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I am trying to design a desktop audio amplifier, and I'd like to better understand the effects of phase shift on my output. I'm trying to design this amplifier to be of the highest quality I can, and as I understand, phase shift cannot be completely eliminated. Is there an approximate level of phase shift that is considered "acceptable" by some standard? For example, a common filter I see recommended for flat phase response is the biquad filter, but even that one has a phase shift that goes like arctan(f), so that a corner frequency even at 100kHz produces significant phase shift in the audible region. What are some good topologies/techniques to reduce phase shift for an audio amplifier?

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  • \$\begingroup\$ Linear phase shift is not audible for humans. Of course if you will be using unobtanium cables in your system then phase shift becomes a concern. \$\endgroup\$ Feb 3 '18 at 19:00
  • \$\begingroup\$ @VladimirCravero But these filters have a phase shift that goes like arctan(f), and thus is not linear. \$\endgroup\$ Feb 3 '18 at 19:02
  • \$\begingroup\$ But you found them because you wanted to eliminate phase shift, which is not necessary in audio application. You are asking a question on wrong premises... \$\endgroup\$ Feb 3 '18 at 19:05
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    \$\begingroup\$ Just thought I'd chime in, linear phase shift is the same as a delay. \$\endgroup\$ Feb 3 '18 at 19:06
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    \$\begingroup\$ Hey OP, I was underestimating your endeavours. Sorry about that, I have found a question that might help you electronics.stackexchange.com/questions/155649/… \$\endgroup\$ Feb 3 '18 at 19:09
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Unfortunately unless you have expensive linear-phase, planar-speakers or similar high quality speakers, the group delay distortion is quite significant in that it distorts the triangulation of the sound source on a stage.

But lets assume you have an anechoic room with perfect speakers.

The phase response is only shifted 50% at the half power point and the pass band must be 2 decades higher if phase shift is critical but by that point the amplitude is now 20 dB attentuated per order of the filter per decade. So our perception tends to ignore that.

My Rule of Thumb for phase response is 1.5 decades of bandwidth above useable bandwidth with less than 10 degree phase shift. For 1 degree such as TV baseband color video, you need at least 2 decades more bandwidth.

The ideal LPF response is a flat group delay found in this filter normalized at @1kHz. enter image description here

. enter image description here

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  • \$\begingroup\$ Hm, okay - so do you think a Bessel filter would do a better job of achieving this kind of response? Right now I am using a Butterworth filter configured differentially and the phase shift seems signficant - here is the circuit I am testing and its response. \$\endgroup\$ Feb 3 '18 at 19:41
  • \$\begingroup\$ @BillyKalfus yes a bessel best approximates linear phase but you have other trade-offs so it depends on your design goals. \$\endgroup\$
    – loudnoises
    Feb 3 '18 at 20:17
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The consensus among researchers who have investigated the effect of non-linear phase shift on music is that it is inaudible. However, golden-eared audiophools would disagree, just on principle.

It's always possible to craft an all-pass network to linearise the phase shift, especially if you are gentle with the filter design and don't have too much group delay variation to start with.

A 'biquad' filter is a particular implementation, a way of building a filter, not a response type. You can implement any of the response types with any of the common filter topolgies.

The main response types are Butterworth (max flat amplitude), Cheby (equiripple amplitude), Bessel (max flat delay), and equiripple delay (which isn't named differently). In practice, a Cheby filter has very little delay variation up to about 30% of its corner frequency, so you might look at a 60kHz design for that. With an all-pass filter, you could use most of the passband.

The problem with the linear phase filters is the passband droop, -3dB at the 'cutoff' frequency, though if your system includes digital processing, a small lift programmed into the DAC would compensate nicely for that.

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  • \$\begingroup\$ If it's inaudible, then phase isn't a big deal to me - I just wanted to make sure that the dispersion between frequency components wouldn't introduce noticeable distortion, as the design I am considering seems to introduce significant nonlinear phase shift. It is primarily a Butterworth filter, which follows my DAC's transimpedance amp low-pass filter (just a capacitor in parallel with the feedback resistor). Here is a schematic and response curve. \$\endgroup\$ Feb 3 '18 at 19:50
  • \$\begingroup\$ I think it's inaudible, most acoustic researchers have shown that it is, but you'll get into a fight with audiophools. \$\endgroup\$
    – Neil_UK
    Feb 3 '18 at 20:31

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