Description
I’ve attached the hand calculation we did to find our Zo that we will input in the code via matlab preferably and Er was provided ..For the report you don’t need to write all of it just the abstract , intro and background.. with some references
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EGRE 310 Lab 3: T-Line Impedance Matching and Tuning
Check Canvas for due dates
Transmission Line Impedance Matching and Tuning
Goals:
Enhance knowledge of transmission lines by exploring the impact of transmission line parameters, load
matching conditions, and frequency on wave propagation and reflection on the line.
Develop a program to compute solutions for different impedance matching networks for a given load and
transmission line parameters and simulate the frequency response of these solutions, and experimentally
verify the effectiveness of these solutions.
Assignment:
Part 1: Simulation Code
Your team is working on designing the necessary hardware to implement a radar system for the coast guard
to help with search and rescue operations. Part of this radar are the microstrip lines that connect to the
antennas used to transmit and receive radar signals. To ensure the most efficient transfer of energy and
minimize the reflections back up the line, the impedance of the transmission line needs to match the
impedance of the antenna.
You will develop a program (use a programming language of your choice) that will provide solutions and
characteristics for two of the major narrow-band impedance matching methods: (1) quarter-wavelength
transformer and (2) single-stub tuning.
The inputs to the program will be
–
Z0 :
r :
ZL :
f0 :
the characteristic impedance of the transmission line (consider only lossless T-lines)
the relative dielectric constant of the transmission line
the complex load impedance for the antenna
the frequency of operation
S-Band radars operate in the range 1 – 6 GHz. Utilize this band for your frequency analysis.
Your program should compute at once the parameters for the two matching techniques (i.e. the output of
one method cannot be used as the input to the other). The output of the software should include all the
following (note that for each method there are two solutions within the /2 electrical length):
1. Quarter-Wavelength Transformer: The distance of the quarter wave transformer from the load (d) (in real
length units) and the characteristic impedance of the quarter-wave transformer (Z/4) for two solutions.
2. Single-stub tuning: (shunt) Stub position, d, and stub length, l, (in real length units) for two solutions both
in the case of short-circuited and open-circuited stubs.
3. Plots of reflection coefficient magnitude, || (reflection from the load+matching network combination back
to the transmission line), as a function of frequency, f, in the vicinity of the operating frequency for the
two methods described above. Plot all solutions for each type of network on a single graph. For each
solution, your program should also provide the bandwidth (f) for || = 0.2 tolerance. Solutions for
different cases should be easily identifiable on your plot.
Part 2: Experimental – single stub tuning
You will implement a single stub (shunt, open) tuner to match a quarter-wave monopole antenna load to a
microstrip line circuit board feed. You will design your matching circuit using the code from Part 1 and
measure the performance of your design using a portable vector network analyzer (NanoVNA). NanoVNA
measures the Reflection coefficient (S11) and the input impedance (Zin) values at different frequencies.
Quarter-wave monopole antenna: Estimate the resonance frequency using the antenna length and
confirm with the reflection measurements using the NanoVNA. Determine the antenna impedance (ZL)
using the NanoVNA.
1
EGRE 310 Lab 3: T-Line Impedance Matching and Tuning
Check Canvas for due dates
The microstrip transmission line: (1.3 mm thick dielectric layer with r = 2.45) Compute eff and Z0 for
the microstrip lines. Use the short-circuit (sc)/open-circuit (oc) method to measure Z0 with the NanoVNA.
Z 0 Z insc Z inoc
(Note that the microstrip line may not have Z0 = 50 .)
Matching circuit: Compute the parameters (d and l) for two single-stub tuning solutions. Create
stubs/strips by cutting the provided 1/4″ wide copper tape to the right length and placing it on the
microstrip transmission line.
The length from the load is the length
measured from the end of the SMA connector
soldered to the board, as this is the point that
the system was calibrated to. Place your stub
such that the distance from the load is
measured from the central line of the stub, and
the stub starts at the central line of the
premade transmission microstrip line.
If your stub is physically too close to the load,
too far from the load, too long or too short, how
can you change the position of the stub to achieve the same input impedance?
Exercise caution when handling the strip. The tape can be torn relatively easily, especially when trying
to remove and replace a strip. You should also press firmly to remove ripples/bubbles in the tape
which cause surface irregularities)
Testing: Measure S11 and Zin of the matched system using the NanoVNA to verify load matching.
If needed, for fine tuning try shortening the length of your stub in 1-2mm increments. Record the final
length of the stub that provided the best characteristics. Take a picture of the board setup for each
solution as well as the plots of S11 and Zin (on the Smith chart) at the resonant frequency. You can
adjust the display range by adjusting START/STOP frequencies.
Compare your final frequency responses (S11 vs freq.) against the data from your simulations.
Your report should address the following questions and have the following deliverables:
A brief discussion of the lumped element model, reflection coefficient, line impedance, and how
transmission line characteristics and circuits impact signal propagation.
Discussion of the ¼-wave transformer and the single-stub tuning methods, and how they achieve
impedance matching with the diagrams/schematics illustrating your solution method, relevant distances,
and other parameters.
– For example, for single-stub tuning, once you have calculated the stub position away from the load,
how would you calculate Zin at that position and use that value to calculate the required length of the
stub? Assume stub and line have real (and equal) Z0 and equal widths.
A brief description of the computer coding method and algorithms used.
Simulation Results and Discussion. Provide at least two representative examples including the outputs
(parameters and plots) of your program developed in Part 1. Comment on the performance of your
matching networks, advantages and disadvantages of various configurations. Which method provides
the better matching characteristics – ¼ wavelength or single stub tuning? Why? (Be specific and
quantitative) You may also discuss any special cases you have encountered.
Experimental designs and results from their performance evaluation. Compare the resonance frequency,
the reflection coefficient, and the -3dB bandwidth before and after impedance matching.
Comparison of experimental results with simulations. Discussion of reasons for any discrepancies.
Copy of code used to perform calculations. (Of course, your code should be your own. You are not
allowed to use code or tools found on the internet)
2
EGRE 310 Lab 3: T-Line Impedance Matching and Tuning
Check Canvas for due dates
Deliverables:
A comprehensive report that has a continuous flow without any breaks or abrupt transitions. Everything
in the report should serve a purpose and the report should reflect what you learned in this lab project. Focus
on critical analysis, justifying your answers/conclusions with data from simulation/calculation/experiment as
well as references (where appropriate). Be sure to provide enough practical information to ensure the reader
can understand what you did and how to interpret the results.
A single Lab Report must be submitted for the team. Each team member is required to submit separately a
one-page Individual Executive Summary. Your Lab Report should contain:
1. An Abstract summarizing the lab and your results/conclusions.
2. An Introduction section that “sets the stage” for your report. You may think of a structure like a funnel,
starting with knowledge understood by a sophomore EE student and gradually becoming more focused until
you get to your specified task.
a. A short discussion/introduction to the problem and the discussion of transmission line properties and the
need for impedance matching
3. A section (can be called Background, theory, or the like, but choose what fits best for you) detailing the
necessary background information to perform the task at hand. Introduce the concepts that you need and
derive the formulas that you will require.
a. E.g. discussion of the specifics of ¼-wave transformer and the single-stub tuning methods, how they
achieve impedance matching, design rules, and relevant formulas for the frequency dependent reflection
coefficient and line/input impedance.
4. A section detailing the Methods and Results produced in the lab as described in the Assignment section.
Explain the experiment that you have designed to test or solve the problem at hand and the logic behind your
approach. Present your results and your analysis/discussion. If there are multiple outcomes, you may elect
to create separate “methods/results” sections for each outcome. Think logically about the order to improve
the flow.
a. Discuss and compare the results of your simulations with two representative examples for the two
matching methods. Discuss and justify the experimental tuning circuit design choices and
characterization results. Compare experimental results with simulations for the antenna matching circuitry
you built. Discuss any discrepancies and potential reasons based on the constraints/approximations you
had. Discuss the frequency response and the bandwidth of operation.
b. In this section you should include sufficient graphs, plots, data to argue your points (see assignment).
Think critically about your results and process when discussing. What worked and did not work? Why?
c. Figures (schematics, simulation screenshots, plots, etc.), tables, and equations must be clearly legible,
neat, and appropriately numbered in the order they appear (e.g. Fig. 1, Fig. 2; Table 1, Table 2; Eq. 1,
Eq. 2, etc.) and must be properly cited in the text of the report (e.g. as shown in Fig. 2 …, Table 1 tabulates
…, According to Eqn. 3 …). All figures and tables should contain sufficiently detailed captions.
5. A Conclusion section which provides a “so what” of the report. Why should someone care about this result?
You may briefly summarize your process and results, but do not just summarize. Aim to add new thoughts
in this section. Did you meet the specifications or constraints? If not, what can you do better?
6. References must be provided at the end of the document. A minimum of 10 references is required for every
report. Your references should consist of published journal papers, textbooks, databases, etc. Items like
Wikipedia, online lecture notes, news articles, etc. will not count towards your 10 references. If you find
something useful in these items, cite the original source, e.g. references at the bottom of a Wikipedia page.
7. A list of your team members, their individual contributions. Provide detailed contributions. If a specific
member is significantly less involved than others are, they will receive reduced credit. Be sure to involve
other members and work together on the project/report.
8. A signature from each member attesting that all members contributed equally to the project.
Page Limit: 8 pages not including references, contribution, and signature pages.
Failure to satisfy these requirements will result in a reduced grade.
3
EGRE 310 Lab 3: T-Line Impedance Matching and Tuning
Check Canvas for due dates
NanoVNA V2 Instructions – Vector Network Analyzer (VNA)
Included in the Kit:
NanoVNA V2
Touch stylus pen
USB 2.0 to Micro USB power cable
Three Calibration Loads: short, 50Ω load, and open (shown on the
right, from top to bottom, respectively).
2 ct. 50Ω coaxial cables, and a 50Ω SMA adapter/female sockets
Confirm all components are included before continuing!
After use, place all components back into the box!
Powering the Device:
The NanoVNA is powered on via the switch located next to the USB port on the front of the device. It is a
rechargeable device and should be plugged in via the USB cable when used for an extended time to ensure it
does not power down mid-session.
Do not disconnect the NanoVNA from its USB port while in use! This will result in a power cycle and erase all
calibration settings.
NanoVNA Display/GUI:
To access the menus of the NanoVNA, either tap the screen with your finger or the stylus, or press the “square”
central button on the top right of the VNA. Menus can be navigated with the stylus or the left/right/square buttons.
Press on “ DISPLAY -> TRACE):
Reflection coefficient – S11 in dB vs. freq. (yellow – TRACE 0)
Transmission coefficient – S21 in dB vs. freq. (blue – TRACE 1),
Input-Impedance displayed on a Smith Chart (green – TRACE 2)
Reflection coefficient phase in degrees vs. freq. (purple – TRACE 3)
The values of each measurement are given on the top ribbon of the
display for the selected marker frequency. By default, there is one
marker (more can be added in the menus) which can be shifted along
the frequency domain using the left and right buttons on the top right of
the VNA or by dragging on the touch screen. As you shift the marker,
you’ll notice the measurement values change. (note that for input
impedance, the real part and a capacitance/inductance value are
displayed on top; you need to compute the complex impedance.)
On the bottom ribbon of the display are the START and STOP frequencies for the range over which you take
measurements. The default range is (100MHz – 900MHz); the maximum range is (50kHz – 4.4GHz). For your
specific application, a frequency range can be selected via MENUS -> STIMULUS -> START/STOP.
Calibration:
To calibrate, access MENUS -> CAL -> CALIBRATE. Note that the CH0 port can be used to measure S11, while
the CH2 port is used to measure S21. For S11, connect the external circuit up till the component whose reflection
you want to measure to CH0. Terminate the external circuit with each calibration load, one at a time, and select
the corresponding OPEN/SHORT/LOAD options (THRU is reserved for S21 measurements). While calibrating,
the on-screen text will turn green, and then the selected load type will be highlighted in black when complete.
Calibration is complete when each of the desired load types is highlighted in black. The measurement plots will
update upon exiting the menus. Do not save calibration, you will need to calibrate every time you change your
measurement circuitry. Why need calibration at all? See for example this link.
4
EGRE 310 Lab 3: T-Line Impedance Matching and Tuning
Check Canvas for due dates
Transmission Line Impedance Matching and Tuning
Goals:
Enhance knowledge of transmission lines by exploring the impact of transmission line parameters, load
matching conditions, and frequency on wave propagation and reflection on the line.
Develop a program to compute solutions for different impedance matching networks for a given load and
transmission line parameters and simulate the frequency response of these solutions, and experimentally
verify the effectiveness of these solutions.
Assignment:
Part 1: Simulation Code
Your team is working on designing the necessary hardware to implement a radar system for the coast guard
to help with search and rescue operations. Part of this radar are the microstrip lines that connect to the
antennas used to transmit and receive radar signals. To ensure the most efficient transfer of energy and
minimize the reflections back up the line, the impedance of the transmission line needs to match the
impedance of the antenna.
You will develop a program (use a programming language of your choice) that will provide solutions and
characteristics for two of the major narrow-band impedance matching methods: (1) quarter-wavelength
transformer and (2) single-stub tuning.
The inputs to the program will be
–
Z0 :
r :
ZL :
f0 :
the characteristic impedance of the transmission line (consider only lossless T-lines)
the relative dielectric constant of the transmission line
the complex load impedance for the antenna
the frequency of operation
S-Band radars operate in the range 1 – 6 GHz. Utilize this band for your frequency analysis.
Your program should compute at once the parameters for the two matching techniques (i.e. the output of
one method cannot be used as the input to the other). The output of the software should include all the
following (note that for each method there are two solutions within the /2 electrical length):
1. Quarter-Wavelength Transformer: The distance of the quarter wave transformer from the load (d) (in real
length units) and the characteristic impedance of the quarter-wave transformer (Z/4) for two solutions.
2. Single-stub tuning: (shunt) Stub position, d, and stub length, l, (in real length units) for two solutions both
in the case of short-circuited and open-circuited stubs.
3. Plots of reflection coefficient magnitude, || (reflection from the load+matching network combination back
to the transmission line), as a function of frequency, f, in the vicinity of the operating frequency for the
two methods described above. Plot all solutions for each type of network on a single graph. For each
solution, your program should also provide the bandwidth (f) for || = 0.2 tolerance. Solutions for
different cases should be easily identifiable on your plot.
Part 2: Experimental – single stub tuning
You will implement a single stub (shunt, open) tuner to match a quarter-wave monopole antenna load to a
microstrip line circuit board feed. You will design your matching circuit using the code from Part 1 and
measure the performance of your design using a portable vector network analyzer (NanoVNA). NanoVNA
measures the Reflection coefficient (S11) and the input impedance (Zin) values at different frequencies.
Quarter-wave monopole antenna: Estimate the resonance frequency using the antenna length and
confirm with the reflection measurements using the NanoVNA. Determine the antenna impedance (ZL)
using the NanoVNA.
1
EGRE 310 Lab 3: T-Line Impedance Matching and Tuning
Check Canvas for due dates
The microstrip transmission line: (1.3 mm thick dielectric layer with r = 2.45) Compute eff and Z0 for
the microstrip lines. Use the short-circuit (sc)/open-circuit (oc) method to measure Z0 with the NanoVNA.
Z 0 Z insc Z inoc
(Note that the microstrip line may not have Z0 = 50 .)
Matching circuit: Compute the parameters (d and l) for two single-stub tuning solutions. Create
stubs/strips by cutting the provided 1/4″ wide copper tape to the right length and placing it on the
microstrip transmission line.
The length from the load is the length
measured from the end of the SMA connector
soldered to the board, as this is the point that
the system was calibrated to. Place your stub
such that the distance from the load is
measured from the central line of the stub, and
the stub starts at the central line of the
premade transmission microstrip line.
If your stub is physically too close to the load,
too far from the load, too long or too short, how
can you change the position of the stub to achieve the same input impedance?
Exercise caution when handling the strip. The tape can be torn relatively easily, especially when trying
to remove and replace a strip. You should also press firmly to remove ripples/bubbles in the tape
which cause surface irregularities)
Testing: Measure S11 and Zin of the matched system using the NanoVNA to verify load matching.
If needed, for fine tuning try shortening the length of your stub in 1-2mm increments. Record the final
length of the stub that provided the best characteristics. Take a picture of the board setup for each
solution as well as the plots of S11 and Zin (on the Smith chart) at the resonant frequency. You can
adjust the display range by adjusting START/STOP frequencies.
Compare your final frequency responses (S11 vs freq.) against the data from your simulations.
Your report should address the following questions and have the following deliverables:
A brief discussion of the lumped element model, reflection coefficient, line impedance, and how
transmission line characteristics and circuits impact signal propagation.
Discussion of the ¼-wave transformer and the single-stub tuning methods, and how they achieve
impedance matching with the diagrams/schematics illustrating your solution method, relevant distances,
and other parameters.
– For example, for single-stub tuning, once you have calculated the stub position away from the load,
how would you calculate Zin at that position and use that value to calculate the required length of the
stub? Assume stub and line have real (and equal) Z0 and equal widths.
A brief description of the computer coding method and algorithms used.
Simulation Results and Discussion. Provide at least two representative examples including the outputs
(parameters and plots) of your program developed in Part 1. Comment on the performance of your
matching networks, advantages and disadvantages of various configurations. Which method provides
the better matching characteristics – ¼ wavelength or single stub tuning? Why? (Be specific and
quantitative) You may also discuss any special cases you have encountered.
Experimental designs and results from their performance evaluation. Compare the resonance frequency,
the reflection coefficient, and the -3dB bandwidth before and after impedance matching.
Comparison of experimental results with simulations. Discussion of reasons for any discrepancies.
Copy of code used to perform calculations. (Of course, your code should be your own. You are not
allowed to use code or tools found on the internet)
2
EGRE 310 Lab 3: T-Line Impedance Matching and Tuning
Check Canvas for due dates
Deliverables:
A comprehensive report that has a continuous flow without any breaks or abrupt transitions. Everything
in the report should serve a purpose and the report should reflect what you learned in this lab project. Focus
on critical analysis, justifying your answers/conclusions with data from simulation/calculation/experiment as
well as references (where appropriate). Be sure to provide enough practical information to ensure the reader
can understand what you did and how to interpret the results.
A single Lab Report must be submitted for the team. Each team member is required to submit separately a
one-page Individual Executive Summary. Your Lab Report should contain:
1. An Abstract summarizing the lab and your results/conclusions.
2. An Introduction section that “sets the stage” for your report. You may think of a structure like a funnel,
starting with knowledge understood by a sophomore EE student and gradually becoming more focused until
you get to your specified task.
a. A short discussion/introduction to the problem and the discussion of transmission line properties and the
need for impedance matching
3. A section (can be called Background, theory, or the like, but choose what fits best for you) detailing the
necessary background information to perform the task at hand. Introduce the concepts that you need and
derive the formulas that you will require.
a. E.g. discussion of the specifics of ¼-wave transformer and the single-stub tuning methods, how they
achieve impedance matching, design rules, and relevant formulas for the frequency dependent reflection
coefficient and line/input impedance.
4. A section detailing the Methods and Results produced in the lab as described in the Assignment section.
Explain the experiment that you have designed to test or solve the problem at hand and the logic behind your
approach. Present your results and your analysis/discussion. If there are multiple outcomes, you may elect
to create separate “methods/results” sections for each outcome. Think logically about the order to improve
the flow.
a. Discuss and compare the results of your simulations with two representative examples for the two
matching methods. Discuss and justify the experimental tuning circuit design choices and
characterization results. Compare experimental results with simulations for the antenna matching circuitry
you built. Discuss any discrepancies and potential reasons based on the constraints/approximations you
had. Discuss the frequency response and the bandwidth of operation.
b. In this section you should include sufficient graphs, plots, data to argue your points (see assignment).
Think critically about your results and process when discussing. What worked and did not work? Why?
c. Figures (schematics, simulation screenshots, plots, etc.), tables, and equations must be clearly legible,
neat, and appropriately numbered in the order they appear (e.g. Fig. 1, Fig. 2; Table 1, Table 2; Eq. 1,
Eq. 2, etc.) and must be properly cited in the text of the report (e.g. as shown in Fig. 2 …, Table 1 tabulates
…, According to Eqn. 3 …). All figures and tables should contain sufficiently detailed captions.
5. A Conclusion section which provides a “so what” of the report. Why should someone care about this result?
You may briefly summarize your process and results, but do not just summarize. Aim to add new thoughts
in this section. Did you meet the specifications or constraints? If not, what can you do better?
6. References must be provided at the end of the document. A minimum of 10 references is required for every
report. Your references should consist of published journal papers, textbooks, databases, etc. Items like
Wikipedia, online lecture notes, news articles, etc. will not count towards your 10 references. If you find
something useful in these items, cite the original source, e.g. references at the bottom of a Wikipedia page.
7. A list of your team members, their individual contributions. Provide detailed contributions. If a specific
member is significantly less involved than others are, they will receive reduced credit. Be sure to involve
other members and work together on the project/report.
8. A signature from each member attesting that all members contributed equally to the project.
Page Limit: 8 pages not including references, contribution, and signature pages.
Failure to satisfy these requirements will result in a reduced grade.
3
EGRE 310 Lab 3: T-Line Impedance Matching and Tuning
Check Canvas for due dates
NanoVNA V2 Instructions – Vector Network Analyzer (VNA)
Included in the Kit:
NanoVNA V2
Touch stylus pen
USB 2.0 to Micro USB power cable
Three Calibration Loads: short, 50Ω load, and open (shown on the
right, from top to bottom, respectively).
2 ct. 50Ω coaxial cables, and a 50Ω SMA adapter/female sockets
Confirm all components are included before continuing!
After use, place all components back into the box!
Powering the Device:
The NanoVNA is powered on via the switch located next to the USB port on the front of the device. It is a
rechargeable device and should be plugged in via the USB cable when used for an extended time to ensure it
does not power down mid-session.
Do not disconnect the NanoVNA from its USB port while in use! This will result in a power cycle and erase all
calibration settings.
NanoVNA Display/GUI:
To access the menus of the NanoVNA, either tap the screen with your finger or the stylus, or press the “square”
central button on the top right of the VNA. Menus can be navigated with the stylus or the left/right/square buttons.
Press on “ DISPLAY -> TRACE):
Reflection coefficient – S11 in dB vs. freq. (yellow – TRACE 0)
Transmission coefficient – S21 in dB vs. freq. (blue – TRACE 1),
Input-Impedance displayed on a Smith Chart (green – TRACE 2)
Reflection coefficient phase in degrees vs. freq. (purple – TRACE 3)
The values of each measurement are given on the top ribbon of the
display for the selected marker frequency. By default, there is one
marker (more can be added in the menus) which can be shifted along
the frequency domain using the left and right buttons on the top right of
the VNA or by dragging on the touch screen. As you shift the marker,
you’ll notice the measurement values change. (note that for input
impedance, the real part and a capacitance/inductance value are
displayed on top; you need to compute the complex impedance.)
On the bottom ribbon of the display are the START and STOP frequencies for the range over which you take
measurements. The default range is (100MHz – 900MHz); the maximum range is (50kHz – 4.4GHz). For your
specific application, a frequency range can be selected via MENUS -> STIMULUS -> START/STOP.
Calibration:
To calibrate, access MENUS -> CAL -> CALIBRATE. Note that the CH0 port can be used to measure S11, while
the CH2 port is used to measure S21. For S11, connect the external circuit up till the component whose reflection
you want to measure to CH0. Terminate the external circuit with each calibration load, one at a time, and select
the corresponding OPEN/SHORT/LOAD options (THRU is reserved for S21 measurements). While calibrating,
the on-screen text will turn green, and then the selected load type will be highlighted in black when complete.
Calibration is complete when each of the desired load types is highlighted in black. The measurement plots will
update upon exiting the menus. Do not save calibration, you will need to calibrate every time you change your
measurement circuitry. Why need calibration at all? See for example this link.
4
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