Please give clear steps! Thanks a lot in advance ! 49. (a) Find the 3dB NLP Butt

Question

Please give clear steps! Thanks a lot in advance !

49. (a) Find the 3dB NLP Butterworth transfer function, H (s) meeting the specs 3dBNLP (cop, Amax) (2T500, 2.2 dB) and (cos, Amin) (2T2000, 22 dB). Then find a min and ac max c using the formulas in the text or as derived in class. (Also, you might do this entire problem in MATLAB and turn in your COMMENTED original code. No comments and clarity, no credit.) (b) Using the circuit below assuming RL 2 2: Vout (s) (i) Compute the transfer function, circuit (s) in terms of the parameter values L and Vin(s) C, and ii) Realize the 3dBNLP transfer function obtained in part (a) as a circuit by equating coefficients, ie., compute the requisite values of L and C so that the magnitude is down 3dB at 1 rad/s. (c) Magnitude and frequency scale the circuit so that the gain is 3 dB down at ae min and final 0.02 AuF after magnitude and frequency scaling. Clearly specify Km and K (d) Plot the magnitude response of the circuit transfer function in both straight gain and dB gain vs f (in Hz). Since the transfer function is a voltage ratio, does magnitude scaling change anything? What about frequency scaling? Does s- out

Explanation / Answer

The code for part(a) can be found at:

https://drive.google.com/file/d/0BzsApW5yffhsR3pFVXV6b2g4SzA/edit?usp=sharing

Run it to get the following plot:

https://drive.google.com/file/d/0BzsApW5yffhsa0NYS0tPekc2QVk/edit?usp=sharing

The given Butterworth filter is of order 2. You can see the values of the various variables at the command line corresponding to the disp(); commands in the file.

For part(b,c)

https://drive.google.com/file/d/0BzsApW5yffhsdng3VnRCanl5Qjg/edit?usp=sharing

https://drive.google.com/file/d/0BzsApW5yffhsWVU4d3J2TTdQYk0/edit?usp=sharing

https://drive.google.com/file/d/0BzsApW5yffhseHhhVmhyOXFtekk/edit?usp=sharing

For part (d)

The code can be found at:

https://drive.google.com/file/d/0BzsApW5yffhsUUxYdDVsck9PZzg/edit?usp=sharing

Run it to get the following plot:

https://drive.google.com/file/d/0BzsApW5yffhsdzczQkUwOWtyN00/edit?usp=sharing

Also, magnitude scaling doesn't change anything as Km gets cancelled in the numerator and the denominator. However, the frequency scaling changes s to s/Kf. This is due to affect of frequency scaling being present only in inductors and capacitors.

Cheers,

Saurav

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