direction is required, twisted
section may be used. It is also called rotator.
(3) WAVE GUIDE TEE: Tees are junctions which are required to combine or split two signals
in a wave guide. Different type of tees are:-
(a) H - PLANE TEE: All the arm of the H- plane Tee lies in the plane of the magnetic field
which divides among the arm. This is thus a current or parallel junction.
(b) E- PLANE TEE: It lies in the plane of electric field. It is voltage or series junction. In this
signal is divided in to two parts having same magnitude but in opposite phase.
(c) MAGIC TEE: If another arm is added to either of the T-junction. Then a hybrid T- junction
or magic tee is obtained. The arm three or four is connected to arm 1&2 but not to each other.
(4) DIRECTION COUPLER: The power delivered to a load or an antenna can be Measured
using sampling technique in which a known fraction of the power is Measured so that the total
may be calculated. A number of coupling units used for such purpose are known as directional
coupler.
(5) ATTENUATORS: It consists of a resistive wane inside the wave guide to absorb
microwave power according to its position with respect to side wall of the wave guide.
Attenuation will be maximum if the wane is placed at center.
a) Fixed Attenuators: In this the position of resistive wane is fixed, it absorbs constant
amount of power.
b) Variable Attenuators: In this the position of resistive wane can be changed with the help
of micrometer.
(6) ISOLATORS: Ferrite is used as the main material in isolator. Isolator is a microwave
device which allows RF energy to pass through in one direction with very little loss, while RF
power in the reverse direction is absorbed.
(7) CIRCULATORS: A microwave circulator is a multi port junction device where the power
may flow in the direction from 1 to 2, 2 to 3, & so on...

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(8) MATCHED TERMINATION: A termination producing no reflected wave at any
transverse section of the wave guide. It absorbs all the incident wave. This is also equivalent
to connecting the line with its characteristic impedance.
(9) SLOTTED SECTION: A length of wave guide in which a non radiating slot is cut on the
broader side. This is used to measure the VSWR.
(10) SLIDE SCREW TUNER: A screw or probe inserted at the top of wave guide (parallel o
E) to develop susceptance the magnitude & sign of which is controlled by depth of penetration
of screw and it can be moved along the length of wave guide.
(11) H – PLANE BEND: An H-plane bend is a piece of wave guide smoothly bends in a plane
parallel to magnetic field for the dominant mode (Hard bend).
(12) E – PLANE BEND: An E-plane bend is a piece of wave guide smoothly bends in a plane
of electric field (Easy bend).
(13) HORN ANTENNAS: The components which radiates & intercept EM energy is of course
the antenna. The open-ended wave guide, in which the open end is flared so that it looks like a
horn, is called horn antenna. There are several types of horns – Sectional E-plane horn,
Sectional H- plane horn and Pyramidal horn.
(14) MOVABLE SHORT: It is adjustable load which moves along the length of wave guide
and adjusted to get SWR.
CONCLUSION: Study of various microwave components has been made.

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EXPERIMENT 2
AIM: To study the RF behaviour of Carbon Composition Resistor.
REQUIREMENTS: MATLAB R2020a
License No:968398
THEORY: Radio frequency (RF) engineering is a subset of electrical engineering that
deals with devices that are designed to operate in the Radio Frequency spectrum. These
devices operate within the range of about 3 KHz up to 300 GHz
An RF module is a small electronic circuit used to transmit and/or receive radio signals on
one of a number of carrier frequencies. RF modules are widely used in electronic design
owing to the difficulty of designing radio circuitry. RF engineering is incorporated into
almost everything that transmits or receives a radio wave, which includes, but is not limited
to, Mobile Phones, Radios, Wi-Fi, and two-way radios.
High Frequency Resistors
Resistance is the property of a material that determines the rate at which electrical energy is
connected into heat energy for a given electric current.
The equivalent circuit of a resistor at radio frequencies is given as
Where :
“R” is the resistor value.
“L” is the lead inductance.
“C” is a combination of parasitic capacitance which varies from resistor to resistor depending
on the resistor’s structure.
Carbon-composition resistors
Carbon-composition resistors are notoriously poor high-frequency performance. A carbon-
composition resistor consists of densely packed dielectric particulates or carbon granules.
Between each pair of carbon granules is a very small parasitic capacitor. These parasites, in
aggregate, are not insignificant, however, and are the major component of the device’s
equivalent circuit.

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MATLAB CODE:
clc;
close all;
c=2e-12;
r=2000;
l=7;
mil=2.54e-3;
d=64*mil;
L=0.002e-6*l*([2.3*log(4*l/d)]-.75);
f=1e6:10e6:500e6;
XL=2*pi*f*L*i
XC=-i./(2*pi*f*c);
Z=(r+2*XL).*(XC)./(r+2*XL+XC);
plot(f,abs(Z));
xlabel('frequency in MHz');
ylabel('Zeq in ohm');
title('RF Behaviour of Carbon Composition Resistor')
OUTPUT:

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OBSERVATION AND RESULT:
It can be observed as per the theory that the impedance/resistance of the Carbon Composition
Resistors decreases as there is an increase in frequency. Compared to Wire Wound or Metal
Film Resistors, Carbon Composition Resistors show signs or poorer performance and higher
frequencies.
CONCLUSION:
Carbon Composition Resistors are simple carbon powder bases resistors that are coated with
ceramic substances and attached to leads that can be seen used in circuits that require
resistors that can withstand high energy pulses. Their resistance is inversely proportional to
the frequency due to the presence of high values of parasitic elements in the equivalent circuit
of the resistors. The RF behaviour of the Carbon Composition Resistor was successfully
studied using MATLAB.

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EXPERIMENT 3
AIM: To study the behaviour of Metal Film Resistor.
License No: 968398
THEORY: A metal-film resistor seems to exhibit the best characteristics over frequency.
Its equivalent circuit is the same as the carbon-composition and wire wound resistor, but the
values of the individual parasitic elements in the equivalent circuit decrease. The impedance
of a metal-film resistor tends to decrease with frequency above about 10 MHz. This is due to
the shunt capacitance in the equivalent circuit.
At very high frequencies, and which low-value resistors (under 50Ω), lead inductance and
skin effect may become noticeable.
The lead inductance produces a resonance peak, as shown for the 5Ω resistance and skin
effect decrease the slop of the curve as if falls off with frequency.

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MATLAB CODE:
clc;
close all;
l=2.5;
d=16*2.4*10^-3;
R=5e2;
C=5e-12;
L=0.002*1*[(2.3*log(4*1/d))-0.75]*10^-6;
f=1e3:1e3:5e9;
jXl=i*2*pi.*f*L;
jXc=[1./(2*pi.*f*C)]*i;
A=[(R.*-jXc)./(R-jXc)];
Zeq=[(A+2*jXl).*(-jXc)]./((2*jXl+A)-jXc);
plot(f,abs(Zeq));
xlabel('frequency');
ylabel('Impedance');
title('Frequency Repsonse of 500 ohm metal film resistor');
OUTPUT:

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The impedance of a Metal Film Resistor decreases as the frequency increases up to a point
(near 0.4 GHz) after which the impedance then increases sharply (till about 0.5GHz) and
continues to decrease as the frequency is increased further.
CONCLUSION:
For a frequency of above 10Mhz, the impedance of the Metal Film Resistor increases
decreases due to the presence of shunt capacitances in the equivalent circuit. At higher
frequencies skin effect becomes more noticeable in these type of resistors due to which the
impedance decreases at very high frequencies. Due to the smaller values of parasitic elements
in the equivalent circuit, the Metal Film Resistors perform better than Carbon Composition
Resistors. The RF behaviour of the Metal Film Resistor was successfully studied using
MATLAB.

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EXPERIMENT 4
AIM: To study the RF behaviour of an Inductor.
License No: 968398
THEORY: Although not employed as often as resistors and capacitors, inductors generally
are used in transistor biasing networks, for instance as RF coils (RFCS) to short circuit the
device to DC voltage conditions. Since a coil is generally formed by winding a straight wire
on a cylindrical former, we know that the windings represent an inductance in addition to the
frequency-dependent wire resistance. Moreover, adjacently positioned wires constitute
separated moving charges, thus giving rise to a parasitic capacitance effect.
The equivalent circuit model of the inductor is as shown below.T he parasitic shunt
capacitance C, and series resistance R, represent composite effects of distributed capacitance
C, and resistance Ra, respectively.
MATLAB CODE:
clear all;
clc;
n=3.5;
mu=4*pi*10^(-7);
sigma=64.5e-6;

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C=0.3e-12;
a=0.0635e-3;
l=0.00254;
r=1.27e-3;
R=(2*pi*r*n)/(sigma*pi*a*a);
L=(10*pi*r*r*mu*n*n)/(9*r+10*1);
N=500;
fmax=10e12
fmin=10e6
f=fmin*((fmax/fmin).^((0:N)/N));
%Z=((j*2*pi.f*L)+R).(j*2*pi.*f*C)./(((j*2*pi.*f*L)+R) +(j*2*pi.*f*C))
Z=1./(j*2*pi*f*C+1./(r+j*2*pi*f*L))
Z_ideal=j*2*pi*f*L;
loglog(f,abs(Z),f, abs(Z_ideal));
title('Impedence of a Inductor as function of frequency') ;
xlabel('Frequency {itf}, Hz');
ylabel('Impedance |Z|, {Omega}');
legend('wire-wound inductor', 'ideal inductor');
OUTPUT:

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The impedance of an ideal inductor increases linearly with respect to the frequency whereas
the impedance of a Wire Wound Inductor increases up to a frequency of 10THz (from graph
obtained) and decreases as the frequency is further increased.
CONCLUSION:
At low frequencies, impedance offered by an inductor is low but increases with an increase in
the frequency. At higher frequencies, the impedance increases, specially in Wire Wound
Inductors due to the “Proximity Effect” which occurs when the wires in the inductor run
close and parallel to each other when eddy currents are induced in the coil due to the
magnetic field created by adjacent coils. This causes the current to be concentrated in a thin
strip in the inductor and thus reduces the cross section just as in the skin effect, thus
increasing its resistance. The RF behaviour of Inductor was successfully studied using
MATLAB.

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EXPERIMENT 5
AIM: To study the RF behaviour of a Capacitor.
License No: 968398
THEORY: In most RF circuits chip capacitors find widespread application for the tuning
of filters and matching networks as well as for biasing active components such as transis-
tors. It is therefore important to understand their high-frequency behavior. Elementary circuit
analysis defines capacitance for a parallel plate capacitor whose plate dimensions are large
compared to its separation as follows:
where A is the plate surface area and d denotes the plate separation. Ideally there is no
current flow between the plates. However, at high frequencies the dielectric materials become
lossy (i.e., there is a conduction current flow). The impedance of a capacitor must thus be
written as a parallel combination of conductance G, and susceptance wC:
In this expression the current flow at DC is due to the conductance G. = (sigma)dielA/d, with
(sigma)diel being the conductivity of the dielectric. It is now customary to introduce the
series loss tangent tanA, = WE/(sigma)diel and insert it into the expression for G, to yield
The corresponding electric equivalent circuit with parasitic lead inductance L, series
resistance R. describing losses in the lead conductors, and dielectric loss resistance R, = 1/G,,
is as shown below:
MATLAB CODE:
l= 1.25e-2;
mu= 4*pi*10^-7;
c= 47*10^-12;

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loss= 10^-4;
sigma= 64.5*10^6;
f=1e6:10e6:1000e9;
mil=2.54e-5;d=16*mil;
a= d./2;Rdc=l./(pi*a*a*sigma);
alpha=sqrt(pi*f*mu*sigma);
delta=1./alpha;Rs=(Rdc*a)./(2*delta);
L=(Rdc*a)./(4*pi*f.*delta);
Re=1./(2*pi*f*c*loss);
Xc=-j./(2*pi*f*c);
A=(Re.*Xc)./(Re+Xc);
Zeq=((2*pi*f.*L*j)+Rs+A);
loglog(f,abs(Zeq),f,abs(Xc));
xlabel('frequency');
ylabel('impedence');
title('RF behaviour of capacitor');
OUTPUT:

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The impedance of an Ideal capacitor decreases linearly as there is an increase in frequency
however for a real capacitor, there is an increase in the impedance value as the value of
frequency is increased.
CONCLUSION:
An ideal capacitor produces a linear decrease in impedance as the frequency increases,
however this is not the case for a real capacitor. This is because at higher frequencies,
dielectric materials become lossy which simply means that there is flow of conduction
current in the component. The impedance, therefore, then becomes the combination of
conductance and susceptance of the capacitor. The RF behaviour of a capacitor was studied
successfully using MATLAB.

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EXPERIMENT 6
AIM: To study Smith Chart as a tool for RF and Microwave Circuit Analysis and plot it in
MATLAB.
License No: 968398
THEORY: The Smith chart provides a graphical representation of Γ that permits the
determination of quantities such as the VSWR or the terminating impedance of a device
under test (DUT). It uses a bilinear Moebius transformation, projecting the complex
impedance plane onto the complex Γ plane:
As can be seen in the figure below, the half plane with positive real part of impedance Z is
mapped onto the interior of the unit circle of the Γ plane.
Properties of the Transformation
In general, this transformation has two main properties:
1) Generalized circles are transformed into generalized circles (note that a straight line is
nothing else than a circle with infinite radius and is therefore mapped as a circle in the
Smith chart)
2) Angles are preserved locally

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Normalization
The Smith chart is usually normalized to a terminating impedance Z0 (= real):
This leads to a simplification of the transform:
Although Z = 50 Ω is the most common reference impedance (characteristic impedance of
coaxial cables) and many applications use this normalization, there is any other real and
positive value possible.
Therefore it is crucial to check the normalization before using any chart. Commonly used
charts that map the impedance plane onto the Γ plane always look confusing at first, as many
circles are depicted.
MATLAB CODE:
% Draw outer circle
t = linspace(0, 2*pi, 100); x = cos(t);
y = sin(t);
plot(x, y, 'linewidth', 3); axis equal;
% Place title and remove ticks from axes
title('Smith Chart')
set(gca,'xticklabel',{[ ]});
set(gca,'yticklabels',{[ ]});
hold on
% Draw circles along horizontal axis
k = [.25 .5 .75];
for i = 1 : length(k)
x(i,:) = k(i) + (1-k(i))*cos(t);
y(i,:)=(1 - k(i))*sin(t); plot(x(i,:), y(i,:), 'k')
end
% Draw partial circles along vertical axis
kt = [2.5 pi 3.79 4.22];
k=[.5 1 2 4];
for i = 1 : length(kt)
t = linspace(kt(i), 1.5*pi, 50);
a(i,:) = 1 + k(i) * cos(t); b(i,:) = k(i) + k(i) * sin(t); plot(a(i,:), b(i,:),'k:', a(i,:), -b(i,:),'k:' )
end

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OUTPUT:
OBERSVATION AND RESULT: The above Smith Chart contains the possible
impedances on the domain of existence of the reflection coefficient.
CONCLUSION: The Smith Chart was successfully plotted and studied using the given
points for RF analysis on MATLAB.

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EXPERIMENT 7
AIM: To design a Rectangular Cavity Resonator for given resonant frequency.
License No:968398
THEORY:
Rectangular cavity resonators are hollow rectangular conducting boxes of width a, height b,
and length d, where d ≥ a ≥ b by convention. Since they are simply rectangular waveguides
terminated at both ends by conducting walls, and the electric fields must still obey the wave
equation, (∇2+ω2με)E=0(∇2+ω2με)E=0, therefore E for TE modes must have the form of the
TE waveguide fields (9.3.27), but with a sinusoidal z dependence that matches the boundary
conditions at z = 0 and z = d; for example, equal forward- and backward-propagating waves
would form the standing wave:
where B = 0 ensures E=0at z = 0, and kz = pπ/d ensures it for z = d, where p = 1, 2, ...
Unlike rectangular waveguides that propagate any frequency above cut-off for the spatial field
distribution (mode) of interest, cavity resonators operate only at specific resonant
frequencies or combinations of them in order to match all boundary conditions. The resonant
frequencies ωmnp for a rectangular cavity resonator follow from the dispersion relation:
The fundamental mode for a cavity resonator is the lowest frequency mode. Since boundary
conditions can not be met unless at least two of the quantum numbers m, n, and p are non-zero,

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the lowest resonant frequency is associated with the two longest dimensions, d and a. Therefore
the lowest resonant frequency is:
Modes: Like waveguides, cavities are also analyzed by solving Maxwell's equations, or their
reduced form, the electromagnetic wave equation, with boundary conditions determined by the
properties of the materials and their interfaces. These equations have multiple solutions, or
modes, which are eigen-functions of the equation system. Each mode is therefore characterized
by an eigen-value, which corresponds to a cut-off frequency below which the mode cannot
exist in the guide. These resonant modes depend on the operating wavelength and the shape
and size of the cavity. The modes of the cavity are typically classified into following types:
1) TE modes (Transverse Electric) have no electric field component in the direction of
propagation.
2) TM modes (Transverse Magnetic) have no magnetic field component in the direction
of propagation.
MATLAB CODE:
clc;
clear all;
f=input('Enter Resonant Frequency');
a=(1/f*sqrt(2*4*pi*10^-7*8.85*10^-12));
disp(a);
l=a;
disp(l);
b=a/2;
disp(b);
disp('The rectangular cavity resonator dimensions are a and b');
OUTPUT:
OBSERVATION AND RESULT: It was observed that for a resonant frequency of
9.8Ghz, the dimensions of the rectangular cavity resonator came out to be: a=4.8124X10-19
and
b=2.4062X10-19
CONCLUSION: A general Rectangular Cavity Resonator was designed and studied
successfully using MATLAB for a given value of resonant frequency. The dimensions of the
rectangular cavity resonator were therefore produced on the basis of the resonant frequency
without taking into consideration the mode of operation for the cavity resonator.

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EXPERIMENT 8
AIM: To plot impedances on a Smith Chart.
License No:968398
THEORY: The Smith Chart, named after its Inventor Phillip Smith, developed in the 1940s,
is essentially a polar plot of the complex reflection coefficient for arbitrary impedance. It was
originally developed to be used for solving complex maths problem around transmission lines
and matching circuits which has now been replaced by computer software.
However, the Smith charts method of displaying data have managed to retain its preference
over the years and it remains the method of choice for displaying how RF parameters behave
at one or more frequencies with the alternative being tabulating the information. Smith chart
can be used to display several parameters including; impedances, admittances, reflection
coefficients, scattering parameters, noise figure circles, constant gain contours and regions for
unconditional stability, and mechanical vibrations analysis, all at the same time.
Types of Smith Charts:
Smith chart is plotted on the complex reflection coefficient plane in two dimensions and is
scaled in normalised impedance (the most common), normalised admittance or both, using
different colours to distinguish between them and serving as a means to categorize them into
different types. Based on this scaling, smith charts can be categorized into three different types;
1) The Impedance Smith Chart (Z Charts)
2) The Admittance Smith Chart (YCharts)
3) The Immittance Smith Chart. (YZ Charts)

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Impedance Smith Chart
The Impedance smith charts are usually referred to as
the normal smith charts since they relate with
impedance and works really well with loads made up
of series components, which are usually the main
elements in impedance matching and other related RF
engineering tasks. They are the most popular, with all
references to smith charts usually pointing to them and
others being regarded as derivatives. The image below
shows an impedance smith chart.
MATLAB CODE:
clc;
clear all;
z1 = 0.1*50 + 1j*(0:2:50);
z2 = (0:2:50) - 0.6*50j;
z0 = 50;
gamma1 = z2gamma(z1,z0);
gamma2 = z2gamma(z2,z0);
s = smithplot(gamma1,'Color',[0.2 0 1],'GridType',"Z");
hold on;
s = smithplot(gamma2,'Color','g','LineStyle','-.','LineWidth',1);
s.Marker = {'+','s'}

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OUTPUT:
OBSERVATION AND RESULT: Based on the impedance and characteristic
impedance data provided in the above-mentioned code, the same was converted to reflection
coefficient using the pre-defined function available in MATLAB. This impedance data was
then plotted on the Smith Plot. We observe a series of plots on the chart as the impedance data
so defined, contained a range of the impedances. (e.g. for z1, the imaginary value of the
impedance ranged from 0 to 50 with increments of 2 after every step.)
CONCLUSION: The Smith Plot was utilized for impedance plots for the given experiment.
The impedance data was provided as input in the code as an array of impedance values and the
same were plotted and studied successfully on the Smith Chart using MATLAB.

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EXPERIMENT 9
AIM: To plot E-H field in a Rectangular Waveguide in dominant mode.
License No:968398
THEORY: A rectangular waveguide is a conducting cylinder of rectangular cross section
used to guide the propagation of waves. Rectangular waveguide is commonly used for the
transport of radio frequency signals at frequencies in the SHF band (3–30 GHz) and higher.
The fields in a rectangular waveguide
consist of a number of propagating modes
which depends on the electrical dimensions
of the waveguide. These modes are broadly
classified as either transverse magnetic
(TM) or transverse electric (TE). In this
section, we consider the TE modes.
The figure below shows the geometry of
interest. Here the walls are located at x=0 ,
x=a , y=0 , and y=b ; thus, the cross-
sectional dimensions of the waveguide are a and b . The interior of the waveguide is presumed
to consist of a lossless material exhibiting real-valued permeability μ and real-valued
permittivity ϵ , and the walls are assumed to be perfectly-conducting.
Let us limit our attention to a region within the waveguide which is free of sources. Expressed
in phasor form, the magnetic field intensity within the waveguide is governed by the wave
equation:
This equation, combined with boundary conditions imposed by the perfectly-conducting plates,
is sufficient to determine a unique solution. This solution is most easily determined in Cartesian
coordinates, as we shall now demonstrate. First we express H in Cartesian coordinates:
Next we observe that the operator ∇2 may be expressed in Cartesian coordinates as follows:

27
In general, we expect the total field in the waveguide to consist of unidirectional waves
propagating in the +z^ and −z^ directions. We may analyze either of these waves; then the
other wave is easily derived via symmetry, and the total field is simply a linear combination
(superposition) of these waves. With this in mind, we limit our focus to the wave propagating
in the +z^ direction.
It can be seen that all components of the electric and magnetic fields can be easily calculated
once E(z) and H(z) are known. The problem is further simplified by decomposing the
unidirectional wave into TM and TE components. In this decomposition, the TE component is
defined by the property that E(z)=0 ; i.e., is transverse (perpendicular) to the direction of
propagation. Thus, the TE component is completely determined by H(z):
and kz is the phase propagation constant; i.e., the wave is assumed to propagate according to
e-jkz
.
MATLAB CODE:
clc;
close all;
% Waveguide dimensions
a = 2.286; % Length in cm in x-direction
b = a/2; % Length in cm in y-direction
f = 45*10.^9; % Frequency of operation 45GHz
c = 3*10.^8; % Velocity of light
% m = 1; % Mode number in X-Direction
% n = 0; % Mode number in Y-Direction
choice = input('Enter choice: 1 for TE and 2 for TM: ');
if choice == 1
m = input('Enter mode value m:');
n = input('Enter mode value n:');
elseif choice == 2
m = input('Enter mode value m:');

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n = input('Enter mode value n:');
else
sprintf('Alert!!! Wrong choice!!!')
end
Amn = 1; % Particular mode Constant
% A10 = 1; % for example
% Wave propagation in Z-Direction
%********************************%
fc = c*100/2*sqrt((m/a).^2+(n/b).^2); % Cutoff frequency calculation in GHz
% lambda = 2*a; %for TE10 mode
lambda = c*100/fc; % Wavelength in cm
epsilon = 8.8540e-12; % Permittivity constant
epsilon_r = 1; % Relative Permittivity constant
mu1 = 4*pi*10e-7; % Permeability constant
mu1_r = 1; % Relative Permeability constant
omega = 2*pi*f; % Frequency of operation in rad/s
M = 40; % Number of points to be poltted
beta = omega*(sqrt(mu1*epsilon)); %Propagation constant
Bx = m*pi/a; %Beta(x)
By = n*pi/b; %Beta(y)
Bc = sqrt(Bx.^2+By.^2); %Beta(c), cutoff wavenumber
Bz = sqrt(beta.^2-Bc.^2);
if choice ==1
if m == 0 && n == 0
fprintf(['TE_',num2str(m),num2str(n), ' mode doesnot exist']);
elseif fc>f
fprintf(['TE_',num2str(m),num2str(n), ' mode cutoff frequency exceeds frequency of
operation; hence mode does not porpagaten']);
sprintf('The frequency of operation is up to: %0.5g',f)
sprintf('The cutoff frequency is: %0.5g',fc)
else
sprintf('The frequency of operation is up to: %0.5g',f)
sprintf('The cutoff frequency is: %0.5g',fc)
% Front View
z = 0;
x = linspace(0,a,M);
y = linspace(0,b,M);
[x,y] = meshgrid(x,y);
% z = linspace(0,2*lambda,M);
%Field Expression for TEmn
% Ex = Amn*(By/epsilon)*cos(m*pi.*x./a).*sin(n*pi.*y./b).*exp(-j*Bz*z);
% Ex = Amn*(By/epsilon)*cos(Bx.*x).*sin(By.*y).*exp(-1i*Bz*z);
Ex = cos(Bx.*x).*sin(By.*y).*exp(-1i*Bz*z);
% Ey = -Amn*(Bx/epsilon)*sin(Bx.*x).*cos(By.*y).*exp(-1i*Bz*z);
Ey = -sin(Bx.*x).*cos(By.*y).*exp(-1i*Bz*z);
Ez = 0;
% Hx = Amn*(Bx*Bz/(omega*mu1*epsilon))*sin(m*pi.*x./a).*cos(n*pi.*y./b).*exp(-
j*Bz*z);

29
Hx = sin(m*pi.*x./a).*cos(n*pi.*y./b).*exp(-j*Bz*z);
% Hy = Amn*(Bx*Bz/(omega*mu1*epsilon))*cos(m*pi.*x./a).*sin(n*pi.*y./b).*exp(-
j*Bz*z);
Hy = cos(m*pi.*x./a).*sin(n*pi.*y./b).*exp(-j*Bz*z);
% Hz = -1i*Amn*(Bc.^2/(omega*mu1*epsilon))*cos(m*pi.*x./a).*cos(n*pi.*y./b).*exp(-
j*Bz*z);
Hz = -cos(m*pi.*x./a).*cos(n*pi.*y./b).*exp(-j*Bz*z);
figure();
quiver(x,y,real(Ex),real(Ey));
title(['Plot of front view for TE_',num2str(m),'_',num2str(n),' E-Field']);
legend('E-Field');
xlabel('x-dimension 0 to a');
ylabel('y-dimension 0 to b=a/2');
figure();
quiver(x,y,real(Hx),real(Hy));
title(['Plot of front view for TE_',num2str(m),'_',num2str(n),' H-Field']);
legend('H-Field');
figure();
quiver(x,y,real(Ex),real(Ey));
hold on
quiver(x,y,real(Hx),real(Hy));
grid on
title(['Plot of front view for TE_',num2str(m),'_',num2str(n)]);
legend('E-Field','H-Field');
% Top View for TEmn
y = b; % Position of x-z plane
x = linspace(0,a,M);
% y = linspace(0,b,M);
z = linspace(0,lambda,M);
[x,z] = meshgrid(x,z); % Create Mesh grid in x-z
% Field Expression for TEmn
% Ex = Amn*(By/epsilon)*cos(m*pi.*x./a).*sin(n*pi.*y./b).*exp(-j*Bz*z);
% Ez = 0;
Ez = zeros(size(real(Ey)));
Hx = sin(m*pi.*x./a).*cos(n*pi.*y./b).*exp(-1j*Bz*z);
% Hx = A10*(Bz/(omega*mu1*epsilon))*pi/a.*sin(pi.*x./a).*exp(-j*Bz*z);
Hy = cos(m*pi.*x./a).*sin(n*pi.*y./b).*exp(-1j*Bz*z);
Hz = -cos(m*pi.*x./a).*cos(n*pi.*y./b).*exp(-1j*Bz*z);
figure();
quiver(z,x,real(Ez),real(Ex));
title(['Plot of Top view for TE_',num2str(m),'_',num2str(n),' E-Field']);
legend('E-Field');
ylabel('x-dimension 0 to a');
xlabel('z-direction');

30
figure();
quiver(z,x,real(Hz),real(Hx));
title(['Plot of Top view for TE_',num2str(m),'_',num2str(n),' H-Field']);
legend('H-Field');
figure();
quiver(z,x,real(Ez),real(Ex));
hold on
quiver(z,x,real(Hz),real(Hx));
grid on
title(['Plot of TOP view of E-H for TE_',num2str(m),'_',num2str(n)]);
% Side View for TEmn
x = a/2;
% x = linspace(0,a,M);
y = linspace(0,b,M);
z = linspace(0,2*lambda,M);
[y,z] = meshgrid(y,z);
% Field Expressions for TEmn
Ez = 0;
Ez = zeros(size(real(Ey)));
Hx = sin(m*pi.*x./a).*cos(n*pi.*y./b).*exp(-j*Bz*z);
Hy = cos(m*pi.*x./a).*sin(n*pi.*y./b).*exp(-j*Bz*z);
Hz = -cos(m*pi.*x./a).*cos(n*pi.*y./b).*exp(-j*Bz*z);
figure();
quiver(z,y,real(Ez),real(Ey));
title(['Plot of Side view for TE_',num2str(m),'_',num2str(n),' E-Field']);
legend('E-Field');
ylabel('y-dimension 0 to b');
figure();
quiver(z,y,real(Hz),real(Hy));
title(['Plot of Side view for TE_',num2str(m),'_',num2str(n),' H-Field']);
legend('E-Field');
figure();
quiver(z,y,real(Ez),real(Ey));
hold on
quiver(z,y,real(Hz),real(Hy));
grid on
title(['Plot of Side view of E-H for TE_',num2str(m),'_',num2str(n)]);

33
OBERSVATION AND RESULT: It was observed that TE is a dominant mode for the
Rectangular Waveguide. In the TE mode the TE10 mode is found to be most dominant and the
same has been used to the plot the E-H field and its various views for the given Rectangular
Waveguide.
CONCLUSION: The various E-H field plots were successfully plotted and studied for the
TE10 mode for a Rectangular Waveguide using MATLAB.

34
EXPERIMENT 10
AIM: To study Microwave Test Bench and measurement of wavelength, frequency, power
and VSWR.
REQUIREMENTS: A PC with Internet Connection
STUDY REPORT:
Introduction: Electrical measurements encountered in the microwave region of the
electromagnetic spectrum are discussed through microwave measurement techniques. This
measurement technique is vastly different from that of the more conventional techniques. The
methods are based on the wave character of high frequency currents rather than on the low
frequency technique of direct determination of current or voltage. For example, the
measurement of power flow in a system specifies the product of the electric and magnetic fields
.Where as the measurement of impedance determines their ratio .Thus these two measurements
indirectly describe the distribution of the electric field and magnetic fields in thesystem and
provides its complete description .This is ,in fact ,the approach to most of the measurements
carried out in the micro wave region of the spectrum. Microwave Bench: The micro wave test
bench incorporates a range of instruments capable of allowing all types of measurements that
are usually required for a microwave engineer .The bench is capable of being assembled or
disassembled in a number of ways to suit individual experiments .A general block diagram of
the test bench comprising its different units and ancillaries are shown below.
1) Klystron Power Supply: Klystron Power Supply generates voltages required for driving
the reflex Klystron tube like 2k25 .It is stable, regulated and short circuit protected power
supply. It has built on facility of square wave and saw tooth generators for amplitude and
frequency modulation. The beam voltage ranges from 200V to 450V with maximum beam
current.50mA. The provision is given to vary repeller voltage continuously from-270V DC to
-10V. Gunn Power Supply:
2) Gunn Power Supply comprises of an electronically regulated power supply and a square
wave generator designed to operate the Gunn oscillator and PIN Modulator. The Supply
Voltage ranges from 0 to 12V with a maximum current, 1A.
3) Gunn oscillator: Gunn oscillator uti1izes Gunn diode which works on the principle that
when a DC voltage is applied across a sample of n-type Gallium Arsenide; the current oscillates
at .microwave frequencies. This does not need high voltage as it is necessary for Klystrons and
therefore solid state oscillators are now finding wide applications. Normally, they are capable
of delivering 0.5 watt at 10GHz, but as the frequency of operation is increased the microwave
output power gets considerably reduced.
4) Isolator: This unattenuated device permits un attenuated transmission in one direction
(forward direction) but provides very high attenuation in the reverse direction {backward
direction). This is generally used between the source and rest of the set up to avoid overloading
of the source due to reflected power.
5) Variable Attenuator: The device that attenuates the signal is termed as attenuator.
Attenuators are categorized into two categories namely, the fixed attenuators and variable
attenuators. The attenuator used in the microwave set is of variable type. The variable

35
attenuator consists of a strip of absorbing material which is arranged in such a way that its
profusion into the guide is adjustable. Hence, the signal power to be fed to the microwave set
up can be set at the desired level.
6)Frequency Meter: It is basically a cavity resonator. The method of measuring frequency is
to use a cavity where the size can be varied and it will resonate at a particular frequency for
given size. Cavity is attached to a guide having been excited by a certain microwave source
and is tuned to its resonant frequency. It sucks up some signal from the guide to maintain its
stored energy. Thus if a power meter had been monitoring the signal power at the resonating
condition of the cavity it will indicate a sharp dip. The tuning of the cavity is achieved by a
micrometer screw and a curve of frequency versus screw setting is provided. The screw setting
at which the power indication dip is noted and the frequency is read from the curve.
7) Slotted Section: To sample the field with in a wave guide, a narrow longitudinal slot with
ends taperedto provide smoother impedance transformation and thereby providing minimum
mismatch, is milled on the top of broader dimension of wave guide. Such section is known as
slotted wave guide section. The slot is generally so many wave lengths long to allow many
minima of standing wave pattern to be covered. The slot location is such that its presence does
not influence the field configurations to any great degree. On this Section a probe inserted with
in a holder, is mounted on a movable carriage. The output is connected to detector and
indicating meter. For detector tuning a tuning plunger is provided instead of a stub.
8) Matched Load: The microwave components which absorb all power falling on them are
matched loads. These consist of wave guide sections of definite length having tapered resistive
power absorbing materials. The matched loads are essentially used to test components and
circuits for maximum power transfer.
9)Short Circuit Termination: Wave guide short circuit terminations provide standard
reflection at any desired, precisely measurable positions. The basic idea behind it is to provide
short circuit by changing reactance of the terminations.
10)VSWR meter: Direct-reading VSWR meter is a low-noise tuned amplifier voltmeter
calibrated in db and VSWR for use with square law detectors. A typical SWR meter has a
standard tuned frequency of 100-Hz, which is of course adjustable over a range of about 5 to
10 per cent, for exact matching in the source modulation frequency. Clearly the source of power
to be used while using SWR meter must be giving us a 1000-Hz square wave modulated output.
The band width facilitates single frequency measurements by reducing noise while the widest
setting accommodates a sweep rate fast enough for oscilloscope presentation.
11) Crystal Detector: The simplest and the most sensitive detecting element is a microwave
crystal. It is a nonlinear, non reciprocal device which rectifies the received signal and produces
a current proportional to the power input. Since the current flowing through the crystal is
proportional to the square of voltage, the crystal is rejoined to as a square law detector. The
square law detection property of a crystal is valid at a low power levels (<10 mw). However,
at high and medium power level (>10 mw), the crystal gradually becomes a linear detector.
FREQUENCY MEASUREMENT
Counters and pre-scalers for direct frequency measurement in terms of a quartz crystal
reference oscillator are often used at lower frequencies, but they give up currently at
frequencies above about 10GHz. An alternative is to measure the wavelength of microwaves
and calculate the frequency from the relationship (frequency) times (wavelength) = wave

36
velocity. Of course, the direct frequency counter will give a far more accurate indication of
frequency. For many purposes the 1% accuracy of a wavelength measurement suffices. A
resonant cavity made from waveguide with a sliding short can be used to measure frequency
to a precision and potential accuracy of 1/Q of the cavity, where Q is the quality factor often in
the range 1000-10,000 for practical cavities. "Precision" and "accuracy".
Precision is governed by the fineness of graduations on a scale, or the "tolerance" with which
a reading can be made. For example, on an ordinary plastic ruler the graduations may be 1/2mm
at their finest, and this represents the limiting precision. Accuracy is governed by whether the
graduations on the scale have been correctly drawn with respect to the original standard. For
example, our plastic ruler may have been put into boiling water and stretched by 1 part in 20.
The measurements on this ruler may be precise to 1/2mm, but in a 10 cm measurement they
will be inaccurate by 10/20 cm or 5mm, ten times as much. In a cavity wavemeter, the precision
is set by the cavity Q factor which sets the width of the resonance. The accuracy depends on
the calibration, or even how the scale has been forced by previous users winding down the
micrometer against the end stop.
WAVELENGTH MEASUREMENT
Wavelength is measured by means of signal strength sampling probes which are moved in the
direction of wave propagation by means of a sliding carriage and vernier distance scale. The
signal strength varies because of interference between forward and backward propagating
waves; this gives rise to a standing wave pattern with minima spaced 1/2 wavelength. At a
frequency of 10 GHz the wavelength in free space is 3 cm. Half a wavelength is 15mm and a
vernier scale may measure this to a precision of 1/20mm.
The expected precision of measurement is therefore 1 part in 300 or about 0.33% The location
of a maximum is less precise than the location of a minimum; the indicating signal strength
meter can be set to have a gain such that the null is very sharply determined. In practice one
would average the position of two points of equal signal strength either side of the null; and
one would also average the readings taken with the carriage moving in positive and negative
directions to eliminate backlash errors. Multiple readings with error averaging can reduce the
random errors by a further factor of 3 for a run of 10 measurements. Measurements of
impedance and reflection coefficient. A visit to your favourite microwave book shows that a
measurement of the standing wave ratio alone is sufficient to determine the magnitude, or
modulus, of the complex reflection coefficient. In turn this gives the return loss from a load
directly. The standing wave ratio may be measured directly using a travelling signal strength
probe in a slotted line. The slot in waveguide is cut so that it does not cut any of the current
flow in the inside surface of the guide wall.
It therefore does not disturb the field pattern and does not radiate and contribute to the loss. In
the X band waveguide slotted lines in our lab, there is a ferrite fringing collar which
additionally confines the energy to the guide. To determine the phase of the reflection
coefficient we need to find out the position of a standing wave minimum with respect to a
"reference plane". The procedure is as follows: First, measure the guide wavelength, and record
it with its associated accuracy estimate. Second, find the position of a standing wave minimum
for the load being measured, in terms of the arbitrary scale graduations of the vernier scale.
Third, replace the load with a short to establish a reference plane at the load position, and
measure the closest minimum (which will be a deep null) in terms of the arbitrary scale
graduations of the vernier scale. Express the distance between the measurement for the load
and the short as a fraction of a guide wavelength, and note if the short measurement has moved

37
"towards the generator" or "towards the load". The distance will always be less than 1/4 guide
wavelength towards the nearest minimum. Fourth, locate the r > 1 line on the SMITH chart and
set your dividers so that they are on the centre of the chart at one end, and on the measured
VSWR at the other along the r > 1 line. (That is, if VSWR = 1.7, find the value r = 1.7). Fifth,
locate the short circuit point on the SMITH chart at which r = 0, and x = 0, and count round
towards the generator or load the fraction of a guide wavelength determined by the position of
the minimum. Well done.
If you plot the point out from the centre of the SMITH chart a distance "VSWR" and round as
indicated you will be able to read off the normalised load impedance in terms of the line or
guide characteristic impedance. The fraction of distance out from centre to rim of the SMITH
chart represents the modulus of the reflection coefficient [mod(gamma)] and the angle round
from the r>1 line in degrees represents the phase angle of the reflection coefficient
[arg(gamma)].
IMPEDANCE MEASUREMENT:
The impedance at any point on a transmission line can be written in the form R+jx. For
comparison SWR can be calculated as
where reflection coefficient ‘R given as
Zo = characteristics impedance of wave guide at operating frequency.
Z is the load impedance
The measurement is performed in the following way: The unknown device is connected to the
slotted line and the position of one minima is determined. The unknown device is replaced by
movable short to the slotted line. Two successive minima portions are noted. The twice of the

38
difference between minima position will be guide wave length. 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, taking ‘1’ as centre,
draw a circle of radius equal to S. Mark a point on circumference of smith chart towards load
side at a distance equal to d/λg. Join the center 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.
Steps:
1. Calculate a set of Vmin values for short or movable short as load.
2. Calculate a set of Vmin values for S-S Tuner + Matched termination as a load.
Note: Move more steps on S-S Tuner
3. From the above 2 steps calculate d = d1~d2
4. With the same setup as in step 2 but with few numbers of turns (2 or 3). Calculate low
VSWR.
Note: High VSWR can also be calculated but it results in a complex procedure.
6. Draw a line from center of circle to impedance value (d/λg) from which calculate admittance
and Reactance (Z = R+jx)nce.
MEASUREMENT OF POWER:
To measure power at high frequencies from 500 MHz to 40 GHz two special type of absorption
meters are popularly used. These meters are,
1. Calorimeter power meter
2. Bolometer power meter
Both these meters use the sensing of heating effects caused by the power signal to be measured.
Introduction to Bolometer power meter:

39
The Bolometer power meter basically consists of a bridge called Bolometer Bridge. One of the
arms of this bridge consists of a temperature sensitive resistor. The basic bridge used in
Bolometer power meter is shown in the Fig 8.14. The high frequency power input is applied to
the temperature sensitive resistor RT. The power is absorbed by the resistor and gets heated
due to the high frequency power input signal. This heat generated causes change in the
resistance RT. This change in resistance is measured with the help of bridge circuit which is
proportional to the power to be measured. The most common type of temperature sensitive
resistors are the thermistor and barretter. The thermistor is a resistor that has large but negative
temperature coefficient.
It is made up of a semiconductor material. Thus its resistance decreases as the temperature
increases. The barretter consists of short length of fine wire or thin film having positive
temperature coefficient. Thus its resistance increases as the temperature increases. The
barretters are very delicate while thermistors are rugged. The bolometer power meters are llsed
to measure radio frequency power in the range 0.1 to 10 mW. In modern bolometer power
meter set up uses the differential amplifier und bridge [orl11 an oscillator which oscillates at a
particular amplitude when bridge is unbalanced. Initially when temperature sensitive resistor
is cold, bridge is almost balance. With d.c. bias, exact balance is achieved. When power input
at high frequency is applied to RT, it absorbs power and gets heated.
Due to this its resistance changes causing bridge unbalance. This unbalance is in the direction
opposite to that of initial cold resistance. Due to this, output from the oscillator decreases to
achieve bridge balance.
MEASUREMENT OF VSWR
High VSWR by Double Minimum Method:
The voltage standing wave ratio of
where Vmax and Vmin are the voltage at the maxima and minima of voltage standing wave
distribution. When the VSWR is high ( , the standing wave pattern will have a high maxima
and low minima. Since the square law characteristic of a crystal detector is limited to low
power, an error is introduced if ≥ 5)Vmax is measured directly. This difficulty can be avoided
by using the ‘double minimum method’ in which measurements are take on the standing wave
pattern near the voltage minimum. The procedure consists of first finding the value of voltage
minima. Next two positions about the position of Vmax are found at which the output voltage
is twice the minimum value.
If the detector response is square

40
where λ g is the guide wavelength and d is the distance between the two points where the
voltage is 2 Vmin.
Measurement of high VSWR:
Select “Unmatched Load” to terminate the slotted line by pressing the button.
1. Use slider to fix the value of “Resistance” and “Reactance” of the load.
2. Locate the position of Vmin and take it as a reference.(If VSWR meter is used in actual
experiment, set the output so that meter reads 3dB).
3. Move the slider (probe of slotted line) along the slotted line on either side of Vmin so that
the reading is 3 db below the reference i.e. 0 db. Record the probe positions and obtain the
distance between the two. Determine the VSWR using equation (2).
4. The simulated value for VSWR can be seen by clicking the buttons “Technique used to
calculate VSWR 1 & 2”.
5. Then match the calculated value with the value displayed in the simulated VSWR
CONCLUSION: The Microwave Testbench was successfully studied. Each block of the
testbench was briefly studied and measurements techniques were realized. For Frequency
measurements, the use of the counters and pre-scalers was observed whereas the measurements
for wavelength were studied by the means of vernier scales attached with a sliding carriage.
The Bolometer power meter and its procedural utilization was realized for the measurements
of power. Impedance and VSWR measurements were observed and the Double Minimum
Method was considered for the latter.

ECE2708 Microwave Engineering Lab Joournal

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