# lec24 (38).pdf - Microwave Integrated Circuits Professor...

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Microwave Integrated Circuits. Professor Jayanta Mukherhee. Department of Electrical Engineering. Indian Institute of Technology Bombay. Lecture -24. Microstrip Matching (contd.), Mason’s Rule, Power Gain Equations.Hello, welcome to another module of this course microwave integrated circuits. In the previous module we had saw how a basic microstrip, how basic matching lumped elements can be done and how using short lengths of high impedance or low impedance microstrip lines they can be used to substitute for inductances and capacitances. But I also mentioned that that is not enough because it may not always be possible to have high impedance or low impedance lines of the desired characteristic impedance. It might not be possible to implement them in a circuit and also the lengths might be too small then that what is feasible. When we look from a purely transmission line point of view, the matching of circuits is similar to the matching using lumped elements but a little different principles are involved.
The signal flow graphs are as we have already discussed about signal flow graphs in the previous modules. At the time of discussing I had mentioned that there are some rules, I had also discussed the ways of simplifying the signal flow graphs and in addition to the methods that we had discussed then, there is also something called Mason’s rules. So, Mason’s rules are somewhat of an easier way of achieving implementation of signal flow graphs and if we go to the slides on the on the monitor then the gain that is…
Suppose we have 2 nodes, if we can come back to the slides on the on the writing slides. Suppose this is a point say G and this is the point say H. And after simplification the gain between G and H is some value K or say T, the gain between G and G to H is T, then and said there are a lot of paths between this node G to H, many complex paths maybe. Then the gain T can be given by a formula this as shown here. This T will be equal to Sigma K PK Delta K upon delta. Now I will just give the definition of this PK, Delta K and delta and we will take an example to understand what these individual terms mean. PK is what is known as the path again of the Kth path between the nodes, delta is the quantity given by this and delta K is the value of delta using loops not touching the Kth parth. So, it might not be very clear but let us see an example. Suppose we have a 2 port network as shown here, S parameters are shown. Then it is corresponding signal flow graphs diagram as we have already seen earlier is given like this and so from this signal flow graphs we have to 1stdetermine how many paths are there. Suppose we consider the path between, the gain between A1 and B1, then how many paths are there between A1 and B1 and how many loops are there in this signal flow graph. So, 1stwe note that this is the path, starting from A1, going like this, this is one path.