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chap13 007

# chap13 007 - 13.40 CHAPTER 13 TRANSMISSION LINES...

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Unformatted text preview: 13.40 CHAPTER 13. TRANSMISSION LINES III/[IIIIII/III/Illllllll.‘ rllill’llllIII/IIIIIIIIII V1+ —> Z°1=10 D 4————— V1- — III/IIIIIIIIIIIIVIII/I’ll! Figure 13.41: A two-way power splitter. a. Looking to the right of the dashed line, the two output transmission lines can be represented as lumped impedances, so the equivalent circuit becomes as shown in Figure 13.42. Find the amplitude V1_ of the reﬂected wave in terms of the input Figure 13.42: Splitting power. wave amplitude V1+ and ﬁnd the fraction of the input power that is reﬂected (give a numerical answer). b. Find the total voltage VT at the point z = 0 in the ﬁgure above in terms of the input wave amplitude V”. c. The total voltage VT found in part (b) must also equal V2... and l/EH. since they are in parallel. Knowing this, ﬁnd the fraction of the input power transmitted in each of the two output transmission lines (give numerical answers). Do all of your fractions (reﬂected and transmitted) add up to unity? They should. d. Suppose you could choose the impedances Z02 and 203 of the output transmission lines to be whatever you wanted. Choose these values such that you simultaneously satisfy the following two conditions: i) No fraction of the input power is reﬂected. ii) The output transmission line with impedance Z02 has twice as much power going into it as the transmission line with impedance Z03. Problem 13.13: A load whose impedance is 300+ j200 ohms is connected to a. coax— ial cable Whose characteristic impedance is 100 ohms. The frequency of the incident wave is 200 MHz and the propagation velocity in the cable is 20/3. 3. Match this load to the line using a single open-circuited stub made out of the same coaxial cable (i.e., ﬁnd the length and position of the stub). Make the stub as short ...
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