Question

53. A 2- order normalized Butterworth filter can be improved by using a so-called Chebeyshev filter The 3dBNLP second order NLP Chebeyshev transfer function is: 0.5012 2 +0.6449s+0.7079 Cheb3dBNLP(s) The Chebeyshev filter has some ripple in the passband but has better roll off, more attenuation in the stop band. If one can tolerate some ripple (sort of like a bouncy car ride) in the passband Chebeyshev filters typically have lower order than Butterworth filters. But, Butterworth filters have NO ripple in the passband The second order Chebeyshev can also be realized by the Sallen and Kev circuit described in the notes and shown below. In the final (Saraga) design, the filter is to have a de gain of dB down frequency of f 1591.55 Hz, and a largest capacitor of 12 nF plot the normalized MAGNITUDE frequency response for 0S 4 rad/s 0.5012 0.7079 (go figure), a 3 (a) In order to understand the behavior of the Chebeyshev transfer function frequency response, (b) The transfer function of the Sallen and Key circuit is given by Hirs)- nd Determine the value Q from the 2 order 3dBNLP Chebeyshev transfer function. Then determine the values of R, R2. C, and C2 for the Sallen and Key circuit that realize the 3dBNLP filter characteristic (c) Use input attenuation to adjust the de gain via a voltage divider with resistances Ri, and R18 that will replace the resistance R (d) Determine K, and Km- The values of R, and Rg can be chosen independently of the other resistors, i.e., with a different magnitude scale factor. See part (e) (e) Given your answers to (d), compute the final values of Rinal, R2 final C final, and C2 Gnal in the cii. Note: R,15 k2 is an acceptable value for this design; what would be the associated magnitude scale factor in 2 out Saraga Design Circuit Parameters: R1-0 ?, R,-T-Q, C-V3 Q F, C.-I F. R-R, and RR can be scaled independently of the rest of the circuit