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I'm needing to improve an existing fourth order active filter design.

The filter amplifies 10-100 kHz signals as desired, however the phase shift is causing problems. 10 kHz signals are phase shifted around 200 degrees, but 100 kHz signals are phase shifted around 600 degrees.

The varying phase shift for desired signals is rather unhelpful. Ideally I would want the same phase shift for the entire frequency range. The magnitude of phase shift itself is of no concern, so increasing the phase shift at 10 kHz so that it is constant up to 100 kHz wouldn't be a problem.

  1. Is there a type of (allpass) filter that introduces a decreasing phase shift? - for instance 360 degrees for 10 kHz and 180 degrees for 100 kHz?
  2. Where should I start, how should I work, when trying to achieve constant phase shift in filter design?
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  • \$\begingroup\$ If you are trying to ensure that the wanted frequencies all stay time referenced to each other then that is not what you are describing. For instance if 1 kHz shifted by 10 degrees then you would want 2 kHz to shift by 20 degrees to main the same relative time between them. Is this what you want? \$\endgroup\$ – Andy aka Aug 30 '18 at 11:45
  • \$\begingroup\$ I think so, what we are seeing is that a repeating event - the falling edge of a mostly sawtooth wave - produces output at the end of the filter that lasts significantly longer than before the filter. \$\endgroup\$ – valki Aug 30 '18 at 12:26
  • \$\begingroup\$ "I think so" - you might want to take a little more time so you can be sure what you want then alter your question but pay heed to any changes you make that might cause a contradiction in the answer already given. \$\endgroup\$ – Andy aka Aug 30 '18 at 13:07
  • \$\begingroup\$ You probably don't want a constant phase shift. It's more likely you want a constant time delay, corresponding to a linear phase shift -- i.e., you want a Bessel Filter. \$\endgroup\$ – Scott Seidman Aug 30 '18 at 13:17
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There are two ways to approach getting a filter with a flat linear phase passband.

a) Flatten the phase of a conventional steep filter. You can design all-pass phase correctors. You don't say what your 4th order filter is, some types have flatter phase than others. It's easier to flatten the first half of the passband where the non-linearity is small, it gets harder as you near the edge of the passband.

You need to start out with as flat a passband phase, which means as wide a passband, as possible, while still meeting your stopband requirement. If you're not using stopband zeroes yet in an elliptic design, then you have a lot of scope for widening the passband, while keeping your attenuation to specification.

b) Flatten the amplitude of a linear phase filter. These have a fairly soggy stopband, which will almost certainly need to be augmented with stopband zeroes. There are published designs for this for up to 8th order, so the basic design should be no trouble.

Do you have a stopband specification? If not, that's the first thing to fix, because otherwise, how will you know how wide you can make your passband?

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