harmonics and single-ended versus balanced audio cables

Ron Resnick said:

What is the length of your single-ended interconnects?

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Most are 1.5ft, but I have some 28ft ones I use for when gear is located farther away, or fun with swapping gear at an event/meeting/test where the rack is away from the speakers. Can't detect difference in sound between them while using my device.

Ron the one situation where you would be transferring any significant 2nd harmonics on the IC's is probably if you had a tube preamp/phono that generated a fair bit of them. Otherwise it'll primarily be the amplifier making them like Don was saying.

I would recommend that interested parties absorb the points that Don and micro are making here, curious also that no comment has been forthcoming in response to Ray's real world test results.

Folsom said:

...the one situation where you would be transferring any significant 2nd harmonics on the IC's is probably if you had a tube preamp/phono that generated a fair bit of them. Otherwise it'll primarily be the amplifier making them like Don was saying.

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Musical Instruments get their characteristic timbre via harmonics generated by the instrument (along with the fundamental).

"The attached figure shows the spectrum of a low A note on a Fender Precision Bass when plucked with a finger, with no EQ applied. You can see the second harmonic at 110 Hz is about 7 dB louder than the fundamental at 55 Hz, and the third harmonic at 165 Hz is about 3 dB louder than the second harmonic."



https://www.gearslutz.com/board/7537435-post10.html

All,

Many of us wrongly conflate differential amplification with a balanced impedance signal interface. They are NOT the same thing, nor does the use of one dictate or require the use of the other. Don's technical comments about this are spot on.

DonH50 said:

The SET amplifier generates the distortion; whether you use a balanced cable or not after that no longer matters, save the potential for noise rejection. I would not bother with balanced cables on a SET, or really in most home systems, as the advantages are not generally required. And, it is real distortion, not something enhanced or obviated by a balanced (differential) cable as you seem to imply. I think you have the impression that differential circuits intrinsically "take away" something from the music but that is not the case; all they remove is extra noise and distortion. If implemented correctly. I could as easily make the argument that single-ended designs mask some of the microdetails in the music and blur transients. For audio circuits I would bet the big differences among components have much more to do with design and implementation details other than the difference between single-ended and differential topologies for the majority, probably the vast majority, of systems. If you have a high-noise environment (which may be more common in these days of dimmer switches and many other noise sources in the home) or have a ground loop, differential may help, but otherwise it is probably a wash.

This is not even a topic of debate in most systems because the benefits of differential circuits go well beyond the distortion and dynamic-range improvements. They also inject less noise into power and ground and are less sensitive to noise from power and ground, typically enable higher slew rates and greater bandwidth with less rail voltage (saving power), etc.

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I agree, but otoh I can easily make the argument that single ended designs preserve fine detail and microdynamics as well...

Ron Resnick said:

(...) But then what is the source of the second harmonic distortion canceled by the balanced circuit and cable topology? (...) ?

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The input stage of the amplifier itself.

microstrip said:

(...) BTW differential mode input does not cancel the existing even harmonics. All circuits add distortion. When we say that "Differential circuits cancel even-order distortion terms" it just means that the added distortion due to differential input will not include even order terms, but the odd order terms will happily be added. (...)

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DaveC said:

I agree, but otoh I can easily make the argument that single ended designs preserve fine detail and microdynamics as well...

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No more so than a differential design but whatever. Fundamentally, for audio, I doubt anyone would know if there were using differential or single-ended circuits in the majority of installations. No point in debating what people hear because it is almost impossible to get a direct comparison of differential to single-ended designs without some other variable changing. For that matter, most audio circuits I have seen utilize both single-ended and differential circuits "inside the box".

***

Ron, throw out the cables, they just convey the signal from one component to another. Consider them ideal, perfect, flawless transmitters from one point to another. Now consider a perfect recording and reproduction chain, only difference being differential vs. single-ended. At the start, the microphone picks up the voice or instrument (I'll ignore direct-plug instruments for now) in all of its (good lord I hope I used the right "its" ) glory, including the full harmonic content (even, odd, and non-harmonic). Apply that perfectly-captured signal to the amplifier chain from mic preamp to speaker outputs. All those electronics will add their own noise and distortion to that perfect source. If the circuits are all single-ended, then the second harmonic will usually be dominant, and there will be both even and odd order harmonics added to the source. If the chain is differential, and let's (oh crud, another apostrophe) say it is perfectly differential so all even-order distortion is suppressed, then the third harmonic will normally be dominant and no even-order distortion will be added to our perfect source. Clearly, I hope, the differential circuit is thus closer to the source, to "perfection" if you will.

Now, what I think you are postulating, is that the added distortion from a single-ended design makes the final sound better. That is possible. To use a (very) gross analogy, a perfect square wave has only odd harmonics, and sounds like a raspy buzz to us. Add in even-order harmonics, the edges of the steps are more rounded, and the sound becomes less raspy and thus "better" to us. It is more distorted, but we may prefer that sound, even knowing it is less true to the source (less "perfect"). That is one reason I like the sound of my old tube gear even though I know it is the extra distortion (among other things) giving me that bit of "false euphoria" (again going to extremes). It is not as true to the source, but sounds better to me.

The big caveat in all of this is that the distortion is so low in modern electronics, at least until the power amps start clipping, that the lower distortion argument for differential circuits is moot in the real world. The advantages of differential circuits in audio are primarily noise rejection and isolation, from within the box (e.g. power supply noise, crosstalk) and without (EMI/RFI). By far the greatest source of distortion in the vast majority of audio systems, at least IME/IMO, comes from the speakers.

HTH - Don

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^This IMHO ^^^^^^^^^^^^^^^^^^^^^^^^^

Ron Resnick said:

So is the even order harmonic distortion which is cancelled by differential circuit topology part of the signal or not?

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No. Distortion is "bad" stuff added to the original signal. Nothing in the original signal is cancelled, just less "bad" stuff is added.

If your original signal is "1" then a single-ended (SE) circuit adds a little bit of "2" and "3" to it. An ideal differential circuit adds a little bit of "3" but no "2".
If you original circuit is "1+2+3" then SE adds a little more 2 and 3; a differential circuit adds only a little more of 3.
In every case the distortion is added to the original signal. It is a distortion of what was there originally, something bad was added, nothing good was taken away.

Ron Resnick said:

Thank you, Ken....I understand Don is explaining that the second harmonic distortion produced by an amplifier is not the same second harmonic distortion canceled by a balanced cable connecting two pieces of equipnent with truly differential signal handling input and output...But then what is the source of the second harmonic distortion canceled by the balanced circuit and cable topology?

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Hi, Ron.

It may help to picture what second harmonic distortion does graphically (meaning, in the time domain) to an otherwise pure sine wave. It literally is an asymmetrical changing of the waveform around the zero crossing point. The positive half of the waveform has a different amplitude or shape from the negative half, with respect to the zero crossing. This asymmetry IS second harmonic distortion. More accurately, even order distortion. Single ended amplification stages tend to exhibit asymmetrical gain, and, therefore amplify signals in an asymetrical manner. Which results in amplified signals exhibiting second harmonic distortion, which is to say, exhibiting an asymmetric shape. That's why second harmonic distortion is so commonly associated with single ended circuits.

Differential bridge amplification circuits reduce second harmonic distortion because each half of the bridge tends to cancel the asymmetry of the opposing half. This cancellation is of the amplification circuit's own internal nonlinearity, not of any distortion of the input signal prior to entering that gain stage. In effect, each half of the bridge distorts in an opposing manner, resulting in better overall linearity, better overall waveform symmetry, together than they each do separately. This second order distortion cancellation effect doesn't just occur with differential bridge topology, it also occurs with complementary symmetry topology. Which is why NPN/PNP and NMOS/PMOS complemenrtary solid state circuits are so popular.

Balanced (impedance) signal interfaces do not cancel distortion. They cancel common mode noise. Distortion and common mode noise are both undesired, yet are totally different factors. Differential signal amplification is not synonymous with an balanced signal interface. They are distinctly different circuit functions. It is fully possible to have an single ended drive over an balanced interface and obtain the exact same common mode noise rejection as with differential drive.

Perhaps this quote from a Texas Instruments application note -Fully-Differential Amplifiers -will help.

Yes but it has to be common mode... otherwise the balanced output doesn't cancel it. So there's some conditions whether or not the cable interfaces matter for 2nd harmonics.

Ken Newton said:

Hi, Ron.

It may help to picture what second harmonic distortion does graphically (meaning, in the time domain) to an otherwise pure sine wave. It literally is an asymmetrical changing of the waveform around the zero crossing point. The positive half of the waveform has a different amplitude or shape from the negative half, with respect to the zero crossing. This asymmetry IS second harmonic distortion. More accurately, even order distortion. Single ended amplification stages tend to exhibit asymmetrical gain, and, therefore amplify signals in an asymetrical manner. Which results in amplified signals exhibiting second harmonic distortion, which is to say, exhibiting an asymmetric shape. That's why second harmonic distortion is so commonly associated with single ended circuits.

Differential bridge amplification circuits reduce second harmonic distortion because each half of the bridge tends to cancel the asymmetry of the opposing half. This cancellation is of the amplification circuit's own internal nonlinearity, not of any distortion of the input signal prior to entering that gain stage. In effect, each half of the bridge distorts in an opposing manner, resulting in better overall linearity, better overall waveform symmetry, together than they each do separately. This second order distortion cancellation effect doesn't just occur with differential bridge topology, it also occurs with complementary symmetry topology. Which is why NPN/PNP and NMOS/PMOS complemenrtary solid state circuits are so popular.

Balanced (impedance) signal interfaces do not cancel distortion. They cancel common mode noise. Distortion and common mode noise are both undesired, yet are totally different factors. Differential signal amplification is not synonymous with an balanced signal interface. They are distinctly different circuit functions. It is fully possible to have an single ended drive over an balanced interface and obtain the exact same common mode noise rejection as with differential drive.

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Great explanation, thanks!

A differential stage cancels even-order harmonic distortion in the differential output. Essentially, it (ideally) does not add even-order distortion terms to the signal as it amplifies it. If the input signal already has even-order terms (distortion or desirable), the differential gain stage will simply amplify them, as it has no way of knowing what is good and bad in the input signal.

Balanced (impedance matched) circuits alone will not in general do that (though it depends upon the circuit topology). Both differential and balanced circuits (which are often combined) reject common-mode noise. There is a lot of confusion on this subject...

This is essentially the same thing that @Ken Newton said above. And is in line with the equations in the link the @microstrip posted. We are all saying the same thing in different ways in hopes one of the explanations will "click". When I was teaching I always tried to have at least three different ways of presenting a concept. Hopefully one of them made sense to everyone, as I never learned to count to four.

Hi Ron

SETs are single ended circuits. When XLR or "balanced" connections are provided, the cables are still single ended because as pointed out by Don and others, only 2 of the 3 wires/pins are used. They are provided only for convenience. What you might get in such an arrangement is a better connector all else being equal which XLR is over RCA. XLR just fits better, has contacts less exposed to air, etc. That's pretty much it really. You won't be scrubbing out anything that the preamp or output section of a single ended source has already created. When a SET amp is receiving via XLR it too would be "using" one hot and would deal with the other hot pin in a few different ways but normally not injecting it into the amp.

Balanced scheme into cable make nothing with signal. If signal distorted before coming to cable, at out cable it will distorted again.

Cable is passive element. It is ideal linear (input-output-level-characteristics) as for AC as for DC. Though have frequency distortions.

However, external noise (out the balance connection) impact to 2 wires of the cable simultaneously. With using balance connection to amplifier these impacts are mutually cancelled, because work in antiphase (sorry, I don't know correct English term).
It is shown at the picture in the post above.

I don't remember what about cancelling by internal-power-supply-unit noise, that spread by wires inside the connected devices.

At my home studio, I have managed to suppress significant noise in monitors via balance connection only.

JackD201 said:

SETs are single ended circuits. When XLR or "balanced" connections are provided, the cables are still single ended because as pointed out by Don and others, only 2 of the 3 wires/pins are used.

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Just out of curiosity is there any reason an SET designer doesn't fit an input transformer to convert balanced input to single-ended? I have a headphone amp where I'm doing the opposite - an input transformer converts a single-ended signal (from a phone) to balanced to drive two complementary SE stages.

opus112 said:

Just out of curiosity is there any reason an SET designer doesn't fit an input transformer to convert balanced input to single-ended? I have a headphone amp where I'm doing the opposite - an input transformer converts a single-ended signal (from a phone) to balanced to drive two complementary SE stages.

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I don't really know of any but it's possible. The SET guys follow a less is more philosophy that extends throughout the entire chain. Using balanced outputs of their sources isn't typical usually because while XLR outputs are sometimes provided with pre amps, XLR inputs are even less common. I'm guessing the scarcity of examples is just a market demand thing.

Your application is much more common, particularly with microphones.