lec21 (43).pdf - Microwave Integrated Circuits Prof Jayanta...

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Microwave Integrated Circuits Prof. Jayanta Mukherjee Department of Electrical Engineering Filter design: Image parameter method, Insertion loss method Mod 05, Lec 21 Hello! Welcome to another module of this course ‘Microwave Integrated C ircuits ’. In the previous modules we had discussed about narrow ban filters and I have said that because of the special properties of the distributed elements like shortened transmission lines it is actually easier to realize resonator as compared to lumps equivalence or equivalence of lumped elements like l and c. Then we also showed some improvement in the design of such resonators using the gap couple ratings and then we discussed how using those elements you can design band pass and stop filters. In this module I will be introducing to another class of narrow band filters called constant K and M derived filters. These filters belong to a class of filters known as image filters. So let us discuss these filters in detail. Now first thing that I want to state about these filters is that now a day’s not many of the filters that are designed, are designed as image filters, but they had a special place in the olden days when synthesis methods were not that developed. So what these methods relay on is having identical sections of similar elements in cascade and the rule is that more the number of sections you have, the better the performance of the filters will be. So the basic fundamental units of this filter is a unit cell and two parameters characterize these cells, one is what is that knows as the image impedance, and the other is known as the propagation constant. So let us discuss these, what are these unit cells.
[Refer Slide Time: 02:30] So in image filters as I said that they can have two different types of image filters one is known as the constant K and the other is known as the m-derived. [Refer Slide Time: 02:50] 11 1 11 22 1 22 i i Z AB Z CD Y Z BD Z AC Y Now, let us see what is this constant K filters. Before discussing this, this type of filter let me a slight diversion and let us just try to establish what is this concept of image impedance. So suppose you have a two port network represented by its ABCD matrix, then the image impedance is defined as that impedance which when connected to any port. Suppose I connect an impedance ZI1 here and this is the impedance ZI2, then ZI1 is said to be the image impedance at port 1 and the input impedance at the port 1 is also ZI1 and ZI2 is said to be the image impedance at port 2, if the input impedance at port 2 is also ZI2. Suppose this is the this is where the voltage and v1 is the voltage at port 1 and v2 is the voltage at v2, I1 is the current at port 1 and I2 is the current at port 2, then it can be showed that ZI1, is equal to AB upon CD which is equal to Y11. Now this is the concept of image impedance.
[Refer Slide Time: 05:10] 2 1 2 1 V D AD BC V A I A AD BC I D Now, coming back to the same network once again, suppose the two ports are terminated by their image impedances, then we can have this relationship between this voltage at port 2 upon voltage upon port 1 like this. Now what is this ratio v2 upon v1 and I2 upon I1?

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