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**Unformatted text preview: **' \
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ECE604 Homework 11
Out: Tuesday, April 13, 2004 (Session 25) Due: Tuesday, April 20 (Session 27)
[Students with tape delays: due according to session number] Problem numbers are from the text by Ramo, Whinnery and Van Duzer (3rd edition, 1994). 1. 8.7a
2) 8.7g
3) 8.8d 4) Start with the gaussian function f(t) given by Eq. 8.16(13). Using this in Eq. 8.16(10),
show that the envleope broadens with 2 as given by Eq. 8.16(14). Hint: Use the
following Fourier transform identity: _ 1/2
J exp (—I‘t2 ) e_Jwtdt = exp (—0)2 /4I‘) 5) 10.3d Hint: Review section 6.4 and note equivalence between 0 and 038”.
6) 10.43 7) A simple air—filled transmission line resonantor may be constructed by shorting both ends
of a transmission line, as pictured below left, for ideal (lossless) resonator. transmission line:
char. impedance Zo, velocity c _ I
Resonator With loss Ideal (lossless) resonator The ideal resonator supports resonant modes such that m half—wavelengths fit within the m?» resonator, i.e., T = L, where m is a positive integer. a) What is the frequency of the mth resonance? b) Now consider a resonator with loss, which we model by replacing one of the shorted
ends with a load RL, where RL << 20. Work out an approximate expression for the
energy storage time and the Q of the mth resonance. You may assume that the
resonant frequencies are approximately the same as for part (a). c) Give numbers for the resonant frequencies and the Q’s for L = 3 meters, Z0 = 509., and RL = 19. 8) In this problem we consider data transmission in two different metal waveguide
structures: (I) the parallel-plate waveguide and (II) the square waveguide. Both
waveguides are taken to be air-filled and lossless. (H)
(I) _ , ,. , ., a=3.c'r_nr—_>‘|>
parallel metalplateS-v .sgqgammeialgui‘de
(Separation a = .6 cm); (Si-ﬂea, = (a) We wish to transmit information using a baseband transmission scheme. Our data rate is R
(units of bits/second), and each bit has durationT = 1/R. For each data bit equal to ‘1’, we
simply transmit a constant DC voltage during time T. For each data bit equal to ‘0’, the
transmitted voltage is zero during the duration T of that bit. (See sketch below, showing - transmitted waveform for data ‘1011’). "time voltage We desire to operate at a data rate R = 100 Mbit/sec (108 bits/sec). For very fundamental
reasons, one of the two waveguide structures is expected to give much better performance.
Which one, and why? (A short answer is sufficient if properly justified). (b) Now we wish to transmit data via binary amplitude modulation of a 6—GHz sinusoid. For
each data bit equal to ‘1’, we transmit a 6-GHz sinusoidal burst of duration T. For each data bit
equal to ‘0’, the transmitted voltage is zero during the duration T of that bit. (See sketch below,
showing transmitted waveform for data ‘1011’). '1 , _ .. . . I6=GH2
T {—T v -' 'si'newave
g0 0 time
D -> Again we desire to operate at a data rate R = 100 Mbit/sec. Comment again on the relative
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- Electromagnet, Trigraph, Resonator, data rate, Acoustic resonance, Waveguide