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Unformatted text preview: ECE 488: RF Circuits and Systems Spring 2009 HOMEWORK 1: AC Circuit Analysis; Impedance Matching; Ladder Program Reference: Lectures 1-3; Chapters 1-2 Due: By 11:15 am January 28 Problem 1. Define the following terms in the context of RF circuits: [10 points] a. Thevenin Equivalent. b. Susceptance. c. Detector. d. Modulator. e. Tank. f. Carrier. g. The frequency range of the VHF band. h. The wavelength range of the UHF band. i. The frequency of one of the latest wireless toys (cellphone, Blackberry, computer, or whatever but specify which). j. The frequency spacing between broadcast AM radio stations. Problem 2: Real inductors have some loss due to the finite conductivity of the wires in their coils. A simple model of an inductor with loss uses a resistor in series with the inductor, as shown in the left-hand portion of Figure 1. The impedance of this model is Z S = R s + j 2 fL S . A lossy inductor can also be modeled as a parallel combination of an inductor with a resistor, as shown in the right-hand portion of Figure 1. For low loss inductors, R P >> R S and L P L S . (Note that in most schematics, the induc- Figure 1: Two models for lossy inductors. tor will be shown without the resistor representing its loss!) [15 points] a. Derive the expression for the impedance Z P of the parallel model in terms of L P and R P . b. Equating Z P to Z S at a given frequency, derive L S in terms of L P and R P . c. Equating Z P to Z S at a given frequency, derive R S in terms of L P and R P ....
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