Determine the transfer function for a low pass filter with t

Determine the transfer function for a low pass filter with the following characteristics:

a cutoff frequency of 100 kHz

a stopband attenuation rate of 40 dB/decade.

a nominal passband gain of 20 dB, which drops to 14 dB at the cutoff frequency

Solution

I\'m going to explain this very mathematically, you could also do this more intuitively (with two first-order low-pass filters and an amplifier).

First you notice that you have to design a low-pass filter of second order (40dB/decade). You can just write down the general equation: H(s) = Av/(1 + as + bs2). Then you look at the other constraints:

As you can see we have three degrees of freedom, but only two constraint equations, so there is an infinite ammount of solutions for your problem. The smart choice is to set a=0 which will greatly simplify your calculations.