2nd order low-pass and high-pass active filters

Thread Starter

Dritech

Joined Sep 21, 2011
828
Hi all,

I need to design a filter to attenuate any signals out of the 5 to 600Hz range (i.e. band-pass filter).
The circuit below was designed to form a 2nd order HPF followed by a 2nd order LPF.
When plotting the frequency response, I am getting a "bump" in the 5MHz range. Is this normal? When seeing a plot like the one below, is this considered as s good filter response?
I would appreciate if you could recommend any improvements to this circuit (ex: change values of some of the components to get a better response etc)

upload_2019-10-6_9-48-26.png

upload_2019-10-6_9-49-32.png
 

LvW

Joined Jun 13, 2013
842
Yes - the observed "bump" in the 5MHz region is "normal" - but only for the chosen lowpass Sallen-Key structure (second stage).
If this "bump" is a problem you should select another topology for this stage - for example "multiloop feedback MFB".

Explanation: For rising frequencies, the "normal" ouput of the opamp B gets smaller and smaller (as desired and expected) - however, at the same time a rising part of the input signal reaches the output directly (not via opamp) through the feedback capacitor C4 (the impedance of C4 gets smaller and smaller for rising frequencies). This is because the opamp has a finite output resistance (which even rises with the frequency) that produces such an (unwanted) output signal caused by the C4 path.
If you use another filter topology for the second stage (without a feedback capacitor), the "bump" will disappear.

Comment (Edit): However, you can reduce the unwanted "bump" by reducing the feedback capacitance C4 (redesign of all components).
 
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Papabravo

Joined Feb 24, 2006
12,389
A couple of questions:
  1. Was this filter designed from a set of requirements?
  2. Was one of the requirements that minimum attenuation in the stopband was 30 dB?
  3. What is the GBW product of the opamp?
  4. Why does it say GAIN on the upper left and PHASE in the lower right. Do you have two different plots on one set of axes
 

crutschow

Joined Mar 14, 2008
23,314
Adding a passive 1st order low-pass RC filter at the input of the active LP filter eliminates the high frequency peak.
With modification of the component values this then becomes a 3-pole filter with an 18db/octave rolloff instead of 12dB (bonus of improved high frequency rejection).

Below is the LTspice simulation of this circuit.
There's no significant peak at high frequencies at the output (blue trace) because the passive R1C3 filter at the input rolls them off significantly (yellow trace) before they get to the op amp active circuitry.

Using such a 3-pole filter also works well for filtering pulse and square-wave signals with fast-rise-times, since it suppresses the high-frequency edge-spikes that otherwise can feed through a 2-pole Sallen-Key low-pass filter.

Here's the tool I used to determine the component values, to change the response rolloff frequency if you like.

upload_2019-10-6_11-53-25.png
 
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Thread Starter

Dritech

Joined Sep 21, 2011
828
@crutschow , thanks a lot for your reply.

I modified both the LPF and the HPF (now both 3rd order). The components shown below were selected.
Do you recommend changing and of the values to prevent the op amps from getting unstable? I did try to reduce the 620nF caps on the HPF, but that is giving me a very high value for R3 (in the mega-ohms range)

upload_2019-10-7_22-55-8.png

upload_2019-10-7_22-56-51.png
 

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crutschow

Joined Mar 14, 2008
23,314
Do you recommend changing and of the values to prevent the op amps from getting unstable?
No.
Why do you think certain values could make it unstable?
The op amp is configured as a gain-of-one follower so it's quite difficult to make the circuit unstable.
I did try to reduce the 620nF caps on the HPF, but that is giving me a very high value for R3 (in the mega-ohms range)
Why did you want to reduce its value?

You can change all values by the same proportional amount to keep all the filter time-constants the same without affecting the filter response.
Thus if wanted R3 to be 1 megohm, you could increase all resistor values by 5 times and reduce all capacitor values by 5 times without a change in the filter response.
 
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LvW

Joined Jun 13, 2013
842
No.
Why do you think certain values could make it unstable?
The op amp is configured as a gain-of-one follower so it's quite difficult to make the circuit unstable.
To me, the last sentence sounds as a gain-of-one-follower would be always stable. Therefore, I like to mention that - in contrary - such a circuit with full feedback is most critical as far as stability is concerned. Remember - there are some opamps which are not unity-gain-stable (stable for gains above "2" or "3".only)
 

LvW

Joined Jun 13, 2013
842
@Dritech...if the damping bump is really a problem for you, why not using another lowpass topology for the last stage (multi-feedback)?
 

crutschow

Joined Mar 14, 2008
23,314
the last sentence sounds as a gain-of-one-follower would be always stable.
I should have added that, if the op amp follower is stable, than it will be generally stable independent of any other feedback from the filter circuit.
if the damping bump is really a problem for you
It's not a damping bump, it's high frequency feed-forward due to the limited op amp frequency response.
See post #2.
The 3-pole LP filter suppresses that feed-forward.
 
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