Hope College PHYS/ENGS 495
Lab Manual for Microwave Engineering I
May 2012
1. The Rectangular Waveguide Resonator
You will test a rectangular cavity resonator and compare your results to the
solution to Problem 9.38 in Griffiths. The copper box measures d x a x b = 1.49” x 1.49”
x 4.0” and has two input ports. You will measure the resonant frequencies and identify
the modes.
The modes of a rectangular waveguide cavity are designated by TEℓmn and TMℓmn.
As was shown in problem 9.38, these modes are degenerate. That is, they have the same
resonant frequencies. For example, TE213 and TM213 have the same resonant frequencies.
Because d=a for this particular resonator, it is also true that TEℓmn and TEmℓn are
degenerate. For example, TE123, TE213, TM123, and TM213 all have the same resonant
frequency.
The radio frequency (RF) signal is generated in a swept frequency synthesizer,
conducted to the cavity resonator by coaxial cable, and enters the cavity through one of
the input ports. If the cavity resonates, then the RF will exit at the other port and
continue by coaxial cable to a network analyzer which plots the transmitted power in
frequency domain.
Using the given dimensions of the cavity (converted to meters) calculate all
resonant frequencies for this cavity that occur below 9 GHz. You can conveniently fill in
the table below. Remember, because the cross-section is square, you do not need to
repeat the calculation for degenerate modes. That is, once you have calculated the
resonant frequency for the TE011 mode, you don’t need to calculate it for the TE101 mode.
Before starting, can you predict which mode will have the lowest frequency?
Hint: n corresponds to b, which is the longest dimension of the cavity.
ℓ
0
0
1
m
1
1
1
n
1
2
1
ℓ
f (GHz)
4.226
1
m
n
f (GHz)
Hope College PHYS/ENGS 495
Lab Manual for Microwave Engineering I
May 2012
Now, measure the resonant frequencies using the swept signal synthesizer and the
network analyzer. Identify the mode using the TEℓmn designation. Why don’t all of the
modes appear? Why do some modes appear as doublets?
f (GHz)
Mode
f (GHz)
Mode
2. The Half-Wave Coaxial Resonator
Just like a vibrating string or an organ pipe, a metal rod suspended in air will
resonate when exposed to an electromagnetic wave whose wavelength is commensurate
with the rod length. When the rod sees a wave, currents will be induced in the rod. Of
course, there can be no current at the ends of the rod, since it would have nowhere to go.
So, oscillating current does not easily exist in the rod unless the current has nulls at the
ends of the rod. If the current has nulls at each end, then there is a current maximum in
the center. A graph of current along the length of the rod will resemble half a sine wave,
and the length of the rod is half the wavelength of the exciting electromagnetic wave.
If a metal rod is suspended in thin air and I want to know the resonant frequency,
I would measure the length of the rod, L, and calculate the frequency, fo, that has
wavelength, 2L. The rod will also resonant at 2fo, 3fo and so on.
If the rod were hanging around by itself in free space, a cross section of its E and
B fields, with the rod coming out of the page, is straight forward to sketch:
The problem with attempting to realize this is that the system is
perfectly leaky. That is, fields fill all of space, and I don’t have a
way to get energy into it. Because the electric fields terminate at
infinity, and the magnetic fields decay as 1/r out to infinity, it
would take an infinite amount of input energy to excite this
resonance. (The magnetic field energy of a wire is . You can
try it using Equation 7.34 in Griffiths.) So, a more practical half
wave resonator is realized in the coaxial configuration:
Now, the electric fields terminate on the outer cavity wall, and
the magnetic fields don’t go to infinity. The electric field is maximum at the two ends of
the rod, and the magnetic field is maximum right in the center, where the current density
is also a maximum. A mode that has this field pattern is called transverse
electromagnetic, or TEM.
2

E

B
Hope College PHYS/ENGS 495
Lab Manual for Microwave Engineering I
May 2012
Electromagnetic Theory of the Coaxial Resonator
According to Gauss’s law, the electric field between the conductors of a coaxial
structure depends only on the radial coordinate, r, (see Example 2.3 in Griffiths)

a
E (r )  Ea rˆ
r
where Ea is the electric field at the surface radius=a of the center conductor. The
magnetic flux density between the conductors of a coaxial structure was found from
Ampere’s law to be

a
B(r )  Baˆ ,
r
where Ba is the magnetic flux density at the surface of the center conductor.
The quality factor Q of a resonator is defined as the ratio of stored energy per
cycle to dissipated energy per cycle
Q
oU
Pd
where o =2fo is the resonant angular frequency. The stored electromagnetic energy
found by integrating B2 over the volume of the resonator (Equation 7.34 in Griffiths,
doubled to account for an equal amount of electric energy) is
1  
U
 B  Bd .
o
The dissipated power is found by integrating K2R over the conducting surfaces, where K
is the surface current density (Section 5.1.3 in Griffiths). Using Equation 6.25 in
Griffiths allows the use of magnetic field H instead of K
Pd  Rs
 
 H  Hda
center
conductor
 Rs
 
 H  Hda .
outer
conductor
Rs  o  / 2 is the surface resistance and  is the resistivity of the conducting
surfaces.
Pre-lab Problem: Derive the expression for Q in terms of Rs, , a and the outer
conductor radius b by evaluating the integrals. You will find the answer below.
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Hope College PHYS/ENGS 495
Lab Manual for Microwave Engineering I
May 2012
Here is a lab exercise.
1. Measure the length of the rod and calculate its lowest resonant frequency.
2. Inspect the coupling antennas. Will they more efficiently couple to the electric or to
the magnetic fields? Position the rod inside the cavity to get efficient coupling.
3. Measure the first two resonant frequencies on the network analyzer. Brainstorm the
reasons why there is a discrepancy between calculation and measurement.
4. Are the resonance peak widths infinitesimal? Measure the Q (=f/f) of the first
resonance.
The Q of the half-wave coaxial resonator is related to the surface resistance, Rs, (or rather,
the real part of the surface impedance) of the copper by
1

Q
1 1
  
ba b
2f o  ln  
a
Rs
where a=center conductor radius, b=outer conductor radius and Rs  f o  . Using
the measured Q, calculate the resistivity, , of copper and compare to its book value of
1.68x10-8 m.
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Hope College PHYS/ENGS 495
Lab Manual for Microwave Engineering I
May 2012
3. Chebyshev bandpass filter paper design
A bandpass filter is modeled using LC resonators which are coupled by
impedance inverters. Because the practical method for tuning filters (called the Dishal
method) involves synchronously tuning the resonator, we will design our filter to have
resonators that all have the same resonant frequency.
Now, the design of a Chebyshev bandpass filter results in resonant elements with
different g values, which then means that every tank circuit is unique. In a physically
realized, distributed element filter, there is no way to set the g values. So we will take an
approach that involves absorbing part of the g values into the coupling circuit. In a
physical distributed-element filter, the coupling circuit is realized not with inductors and
capacitors, but with electromagnetic proximity. Two resonators with significant electric
field overlap are said to be negatively coupled. Two resonators with significant magnetic
field overlap are said to be positively coupled. We will control the “sign” and strength of
this coupling by using a capacitive  network between the tank circuits. The  networks
will control the strength of coupling between resonators and will allow all of the
resonators to be identical by absorbing excess g value.
An oddity that you will need to accept in filter design is the “negative capacitor.”
Of course, there is no such thing, but the circuit simulator does not know that. This will
allow the coupling network to absorb g-value from the resonator. Sometimes absorbing
excess g value involves giving back g value to the tank circuit, which then involves a
positive capacitor. To get the right g values, the capacitive  networks will include a
mixture of positive and negative capacitors.
To complete the design process, write a Maple program to compute the g values
using the Chebyshev synthesis equations. Also compute the coupling bandwidths,
Kij=(fu-fL)/fo(gigj)0.5, where fo=(fLfu)0.5. The inputs for synthesis are the start frequency, fL,
the stop frequency, fu, the passband ripple and the number of poles (e.g. number of
resonators.) With these g values you can then lay out a filter circuit in Genesys.
Here are the filter specifications:
N
fL
fu
Lr
3 poles
3.45 GHz
3.60 GHz
0.1 dB
Normally, an engineer is presented with a set of rejection specifications and challenged to
find the filter that meets those specifications. For this first exercise, we are proceeding
with the number of poles as a given.
Simulate this filter in Genesys. Set an optimization criterion on S11 of -16 dB.
Submit the S-parameter graph (S21 and S11) including a close-up of the passband clearly
showing the ripple. Plot the group delay as well. Isolate the input resonator and
determine the external Q. Include finite Q by assigning a Q value of 500 to the tank
capacitors.
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Hope College PHYS/ENGS 495
Lab Manual for Microwave Engineering I
May 2012
4. Three-pole bandpass filter electromagnetic simulation
You will use IE3D to layout the three-pole filter that you designed in the previous
lab. The substrate should be something that is available in the Microwave Lab, so look
and see what there is. You will use one of several varieties of Rogers Corp. RT Duroid
copper clad circuit board. The key characteristics that you will need for the board are the
dielectric constant, the dielectric thickness, and the copper thickness.
Once you have the information about the board, you need to design a resonator.
Let’s not get fancy with this first design. The resonators should be straight lines. Design
a line in IE3D that resonates at 3.524 GHz, the geometric mean of fL and fu. Pick a line
width, w, of 500 m. You can change that if you find a good reason. Vary the length, L,
until the desired resonance is achieved. Determine the unloaded Q of this resonator. Go
back to your Genesys model and put in this Q value for the tank capacitors.
Now you need to determine the resonator separations that yield the desired
coupling. Adjust the resonator separation to achieve the coupling bandwidths calculated
in your Maple program. You can vary the resonator separation, d, and the offset, s.
Increasing d results in weaker coupling. Increasing s is more complicated. When s is
zero you will find there to be very little coupling. As you increase s you will probably
find the coupling (as determined by the separation of the two resonance peaks) to
increase.
This is because the
negative coupling that results from
electric field overlap is being
extinguished, resulting in only
positive coupling. In fact, there
should be some finite value of s
just to ensure that the coupling is
sufficiently positive.
Once you have determined the necessary separations between the three resonators,
you need to design the input coupler. There are several ways to do this. Let’s try the tap
coupler. Determine the necessary width to have a 50  line on your circuit board. Add a
50  line to the IE3d model. One end of the line should come into contact with the
resonator. The other end should be defined as
the input port. Add another line to use as a test
port. This line does not need to be 50 ,
although it certainly can be. The other end of
the test probe should be defined as the output
port. Simulate the resonator and determine the
loaded Q. Vary the length until it is resonating
at 3.524 GHz. Vary x until the loaded Q equals
the external Q that you determined from the
Genesys simulation in the previous lab. As x varies, the resonant frequency will again
vary, forcing minor adjustments to the length. Keep iterating until both the resonant
frequency and the loaded Q are right.
Upon determining the correct value of x, you are ready to put everything together.
Draw the three resonators in IE3D with the separation and offset that you had determined.
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Hope College PHYS/ENGS 495
Lab Manual for Microwave Engineering I
May 2012
Add the 50  lines at the value of x to the input and the output resonator. Run the
simulation in IE3D and plot the S-Parameters, S11 and S21 in decibels.
You will find that the results are not so great. Perhaps S11 is poor, where poor
means that in-band S11 creeps above 15 dB in places. Perhaps there is a large ripple in
the passband. These are due to the fact that when it all goes together the resonators are
no longer tuned. Now begins a time of trial and error. Vary the values of L for the
resonators, beginning with the middle resonator and see what changes improve the
response of the filter. Eventually you will have a good S-parameter result and you will
then be finished with this design.
Before going any further, locate a fixture in the lab that this filter will fit on.
Adjust the layout in IE3D so that the input and output ports meet at the SMA connectors.
Actually, you may wish to do this first.
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Hope College PHYS/ENGS 495
Lab Manual for Microwave Engineering I
May 2012
5. Fabrication and test of the bandpass filter.
The following is a procedure for generating a mask from IE3D, making the mask, and
using photolithography to transfer the mask to the circuit board. This procedure was
compiled by Isaac Angert, with some modifications made by Andrew Bunnell.
Photolithography Procedure
Supplies
PC197-8 positive photoresist from Injecorall
RO3003 (or similar p/n) circuit board from Rogers Corp.
Laser printer transparency
Liqui-Nox detergent
Scotch-Brite pad
Sodium Hydroxide developer
R.O. or D.I. water
Sodium Perchlorate etchant
Equipment
PC with IE3D and DWG TrueView
Laser printer
Erlenmeyer flask
Plastic tray
Glass tray
Air brush
Drying oven
UV lamp
Yellow light
Glass plate
This document can be used as an addendum to the Hope College
document “Making a Circuit Board” by T. Geipel, 2005. This document
is a self-contained procedure, with additional instructions for application
of photoresist, and instructions for preparing your mask using IE3D.
1.
Lay out the design in MGRID. Make sure the line fits on the
available board size, usually 6x9”. By now, the design should have been
simulated.
2.
From MGRID, export the layout to a *.dxf file. Open the *.dxf
file in DWG TrueView 2009, a free program from Autodesk. The
geometry is printed with the following settings:
(See Mask Generation below for more detailed instructions)
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Hope College PHYS/ENGS 495
Lab Manual for Microwave Engineering I
May 2012
View must be set to “conceptual” before setting print options! Failure
to do this will result in a wireframe mesh being printed by default.
Plot Scale:
1:1
Drawing orientation:
Portrait
Plot area/what to plot:
extents
Plot offset:
center plot
Plot style table (pen assignments):
None
Shaded viewport options:
As displayed
Plot options:
Uncheck “plot with plot styles” and “plot object lineweights”
Failure to do this will result in ~0.3mm being added to each dimension
printed!
3.
Print a transparency
The document is printed to a 8.5x11'' transparency (standard office
supplies, available in the physics office on third floor). It is found that the
laser printers do not deposit enough toner onto a sheet to completely block
light from passing through (which is critical for our application). Send
several copies to the printer and print over the same transparency multiple
times with your pattern. Three times is sufficient. This introduces some
error into the designs as the printer does not print to exactly the same
places each time. Still, the printer does a remarkable job lining up the
pages to fairly high precision. Cut the transparency to size.
4.
Clean the board
Using Liqui-Nox detergent and a Scotch-Brite pad, scrub both sides of the
board. You know you are finished when the copper shines and the water
runs off in sheets. Rinse the board in D.I. or R.O. water. Cut the board to
size.
5.
Apply photoresist to the board
Wear a lab coat and gloves! We have used the Rt/Duroid (pt. # RO3003)
from Rogers corp. This material does not come pre-coated with
photoresist. It needs to be coated using the airbrush. The photoresist
currently in stock (Injectorall Positive Photoresist, PC197-8) comes in a
tin bottle and is red in color. Operation of the airbrush is straight forward;
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Hope College PHYS/ENGS 495
Lab Manual for Microwave Engineering I
May 2012
consult the instructions in the box. The airbrush may become clogged and
require disassembly and cleaning. It is recommended to run a small
amount of acetone through the brush to check that it is not clogged before
loading the photoresist (the resist is thick, and sticky and you'll be using it
in the dark—check for problems ahead of this step!). Clean the brush with
acetone and run some acetone through it after using. The brush should be
hooked up to the air in the hood, preferably through the regulator and oil
filter mounted on the right side of the hood. 30psi works well.
Application, drying and exposing of the board must be done under red or
yellow light. Wavelengths that the resist is sensitive to are given on the
bottle. The resist should never see overhead lights. If you do not plan to
etch to both sides and wish to keep copper on one side for a ground plane,
you must coat both sides of the board and only expose one side. It is
suggested to cut the board before you apply the resist. We have been using
12x9'' board, which needs to be cut to 6x9'' to fit into the bubbler. Sizes
much larger than 6x9'' will pose a problem. The resist is applied lightly to
the board in several thin coats. Heavier coats don't present too much
difficulty, but use up the developer faster and take longer to develop. If the
resist begins to form drops that run off the board, it is too thick.
Application should not be nearly this heavy. After application, dry the
resist at ~50C for 15-20min.
6.
Expose the board
Tape the transparency to a clean piece of glass and align this mask over
the board. Weigh down by placing lead weights on the edges of the glass.
The transparency should be touching the board, underneath the glass, not
on top. Expose for 10 min under 275W UV/visible light (a brilliant white
with purple tint). You should ready the developer in a tray while exposing.
(Prepare dilution before starting) After 10min, turn off the exposing lamp.
7.
Develop the board
Keep that lab coat and gloves on! After exposure to UV, soak the board in
a shallow bath of sodium hydroxide (in the plastic tray). The exposed
resist, which has been broken up at the molecular level, will dissolve.
Wash in DI water. The remaining resist polymer hydrolyzes and fixes to
the board. Place the board in the developer. The resist that was exposed
to light will be removed. This takes ~3min, less if the developer is fresh.
Fill the glass tray with tap water and after developing, place the board in
the glass tray to clean off the developer.
8.
Etch the board
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Hope College PHYS/ENGS 495
Lab Manual for Microwave Engineering I
May 2012
You should prepare an etchant solution in an Erlenmeyer flask and heat it
on a hot plate to about 120oF before starting this process. The heater is not
needed in the bubbler, provided the etching is reasonably quick.
Temperatures and times in this whole process have considerable error
tolerances. The etchant should be at ~110oF. After developing, rinse the
board and place in the bubbler with warm etchant. Attach the bubbler to
the air from the hood. The bubbles help to ensure a uniform etch. Again,
it is suggested to use air from the filter/regulator. Etching times vary
depending on temperature and how many times the etchant has been used.
Times have been as little as 7 min at 120F with fresh etchant. Watch the
process closely until you have a sense of how long it will take.
Note: Etchant and developer go bad over time. Mix fresh if unsure how
old these chemicals are. We have used sodium perchlorate as an etchant,
which starts out clear and turns blue over time as copper salts form.
We've found that if the resist is not completely dried it will be removed by
developing regardless of whether it was exposed to light or not. The resist
will take much longer to dry in places where it has accidentally beaded
into drops due to too thick a coat. Bends in the board should be
straightened beforehand. Warped boards can cause trouble during
exposing if the transparency does not lay flat against the board. This is
mostly a concern for very thin lines.
Mask Generation
1.From MGRID, export your geometry to DXF
2.In order to properly print a DXF to scale, use TrueView
a. You should be able to find TrueView on the local drive under
Autodesk
b. Or Download it from Autodesk
c. Open TrueView
3.Set-up within TrueView
a. Click on the red icon to open a file (The Zoom Extents button
frames it well. Change colors to black by clicking the right black.)
b. Find the Layer Properties manager button to change colors. Set the
line color to black. Very black.
c. Check the following plot settings:
View must be set to “conceptual” before setting print options! Failure
to do this will result in a wireframe mesh being printed by default.
(This might change the view a little bit.) There is a pull down View
Manager menu at the top of the screen where you will find this.
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Hope College PHYS/ENGS 495
Lab Manual for Microwave Engineering I
May 2012
Plot Scale:
uncheck “fit to paper”
Set 1:1
Drawing orientation:
Portrait
Uncheck:
“Plot with plot styles”
“Plot object line weights”
Failure to do this will result in ~0.3mm being added to each dimension
printed!
Plot area/what to plot:
extents
Plot offset:
center plot
Plot style table (pen assignments):
None
Shaded viewport options:
As displayed
Quality
Maximum
Save the page set-up since you are printing twice.
After you have fabricated your board you need to fixture it and connectorize it.
Fit the board onto the fixture and solder the SMA connectors.
Perform a full two-port calibration on the vector network analyzer over the range
of 2.7 GHz to 5 GHz and perform an S-parameter (S11 and S21) sweep of the filter. What
is the group delay distortion? What is the in-band VSWR? How successfully do your
skirt rejections meet the design expectation? What is the ultimate rejection? What is the
spurious-free frequency range? Plot your S-parameters and group delay using the HP
plotter.
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Hope College PHYS/ENGS 495
Lab Manual for Microwave Engineering I
May 2012
6. Amplifier Nonlinearity
The objective here is to measure the output third order intermodulation distortion
(IMD) of a low noise amplifier and to determine the amplifier’s output third order
intercept point (IP3o).
1. Choose a low noise amplifier. Bias it to its specified level and perform a sweep over
its specified frequency range using the scalar network analyzer with the signal generator
output set to -30 dBm. To do this, set the swept signal generator to -10 dBm and add a 20
dB attenuator at the swept signal generator output. Plot the S21 and S11 with the HP
plotter. What is the unsaturated gain? Are you working with a single stage LNA or a
two stage LNA?
2. Choose two carrier tones, f1 and f2, separated by 100 MHz, both located somewhere in
the operating range of the LNA. You will perform all measurements at these frequencies.
3. Set up a table with three columns: Input Power (dBm), Output Power (dBm), and 3rd
order IMD (dBm). f1 and f2 will be set to the input power level. You will measure the
output of f2 for the output power column. The power of the upper 3rd order IMD spur at
2f2-f1 will be measured for the IMD column.
4. Set up a circuit using two signal generators, a combiner, the device under test (DUT)
and the spectrum analyzer.
5. Fill in your table for input powers ranging from -30 dBm until the amplifier is
saturated.
6. In Origin, plot Output Power versus Input Power. On the same graph, plot 3rd order
IMD versus Input Power. Identify the 1 dB compression point and the IP3. What is the
slope of IMD (dB) versus Input Power (dB)?
7. Can you find a rule that will allow you to determine the IP3 with a measurement at
one power level only?
8. Using this rule, vary the bias voltage from the turn-on level up to the specification
voltage and measure unsaturated linear gain and the IP3, both versus bias voltage.
13