The frequency response of a Butterworth filter is not supposed to have any peaking. SPICE claims the contrary.
I came across an online datasheet for some op-amps where I found two schematics that intrigued me. Screen-shotting them together resulted in the following montage (Figure 1).
Figure 1 Two published filter circuits that caught the author’s eye.
Doing a quick Google search on the term “Butterworth Filter Response” yielded the following two paragraphs.
The Butterworth filter is a type of signal processing filter designed to have a frequency response that is as flat as possible in the passband. It is also referred to as a maximally flat magnitude filter.
As the ripple increases (bad), the roll-off becomes sharper (good). The Chebyshev response is an optimal trade-off between these two parameters. When the ripple is set to 0%, the filter is called a maximally flat or Butterworth filter (after S. Butterworth, a British engineer who described this response in 1930).
This was nothing new, but I just wanted to confirm for myself that the frequency response of a Butterworth filter is not supposed to have any peaking.
Putting these two filters into a SPICE simulation led to something unexpected (Figures 2 and 3).
Figure 2 This SPICE simulation of the low-pass filter circuit seemingly shows peaking.
Figure 3 This SPICE simulation of the high-pass filter circuit also seemingly shows peaking.
Both simulations show peaking in their frequency responses, which for a Butterworth filter is not supposed to be the case. I then modified the circuits as shown in Figures 4 and 5, with the simulation results again also included in the graphics.
Figure 4 This SPICE simulation of the modified low-pass filter circuit is absent any peaking.
Figure 5 This SPICE simulation of the modified high-pass filter circuit is also absent any peaking.
One change to each filter, highlighted in the graphics, seemed to correct the peaking issue. Whether the modified filter coefficients are truly Butterworth might be questioned, but for all practical purposes, these two changes seem good enough.
The applicable caveat is that if you really do need a Butterworth or Chebyschev or Bessel or Elliptical or…. filter frequency response, don’t just blindly follow whatever example you might find printed, no matter who wrote it. Check your design independently of any supplier’s application note(s).
An approximation might not be good enough to serve your needs.
John Dunn is an electronics consultant and a graduate of The Polytechnic Institute of Brooklyn (BSEE) and of New York University (MSEE).
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