# How to convert Sallen-Key Low pass filter to Signal Flow Graph

Oct 9, 2017
1

#### LvW

Apr 12, 2014
604
The circuit consists of a fixed-gain amplifier (opamp with R3, R4) and a positive feedback function. Hence, where is the problem to find the signal-flow graph?

#### Audioguru

Sep 24, 2016
3,656
There are two RC lowpass networks, R1 and C1 and R2 and C2. Each RC network has an output of -3dB at the cutoff frequency.
Actually, the positive feedback occurs only near the cutoff frequency so that the -6dB response is boosted to be -3dB and the cutoff is sharp instead of droopy.

#### LvW

Apr 12, 2014
604
There are two RC lowpass networks, R1 and C1 and R2 and C2. Each RC network has an output of -3dB at the cutoff frequency.
.
No - it is obvious that the feedback network consists of a band pass (highpass C1-R1, lowpass R2-C2).
As a consequence, there is no lowpass -6dB response.

#### Audioguru

Sep 24, 2016
3,656
No - it is obvious that the feedback network consists of a band pass (highpass C1-R1, lowpass R2-C2).
As a consequence, there is no lowpass -6dB response.
I disagree. C1-R1 is a lowpass, not a highpass.
If C1 connects to ground instead of the the opamp output then there is no boost and the output at the cutoff frequency will be -6dB and the slope will gradually be 12dB per octave.

Last edited:

#### LvW

Apr 12, 2014
604
We are discussing the FEEDBACK network. Hence, you have to look into the circuit from the opamp output.
You cannot deny that - in this case - the feedback network resembles the well known highpass-lowpass CR-RC bandpass characteristic. This is a well-known property of a positive-gain Sallen-Key lowpass.

Last edited:

#### Audioguru

Sep 24, 2016
3,656
The bandpass circuit occurs only near the cutoff frequency to boost the response so that it has flat levels at low frequencies, -3dB at the cutoff frequency instead of a droopy -6dB and a sharp 12dB per octave slope at higher frequencies. Above the cutoff frequency both RC networks are lowpass filters.

#### LvW

Apr 12, 2014
604
The bandpass circuit occurs only near the cutoff frequency to boost the response so that it has flat levels at low frequencies, -3dB at the cutoff frequency instead of a droopy -6dB and a sharp 12dB per octave slope at higher frequencies. Above the cutoff frequency both RC networks are lowpass filters.

I dont understand your position.
A bandpass is a bandpass - full stop.
Just one question, which can be answered with yes/no:
Do you agree that - between the ouput pin and the non-inv. input of the opamp - there is the classical four-element ladder network C1-R1-R2-C2 ? And this is the well known RC-bandpass.

How can you say that "Above the cutoff frequency both RC networks are lowpass filters"?

At first, we dont have two RC-networks because you are not allowed to separate them, because they influence each other.
Secondly, the series cap C1 - of course - has highpass properties. I don`t think that you will argue against this.

#### Audioguru

Sep 24, 2016
3,656
I see the circuit as two lowpass RC networks at frequencies above cutoff like this:

#### Attachments

• Sallen-Key lowpass filter.png
14.3 KB · Views: 166

#### LvW

Apr 12, 2014
604
OK - I know what you mean. But that does not answer the question.
The question concerns the corresponding signal-flow diagram (which shows forward and backward ways.).
That is the background we are speaking about FEEDBACK.
And - it does not matter how the circuit looks like without feedback.
It is a fact that the Sallen-Key lowpass has a feedback function that resembles a bandpass.
This is the background for realizing a complex pole pair.

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