# Node Analysis of 2nd order Sallen-Key question

#### Techspec2

Joined Oct 15, 2015
10
Hello,

Im trying to figure out how the author of this ( The Sallen-Key filters (hmc.edu) ) (the very first/top problem)came to the conclusion Va = Vout((Z2+Z4)/Z2)).I was able to come up with same exact node analysis equations,but trying to solve them I get different results.

So: Va-Vout = Vout(Z2/Z4) -----> Va = Vout((Z2+Z4)/Z2)) I would just like to know how they got to this

My: Va = Vout(Z2/Z4) + Vout and simplified version : Va = Vout[(Z2/Z4) + 1]
Im sure im just overthinking this,but any help is appreciated.

#### Techspec2

Joined Oct 15, 2015
10
Just noticed Va= Vout((Z2+Z4)/Z2) is a voltage divider.And sub this and other equation and simplify....smh....

#### Papabravo

Joined Feb 24, 2006
20,993
Funny how the guys who publish things tend to double check and recheck their work with some degree of reliability.

#### Techspec2

Joined Oct 15, 2015
10
Funny how the guys who publish things tend to double check and recheck their work with some degree of reliability.
Couldnt tell you if this is true, but was just frustrated lol.But thanks for taking the time to reply.

#### Papabravo

Joined Feb 24, 2006
20,993
Couldnt tell you if this is true, but was just frustrated lol.But thanks for taking the time to reply.
I had to stare at it a bit the first time saw it as well.

#### Techspec2

Joined Oct 15, 2015
10
I had to stare at it a bit the first time saw it as well.
This makes me feel abit better lol.

The way the author put those 2 equations side-by-side made it more difficult for me.

And I plan on solving it the original way I stated in beg. of post:

Va = Vout[(Z2/Z4) + 1] ,I have 2 nodes and 2 equations , should be do-able,but the author stumped me lol and I need a break.Too many Laplace Transforms and transforms in general.

#### Papabravo

Joined Feb 24, 2006
20,993
I seem to remember that Van Valkenburg (Analog Filter Design, 1982) had an especially lucid description of the analysis of the Sallen-Key topology. I don't remember if it was the 2-pole or the 3-pole, but I'm sure I could dig it up if it would be useful to you.

#### Techspec2

Joined Oct 15, 2015
10
I seem to remember that Van Valkenburg (Analog Filter Design, 1982) had an especially lucid description of the analysis of the Sallen-Key topology. I don't remember if it was the 2-pole or the 3-pole, but I'm sure I could dig it up if it would be useful to you.
If you want too then heck yeah,But I didnt know this book existed thanks! Gunna buy soon. Its nice to check your work compared to others as a triple check.

#### Papabravo

Joined Feb 24, 2006
20,993
If you want too then heck yeah,But I didnt know this book existed thanks! Gunna buy soon. Its nice to check your work compared to others as a triple check.
I dug it up and it was for the 2nd order case. Enjoy.

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