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Microwave Integrated Circuits Professor Jayant Mukherjee Department of Electrical Engineering Indian Institute of Technology, Mumbai Lecture Number 27 Gain Circles Hello! Welcome to another module of this course Microwave Integrated Circuits ”. In the previous modules for the past few weeks we had covered the topic of stability and as I had said stability is the very important aspect of amplifier design, and in this module we will be covering about amplifier, about amplifier gain how to design an amplifier with a given gain. So already we have discussed about the various types of gain that we talk about, among them the transducer gain is the most effective; it is the most practical definition of gain. But then problem with transducer gain is that we cannot design gamma S and gamma L independently, hence to get rid of that problem we have some other definitions of gain like operating power of gain and available power gain, and then I had also mentioned for the unilateral case that is when S 1 2 is equal to 0, the definition of the transducer gain can be somewhat simplify. So let us start the discussion today on how to design for the unilateral case where we have S 1 2 is equal to 0. 0 2 2 1 0 1 TU S L i i ii i G G G G G S   Now, this GS or GL, I can write by the general term like this. Now for an unconditionally case stable case we have seen that SII modulus should be lesser than 1, this is of course considering that this case where the stability circle is encompassing the center of the switch now for this case we have SII lesser than 0 and our GI is between 0 and some value GI max. Now if we define a term small GI which is defined as follows
max max 2 max * 2 2 2 1 1 0 1 , 1 1 1 1 1 1 i i i i ii i i i i i i i i ii i ii i i ii i ii i G g G G S G g G g C R g S C S g g S R S g   Say capital GI is the gain that you want to achieve and GI max is the value of the maximum gain, maximum value of GI where GI is either GL or GS. Then we know that GI max is given by this equation, and GI will verify this equation. This intern verifies that GI, small gi is between 0 and 1. Now the locus of those values of gamma I which give constant GI now that is a circle and the equation for that locus is given by this where CI, RI is given is like this. Now the center of all the circles for the various values of GI are located between 0 and SII star so if we draw a line between SII conjugate and the center then all the centers will be lying on that line now other observation be may we see is that GI is equal to 1 for gamma I equal to 0. see in other words GI is equal to 0dB there is no gain for gamma I equal to 0. So if now go to the slides on the monitor we see that if we draw these circles then it will the circles will look something like this actually.

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