Here we go again: Isolator EQ design - phase shift effect

[xenon789]

Hello everyone, I'm currently in the process of deciding which EQ topology to implement for my rotary mixer. My objective is to achieve full kill attenuation while incorporating three essential controls: low, mid, and high. In my quest for information, I've extensively explored various resources, including service manuals. One particular circuit that has caught my attention is the ESP isolator circuit, which can be found at the following link (https://sound-au.com/articles/eq.htm#s9). This circuit strikes a balance between complexity and performance that aligns with my goals.

However, there's a crucial aspect I'm grappling with—namely, the impact of phase shift on the output signal. I conducted simulations of the circuit in the frequency domain using LTSpice, and the results showed a satisfyingly flat response but also a notable phase shift. To delve deeper, I decided to inject both square and triangle waves into the isolator, maintaining the knobs at the 50% mark. What I observed was a distinct alteration in the signal compared to the input waveforms.

Now, there are differing opinions on whether this phase shift is perceptible to a listener. Some argue that it might go unnoticed, but I find it challenging to fully trust this notion without conducting practical tests. Also at the bottom at the page Elliot wrote:

Phase response wasn't even mentioned in any of the descriptions, because it's extremely variable. All equalisers cause phase shift, and the change of phase is much more rapid with a high Q circuit. We can hear the frequency response variation caused by any equaliser, but the phase shift is not audible. There is any number of people who claim that phase is audible, but the claim belies the fact that most programme material has had at least some equalisation, and therefore has phase that varies from the original either for particular instruments and/or for the complete mix. No double-blind test has ever shown that phase shift is audible, provided it's static. Varying phase shift is used to create vibrato (cyclically varying pitch) which is audible, and is used as an 'effect' with many electric musical instruments.

To me, the impact of the phase shift appears significant enough that it could potentially affect the listening experience. If not, is there a scientific explanation to it?

 

[Ludus Tonalis]

I have simulated this circuit and can confirm your result. It is strange, to my eyes at least, that set to a (nearly) flat frequency response, there is a 300+ deg. phase shift. My expectation would be zero phase shift for a flat response, and one can't help feeling that there is something wrong with the circuit. Personally, I wouldn't touch it with a (barge) pole.

I've attached a zipped folder with two versions of a three-way EQ circuit that is inspired by an article in HiFi News many years ago called the Versatile Synthesised Tone Control. My version uses just two capacitors to derive three level-adjustable bands. The LF band is built on a simple low-pass circuit. The HF band is built on a high-pass filter. The killer feature of this circuit is that the mid band is created with no further filters, rather it is derived by subtracing the low and high bands from the wide-band input. When the three bands are mixed, if the controls are set for a flat response, then there is no phase shift.

Version 2 expands on version 1 by making the crossover frequencies adjustable. This requires dual-gang pots for the two frequency adjustments, so the circuit would be difficult to make in a stereo version, as this would require quad-gang potentiometers. The circuit is, however, quite feasable for a mono mixing desk strip, or a mono instrument amplifier.

 

[Ludus Tonalis]

Some example fr responses from both versions.

Version 1


Version 2

 

[xenon789]

Hi @Ludus Tonalis, very interesting, thanks for sharing. For those interested I found the article you mentioned:https://www.worldradiohistory.com/hd2/IDX-Audio/Hi-Fi-News-UK/IDX/80s/Hi-Fi-News-1982-12-IDX-62.pdf

It looks like this approach keeps phase coherency. However, there is still something puzzling my mind. The fact that many well known commercial DJ mixers use the ESP circuit or a variation of it. Here the Vestax PMC-CX, one of the most respected products out there:

If you look for the Allen Heath Xone:42 service manual you will also see a very similar circuit to ESP. I simulated all three and they all have the same phase characteristics. I started reading some documentation on EQs and the common viewpoint is that all EQ introduce a certain amount of phase shift but in application like music playback this cannot be noticed.

And to test this I have imported two wave files (bells and square wave) into my LTSpice simulation and saved the output. Guess what, despite the phase shift the two samples sound exactly the same.

From the great book Small signal audio design on Phase perception:

You don’t have any. Under realistic conditions human hearing cannot detect phase shift, which is just as well, because most of what you hear will have been phase shifted all over the place by loudspeakers and subsequent room reflections. Being able to hear phase would probably be hopelessly distracting and, from an evolutionary point of view, useless. It’s not, as far as I can see, going to help you detect the tiger stalking you through the undergrowth, whereas stereo location with binaural hearing might. It’s definitely “might”, because tigers, despite their large size, can move with terrifying stealth. We are talking here about having one part of the audio spectrum phase shifted with respect to another. An example was given in the previous section: a -3 dB cutoff frequency of 40 kHz gives a phase lag at 10 kHz of 14 degrees relative to low frequencies. Raising the cutoff to 100 kHz reduces this to 5.7 degrees. Neither is perceptible. If the phase shift is proportional to frequency, then the group delay is constant with frequency and this is a linear-phase system, as described above; we just get a pure time-delay with no possible audible consequences. However, in most cases the phase shift is not remotely proportional to frequency, and so the group delay varies with frequency. This is sometimes called phase distortion or group-delay distortion, which is perhaps not the ideal term, as “distortion” implies nonlinearity to most people, while here we are talking about a linear process.

 

[xenon789]

@Ludus Tonalis forgot to comment, the drawback I see in this alternative circuit is the fact that it is made of first order filters, with 6dB per octave. This would give different results compared to the common isolators used in mixers.

 

[Ludus Tonalis]

I had no idea that the article was available online - good find. In case anyone else is interested in seeing the original article, it is spread across three pages at:

https://www.worldradiohistory.com/hd2/IDX-Audio/Hi-Fi-News-UK/IDX/80s/Hi-Fi-News-1982-12-IDX-62.pdf
https://www.worldradiohistory.com/hd2/IDX-Audio/Hi-Fi-News-UK/IDX/80s/Hi-Fi-News-1982-12-IDX-63.pdf
https://www.worldradiohistory.com/hd2/IDX-Audio/Hi-Fi-News-UK/IDX/80s/Hi-Fi-News-1982-12-IDX-65.pdf

My own version, FWIW, is a minor improvement on the original in that I reorganised/rationalised/simplified the filters and was able thus to get rid of one of the capacitors, but with exactly the same frequency response. This opened the route to adjustable turnover frequencies, which would be much more difficult with the original circuit.

As to the audibility of phase distortion, Self is almost certainly right; at least in the context of music, phase shifts are next-to-impossible to detect audibly.

Looking at Rod Elliot's Isolator circuit, although the HP and LP filters are well-behaved equal component Sallen and Key filters, the mid section looks like a bit of a kludge, seemingly cobbled together empirically to get the flattest response with all controls central. It is the mid section that causes the large phase distortion.

It is, however, possible to derive the mid section by subtracting the HP and LP section o/ps from the unfiltered signal. The mid section only has first-order slopes, unlike the HP and LP sections, which have second-order slopes, but one is now guaranteed: a) the mid section exactly fills the "gap" between the two outer sections, regardless of the frequencies chosen; b) the frequency response is guaranteed to be ruler flat with zero phase distortion with the controls all controls central and regardless of the frequencies chosen. Moreover, dual pots can now be used to control the turnover frequencies - the mid section automatically expands or contracts to "fill the gap".

Enjoy...

 

[Ludus Tonalis]

@Ludus Tonalis forgot to comment, the drawback I see in this alternative circuit is the fact that it is made of first order filters, with 6dB per octave. This would give different results compared to the common isolators used in mixers.

Personally, I don't think that first-order filters are a drawback for EQ - but the circuit posted in my previous reply mostly gets round this.

 

[Mark Tillotson]

Couldn't a state variable filter be used? I guess thats only one pole (or is it a zero?) per section though. Perhaps stack a couple of them with buffers and combiners for each? Should be able to get flat frequency and phase though.

 

[treefella]

Maybe this Rane Paper is helpful regarding minimum phase in equalizers 😉

https://www.ranecommercial.com/legacy/pdf/ranenotes/Exposing_Equalizer_Mythology.pdf