Active low pass filter DC-20Khz, 40dB/decade

[jonnybgood]

In a tutorial I was asked to design an Active low pass filter DC-20Khz, 40dB/decade with a maximally flat response. I decided to go for a sallen key configuration with Butter-worth coefficients.

I chose an op amp suitable for audio applications: LT1028. My working is attached in pdf. My simulation shows that I got the correct values since I have a cut off (-3dB) at 20Khz and a roll of rate of 40dB/decade.

I derived the TF to a form suitable for drawing the bode plot by hand manually. I have a difficulty in drawing the bode plots because the values are not making sense. Am i doing something wrong in my working?

 

[LvW]

Jonnybgood, I think there is nothing wrong in your design.
However, there is one point you have to consider:

The formulas and the transfer function assumes an IDEAL opamp.
But in your simulation you have used a real opamp model (with non-ideal parameters). And that was the correct way to prove the design.
But you cannot expect that the transfer function (BODE plot) looks like the ideal Plot if you use a real opamp.

There are two major reasons the real plot does not look like the idel one:
* The finite gain and bandwidth of the real opamp
* The finite output resistance Rout of the real opamp model.
A part of the input signal is coupled DIRECTLY to the output via C2 and causes the rising part of the output voltage across Rout for rising frequencies.
This effect for higher frequencies is a known disadvantage of the S&K topology.