20102ee161_1_Homework05_solution

# 20102ee161_1_Homework05_solution - 53 Problem 8.36 A TE...

This preview shows pages 1–5. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 53:: Problem 8.36 A TE wave propagating in a dielectric-ﬁlled waveguide of unknown permittivity has dimensions a : 5 cm and b : 3 cm. If the x-component of its electric ﬁeld is given by Ex : —36cos(407tx)sin(100rty) -sin(2.4rt X 101% — 52.9w). (V/m) determine: (a) the mode number, (b) 81. of the material in the guide, (c) the cutoff frequency, and (d) the expression for Solution: (a) Comparison of the given expression with Eq. (8.1'10a) reveals that H? TE _ : 401T, hence m : 2 a ? : 1007:, hence I? : 3. Mode is TE23. (1)) From sin(oor * [32), we deduce that o) = 2.4:: >< 1010 rad/s, B = 52.97: rad/m. Using Eq. (8.105) to solve for 81-, we have 5; [Ba (TV + (W = 2.25. (C) _ c _3><108 "p" 7 V2.25 2 2 2 2 (a) db) : 10.77 GHZ. : 2 x 108 m/s. (d) ZTE = Z'U/V '1 — (53/02 _ 7 i 81. 3 . 2 7 1 — ﬂ : 569.9 9. ..F 12 Hence, H _ Ex- .1" _ ZT = —0.063 c05(407tx) sin('1001't_v) sin(2.4rt >< '1010r— 52.9112) (A/m). Problem 8.40 A narrow rectangular pulse superimposed on a carrier with a frequency of 9.5 GHZ was used to excite all possible modes in a hollow guide with a : 3 cm and Z7 : 2.0 cm. If the guide is 100 m in length, how long will it take each of the excited modes to arrive at the receiving end? Solution: With a : 3 cm. I) : 2 cm. and Hpo : c : 3 X 108 m/s, application of Eq. (8.106) leads to: f10 : 5 GHz f01 = 7.5 GHZ fll : 9.01 GHZ f20 = 10 GHZ Hence, the pulse with a 9.5-GHZ carrier can excite the top three modes. Their group velocities can be calculated with the help of Eq. (8.1 14), “g : CV 1* (ﬂint/.ﬂzs which gives: 0.856 = 2.55 X '108 m/s, for T1310 Hg : 0.616 : 1.84 X 108 Ms. for T1301 0.320 : 0.95 X 108 rn/s. for T1311 and TMH Travel time associated with these modes is: 0.39 ,us. for TEN : 0.54 ,us. for T1301 1.05 ys. for TEN and TM-l 1. d 100 T : — : Hg Hg ...
View Full Document

## This note was uploaded on 06/01/2010 for the course EE EE161 taught by Professor Wang during the Spring '09 term at UCLA.

### Page1 / 5

20102ee161_1_Homework05_solution - 53 Problem 8.36 A TE...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online