Reproduction of Low-Frequency Square Waves by Audio Amplifiers (and DAC)

[Onurb]

I am interested in the reproduction of low frequency square waves for audio and also, for PEMF therapy( square waves < 20 Hz). I don't want to discuss PEMF therapy here and focus on audio.


I have found a Harman Kardon document about low frequency square wave reproduction (page 3):
"
We shall initially examine the 20Hz square wave for three reasons. First, 20Hz is the traditional lower limit of human hearing and it makes sense to determine an amplifier's ability to function at this point. Second, the 20Hz square wave permits us to see out to about 200Hz (covering the entire bass and mid-bass region). Finally, we can see that problems at frequencies lower than 20Hz influence frequencies above that point. At 20Hz, square wave deformation is in the form of tilt. In moderate cases, the tops and bottoms of the waveform will tend to slope toward one another with the tilt increasing with more severe problems. In extreme cases the tilt is precipitous, and in the worst cases the square wave begins to look like an interrupted sine wave. Excessive tilt reveals low frequency loss, or poor power supply regulation with resultant phase shift. The distortion is clearly audible and bass and mid-bass sound becomes dull and boomy.
"


I measured several amplifiers and DACs and posted my measurements on the AVS forum ("Amp Measuring: Sinbosen D2-4200", page 4 and 5).


The best 5 Hz square wave I measured was produced by a Technics SG 30:

Here is an example of a heavily distorted square wave (SenMicre NX42000:

I'm definitely missing the know-how and gear to properly measure amplifiers and DACs myself. It would be fantastic if future reviews on Audio Science Review could incorporate measurements of low square wave reproduction. I'm really curious to see those results!



Bruno

 

[MaxwellsEq]

I am interested in the reproduction of low frequency square waves for audio and also, for PEMF therapy( square waves < 20 Hz). I don't want to discuss PEMF therapy here and focus on audio.


I have found a Harman Kardon document about low frequency square wave reproduction (page 3):
"
We shall initially examine the 20Hz square wave for three reasons. First, 20Hz is the traditional lower limit of human hearing and it makes sense to determine an amplifier's ability to function at this point. Second, the 20Hz square wave permits us to see out to about 200Hz (covering the entire bass and mid-bass region). Finally, we can see that problems at frequencies lower than 20Hz influence frequencies above that point. At 20Hz, square wave deformation is in the form of tilt. In moderate cases, the tops and bottoms of the waveform will tend to slope toward one another with the tilt increasing with more severe problems. In extreme cases the tilt is precipitous, and in the worst cases the square wave begins to look like an interrupted sine wave. Excessive tilt reveals low frequency loss, or poor power supply regulation with resultant phase shift. The distortion is clearly audible and bass and mid-bass sound becomes dull and boomy.
"


I measured several amplifiers and DACs and posted my measurements on the AVS forum ("Amp Measuring: Sinbosen D2-4200", page 4 and 5).


The best 5 Hz square wave I measured was produced by a Technics SG 30:
View attachment 450047

Here is an example of a heavily distorted square wave (SenMicre NX42000:
View attachment 450051


I'm definitely missing the know-how and gear to properly measure amplifiers and DACs myself. It would be fantastic if future reviews on Audio Science Review could incorporate measurements of low square wave reproduction. I'm really curious to see those results!



Bruno

Hi and welcome to ASR!

One of the challenges you will encounter is that everything below 20Hz is effectively "undefined". Since none of us can hear it, there's no need to reproduce it and (e.g. waste energy). So an amplifier would not be a failure if it did not produce an adequate square wave at 5Hz. Reviewers won't measure it, hear it or comment on it

Furthermore, DC is potentially very risky to pass through, so most gear has a filter close to zero Hz which may well have a phase impact up to 20Hz.

 

[ChrisG]

Going to disagree with Maxwell above. We absolutely can detect below 20Hz, but our hearing system isn't very good at it. It's more of a tactile sensation, and IMO worth reproducing.


A 20Hz square wave, though, is trivial to reproduce. You just need a flat frequency response to 20Hz. The SenMicre amp seems to have a highpass in place which is reducing the level at 20Hz, which will give the waveform shown.

Here's an example:

Top is a 20Hz square wave, bottom is with a 20Hz -6dB/octave highpass.


Unless you're running a 20Hz square wave tone through the amplifier at full power to really give it some pain, IMO there's not much to discover here.

 

[MaxwellsEq]

Going to disagree with Maxwell above. We absolutely can detect below 20Hz, but our hearing system isn't very good at it. It's more of a tactile sensation, and IMO worth reproducing.

We are actually in agreement! I accept that we can sense pressure waves below 20Hz, but I deliberately stated "... none of us can hear it...", which you agree with above. The mechanism for experiencing 15Hz is different from 150Hz.

The point I was making is that reproduction below 20Hz is undefined. By this I mean that no standards authority for audio systems sets specifications against which I can measure a device for compliance. For example, Red Book CD can store signals down to DC, but the specifications only mention 20Hz.

So two different, fully in-spec CD players may replay 10Hz completely differently. Neither is "faulty". Similarly, a phono preamplifier that rolls off below 30Hz is sensible.

Finally a power amplifier that blocks DC is generally a good idea. Since such a filter may have level and phase impacts up to 20Hz, it means that reviewing amplifiers using 5Hz square waves tells us little about how they reproduce music - just because amplifier A produces a clean 5Hz square wave tells us nothing about it's ability in the normally specified audio range.

 

[Onurb]

I choose to show the 5 Hz square wave because the distorted wave is more visible. Square waves at 20 and 50 Hz can be distorted as well. I have other measurements that I did not copy&paste from the AVS forum thread I did mention above. Have a look here.

Moreover, I have found an amplifier (IMG Stageline STA-2000D) for which the low frequency square wave distortion increases with the volume level.

I have also found that DACs can distort square waves in a similar way. See this link

 

[MaxwellsEq]

I choose to show the 5 Hz square wave because the distorted wave is more visible. Square waves at 20 and 50 Hz can be distorted as well. I have other measurements that I did not copy&paste from the AVS forum thread I did mention above. Have a look here.

Moreover, I have found an amplifier (IMG Stageline STA-2000D) for which the low frequency square wave distortion increases with the volume level.

I have also found that DACs can distort square waves in a similar way. See this link

Excellent. Is any of this audible?

 

[morillon]

Some magazines systematically presented square signals but typically at 40hz for amplifiers...
(see formerly in the case of phono cartdrige... 10khz)
;-)

 

[Azrael]

It's been a while since I learnt anything about signal theory, but a square wave contains a bunch of frequencies in addition to the fundamental frequency, and the more "perfect" the rectangles are, the more they contain, doesn't it?

 

[Onurb]

Excellent. Is any of this audible?

I haven't not performed any audio tests. I don't know which bass rich program would be affected by affected by a poor square signal reproduction. The only information that I have is the report from Harman Kardon (see my first post for the link).


Here is a screenshot of page 3 of the Harman Kardon report:

 

[Onurb]

I have also found that DACs can distort square waves in a similar way. See this link

One of the DAC I tested, the Armature Oberon, which has a good square wave reproduction, has, according to the manufacturer page, a class A output stage.

 

[ChrisG]

I choose to show the 5 Hz square wave because the distorted wave is more visible.

Yes, because there's often a highpass filter which is in full effect by 5Hz.

I have also found that DACs can distort square waves in a similar way. See this link

Yes, because they may also have a highpass filter in place.


The waveforms I posted are digitally generated and therefore theoretically perfect. They're not being "distorted" by equipment, because no equipment is connected.

 

[ChrisG]

It's been a while since I learnt anything about signal theory, but a square wave contains a bunch of frequencies in addition to the fundamental frequency, and the more "perfect" the rectangles are, the more they contain, doesn't it?

Yep, a square wave is the infinite series of odd harmonics.

However, if you adjust the level of the harmonics, you'll find weirdness can creep in. In the case of a HF bandwidth limitation, you'll see some ripple just before/after the vertical edges.
The case we're looking at here is that the 20Hz level has been reduced, probably with a bit of phase shift in there as well. It shouldn't be surprising that the 20Hz fundamental is responsible for the bulk of the "keeping the horizontal bit horizontal", since the 20Hz wave would peak at the centre of the square.

Here's a really good video which covers a lot of signal processing stuff, focusing mainly on digital audio, but with enough analogue that you'll almost certainly find it useful: https://xiph.org/video/vid2.shtml

 

[KSTR]

The case we're looking at here is that the 20Hz level has been reduced, probably with a bit of phase shift in there as well. It shouldn't be surprising that the 20Hz fundamental is responsible for the bulk of the "keeping the horizontal bit horizontal", since the 20Hz wave would peak at the centre of the square.

Actually, it is the phase shift that makes for most of the deforming, the amplitude plays a much lesser role. Below two versions, the first with the normal analog (minimum-phase) filter and second one with the linear-phase variant. Shown is a 5Hz square with two 1st order filter sections at 5Hz in series.

The second pass was applied in time reverse for the linear phase version (no phase-shift introduced by the filter) and this looks much nicer.

And we can see better what you wrote correctly, the bulk of the level at the center of the roofs comes from the fundamental, which is 6dB down in this case. This does not create a corresponding exact same drop of level at the bottom of the valley, though (as the math is a bit complex) but one immediately gets the concept.

 

[MatrixS2000]

It's been a while since I learnt anything about signal theory, but a square wave contains a bunch of frequencies in addition to the fundamental frequency, and the more "perfect" the rectangles are, the more they contain, doesn't it?

Yup, you need the odd harmonics where the 3rd harmonic is ⅓ the power of the fundamental, the 5th is 1/5, the 7th is 1/7 etc to infinity to create a perfect square wave.

EDIT: I see @ChrisG already mentioned this.

 

[MatrixS2000]

However, if you adjust the level of the harmonics, you'll find weirdness can creep in.

Yes because of the above. The power of each harmonic plays a role and to get a perfect square wave you need to follow the above.

 

[raindance]

One of the DAC I tested, the Armature Oberon, which has a good square wave reproduction, has, according to the manufacturer page, a class A output stage.

Same as pretty much every DAC. There's no need for other classes because they're not trying to generate power.

 

[SIY]

The frequency response measurement contains all the information you need to know what the square waves are going to look like since 99.99999% of audio amps are minimum phase. It's just the Fourier theorem.

 

[Keith_W]

Since a square wave is the sum of the fundamental + an infinite amount of odd-order harmonics, its shape can be altered by low-pass and high-pass filters, as well as any form of phase distortion. Here are a few examples that I quickly threw together:

20Hz square wave convolved with a 1Hz high-pass filter. This simulates what happens when the amplifier can not pass DC.

20Hz square wave convolved with a 10Hz high-pass filter. This is what happens if you have a really bad amplifier that can not reproduce low bass. The tilt has become much worse.

20Hz square wave convolved with a 200Hz low-pass filter. This simulates what happens when the amplifier is bandwidth limited.

20Hz square wave convolved with 1Hz HPF and 200Hz LPF (can't pass DC and bandwidth limited).

 

[nagster]

Is the explanation of square waves in this video correct? I think it's an important basic concept, so I'm a little concerned about this being an official video.
(However, I'm watching YouTube's auto-translated subtitles, so it's possible that I misunderstood. I apologize if that's the case.)

Whether or not he wants to use square waves is up to him. However, his explanation of square waves themselves differs from what everyone else has posted here and from my own experience.
For example, the inclined waveform around 04:20 is, in my experience, a waveform that is often seen on an O-scope when using capacitor coupling. This seems consistent with him setting the AP to AC coupling, but his explanation is different.

Square Wave Testing of Audio Products (Video Tutorial)

The topic of using square waves to test audio products comes up quite frequently. Turns out that it is not a very useful signal for this application due to its nature and how our audio systems work. In this video I explain and demonstrate the signal processing behind square wave and reasons...

www.audiosciencereview.com

 

[Cbdb2]

Is the explanation of square waves in this video correct? I think it's an important basic concept, so I'm a little concerned about this being an official video.
(However, I'm watching YouTube's auto-translated subtitles, so it's possible that I misunderstood. I apologize if that's the case.)

Whether or not he wants to use square waves is up to him. However, his explanation of square waves themselves differs from what everyone else has posted here and from my own experience.
For example, the inclined waveform around 04:20 is, in my experience, a waveform that is often seen on an O-scope when using capacitor coupling. This seems consistent with him setting the AP to AC coupling, but his explanation is different.

Square Wave Testing of Audio Products (Video Tutorial)

The topic of using square waves to test audio products comes up quite frequently. Turns out that it is not a very useful signal for this application due to its nature and how our audio systems work. In this video I explain and demonstrate the signal processing behind square wave and reasons...

www.audiosciencereview.com

Well hes mostly right. He was wrong about the tilt, its from the 10hz hipass filter he has on, not the lopass, so yes like a coupling cap. He also said a perfect square wave has infinite power, which is also wrong. Its power is the same as a DC voltage with the same level. I agree mostly with what he says but I still like to see it.