lec22 (44).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 -22. Filter synthesis, Kuroda’s identity. Hello, welcome to another module of this course microwave integrated circuits. In the previous 2 modules we had covered the various techniques for filter synthesis. In 2 modules that we had introduced, he had introduced you to the concept of narrowband filters using the resonators. And in the last module we had discussed about image filters. Now both the narrowband and image filters as we had seen, they rely on certain set structures, for example in the narrowband filter case, there were resonators. And for the image filters, there was the concept of unit cells. The synthesis techniques were very limited, for example in a narrow band filter case, we could only change some gap, introduce a gap, put it in shunt or in… Or put a transmission line element in Cascade and something like this. And for image filters we see this that our design is limited to just designing the unit cells. And basically they were just 2 types of unit cells that we discussed, one was the constant K and the other was M derived. But really there is no way of designing the response. So, in this module we shall be talking about designing particular frequency response. How to design a filter that will provide us a particular desired frequency response? (Refer Slide Time: 1:51)
So, let us see how to do that. Recall I had introduced you to the concept of insertion loss and oa few modules back. So, LI, this insertion loss is given by this relationship and for say a low pass filter, LI should be high, should be low in the passband and high in the stop band. So, if we make a plot between LI and omegaC and suppose OmegaC is our cut-off frequency, then it means that the insertion loss should increase to a maximum of 3 DB for frequencies less than omega C and beyond omega C, it would increase. So, this is our passband and beyond omega C, we have our stop band. Now the technique for this synthesis is based on this insertion loss. Suppose we are given a certain insertion loss, what circuit can be realised, can be designed so that a particu lar insertion loss characteristic is… (Refer Slide Time: 3:21) The procedure is very similar to the procedure that I had described while designing impedance matching networks. In the impedance matching networks, we 1 st had found out a relationship for, gamma in omega and then we had equated it to a prototype gamma in omega. So, this was our prototype function. So, either it was a binomial or Chebyshev and this was from circuit analysis. So, this was the case for impedance matching now for this filter synthesis also, the principle will be the same. We will be given a certain S21 or certain insertion loss transfer function and we will be equating it to a prototype case.

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