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Microwave Integrated Circuits Professor Jayanta Mukherjee Department of Electrical Engineering Indian Institute of Technology Bombay Module 7 Lecture No 28 Gain Circles (contd.) Hello, welcome to another module of this course, microwave integrated circuits. In the previous module, we are in week 7 now. In the 1 st module of week 7, we had covered about design using the gain circle for the unilateral phase using the transducer gain as our specification for the gain. And then we had seen what we had also discussed about the unilateral figure of merit to show how good an approximation, the unilateral approximation was. I had also mentioned in the previous module that next we will be covering the bilateral case. That is the case when we do not make the unilateral approximation. So let us see how, what we can actually do. Now one thing I would like to state for the bilateral phase is that unlike the unilateral case there is not much design flexibility. I mean what we can achieve mathematically is to specify the maximum gain that we can get unlike the unilateral approximation case where you could specify a particular gain and then draw a load side and source side gain circle. In the bilateral case, we cannot do that. (Refer Slide Time: 1:39) Now if the device unconditionally stable that is A greater than 1 and B greater than 0 or Delta less than 1 then for conjugate maths, we have to have and gamma L should be equal to now we
know what is the equation for gamma in and the equation for gamma out and if we solve these 3 equations simultaneously then the solution that we will get is given like this. 2 2 1 1 1 1 2 2 2 2 2 2 2 2 2 1 11 22 2 2 2 2 22 11 * 1 11 22 * 2 22 11 4 2 4 2 1 1 MS MS B B C C B B C C where B S S B S S C S S C S S         Where th is B1, Bs and Cs are given by… Now if we substitute these values into the gain equation then the value of gain we call the gaming question for the non-unilateral case that is when we do not make that is when S12 is not equal to 0. I’m not repeating that equation but if we substitute these values of gamma S and gamma ML in that equation, what we get is actually the maximum possible game, maximum possible value of GT for the bilateral case. And that value of GT, that maximum value of GT that we get is given by
(Refer Slide Time: 4:56) 2 21 max 12 max max max 21 21 21 max 2 12 12 12 1 1 1 T T P A T S G K K S G G G S y z G S y z K K Now we can show, we have already talked about GP that is the power gain or the operating power gain and GA is the available power gain. Now we can show that GT Max will be equal to GP Max which is equal to GA Max. Now this can also be simplified like this. Now just dividing the numerator and denominator by K+ square root of K square -1, what we will get is this. This S21 upon S12 is equal to any of the values. That is this is also equal to Y21 upon Y12. You can verify that from the conversion formulas for between Z and S parameters. Now, we saw that this is the case for the unconditionally stable case.
max
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