Variable impedance - what's the audible impact

[DonH56]

Stupid question time: Is it true or not that load dependence of amplifiers impacts frequency response only at higher frequencies?

I ask because the subject of this thread is "what's the audible impact" of "variable speaker impedance."

And as we know from other threads, a major bone of contention is whether it's necessary or useful to test amplifiers with complex loads. The idea behind testing amps with complex loads is that if you do so, then a load-dependent amp won't just have a slight high-frequency peak or rolloff as it does with a constant resistive 4-ohm or 8-ohm load. The idea is that it will instead have nonlinearities throughout the audible range, as the load's impedance varies.

However, my understanding is that this is not the case - my understanding is that a variable load will only impact a load dependent amp's response in the highest couple of octaves in the audible range.

Would love it if one of our more knowledgeable members would be willing to answer this, as I think it would help clear up a lot of confusion (and help sweep away the FUD around this issue speed by a few of our members).

Simple answer is "no" but of course things are rarely that simple. That really relates to two things: how a speaker's (load) impedance changes over frequency, and how an amplifier's output impedance changes over frequency.

Most speakers exhibit a fairly wide variance in output impedance over frequency, complicated by the phase angle that can make things worse. There can often be dips at the crossover frequencies as power is shifted from one driver to another. Ported designs usually have a dip in impedance at the port resonance frequency where the active driver is basically static (resonance "holds" the woofer still) and output comes from the port. The panels of ESLs are basically big capacitors so their impedance falls with frequency, often to 1 ohm or less at very high frequency. Planar dynamic (Magnepan) and ribbon (Apogee) speakers are almost purely resistive so flat in impedance over frequency except where the crossover adds a bit of a "bump". Hybrids may include a ported woofer with an ESL so have dips at high and low extremes. Etc.

Every real amplifier is load-dependent, the question is how much (and thus does it matter)? The output impedance of the active devices inside the amplifier generally goes up with frequency, but how much and how high depends very much upon the devices and the internal design. Feedback works to greatly reduce the output impedance and is what leads to very high damping factors (low output impedance). The amplifier's feedback factor depends upon its internal (open-loop) bandwidth, however. As frequency goes up, internal gain reduces, feedback goes down, and output impedance rises. You can see this in the thread I linked earlier.

Amplifier feedback, gain, and bandwidth are design choices. Some amplifiers have little or "no" feedback (there is always a little due to device parasitics in the real world) and may have flat (but high) output impedance over the audio band. Most SS amplifiers have high feedback and thus low output impedance rising with frequency. Tube amps usually have lower internal gain plus an output transformer that raises their output impedance across frequency, again rising at higher frequency. Modern class D amplifiers tend to be self-oscillating with very high gain and feedback leading to extremely low output impedance over a broad frequency range. Class D also requires an output filter to suppress the high switching frequency and, even in the feedback loop, that can raise the impedance and introduce a faster high-frequency rise than if the filter was not there -- though still have very low output impedance over the audio band.

This brings us to "synergy". An amplifier with high output impedance paired to a speaker with little variation over frequency will not significantly change the frequency response. My classic example is tube amps and Magnepans. ESLs require an amp that can handle low HF impedances, but HF roll-off may be pleasing to some, so preference may influence the amp choice. Speakers with wide impedance changes will exhibit more frequency response variation when paired with amplifiers having high (or changing) output impedance, but again preference enters into people's choice. If the amplifier rolls off some frequencies and emphasizes others due to the speaker's impedance profile, or the speaker itself varies its output over frequency, some may prefer an amplifier that reduces or enhances the speaker's intrinsic response.

I think (but am not a speaker designer) that most speakers assume an ideal voltage source as a driver and thus an amp with low output impedance (high damping factor) that is flat over (audio) frequency is desirable. But often enough I read in reviews and manufacturer's comments how they designed or "voiced" the speaker for certain amplifiers so who knows? Flat response used to be a goal, but lately things seem to have deviated, at least for some amp and speaker designers.

HTH/IME/IMO/FWIWFM/etc. - Don

 

[NTK]

Your highest possible grade is a "C".

There is a throttling valve in a carburetor. Without Bernoulli a carburetor would not function

The energy upstream in the fluid flow will always be equal to the energy downstream in the flow plus the energy loss between the two points. Here is your conservation, energy in equals energy out including friction loss.
Bernoulli is still at work.

So, you are so confused that you can't tell the flow regime a flow restrictive valve, e.g. a metering valve, works in versus that of a purposedly designed venturi in a carburetor? You have any idea of the difference in their Reynolds numbers? And somehow your Dunning-Kruger makes you think you are qualified to assign grades in fluid mechanics

The analogy between current flow across a resistor and fluid flow across a valve isn't perfect, since flow rate is to a first order approximation proportional to the square root of Δp (again, in the right flow regime, link).

Anyhow, I ain't wasting more time with you, other than calling out your error to the other people reading this thread. Bye.

 

[tmtomh]

Yes and no. No in that there is no such generic rule. Yes in that class D amps with this issue have a rising output impedance with frequency. It is for that reason that the worst case impact is at the highest frequency.

Thanks Amir - and thanks @DonH56 , for your replies.

So to be clear, when it comes to the Class D amps we often see reviewed here, the ones that exhibit measurable load dependency show peaks or dips only in the higher frequencies - and the localization of these nonlinearities to the higher frequencies is not because they’re tested with a simple resistive load, yes? If tested with a variable load, we would expect their response to remain linear in the low and mid frequencies, because these amps’ output impedance would remain low at those frequencies regardless of the load - correct?

 

[solderdude]

Thanks Amir - and thanks @DonH56 , for your replies.

So to be clear, when it comes to the Class D amps we often see reviewed here, the ones that exhibit measurable load dependency show peaks or dips only in the higher frequencies - and the localization of these nonlinearities to the higher frequencies is not because they’re tested with a simple resistive load, yes? If tested with a variable load, we would expect their response to remain linear in the low and mid frequencies, because these amps’ output impedance would remain low at those frequencies regardless of the load - correct?

Yes.
At higher frequencies (with class D with sizable low pass filters) there are voltage division and resonance issues (not damping) because of the inductance on the output of the amp combined with the XO filter/tweeter.
A 'similar' thing can happen with tube amps using output transformers.

 

[tmtomh]

Yes.
At higher frequencies (with class D with sizable low pass filters) there are voltage division and resonance issues (not damping) because of the inductance on the output of the amp combined with the XO filter/tweeter.
A 'similar' thing can happen with tube amps using output transformers.

Thanks! So when it comes to Class D (and some tube amps), the “we need to see how the amp behaves with a real/complex load” claim is not valid. Or, to put it another way, if a complex load makes such an amp’s response “wiggly” instead of smooth, it would do so only in that same high-frequency region where tests with a simple load already shows a smooth peak or dip.

I just think it’s important for the facts around this particular part of the impedance question to be clear to everyone, given what’s been claimed in some of the long other threads about Class D and load dependency.

 

[solderdude]

Thanks! So when it comes to Class D (and some tube amps), the “we need to see how the amp behaves with a real/complex load” claim is not valid. Or, to put it another way, if a complex load makes such an amp’s response “wiggly” instead of smooth, it would do so only in that same high-frequency region where tests with a simple load already shows a smooth peak or dip.

Yes, at least when we are talking about some class-D designs, the ones where Amir's measurements show a low resistor dependent frequency response.
This is related to the overall design and the switching frequency (and thus output low pass filter) and assuming the output resistance of the amp is low from sub-lows to at least upper mids.
There are class-D designs that are not very load dependent.

Real world loads can differ from some 'complex' loads and resistive loads. When we we see a FR deviation with different loads one can be pretty certain there will also be differences using real word loads or complex loads.
The shown effect with resistive loads, however, are only indicative something is going on there and might well be different when used with a speaker.
It could be worse, it could be less worse.

The "we need to see how the amp behaves with a real/complex load” in that respect might certainly be true.

I just think it’s important for the facts around this particular part of the impedance question to be clear to everyone, given what’s been claimed in some of the long other threads about Class D and load dependency.

 

[tmtomh]

Yes, at least when we are talking about some class-D designs, the ones where Amir's measurements show a low resistor dependent frequency response.
This is related to the overall design and the switching frequency (and thus output low pass filter) and assuming the output resistance of the amp is low from sub-lows to at least upper mids.
There are class-D designs that are not very load dependent.

Real world loads can differ from some 'complex' loads and resistive loads. When we we see a FR deviation with different loads one can be pretty certain there will also be differences using real word loads or complex loads.
The shown effect with resistive loads, however, are only indicative something is going on there and might well be different when used with a speaker.
It could be worse, it could be less worse.

The "we need to see how the amp behaves with a real/complex load” in that respect might certainly be true.

Thanks! Not to belabor, but the kinds of claims I’m talking about are ones that have suggested that load-independent Class D amps might be revealed to actually be load-dependent if only they were tested with more realistic, complex loads.

 

[solderdude]

Highly unlikely.
I would like to see proof of that.
Such as an amplifer measurement with a 'difficult' load.
When we are talking about increased distortion in the upper treble range one has to take into account that even H2 is likely to be outside of the audible range.

 

[tmtomh]

Highly unlikely.
I would like to see proof of that.
Such as an amplifer measurement with a 'difficult' load.
When we are talking about increased distortion in the upper treble range one has to take into account that even H2 is likely to be outside of the audible range.

You are preaching to the choir - I’d like to see proof of it too, and none has been forthcoming.

 

[DonH56]

Every amplifier has some degree of load dependence. I assume this is related to Pavel's experiments highlighting various class-D amplifiers under certain load conditions. That is not a debate likely to be resolved here.

 

[DualTriode]

I ain't wasting more time with you

For some reason I want to believe that this stuff is easier to understand.

I can assign grades because I have been teaching piping and control systems for years.

To keep it simple for you, fluid flow does not follow Ohm's Law and there is a inverse relationship between velocity and static pressure.

The quiz question:
Where/how would velocity and static pressure fit into Ohm's Law?

 

[Ken Tajalli]

For some reason I want to believe that this stuff is easier to understand.

I can assign grades because I have been teaching piping and control systems for years.

To keep it simple for you, fluid flow does not follow Ohm's Law and there is a inverse relationship between velocity and static pressure.

of course it doesn't , but as a common sense visualization , the simple drawing is useful.

The quiz question:
Where/how would velocity and static pressure fit into Ohm's Law?

playing your game:
- velocity alone, nothing . electricity has one speed.
- pressure is, potential difference.
- flow rate is current.
Static pressure, is charge.
All of the above are not exact, but loosely similar .

 

[NTK]

The quiz question:
Where/how would velocity and static pressure fit into Ohm's Law?

Okay. Let's see how to solve a pipe flow network problem with "Ohm's law".

Here is a simple pipe flow network. The rectangular boxes are valves. To not complicate matters too much, I'll assume flow restrictions in the rest of the components (pipes and tees) are negligible compared to those of the valves. This does resemble an electrical resistor network, doesn't it?

The P's indicate the pressures (analogous to voltages) at each of the nodes, and Q's are the flow rates across the valves (analogous to electrical currents, only QB is shown). What is left is find the electrical equivalent of the valve flow resistance from the valve coefficients C_v.

Back to the Swagelok valve sizing tech bulletin I linked to in post #22. The expression of the "equivalent resistance" for valve VB is given by R_B. Note that there is nothing in Ohm's law that said resistance has to be a constant and not a function of the upstream and downstream voltages (or pressures). It just makes the problem nonlinear, which is what the vast majority of fluid dynamics problems are.

So, to solve this flow network problem, we'll set it up using mathematical graph (see next post). The typical nonlinear numerical techniques can be used:

1. Make educated guesses of the pressures of each node, calculate the R's
2. Solve it like a linear resistor networks using Ohm's law and find the P's and Q's (analogous to V's and I's)
3. Update the R's with the newly calculated P's
4. Iterate until convergence

See Ohm's law at work?

Notice that Bernoulli didn't shown up to this party. But no worry, DT will show us how.

Now it is your turn, DT. Teach us how to solve this pipe network problem using Bernoulli.

 

[NTK]

If you are unfamiliar with what mathematical graphs are, here is a Professor Gil Strang (MIT OCW 18.085) video to get you started.

 

[dlaloum]

'hard to drive' for amplifiers that are designed for 8ohm speakers and maybe even for some amps that should not be used below 4ohm.
The 'hard to drive' is not really the case though, that is more related to sensitivity (efficiency) but could be a 'challenging' load for some amps.
2.5ohm will draw almost double the current (at the frequencies it dips to that value) as a 4ohm load would.

Some amplifiers may go into current limiting, some simply will not deliver the desired output voltage it can deliver in 4ohm or higher.

If the speaker only dips that low in the mids or treble there is not much of a problem but in the bass, where most energy is, the amp could overheat or clip at high listening levels.
So the audible impact would only be noticeable at higher SPL and only compared to amps that could drive 2ohm at the same level as 4ohm. Not many amps do.

Not true, my 100w integra AVR made my setup sound confused/congested, collapsed the soundstage/imaging, and all at 72db average level at mlp.

Switching to either my quad or crown power amps immediately resolved the problem.

My speakers have 2 dips, one to 3 ohm and the other to 1.6 ohm.

The effect on the 8 ohm rated / designed for, AVR , was quite noticeable.

I do wonder whether amp stability is the problem when going below 2 ohm, and triggering distortion as a result...

The Quad doesn't put out much at 2 ohm, but it is enough ( 90w )

 

[DualTriode]

a pipe flow network problem with "Ohm's law".

Okay your hydraulic network is more complex than you can use Ohm's Law to solve. This is where we started this conversation.

Your proposed network might have some similarity to a city underground water supply . The city does have some good models made with flow measurements over years.

The assumption that line losses are unimportant is completely wrong.

Fire Codes require that buildings so many floors tall or wood frame construction be fire sprinkled. That can be a lot of gallons of water with operating pressures outside the norm with or without a fire pump to fight a fire.

Fire sprinkler systems are hydraulically calculated with software more complex than your matrix with assumed negligible line losses.

The calculation begins with a measurement of supply static and residual pressures at the closest fire hydrants. Static is measured at hydrant #1 with no flow. With hydrant #1 flowing wide open the velocity is measured with a pitot tube and the GPM flow rate is calculated. Then the residual pressure is measured at hydrant #2.

For another thread we will talk medical vacuum pipe sizing. We will turn pressure on its' head. (joke)

I am finished here or someone will throw rocks.

Thanks DT

 

[NTK]

I am finished here or someone will throw rocks.

It is not a surprise that you are so lacking in self awareness that you didn't realize you are the one who came into this thread throwing rocks.

Hello,

I take exception, your analogy of water flow Is incomplete and confusing at best.

Bernoulli is scratching his head trying to make sense of it.

Using your analogy air may even be sucked in between the "valves" that you illustrate.

 

[fpitas]

Yeah, we got derailed from discussing a useful audio topic.

 

[tmtomh]

People love to talk about stuff they know about, regardless of whether or not it’s on topic.

 

[DualTriode]

What is audible, with some inexpensive Class D designs - exp. all TPA3255 amplifiers - there is difference in frequency response in higher frequencies with higher impedances. So it is the impedance at ~10kHz and above that matters.

What is audible about it to your ears? SPL?

Class D amplifiers have all that filtering up high to get rid of the all that switching stuff. Add a higher resistance load and it interacts with the CL filtering and increases relative voltage output. You might be able to hear the added SPL. Then again the added output voltage my compensate for the tweeter reduced output at HF.

Related:

It is interesting that the measurements of Class D amplifiers are made with additional filtering.
To measure Class D amplifiers the APx555 requires additional HF filtering to get stable meaningful numbers. Does that additional filtering remove anything audible?

Acoustic measurements with a quality GRAS microphone with and without the AP AUX-040 filter?

Thanks DT