A circuit board inside of a GPS receiver is being designed to operate at 1.6 GHz. The circuit layout calls for a 8 pF capacitor as part of a low-pass filter, however a lumped element capacitor is not available at this frequency. Instead the circuit designer decides to utilize a short circuited transmission line to create the similar reactance as the capacitor at1.6 GHz. Lossless 75 Ohm micro strip lines are utilized on the 3 mm thick circuit board, which is made of a material withε4ε0=, μμ0=.
a) How long should the shorted line be to create an effective 8 pF capacitor at 1.6 GHz?