Design a 5GHz full-wavelength microstrip resonator in ADS using 50Ohm physical lines (TLINP) assuming an attenuation of 1.4dB/m and an effective dielectric constant K = 2.1. The resonator is terminated in an open circuit and coupled to an input 50 Ohm line through a series capacitor.

a. Find the theoretical length of the line that makes it resonate at 5GHz, assuming no coupling exists.

b. Choose capacitance values so that the coupled resonator is i) critically coupled, ii) overcoupled, and iii) undercoupled. Show the magnitude and phase of S11 in each case.

c. Are the resonance frequencies observed in each case of (2.b) the ones expected?.

d. Provide an explanation of what happens in (2.c) using a theoretical model