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# hw09 - ECE 488 RF Circuits and Systems Spring 2009 HOMEWORK...

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ECE 488: RF Circuits and Systems Spring 2009 HOMEWORK 9: PLL, Coupled Resonators, Directional Couplers, and Two Ports Reference: Lectures 20, 22, 25, 26; Chapters 14, 18, 19 Due: April 8 Problem 1: Determine the source of numerical constants in the equation for V3 in the PLL problem of your previous homework (Problem 5 of Home- work 8), i.e., how is 0.141 and 0.01 related to R 1 , R 2 , and C . Note: V3 in the program is V2 in the circuit of Figure 14-5 in Hagen . Apology: I should have given this question as part of the PLL problem in Homework 8; it might have helped. [20 points] Problem 2: Figure 1 shows a Butterworth band- pass filter. The component values are as listed in the figure caption. [20 points] a. What is the center frequency of the filter? b. Convert the filter to use 2 μ H inductors for the three resonators. (You will need to use the cou- pled resonator technique to convert the series res- onator to a parallel configuration.) Add components to convert the generator and load impedances back to R L =100 Ω. Be sure to draw and label your final design.
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