DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING INDIAN INSTITUTE OF TECHNOLOGY ROOKEE

EC-631 Prob. Sheet-5

1. A GaAs FET has the following S-parameters at 2 GHz, with bias voltage Vgs = 0 and Z0 = 50 :

11 12 21 220.894 60.6 , 0.02 62.4 , 3.122 123.6 , 0.781 27.6S S S S

(i) Determine the stability of the transistor by using K- test and the -test. (ii) Plot the input and output stability circles on the Smith Chart and identify the stable and

unstable regions. (iii) Determine the value of the series stabilizing resistor that is to be connected at the input

end. (iv) Determine the new S-parameters of the two-port consisting of the series resistor and the

transistor. (v) Test the stability of the stabilized transistor using K- test and the -test and again draw the

input and output stability circles to verify stability.\ (vi) Repeat parts (iii), (iv), and (v) for a shunt stabilizing resistor which can be connected at the

output of the transistor.

2. A GaAs FET has the following S-parameters with Z0 = 50 :

f(GHz) S11 S21 S12 S22

3.0 0.8 89 2.86 99 0.03 56 0.76 41 4.0 0.72 116 2.6 76 0.03 57 0.73 54 5.0 0.66 142 2.39 54 0.03 62 0.72 68

(i) Investigate the stability of the transistor at all the three frequencies using K- test and the

-test. (ii) In case the transistor potentially unstable at any of these frequencies, draw the stability

circles and stabilize the transistor by using a shunt resistor at the output. Determine the new S-parameters at that frequency and test the stability again.

(iii) Design an amplifier at 4 GHz for maximum gain. (iv) For the amplifier designed in part (iii), compute and plot the gain (dB) and the return loss

(dB) seen by the input generator as a function of frequency from 3 5 GHz. For generating the data at frequencies between 3 - 4 GHz(at 3.1, 3.2, 3.3 GHz) and 4 - 5 GHz at 4.1, 4.2, 4.3, GHz), use linear interpolation for determining the S-parameters.

3. Design an amplifer to have a gain of 11 dB at 4 GHz. Plot the constant gain circles for GS= 2 dB and 3

dB, and GL= 0 dB and 1 dB and make an appropriate decision for choosing GS and GL. For the amplifier so designed, calculate the input return loss and overall amplifier gain from 3 to 5 GHz. Use the following S-parameters with linear interpolation:

f(GHz) S11 S21 S12 S22

3.0 0.8 90 2.8 100 0 0.66 50 4.0 0.75 120 2.5 80 0 0.6 70 5.0 0.71 140 2.3 60 0 0.58 85

4. For the transistor given in problem 2, determine the unilateral figure of merit at 4 GHz and

determine the error in the gain(dB) that can be expected if the transistor is assumed to be unilateral. Design an amplifier at 4 GHz for maximum gain assuming the transistor to be unilateral. Plot the gain and input return loss over the 3 5 GHz range and compare your results with the results of problem 2.