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Unformatted text preview: ECE 166 Prof. Gabriel M. Rebeiz Final Exam — ECE 166
Microwave Circuits and Systems
Monday December 8, 2008
3:006:00 pm — PCH 122 Exam Rules:
1. There are 6 problems in this exam. Solve all problems.
2. Absolutely no cooperation is allowed between any students. The only peeple who can answer questions are Prof. Rebeiz and the TAs. 3. Open book. open notes. open anything. It is advisable to bring a summary sheet to the exam. 4. Blue book required. Bring your own Smith Chart (maybe 4 or 5), compass and ruler. 5. Simple (nonprogrammable) calculators are recommended. 6. No name, no grade. No units, no grade. 7. Use blue or black lNK only. Nothing in pencil will be graded except if used on the Smith
Chart. 8. Partial answers will result in partial credit. Answers (even if correct!) with no clear solutions or how you got there will result in zero credit.
9. Wrong answers with a good explanation of why they are wrong will result in partial credits. 10. This exam is graded out of 100. Problem 4 (SParameters: 15 points) Consider the following 4port networks with scattering parameters [S A] and [SB]. The networks are passive and linear. All ports are matched except for S“ (Srm = 0 except for 811). Also, $13 = 0 for both A and B
networks.  Calculate 811, Sn for the combined network. Problem 5 (Gain and Noise: 10 points) Consider the direct sampling receiver. The lowpass filter has a gain of 1 dB at 1 GHz (resistive) and 40
dB at 3 GHz (reactive). a) Calculate the system level gain and noise ﬁgure referenced to plane A at 1 GHz and 3 GHz. b) The antenna temperature, TA, is 300K. Calculate the output noise power at 1 GHz and 3 GHz for a
system bandwidth of 1 MHz. A ‘ b T m
63310415 Gem, 4
NR = 21% M12}; =E7Cw.) NP: 9046 Problem 6 (Ampliﬁer Design: 25 points) G = 4043 a) Design a unilateral ampliﬁer at 10 GHz using single stub matching. Choose the shortest possible stub
length (you can use open or shorted stubs). All stubs are 50 Q. The generator and load are both 50 Q. SI 1: 0.3(90 deg), 521:8.0(+120 deg), 31220, 822 = 0.5(150 deg)
b) Calculate the gain of the unilateral ampliﬁer at 10 GHz. c) This transistor is replaced with another device which has the same Sparameters except that
SlZ=0.05(+60 deg). What will the new gain become? Problem 1 (Matching: 20 points) a) Design an LC matching network for maximum power transfer. Determine XC and XL, and also the
L and C values at 3 GHz. b) Calculate the available power from the source for Vg=l V(rms).
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20 J'0J‘* 2'” " ‘ Va M IV (007')ch Problem 2 (Transmission Lines: 10 points) a) Plot the SI 1, 822 and 821 on a Smith Chart for f=0 to inﬁnity. b) Plot the time domain signal at points A and B for an input wave, Vol+=u(t). Problem 3 (Scattering Matrix: 20 points) a) Derive the Scattering matrix for the following 4port circuit. Use symmetry and reciprocity to
greatly simply your calculations. All ports have a characteristic impedance of 20. b) For ailz=1, what is the power dissipated in the network if all ports are matched? Do this using the
scattering matrix. c) For al2=1, what is the power dissipated in the network if alf‘ports are short—circuited? Do this using the scattering matrix. 2}?" q. 1 225 7 2.  7?» ...
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