Nguyen_Lab4

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Apr 3, 2024

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Experiment Report due day: November 05, 2023 Lab 4: Waveguide MICROWAVE ENGINEERING EEL 4436C Quang Nguyen

Lab 4 Quang Nguyen Page 1 of 12 Lab Results Quarter-Wavelength Transformer 1. (5 pts) Plot the S-parameters for the structure without the quarter-wavelength transformer. (You must run a sweep to plot the S-parameters)

Lab 4 Quang Nguyen Page 2 of 12 • We can see impedance mismatched at 12 GHz: S11 = S22 = -6.1 dB S12 = S21 = -1.2 dB 2. (10 pts) List the dimensions of your quarter-wavelength transformer. Show a screen capture of the final structure with the quarter-wavelength transformer. • The Impedances recorded at 2 ports:

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Lab 4 Quang Nguyen Page 3 of 12 At port 1: Input microstrip line Zo = 97.6 Ω At port 2: Output microstrip line ZL = 32.2 Ω = (97.6 *32.2) 0.5 = 56.06 Ω • Using the below equations from the book with parameters ϵ r =2.1 (Teflon) given, substrate height d = 2mm, microstrip line thickness 0.017 mm, the width of quarter wavelength is approximately 4.885 mm

Lab 4 Quang Nguyen Page 4 of 12 Length = λ/4 = 0.01 8786 m / 4 = 0.0046964m = 4.697 mm • Final structure with the quarter-wavelength transformer:

Lab 4 Quang Nguyen Page 5 of 12 3. (10 pts) Plot the S-parameter for the structure with the quarter-wavelength transformer. • S11 parameter with width and length calculated • S11 parameter with width and length adjustment making the matching close to 12 GHz. 4. (5 pts) Does the best matching occur at 12 GHz? If not, what is the reason? • From the plot of S11, the best matching does not occur at 12GHz. They occur at 11 GHz (calculation dimensions) and 12.5 GHz (adjusted dimensions) • The best matching does not occur at 12 GHz because the physical dimensions of the quarter-wavelength transformer calculated are not perfectly matched with the quarter-wavelength requirement at 12 GHz resulting in an impedance mismatch. It also could be due to simulation accuracy. 5. (5 pts) What is the reflection coefficient at 12 GHz? What is the SWR at 12 GHz? • From the plot of S11 above, the reflection coefficient at 12 GHz is about -19dB which is equivalent to 0.1122 linear.  Γ =0.1122 

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Lab 4 Quang Nguyen Page 6 of 12 From the software, we also can see the reflection coefficient is 0.1119.(close to our calculation) • The SWR at 12 GHz can be calculated as the formula: SWR = (1+0.1119) / (1-0.1119) = 1.252 • We also can see it from the SWR plot. 6. (5 pts) You might see a peak in S11 within the matching bandwidth which is unexpected. This is called box resonance. How do you remove it by explaining? (10 pts) Prove your method by doing another HFSS simulation. • Box resonance, also known as enclosure resonance or cavity resonance, can occur in our structure. It's an unintended effect where the electromagnetic waves get trapped within the structure, causing resonance at certain frequencies. • We can do several ways to remove box resonance: absorb material, modify the structure, or change the boundary conditions. • In our case, we will change the boundary conditions of the airbox which was not assigned a boundary resulting in the outward radiation effect. By reassigning the the radiation boundary for the airbox, we get the plot of S11:

Lab 4 Quang Nguyen Page 7 of 12 7. (5 pts) Does the quarter-wave transformer work in the reverse direction? That is, if port 2 is the input port, is the impedance matching still achieved? • After switching port 1 and port 2, the plot of S11 obtained below: • The plot still looks the same as before switching, so the quarter-wave transformer still works in the reverse direction, and the impedance matching is still achieved. 8. (5 pts) Show a screen capture of the mesh in both air and substrate regions. Which region has a denser mesh? What is the reason? • The mesh in the air region and substrate region

Lab 4 Quang Nguyen Page 8 of 12 We can see the mesh in the substrate region is denser than the air region because the substrate has a higher dielectric constant (εr) than ai r, and the impedance matching between the transmission line and the substrate. Single-Stub Matching Network 9. (5 pts) Plot the S-parameters for the structure without the single stub matching. 10. (20 pts) Show all your design steps and details on the Smith Chart. For your final design, what is the distance from the impedance mismatch to the nearest edge of the stub? What is the length of the stub? Show a screen capture of your final design.

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Lab 4 Quang Nguyen Page 9 of 12 From above solutions table, We got Zo = 59.6 Ω , Zl = 127.8 Ω , wavelength = 0.04544m= 45.44mm • Below is the screen capture of final design: The design steps on Smith chart showed below:

Lab 4 Quang Nguyen Page 10 of 12

Lab 4 Quang Nguyen Page 11 of 12 11. (10 pts) Plot the S-parameters for the structure with the single-stub matching network. • For the first solution: d1 = 0.7mm, l1 =17.46 mm • For the second solution d2 = 15.2mm, l2= 4.81mm 12. (10 pts) Does the best matching occur at 5 GHz? If not, what is the reason? • The best matching occurs at 5GHz for the second solution. • The best matching does not occur at 5GHz (about 4.7 GHz) for the first solution. The reason could be an approximation in calculating by Smith chart and the simulation accuracy.

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Lab 4 Quang Nguyen Page 12 of 12 13. (5 pts) Does the single stub match work in the reverse direction? • After reverse direction, the S plot for the first solution: • After reverse direction, the S plot for the second solution: • From the above plots, we can see the single stub match work in the reverse direction.