a.) A microstrip directional coupler will be designed for 845 MHz compatible with 50 ohms. A substrate with a dielectric constant of 3 and a thickness of 1.58 mm was chosen for this design. For 50 ohms, assume the line width as 4 mm everywhere. Calculate the mainline length of the directional coupler to be designed.

b.)Calculate the return loss, coupling, directivity and isolation values in dB for the directional coupling circuit, for which the scattering parameters (S-parameter) matrix at the operating frequency is given below. Here, gate number 1 is the entrance gate, gate number 2 is the transmission (exit) gate, gate number 3 is interconnection gate, and gate number 4 is the isolation gate.

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c.)Plot the scattering parameters amplitudes of the directional coupler given the scattering matrix at the operating frequency in case b), depending on the frequency. Use the exact values of the directional coupler at the operating frequency in the drawing. You can use symbolic values for other frequencies in accordance with a narrow-band directional coupler. Take the necessary precautions to make each Sparameter understandable in your drawings (using colored pencils, using a different line style, etc.)

[0,1464/162,5 0,9637241,35 0,0811/125,52 0,0122-174,47 0,94/41,68 0,1561/162,3 0,0109/174,8 0,0806/89,36 [$]= 0,0817/125,5 0,0112/166,4 0,145/2113 0,9329-7,088 0,0128/179,4 0,0802289,44 0,93782-7,016 0,1453/113,6