311ps3 - PROBLEM SET 3 ECE 311 Autumn Quarter 2011 Assigned...

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PROBLEM SET 3 ECE 311 Autumn Quarter 2011 Assigned: Friday, Oct. 7th Due: Friday, Oct. 14th in class Instructor: Joel T. Johnson Problem 1 A circuit board inside of a GPS receiver is being designed to operate at 1.6 GHz. The circuit layout calls for a 4 pF capacitor as part of a low-pass filter, but a lumped element capacitor is not available at this frequency. Instead the circuit designer decides to use a short circuited transmission line to create the same reactance as the capacitor at 1.6 GHz. Lossless 80 Ohm microstrip lines are used on the 2.5 mm thick circuit board, which is made of a material with , . (a) How long should the shorted line be to create an effective 4 pF capacitor at 1.6 GHz? (b) What effective capacitance does the transmission line create at 1.55 GHz? At 1.65 GHz? (c) If only a 10% deviation from the specified capacitance is tolerable over this band, is your design allowable? Problem 2 An FM radio broadcast station operates at 91 MHz. Power is sent to the broadcast antenna through a lossless, air-filled 50 ohm transmission line. The antenna at the load
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