THE UNIVERSITY OF BRITISH COLUMBIA

Physics 401 Assignment # 9:

LOOSE ENDS & COAX CABLES

Wed. 8 Mar. 2006 - finish by Wed. 15 Mar.
1. Cutoff Frequencies: Explain in words why there is a lower limit on the frequencies of EM waves that will propagate freely either through a tenuous plasma or down a rectangular waveguide. Why is there no cutoff frequency (neither upper nor lower) for wave propagation down an ideal coaxial cable?

2. Rectangular Waveguide with Dielectric: Show that if a hollow rectangular waveguide of the type shown in Griffiths' Figure 9.24 is completely filled with a dielectric of permeability , its cut-off frequency is lower than if it were empty, by a factor of :

Thus, for a given operating frequency, a dielectric filled waveguide can be smaller than an empty one.

3. (p. 412, Problem 9.31) - Coax Cable:1
1. Show directly that Eqs. (9.197) satisfy MAXWELL'S EQUATIONS (9.177) and the boundary conditions (9.175).
2. Find the net charge per unit length, , and the net current, I(z,t), on the inner conductor.

4. Coax Impedance:

In class, we derived the electric and magnetic fields in a coaxial transmission line. From those we deduced the characteristic impedance of a coaxial cable:

where a is the radius of the inner coax line and b is the radius of the outer coax cylinder, as shown.

In general, the characteristic impedance of a transmission line is given by

where and are the inductance and capacitance per unit length, respectively.

Show that the characteristic impedance of this coax line satisfies this definition by calculating and explicitly, and then Z.

Jess H. Brewer
2006-03-05