# Sallen Key Filters

#### Dhana

Joined Mar 1, 2006
1
Hi all, this looks like a great site and I look forward to being a member of it. My questions today are as follows.

This is part of an examination question. Basically, a diagram of a Sallen Key filter with 2 equal resistances and 2 capacitors was given. The gain of the amp is unity and it is assumed that this circuit is used to approximate a 3rd order Butterworth filter. Now I understand that this will give a transfer function with a quadratic term, basically a second order block to which another Sallen Key filter will be added to make it a 3rd order filter. The capacitances in the 2nd order block can be determined easily enough by comparing the transfer function of a second order B-worth filter. But how does one find the capacitance for the 1st order block added onto it? Does one compare the co-efficients of a 1st order B-worth to get it?

I can provide additional info if necessary.

Many thanks.
Dhana

#### Papabravo

Joined Feb 24, 2006
20,377
Originally posted by Dhana@Mar 1 2006, 07:18 PM
Hi all, this looks like a great site and I look forward to being a member of it. My questions today are as follows.

This is part of an examination question. Basically, a diagram of a Sallen Key filter with 2 equal resistances and 2 capacitors was given. The gain of the amp is unity and it is assumed that this circuit is used to approximate a 3rd order Butterworth filter. Now I understand that this will give a transfer function with a quadratic term, basically a second order block to which another Sallen Key filter will be added to make it a 3rd order filter. The capacitances in the 2nd order block can be determined easily enough by comparing the transfer function of a second order B-worth filter. But how does one find the capacitance for the 1st order block added onto it? Does one compare the co-efficients of a 1st order B-worth to get it?

I can provide additional info if necessary.

Many thanks.
Dhana
[post=14515]Quoted post[/post]​
Do you know the coefficients of the third order Butterworth response?

Remember that transfer functions apply to linear systems which means that the principle of supperposition applies. It does not matter if the first order filter feeds the second order filter or the other way around with ideal components. The third order transfer function will be the same in either case. You can also argue that the poles do not change their location if the blocks are rearranged.

So if you know the thrid order polynomial and you know the second order polynomial then you should be able to divide one by the other to get the first order polynomial. That first order polynomial should give you the the product of an R and a C. Then you should try to pick a C, and compute an R because there are more choices of values for R than there are for C.

With real components there is always a chance you will pick a pair of values that produce an unwanted side effect. The most common side effect in filters is where one section loads another section and changes its response. When you are all done you need to check the entire system and not just the individual pieces.