How to choose the transfer function?

Question

Greetings from a physics student.

I have to do an activity which aim is to design a filter in frequency. To do so, I need a transfer function (gain, poles and zeros) that must meet the following conditions:

• The frequency response must pursue a specific functionality (high pass, low pass, band pass, band deleted, double band pass, etc.).
• The frequencies of the transfer function factors (poles and zeros) should be chosen as appropriate for that frequency response.
• The total order of poles plus zeros shall be a minimum of 5 and a maximum of 7.
• There may be poles at the origin or zeros at the origin (not both at the same time), with a maximum of 2.
• There must be at least one quadratic factor in the transfer function.

Then I have to do Bode's plots but I control that part. I am struggling with the choice of the function because we lost a lot of classes due to COVID-19 so I came here for a bit help.

Thanks!

Answer 1

I would first check out these links:

Matlab Low Pass Filter

Analog Filter Design

Butterworth

That will give a good indication on how to design filters. The main one is the butterworth because it returns transfer function coefficients in the numerator and denominator. You can use matlab to factor to get poles and zeros, along with changing the order of the filter. The quadratic factor will naturally come in higher order transfer functions, and if it doesn't, play around with the cutoff frequency or order until you see a squared term. A sample run is in the third link as well from matlab.

Some helpful commands as well:

• tf()

• freqz()

• bode()