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# hw8solutions - S'a/q~l~ion ECE604 Homework 8 Out Tuesday...

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Unformatted text preview: S'a/q~l~ion ECE604 Homework 8 Out: Tuesday, March 8, 2005 Due: Tuesday, March 22, 2005 Problems given by number are from the text by Ramo, Whinnery and Van Duzer (3rd edition, 1994). 5.5d 5.5e 5.6a 5.7c 5.7d 5.7f 5.8d 5.86 attached 990999999N!‘ p—i CD . attached 9. Consider a parallel plate transmission line made of perfectly conducting plates. The plates are 5mm wide and spaced by 250 um and the medium between the plates is air. The characteristic impedance of the transmission line is denoted by Z0. At one end the transmission line is connected to a short circuit, while at the other end the transmission line is connected to amatched load (RL = 20). The transmission line is driven by a current sheet sinusoidally varying at a frequency of 10 GHz, separated a distance d from. the short circuit. The total length of the transmission line is 10 cm. perfectly conducting plates (extend 5 mm into paper) current sheet ,I (extends 5 mm into paper) , short circuit a) Where should the current sheet be placed to maximize the power delivered to the load resistor RL? (What is the value of d?) A short answer is acceptable provided it is justified. b) Now the short circuit at z = 0 is replaced by an open circuit. Now where should the current sheet be placed to maximize the power delivered to the load resistor? Problem 10 In class, we solved for the time-dependent response v(t) at the input to a transmission line of characteristic impedance 20, for the special case of a matched source impedance (ZS = 20), and ZL = 00 (open circuit), by using the impedance transformation equation, eq. (5.7.13) as a function of frequency (1). The result was that this Fourier domain approach yielded the same result as the simple time domain approach of section 5.5. For this problem, we allow both ZL and ZS to be arbitrary. We will consider v(t), the time- dependent voltage at the input end of the transmission line. a) Use the impedance transformation formula to give an expression for \7 (to) , the Fourier transform of v(t), in terms of the frequency (1). In particular, if we write \7 (so) = \A/in (0)) H((:)) , give an expression for the frequency response H(w). Here A Vi ((1)) is of course the Fourier transform of the input voltage v(t). b) Assume now that 2;, 2,, and Z0 are frequency independent. Explain how your expression from (a) gives rise to an impulse response function, h (t) = 2: I H(0)) ejwtdu) consisting 75 of a series of impulses, spaced in time by At = ZLJE . c) Suppose ZL is now allowed to be frequency-dependent. Give a short, qualitative description of how the response changes. - L54. As in '59; 55c - 4mg. mam». 'dcs‘mma-«ig be. mﬂev‘ed 2; superpcmhw 0? W0 eﬂual h‘mau’ak‘ 00%: A‘ﬁf\¥u&\°n, one. Manna “ID We. 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