Designing a 3-Section Coupler

[Fascheue]

Homework Statement:

Design a 20±1 dB parallel line 3-section coupler with a center frequency of 3 GHz and a bandwidth of 4 GHz between 1 GHz and 5 GHz. The design should meet the following specifications: Coupling at 3 GHz at 20±1 dB, Directivity at design frequency 15±2 dB, insertion loss at design frequency 1.5 dB maximum. Include in your report coupling, directivity, isolation, reflection co-efficient, and insertion loss of the coupler. Use either binomial or equal ripple response.
Students are supposed to use RF design software (ADS) for design. Use Rogers RT/Duroid 5880 boards for the project.

Start with hand calculation. Perform circuit level simulation (linecalc) including layout parasitics (bends), fine tune with the EM simulation for better accuracy. You have to use capacitive and/or inductive compensation (Read the uploaded papers) to meet the directivity specification. An example EM simulation of single section coupler is available. Compare the different simulations and finalize the design and layout for best performance.

Relevant Equations:

Cn’ = 0

For a maximally flat three-section coupler, by setting the nth derivative of C with respect to theta to 0 then solving the resulting system of equations, I got C1 = C3 = .0125 and C2 = .125.

I’m not sure where to go next. What other parameters do I need to calculate before working in ADS? Any pointers in the right direction would be appreciated.