Consider a round wire transmission line above a flat ground plane. For a wire diameter, d, and height, h, above the ground plane, calculate the following:
a) Find an expression (equation) for the characteristic impedance, Z0, and phase velocity, vp, for the transmission line if the line is surrounded by dielectric with relative permittivity er.
b) Given values for d = 0.025 mm, h = 0.5 mm, and er=e0, calculate numerical values for Z0 and vp.
c) Assume that the transmission line (signal line) material is gold and that the ground plane is copper and find the skin depth and sheet resistance for these materials at 10 GHz and use these values to obtain the resistance per unit length of the transmission line and the loss coefficient in both nepers and in dB per cm.
d) Find the input impedance to a section of the above transmission line that is a quarter of a wavelength long at 10GHz (air dielectric) and is terminated by a perfect 1 ohm resistive circuit.