本次代写是射频电路相关的一个assignment

Assignment 1

Question 1

A coaxial cable has a core conductor with a radius of a, and an inner radius of the sheath is b, as shown
in the figure. The space between the core and the sheath is filled with a concentric layer of polyethylene
insulation with  relative permittivity  εr and  relative permeability Ur. A  voltage  is applied between  the
sheath and core at one end of the cable, whilst the other end is open‐circuited.

(a) Derive an expression for the magnitude of the electric field in the dielectric layer as a function of
radius.

(b) Show that the capacitance per unit length of the cable is given by

(c) Given the resistivity of the inner and the outer conductor are 1 and 2, respectively, calculate the
resistance per unit length of the cable.

(d) Given the resistivity of the dielectric layer is diel, calculate the conductance per unit length
between the two conductors.

(e) Calculate the inductance per unit length of the cable.