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ECE 166 Hwk5-Fall 2009

# ECE 166 Hwk5-Fall 2009 - ECE 166 — Microwave Circuits and...

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Unformatted text preview: ECE 166 — Microwave Circuits and Systems Homework #5— Due Thursday November 19, 2008 (Couplers, Temperature and Noise Figure) Problem 1: Consider a hybrid (90deg) coupler connected to two variable capacitors. A variable capacitor at microwaves can be achieved using a reverse-biased Schottky diode (ie, a varactor). The reverse bias modulates the depletion region and changes the diode capacitance. a. Plot the reﬂection coefﬁcient of the load assuming that jX varies between —j 150 to —j30 \$2 for a reverse bias of 2-20V. Assume a series resistance of 5 52. What is the phase difference between these two conditions? Plot several X on the Smith chart. (Ignore the coupler for now). b. Insert an inductance in series with the varactor with a value +j90 9. Repeat (a). What do you find? Calculate 811 and \$31 for the entire system (take the inductor into account) at X=—j 150 to —j3{} Q. cl. Calculate \$11 and 831 for the entire system assuming a 10% mismatch between the capacitors rcactances (it does not matter which One is higher). Do it for X=-j150, -j90, -j30 Q. What do you ﬁnd? 9 Problem 2: Consider the 4-way power amplifier using passive T-junctions and using Wilkinsons (two cases). a) Derive the 5-port S-matrix of the T—j unction network and the Wilkinson network. b) All amplifiers are matched and have a voltage gain of 10 . Amplifier 2 fails as an open circuit. Derive the new input and output reflectiOn coefﬁcients in both cases. T‘juhciion Problem 3: a) Calculate the gain, noise ﬁgure and effective noise temperature as seen from the reference planes labeled on the ﬁgure. The ﬁlters act like attenuators at room temperature in the passband and as zero loss, zero noise reactive elements in the stop band. b) Calculate the output noise power, P0, in a l MHZ bandwidth if a matched resistor at 300K is attached to the antenna port (the antenna “sees” and acts as a 300 K load). For an input of J30 dBm, what is the signal to noise ratio? (0 dBm = 1 mW). .. gamete wavr pf“ -_ 1.. _ a P Béat‘nglm 6:“3M Gzé’ow Nl'SSQJQJ HF: 30142: phrase WT 9‘96 Tx 6: _ we ‘5 “M Problem 4: (:1) Calculate the gain, noise figure and effective noise temperature as seen from the reference planes labeled on the figure. Take into account the PA broadband noise. c) Calculate the output signal power, P,, if a -92 dBm signal is input at the antenna. Also calculate the Output noise power, P0, in a 5 MHz bandwidth, if a 300 K matched resistor is attached in place of the antenna. What is the SEN ratio? l)kang wﬁfeana’ 2 limp “The Tw23,arﬁqaaot,’f —2rl£2 aléIb [ewe €7u-évdew1“ NF?) ...
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