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Microwave Integrated Circuits Professor Jayanta Mukherjee Department of Electrical Engineering Indian Institute of Technology Bombay Module 6 Lecture No 26 Amplifier gain stability (contd.) Hello, welcome to another module of this course, microwave integrated circuits. We are now in the week 6. This is module 4, week 6. In the previous module, we had discussed about stability and what are the conditions for unconditional stability and what is the condition for just keeping the circuit stable. So let us review once again what we mean by stability. 11for all111INSLoutINL We saw that if gamma in modulus is lesser than 1, or gamma out modulus is lesser than 1 for all mod gamma S lesser than 1 and what gamma L lesser than 1. So this is the stability criteria that gamma in should and gamma out modulus should be lesser than 1 for all gamma S and gamma L modulus lesser than 1. If modulus of gamma in or gamma out is more than one, then it is not stable. So this is the condition for unconditionally stable. Fine? So then, can we say that the condition that gamma in which is a function of gamma L modulus becomes equal to 1 this is the boundary between unconditional stability and potential instability. Gamma in is a function of gamma L modulus equal to 1 is a boundary between unconditional stability and potential instability. What does that mean actually? It means that when gamma in as a function of gamma L so those values of gamma L for which gamma in modulus becomes equal to 1 is that boundary. So if we can find out the locus of those points, or locus of gamma L which modulus gamma in is equal to 1, then we find out which is that boundary. If we want to derive the equation for that lacus let us see what it is, so the condition that is we have to satisfy is. Now the gamma in as we have seen earlier can be written as. After lot of mathematical manipulation what we can write is. First thing that you have to notice is this term is a constant let us say called CL this is a vector quantity.
12211122**221112212222221111INLLLLLLLLSSSSSSS SSSCR  This term is also a constant let us called it RL. This whole term can be written like ,this whole equation simplified like this. This is an equation of a circle. In other words that I was mentioning between stability and instability between unconditional stability and potentially instable circuit is a circle. This the equation of this ,this equation of circle that is just mentioned is also known as the output stability circle. It is called output stability circle because here the circle is dependent on gamma L which is the output impedance connected to the output of the amplifier. Similarly you know similarly we can also have the input stability circle which is analogous to the output stability circle, but instead of gamma IN becoming to zero we will have gamma out modulus equal to 1.

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