Comparison of power amplifier distortions and FR into complex speaker dummy load

[dominikz]

I agree but surely if EQ frequency correction is assumed it should be stated. Differences in FR are clearly fairly important differences.

Indeed - but we should qualify the extent of these differences - even pretty 'bad' amplifiers in this sense (high output impedance) typically result in around ~1dB variation in FR across the audible spectrum, one 'bad' example here:

Amplifier output impedance:

Loudspeaker impedance:

Resulting amplifier FR deviations:

You see that the FR deviation across the whole spectrum is ~1dB maximum even in this severe case. Audible for sure, but subtle and definitely not terribly offending.
In practice IMHO it makes no sense to correct even for this, as most of the variation is in the low frequency region where one will typically anyway apply EQ based on in-room-measured loudspeaker response (to fix room resonances). ~1dB differences in amp response then become completely insignificant.

With amplifiers that have much lower output impedance (e.g. Hypex, Purify, Benchmark, new Topping amps etc...) the FR deviations will become much smaller (here's a nice article and spreadsheet from Benchmark that shows how this can be calculated) - so it is realistic to expect around 0,2-0,3dB variations with well performing amps. Probably no need to EQ the amplifier response anymore with such low variations

Thing is the amps did sound distinctively different and if they all sound the same that shouldn't be true.

This is why I said:

often misquoted "all amplifiers sound the same" argument

To my understanding the "all amplifiers sound the same" argument is often linked to the famous Richard Clark $10,000 Amplifier Challenge - you will see the challenge conditions also specify the use of EQ to remove FR deviations between amps (such that may also come from differing load dependence between amps). This is of course completely reasonable - the challenge was in my view well thought-out.

Maybe we should instead be saying "all non-broken amplifiers sound the same with a little EQ, assuming no-clipping condition and identical levels". A mouthful - no wonder people shortened it

Am I right in thinking that some amplifiers will have varying FR depending on the load? If so, does this not mean that it cannot be simply sorted out via EQ? ie if you have a changing FR, you need a corresponding changing EQ correction?

The FR deviations will be fully determined by the amp-loudspeaker combination and therefore are static as long as you use the same combination. I.e. the theoretical amp corrective EQ does not need to change for as long as you use the same amp-loudspeaker combination.

 

[Chr1]

Indeed - but we should qualify the extent of these differences - even pretty 'bad' amplifiers in this sense (high output impedance) typically result in around ~1dB variation in FR across the audible spectrum, one 'bad' example here:

Amplifier output impedance:

Loudspeaker impedance:

Resulting amplifier FR deviations:

You see that the FR deviation across the whole spectrum is ~1dB maximum even in this severe case. Audible for sure, but subtle and definitely not terribly offending.
In practice IMHO it makes no sense to correct even for this, as most of the variation is in the low frequency region where one will typically anyway apply EQ based on in-room-measured loudspeaker response (to fix room resonances). ~1dB differences in amp response then become completely insignificant.

With amplifiers that have much lower output impedance (e.g. Hypex, Purify, Benchmark, new Topping amps etc...) the FR deviations will become much smaller (here's a nice article and spreadsheet from Benchmark that shows how this can be calculated) - so it is realistic to expect around 0,2-0,3dB variations with well performing amps. Probably no need for EQ the amplifier anymore with such low variations


This is why I said:


To my understanding the "all amplifiers sound the same" argument is often linked to the famous Richard Clark $10,000 Amplifier Challenge - you will see the challenge conditions also specify the use of EQ to remove FR deviations between amps (such that may also come from differing load dependence between amps). This is of course completely reasonable - the challenge was in my view well thought-out.

Maybe we should instead be saying "all non-broken amplifiers sound the same with a little EQ, assuming no-clipping condition and identical levels". A mouthful - no wonder people shortened it


The FR deviations will be fully determined by the amp-loudspeaker combination and therefore are static as long as you use the same combination. I.e. the theoretical amp corrective EQ does not need to change for as long as you use the same amp-loudspeaker combination.

Great, thanks. My knowledge of electronics is minimal so apologies for any wrong assumptions here. I was wrongly under the assumption that an amplifiers FR could change dynamically with difficult speakers and therefore any correction via EQ would need to change correspondingly. Thanks for help in understanding this.

 

[BoredErica]

You see that the FR deviation across the whole spectrum is ~1dB maximum even in this severe case. Audible for sure, but subtle and definitely not terribly offending.
In practice IMHO it makes no sense to correct even for this, as most of the variation is in the low frequency region where one will typically anyway apply EQ based on in-room-measured loudspeaker response (to fix room resonances). ~1dB differences in amp response then become completely insignificant.

With amplifiers that have much lower output impedance (e.g. Hypex, Purify, Benchmark, new Topping amps etc...) the FR deviations will become much smaller (here's a nice article and spreadsheet from Benchmark that shows how this can be calculated) - so it is realistic to expect around 0,2-0,3dB variations with well performing amps. Probably no need to EQ the amplifier response anymore with such low variations

Thank you for the even-handed analysis.

The FR deviations will be fully determined by the amp-loudspeaker combination and therefore are static as long as you use the same combination. I.e. the theoretical amp corrective EQ does not need to change for as long as you use the same amp-loudspeaker combination.

Are there any general rules to consider? For example, do high frequencies tend to get pushed higher when speaker impedance is low at 10khz-20khz? When phase increases a lot in that range? etc. Without a test for my speaker + amp specifically it'd be nice if we can look at impedance/phase chart and guesstimate how much trouble the speakers might be for a cheap amp.

 

[SIY]

Are there any general rules to consider? For example, do high frequencies tend to get pushed higher when speaker impedance is low at 10khz-20khz? When phase increases a lot in that range? etc. Without a test for my speaker + amp specifically it'd be nice if we can look at impedance/phase chart and guesstimate how much trouble the speakers might be for a cheap amp.

If you can get curves of the amp output impedance versus frequency (usually relatively flat, then rising in the top octave) and know the speaker's impedance versus frequency (available in just about any review or from the manufacturer), you can set it up in Excel and do the basic voltage divider calculation. Engineering types use SPICE, but I'm not one of them.

The only tricky part is using both magnitude and phase (again, usually shown in manufacturer's data and reviews), but there's not a huge error in ignoring this for amplifier source Z. Excel does complex numbers so you don't have to.

 

[dominikz]

Thank you for the even-handed analysis.


Are there any general rules to consider? For example, do high frequencies tend to get pushed higher when speaker impedance is low at 10khz-20khz? When phase increases a lot in that range? etc. Without a test for my speaker + amp specifically it'd be nice if we can look at impedance/phase chart and guesstimate how much trouble the speakers might be for a cheap amp.

In principle if amplifier output impedance is high, and speaker impedance is low in a specific frequency region, you will see a dip there.

Still, usually the amplifier output impedance doesn't deviate nearly as much as the loudspeaker impedance across frequencies, so I'd be most concerned with just keeping the overall amplifier output impedance as low as possible to minimize any load dependence.
Of course, that alone will not tell you if the amplifier is suitable to drive any loudspeaker. E.g. amplifier cooling efficiency and current capability will surely also come into play for low-impedance loads.

Personally, I find the Benchmark spreadsheet (link) a really nice resource to get a good general idea of the FR magnitude deviations one might expect with a certain amplifier/loudspeaker pairing. This assumes you know only the basic information on loudspeaker impedance (nominal and min/max values), amplifier nominal output impedance and the speaker wire gauge and length.

If you still want to investigate deeper, it is not that difficult to make a more complete calculation with REW and some spreadsheet tool like Excel.
Here's a nice online resource showing the main principle or voltage division circuits: link.

The main equation is:
Vout=Vin*[R2/(R1+R2)]

Vout in the above equation is the voltage measured on loudspeaker terminals
Vin is the voltage without any load connected (i.e. open-circuit voltage)
R1 is the amplifier's complex output impedance
R2 is in our case the loudspeaker's complex impedance

(Note that in EE literature 'R' is usually used for pure resistive elements, while complex impedances are usually marked with 'Z' instead.)

Let me show you an example of this calculation on my previous example of Denon RCD-N9 driving Revel M16 loudspeakers.

Here's the measured impedances of Denon and Revel, and the calculated voltage division factor [R2/(R1+R2)]:

Due to scale it is difficult to see the wiggles in the calculated [R2/(R1+R2)] factor, but you can still see how they correlate with the loudspeaker and amplifier impedance curves.
Also, please note that I don't have phase data for the amplifier output impedance (phase=0° assumed), so there is some error above ~4kHz where output impedance phase is almost certainly deviating from zero.

Next we convert the calculated [R2/(R1+R2)] factor to dBs with 20*log[R2/(R1+R2)] and then multiply the amplifier's open-circuit FR with this.
Then we can finally compare this calculated FR to the FR that was actually measured on the loudspeaker terminals:

As you see, there is a really good match between calculated and measured FR up to about ~2kHz where we start to see more difference, up to a maximum of 0,5dB deviation. This should be the error introduced by assuming 0° phase for the amplifier output impedance across the spectrum.

Hope this helps!