Midterm Test
Design of three-section branch line coupler
原本参数有问题，修改了一下
Problem
Q7: Design a wide band branch line coupler operating at 2.6 G H z 2.6 GHz 2.6GHz with a coupling level of 10 d B 10 dB 10dB as shown in figure below. The characteristic impedances of the quarter-wavelength ( θ a 1 = θ a 2 = θ b 1 θ_{a_1} = θ_{a_2} = θ_{b_1} θa1=θa2=θb1$ = θ_{b_2} = 90°$) transmission lines are Z a 1 = 54 Ω Z_{a1} = 54 Ω Za1=54Ω, Z a 2 = 58.3 Ω Z_{a2} = 58.3 Ω Za2=58.3Ω and Z b 1 = Z b 2 = 143 Ω Z_{b1} = Z_{b2} = 143 Ω Zb1=Zb2=143Ω. Assume the device is to be implemented in microstrip, with a 0.787 0.787 0.787 mm substrate thickness, a dielectric constant of 2.33 2.33 2.33.
Q: Do these results indicate that your designs are correct? Explain why you think so.
Q: Compare these values between the ADS simulation results and HFSS simulation results. Some of these values are close, while some values are quite different. Explain why this is so.
Q: How this coupler is different than the conventional branch-line coupler.
I used to use the given characteristic impedances to do the simulations. But it soon turned out that these previous parameters could only give 3dB coupler instead of 10dB coupler.
Therefore I serched the Internet and used new characteristic impedances below:
| Z 1 ( Ω ) Z_1(\Omega) Z1(Ω) | Z 2 ( Ω ) Z_2(\Omega) Z2(Ω) | Z 3 ( Ω ) Z_3(\Omega) Z3(Ω) | Z 4 ( Ω ) Z_4(\Omega) Z4(Ω) |
|---|---|---|---|
| 609.0 | 48.6 | 197.3 | 47.0 |
Remark: Only value of impedances are changed. The circuit maintains operating at 2.6 G H z 2.6GHz 2.6GHz and the device is still implemented in microstrip with 0.787 0.787 0.787 mm substrate thickness, a dielectric constant of 2.33 2.33 2.33.
Reference: Handbook of Research on Recent Developments in Electrical and Mechanical Engineering Page 9 9 9, Table 3 3 3.
ADS Design
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Use line calculator to compute width and length. (Using loss tangent = 0.002 0.002 0.002 )
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Draw the circuit below:
- Simulation Result:
HFSS Design
- Dimensions for 10 10 10dB branch line coupler:
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Using the above parameters, we could draw the schematic below:
Details for the design are shown in the appendix.
- Unite FLs and TLs to simulate the program, we could get the below result:
Answers & Anaysis
Q: Do these results indicate that your designs are correct? Explain why you think so.
A: These results indicate that my designs is correct.
proof:
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For both ADS and HFSS designs, observe the S-paramter plot (Figure 2 and Figure 6).
It could be observed that S 13 ≈ − 10 d B S_{13} \approx -10dB S13≈−10dB at 2.6 G H z 2.6GHz 2.6GHz in both cases.
And recall the lecture that coupling factor is defined as:
C = 10 l o g 10 P 1 P 3 C=10log_{10}\frac{P_1}{P_3} C=10log10P3P1.
We can prove that: KaTeX parse error: \tag works only in display equations.
According to S 13 ≈ 10 S 23 S_{13} \approx 10S_{23} S13≈10S23, we could deduce that amplitudes of Port 2 and Port 3 have a ratio of 10:1. KaTeX parse error: \tag works only in display equations
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For both ADS and HFSS designs, observe the phase plot (Figure 3 and Figure 7).
Port 2 and Port 3 have 9 0 ∘ 90^{\circ} 90∘ phase different. KaTeX parse error: \tag works only in display equations
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Combining the conditions 1~3 could lead to a conclusion that these two designs are 10 d B 10dB 10dB branch-line couplers.
Q: Compare these values between the ADS simulation results and HFSS simulation results. Some of these values are close, while some values are quite different. Explain why this is so.
A: General results are quite similar(S parameters at 2.6 2.6 2.6 GHz, phase difference, and etc). But some curve shapes are not similar. This is might because:
- ADS and HFSS have differrent soultion setups and parameter settings. (I almost used the default.)
- ADS simulation is relatively more ideal than HFSS simulation.
- ADS yields to circuit simulation (Transmission line) while HFSS yields to micriostrip structures. In other word, the simulation result for ADS is much more ideal. Therefore the simulation result for HFSS is more close to the experimental result.
Q: How this coupler is different than the conventional branch-line coupler.
A: There are three states in this coulper while there just single section in conventional branch-line coupler. We could also consider this coupler as cascaded branch-line couplers. This change could lead to higher impedance and much greater microstrip line width.
Experience
- Adjusting the parameters are quite struggling for me. I searched many references online and fortunately got the right charactersictic impedance parameters.
- Using some mathematical equations to analyze the problem is quite useful to understand the problem.
Appendix
Details for HFSS design: