About HPF/LPF & Phase

Thread Starter

Alexwfm

Joined Mar 10, 2021
4
Hello everyone,

I was trying to design a circuit where I split an audio signal in two channels: one which is a low pass filtered version of the original and the other which is a high pass filtered one. Both LPF and HPF are 2nd order and have same fc.
The idea was to merge the two signals back at the end of the circuit, after the high end signal gets minor level adjustments. Though when I do this, using a simple summing opamp, I happen to have a notch in the frequency response precisely at fc, which I realised it's where the phase of the two signals is +90 and -90 respectively.

I tried inverting one of the signals 180 degrees to make the frequencies at fc in phase, but there's still some weird modulation due to phase happening at fc which also compromises the flatness of the frequency response. And also the signal's low end would be out of phase with the rest of the audio band which I'd rather avoid.

I was wondering if anyone knew how would I be able to restore the filtered low end in the high end signal, archieving a flat response at the end?


Thank you in advance for any help, stay safe!

A
 

Audioguru again

Joined Oct 21, 2019
2,858
Yes, a 2nd order Butterworth lowpass and a 2nd order Butterworth high pass (and all other even-order Butterworth filters) make a phase-cancellation notch at their crossover frequency. If you invert one side then you have a +3dB boost at the crossover frequency. Using a Linkwitz-Riley alignment (less Q than a Butterworth) eliminates the +3db boost when one side has its phase reversed.

I use 3rd order Butterworth crossovers instead.
 

Thread Starter

Alexwfm

Joined Mar 10, 2021
4
Thanks for the suggestion! I've just simulated on LTspice a 3rd order butterworth crossover and the signals summed up nicely with a minimal bump at fc.
I'll try to see if I can just add an additional RC stage in front of the discrete 2nd order HPF to turn it into a 3rd order filter. Hopefully that will work, I'm expecting the real life version not to be as linear as the simulation.
 

Tesla23

Joined May 10, 2009
435
If you get a flat enough response by experimenting then fine.

There is a theory that will give you a flat response as Audioguru said, use Linkwitz-Riley theory, just duplicate your butterworth filters in each channel. This was discussed in this thread (it was a very long thread so I linked part way through):
https://forum.allaboutcircuits.com/threads/q-of-3rd-order-filters.168519/page-9#post-1517446

Typically if you sum butterworth filters you get a bump as shown, using L-R theory you get a flat response.
1615413121066.png
 

Thread Starter

Alexwfm

Joined Mar 10, 2021
4
Thank you for the link, it looks very tempting. I'm only hesitating on the idea of having to add another two stages so I think I'll try to see how the 3rd order Butterworth configuration works in real life.

For what I've understood, each configuration as in Butterworth or Chebyshev must be about 2nd and higher order filters as the configuration itself is about the positioning of poles which you can't do if you only have one. So by seeing the slope on the graph above I'd suppose that's a 2nd order filter? Wouldn't a double Butterworth filter be 4rd order from the sum of two 2nd order filters? I was wondering then what the graph would look like with the sum of two 3rd order Butterworths.
 

Audioguru again

Joined Oct 21, 2019
2,858
Two 2nd-order butterworth filters in series made a 4th-order filter with a low Q which is what Linkwitz-Riley uses to make a flat frequency response of a crossover.
Two 3-order Butterworth filters each are down -3dB at the crossover frequency so they add to produce no gap.
 
Top