assignment3

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1 ECE145C (undergrad grad)/ ECE218c: Problem set #3 Exercises in nodal analysis, MOTC, and broadband circuits Problem 1 Take a highly simplied model of a bipolar transistor as below Cbe gmVbe B E C Where kT qI g c m / = and f m be g C τ = , and apply it to the amplifier below. Lets assume a transistor with a 500 GHz ft, hence a f τ of 0.32 ps. The bias tees shown have infinite L and C, and the generator, load and termination resistors are 0 Z (e.g 50 Ohms). Vcc is fairly unimportant, but lets make it 10 volts. amplifier termination termination darlington cell Vcc 10 mA 10 mA generator load Q1 Q2 Vgen Vout Vin a) Using Nodal analysis, calculate the input impedance of the Darlington cell. To simplify the analysis, the input termination and the generator are removed in this calculation. The result should be (i) perhaps surprising and (ii) worrying. By hand, sketch the trajectory of S11 on a smith Chart b) Using hand analysis, compute S21=2Vout/Vgen at mid-band. Use the method of

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