Classical Electrodynamics · Problem 8.3

Radiating Systems, Multipole Fields and Radiation — John David Jackson

Physics — E&M · parallel-strip-microstrip-transmission-line

Problem

(a) A transmission line consists of two identical thin strips of metal, shown in cross section in the sketch. Assuming that b≫ab \gg a, discuss the propagation of a TEM mode on this line, repeating the derivations of Problem 8.2. Show that P=ab2μϵ∣H0∣2,γ=1aσδϵμ,Z0=μϵ(ab),R=2σδb,L=(μa+μcδb)P = \frac{ab}{2}\sqrt{\frac{\mu}{\epsilon}}|H_0|^2, \quad \gamma = \frac{1}{a\sigma\delta}\sqrt{\frac{\epsilon}{\mu}}, \quad Z_0 = \sqrt{\frac{\mu}{\epsilon}}\left(\frac{a}{b}\right), \quad R = \frac{2}{\sigma\delta b}, \quad L = \left(\frac{\mu a + \mu_c\delta}{b}\right) where the symbols on the left have the same meanings as in Problem 8.2. (b) The lower half of the figure shows the cross section of a microstrip line with a strip of width bb mounted on a dielectric substrate of thickness hh and dielectric constant ϵ\epsilon, all on a ground plane. What differences occur here compared to part a if b≫hb \gg h? If b≪hb \ll h?

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