HW8 - UNIVERSITY OF CALIFORNIA Santa Barbara Department of...

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UNIVERSITY OF CALIFORNIA Santa Barbara Department of Electrical and Computer Engineering Problem Set No. 8 Issued: November 21, 2007 Fall 2007 Due: November 28, 2007 ECE 201A 1. Metal Air Dielectric Metal The Microstrip transmission line shown in the Figure above is widely used in Monolithic Microwave Integrated Circuits (MMICs). The purpose of this problem is to show that such structures cannot support TEM waves. The problem also identifies the conditions for a TEM mode to exist. (a) Prove that the electric field obeys the differential equation in a uniform dielectric medium. ∇+ = 22 0 0 G G EE ωμε (b) In an axially uniform structure traveling waves that have the z dependence as exp( ) jz β exist. Then the previous equation reduces to = T 0 2 0 G G () ωμε β where T is the transverse component of the operator. A TEM wave has no longitudinal components of E and H, no field components in the direction of propagation. Thus E and H are purely transverse i.e., E = E T and H = H T (c) Prove that ∇× = TT E G 0 Therefore
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G Ex
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This note was uploaded on 12/02/2009 for the course ECE 000 taught by Professor O during the Spring '09 term at UCSB.

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HW8 - UNIVERSITY OF CALIFORNIA Santa Barbara Department of...

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