MIT6_013S09_pset09

MIT6_013S09_pset09 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science 6.013 – Electromagnetics and Applications Problem Set 9 (four problems) Suggested Reading: Course notes: Sections 9.3.1-2; 9.4; 10.3.1-2, 10.3.5; and 11.4.1-11.4.2 Problem 9.1 x z measuring approximately 7 × 12 meters at their conducting walls. Over what frequency range [Hz] will these waveguides propagate one and only one (a) Boston’s big dig created new traffic tunnels, some y mode? What is the name of this mode? (b) What are the cutoff frequencies f m,n [Hz] for the TE 11 , TE 01 , and TM 11 modes for these tunnel waveguides? (c) What is the waveguide wavelength λ g for the TE 10 mode in these tunnels at 15 MHz? (d) We can consider the waves at 15 MHz to be plane waves reflecting from the tunnel sidewalls at some incidence angle θ i ; what is the value of θ I for the TE 10 mode? (e) Write a general expression for the magnetic field H(x,y,z) for the TM 11 mode in terms of the waveguide dimensions b, a. (f) For the TM 11 mode, where might long slots be cut in these waveguide walls without significantly perturbing wave propagation?
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MIT6_013S09_pset09 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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