Power and impedance

[dincz]

I've noticed quite a bit of variation in various heads and power amps in terms of how much more power they will deliver when speaker impedance is halved. In an ideal world, an amp with a perfect power supply would deliver twice as much power into a 4 ohm load as into an 8 ohm. The degree to which an amp falls short of this ideal seems to me to be an indication of the shortcomings of its power supply.

Any thoughts?

[warwickhunt]

I couldn't argue with your hypothesis that there may be some link but most amps that I've owned haven't followed the doubling of power for the halving of impedance; it's been closer to, half impedance - power up by approx 50% i.e. 500w @ 8ohms / 750w @ 4ohms. 260w @ 8ohms / 400w @ 4ohms. 170w @ 8ohms / 250w @ 4ohms etc. In fact I can't think of a single amp that I've tried or owned that does the near double.

[dincz]

[quote name='warwickhunt' post='1077733' date='Jan 4 2011, 08:32 PM']In fact I can't think of a single amp that I've tried or owned that does the near double.[/quote]

Agreed and I wouldn't expect to find one. My amp is pretty much the same as yours - halving impedance gives 50% more power. Even a Crown XLS1000 gives only 57% more into 4 ohms than into 8.

[thinman]

Isn't it often to do with the amp's power supply not being able to deliver enough current to deliver double the current when the impedance is halved?

To reach double the quoted 8ohm power at 4 ohms and double again at 2 ohms would mean much beefier, and expensive power supplies.

There's probably other reasons too!

[dincz]

[quote name='thinman' post='1077818' date='Jan 4 2011, 09:25 PM']Isn't it often to do with the amp's power supply not being able to deliver enough current to deliver double the current when the impedance is halved?

To reach double the quoted 8ohm power at 4 ohms and double again at 2 ohms would mean much beefier, and expensive power supplies.

There's probably other reasons too![/quote]

Exactly. That's what I meant about "an ideal world" and "a perfect power supply". So I'm wondering how valid it is to look at the percentage increase as an indicator of how well engineered an amp is. For class A/B, I'd expect weight (big transformer) to be an indicator as well (unless it's a switch mode supply of course).

Edited January 4, 2011 by dincz

[thinman]

[quote name='dincz' post='1077902' date='Jan 4 2011, 09:15 PM']Exactly. That's what I meant about "an ideal world" and "a perfect power supply". So I'm wondering how valid it is to look at the percentage increase as an indicator of how well engineered an amp is. For class A/B, I'd expect weight (big transformer) to be an indicator as well (unless it's a switch mode supply of course).[/quote]


Wouldn't the need for a much larger transformer assume that the power output is measured over a relatively longer period? Short-term peaks can be handled by the resevoir caps.

I'm not sure what the standard is for measuring output in terms of time - I doubt many commonly available amps could sustain their maximum for long!

[flyfisher]

If an amp is rated at, say, 500W into 4 ohms then surely the PSU must be capable of delivering that amount of power otherwise the manufacturer is telling porkies.

I'm not sure about the OP's assumption that an amplifier should be able to deliver twice as much power into a 4 ohm load as into an 8 ohm load. This might be the case if the amp itself had a zero output impedance, but that isn't very likely. In practice, the amplifier [u]will[/u] have an output impedance and this will mean the power into differing loads will not be a linear relationship.

Consider these numbers:

Amp output voltage = 10V in all cases

Amp output impedance = 0 + 8 ohm speaker = 8 ohms = 10/8 = 1.25 Amps = 12.5W = 100% power
Amp output impedance = 0 + 4 ohm speaker = 4 ohms = 10/4 = 2.50 Amps = 25.0W = 200% power

So, for an amp with zero output impedance the output power IS linear with respect to the speaker load.
But, allowing for the amplifier output impedance:

Amp output impedance = 2 + 8 ohm speaker = 10 ohms = 10/10 = 1.0 Amps = 10.0W = 100% power
Amp output impedance = 2 + 4 ohm speaker = 6 ohms = 10/6 = 1.67 Amps = 16.7W = 167% power

Amp output impedance = 4 + 8 ohm speaker = 12 ohms = 10/12 = 0.83 Amps = 8.3W = 100% power
Amp output impedance = 4 + 4 ohm speaker = 8 ohms = 10/8 = 1.25 Amps = 12.5W = 151% power


Thus, any amplifier with a finite output impedance cannot deliver twice the amount of power just because the external load is halved.
None of this has anything to do with the capability of the PSU.

(I think!).

[thinman]

[quote name='flyfisher' post='1077918' date='Jan 4 2011, 09:28 PM']If an amp is rated at, say, 500W into 4 ohms then surely the PSU must be capable of delivering that amount of power otherwise the manufacturer is telling porkies.

I'm not sure about the OP's assumption that an amplifier should be able to deliver twice as much power into a 4 ohm load as into an 8 ohm load. This might be the case if the amp itself had a zero output impedance, but that isn't very likely. In practice, the amplifier [u]will[/u] have an output impedance and this will mean the power into differing loads will not be a linear relationship.

Consider these numbers:

Amp output voltage = 10V in all cases

Amp output impedance = 0 + 8 ohm speaker = 8 ohms = 10/8 = 1.25 Amps = 12.5W = 100% power
Amp output impedance = 0 + 4 ohm speaker = 4 ohms = 10/4 = 2.50 Amps = 25.0W = 200% power

So, for an amp with zero output impedance the output power IS linear with respect to the speaker load.
But, allowing for the amplifier output impedance:

Amp output impedance = 2 + 8 ohm speaker = 10 ohms = 10/10 = 1.0 Amps = 10.0W = 100% power
Amp output impedance = 2 + 4 ohm speaker = 6 ohms = 10/6 = 1.67 Amps = 16.7W = 167% power

Amp output impedance = 4 + 8 ohm speaker = 12 ohms = 10/12 = 0.83 Amps = 8.3W = 100% power
Amp output impedance = 4 + 4 ohm speaker = 8 ohms = 10/8 = 1.25 Amps = 12.5W = 151% power


Thus, any amplifier with a finite output impedance cannot deliver twice the amount of power just because the external load is halved.
None of this has anything to do with the capability of the PSU.

(I think!).[/quote]


Actually, my maximum power transfer theory is seeping back - that does seem correct.

[thinman]

[quote name='thinman' post='1077936' date='Jan 4 2011, 09:38 PM']Actually, my maximum power transfer theory is seeping back - that does seem correct.[/quote]

Having had a quick scan round typical output impedances tend to be a lot lower than 2 ohms - less than 0.5 ohm seems common. So the amp's impedance does account for some of the degradation but I suspect a bit of corner cutting on the PSU front accounts for some degradation depending on how the measurements are taken.

[flyfisher]

[quote name='thinman' post='1077936' date='Jan 4 2011, 09:38 PM']Actually, my maximum power transfer theory is seeping back - that does seem correct.[/quote]
That was my first thought, but I seem to recall that only really applies in transmission line systems, i.e. typically in far higher frequency applications than audio.

I had a quick look for output impedance specs but I couldn't find anything (=didn't try hard enough ). I've read conflicting stuff about amplifier output impedances though. One school of thought seems to go for very low figures because it is supposed to give better 'damping' of the speaker, resulting in a 'tighter' sound, especially at bass frequencies. Another school of thought seems to suggest that speaker damping is best achieved by getting the enclosure right in the first place! (that's getting outside my comfort zone though).

It would be interesting to see the output impedance specs for a range of amps and then compare the figures with the rated outputs at 4 and 8 ohms.

I'm not denying the PSU theory, BTW, and it's certainly possible for power output to be limited by a poorly rated PSU but, to my mind, such a thing would be the result of bad design or an over-optimistic (to be kind!) marketing department, both of which are pretty heinous crimes in my book.

Edited January 4, 2011 by flyfisher

[TimR]

Amplifiers are current devices, not voltage devices.

The power is limited by the current it supplies.

If the voltage rail maximum is 50v then into 8ohms you get 312watts which is 6amps give or take.
With the voltage rail still at 50v then theoretically into 4ohms you'll get 625watts but if the amp is limited to 11amps then you can only get 484watts.

It's not the transformer it's just the way that the transistors or valves work.

[TimR]

Its not a case of not being able to get double the power out of 4ohms, more a case of being able to get more than half out of 8ohms.

[flyfisher]

[quote name='TimR' post='1078010' date='Jan 4 2011, 10:24 PM']Amplifiers are current devices, not voltage devices.

The power is limited by the current it supplies.

If the voltage rail maximum is 50v then into 8ohms you get 312watts which is 6amps give or take.
With the voltage rail still at 50v then theoretically into 4ohms you'll get 625watts but if the amp is limited to 11amps then you can only get 484watts.

It's not the transformer it's just the way that the transistors or valves work.[/quote]

Fair point about the power being limited by the current the amp can supply, but surely that's a practical limitation determined by the designer? It's not a theoretical limitation is it?

Your example is fine, but why the arbitrary limit of 11 amps? If the amp could supply 12.5A (or more) then it would deliver 625W.

Perhaps it's just an economics thing?

Incidentally, are you saying the amp output impedance itself can be entirely discounted ?

[Bill Fitzmaurice]

[quote name='dincz' post='1077700' date='Jan 4 2011, 02:16 PM']The degree to which an amp falls short of this ideal seems to me to be an indication of the shortcomings of its power supply.

Any thoughts?[/quote]
It's not a shortcoming, merely the reality of how amps work. At low signal levels current does double into a halved impedance load, so power doubles as well. But at full power the actual current delivery increase, and therefore power increase, averages only 70%. That translates into an actual full power level increase of only 2dB. That small figure, combined with the fact that few speakers can actually make use of more than half their rated power before reaching their mechanical limits, makes the oft seen "I want a 4 ohm speaker to get all the watts out of my amp" a generally fruitless quest.

[dincz]

[quote name='Bill Fitzmaurice' post='1078727' date='Jan 5 2011, 05:09 PM']It's not a shortcoming, merely the reality of how amps work. At low signal levels current does double into a halved impedance load, so power doubles as well. But at full power the actual current delivery increase, and therefore power increase, averages only 70%. That translates into an actual full power level increase of only 2dB. That small figure, combined with the fact that few speakers can actually make use of more than half their rated power before reaching their mechanical limits, makes the oft seen "I want a 4 ohm speaker to get all the watts out of my amp" a generally fruitless quest.[/quote]

"Shortcoming" was probably the wrong word. Ideal worlds and zero-impedance power supplies don't and can't exist, and I'd say that a manufacturer who achieves a 70% increase in maximum power with a halving of load impedance is doing a brilliant job. Most don't reach 70%.

Regarding the impedance of the output stage - it certainly has an effect but is typically only tenths of an ohm. Sagging power rails are the major culprits.

Edited January 5, 2011 by dincz

[flyfisher]

[quote name='dincz' post='1079082' date='Jan 5 2011, 07:58 PM']Regarding the impedance of the output stage - it certainly has an effect but is typically only tenths of an ohm.[/quote]
Is a low output impedance also possible with a valve amp? I understand they use transformers to match the high-impedance valve outputs to low-impedance speakers, but am not sure how low they can get with this approach.

[thinman]

[quote name='flyfisher' post='1079415' date='Jan 6 2011, 01:45 AM']Is a low output impedance also possible with a valve amp? I understand they use transformers to match the high-impedance valve outputs to low-impedance speakers, but am not sure how low they can get with this approach.[/quote]

Not sure it makes much difference. We seemed to think that the fact the output at one speaker impedance is not double that at half that speaker impedance due to a combination of power supply inadequacy and the ratio of speaker impedance to amp output impedance.

Just because there's a transformer between the output stage and speaker doesn't really change that - the power supply still has to supply the same amount of power and the impedance ratio between the output stage and transformer will also change.

Or maybe that's b*ll*cks.

[flyfisher]

Hmm. Not sure. PSU inadequacy seems, to me, to be an economic issue rather than a purely technical issue, i.e. the limitation [u]could[/u] be eliminated by design.

But if the amplifier output impedance wasn't very, very low (relative to the speaker impedance) then the power output across 4 ohms could never be double that at 8 ohms - as per my earlier example calcs. I think.

If that's correct, then the valve amp question will depend on the output impedance achievable when using an output transformer. If it can be very, very low, then I agree with you that there should be little, if any, difference between a valve or a solid state amp - but I'm not at all sure about the current state of the art with impedance matching transformers at audio frequencies.

Digital and video electronics is more my area of direct experience, so the nitty-gritty of audio amplifier design is getting a bit out of my comfort zone. An interesting discussion though.

[Bill Fitzmaurice]

[quote name='flyfisher' post='1081561' date='Jan 7 2011, 04:57 PM']Hmm. Not sure. PSU inadequacy seems, to me, to be an economic issue rather than a purely technical issue, i.e. the limitation [u]could[/u] be eliminated by design.[/quote]I believe that it's not the PSU, it's the output devices. Somewhere in my files I've got the reason why amps can't double their full power output when the load impedance is halved. Of course I can't find it when I need it. If it could be done you'd see it done, and it isn't.

[TimR]

It's not the power supply. It's the characteristic of the device that is amplifying the current. The power supply just supplies the current and voltage to that device. The current still has to pass through it.

If you want a more powerful amplifier then you just get a bigger device, but that means more cost. Hence more power = more cost.

You're still looking at it from the wrong angle. The maximum power is determined by the maximum current through that device. The 8ohm power is then a function of the full power at 4ohms. It's not that you can't get double through 4ohms it's that you get more than half at 8ohms. As Bill intimated earlier. The power output is not linear. This is why you get power compression at the top end of the amplifiers range.

[Mr. Foxen]

I think heat sinking is factor too. Running more power means it all warms up and the transistors don't work as well hot, I'd guess their internal impedance increases. And beeinf up heat sinks is a big weight gain (see Peavey amps that run to 2ohm).l

[TimR]

[quote name='Mr. Foxen' post='1081654' date='Jan 7 2011, 11:38 PM']I think heat sinking is factor too. Running more power means it all warms up and the transistors don't work as well hot, I'd guess their internal impedance increases. And beeinf up heat sinks is a big weight gain (see Peavey amps that run to 2ohm).l[/quote]

The opposite. Silicon has a negative temperature co-efficient of resistance once it gets over a certain temp it will go into thermal runaway. Hotter it gets the more current it passes, the more current it passes the hotter it gets - queue blue smoke.

There are lots of ways to try to stop this such as by piggybacking transistors so that as they get hot one drains the current away from the other. This again impacts on the current the amplifier can drive.

Edited January 8, 2011 by TimR

[flyfisher]

I don't think heat sinks are a factor because you can't get more power out of an amplifier just by increasing the size of the heat sink. Additional power could only come from a slightly different design, which would cause more heat to be generated, which would then require more heatsink capacity. If the heatsink is too small for the design then the amp would overheat and break (or more likely go into thermal shutdown). Sure, there are sometimes good reasons for having a small heatsink, in which case the design has to be amended accordingly, but the heatsink itself plays no part in the circuit design itself.

[b]TimR[/b] is correct to remind us:

[i]You're still looking at it from the wrong angle. The maximum power is determined by the maximum current through that device. The 8ohm power is then a function of the full power at 4ohms. It's not that you can't get double through 4ohms it's that you get more than half at 8ohms.[/i]

Of course we can get full power from an amp by using a 4 ohm speaker (if that's the rating), because that, by definition, [u]is[/u]the full power output.

The issue is why we get more than 50% power output when the load is doubled, i.e. why isn't the output halved when the load is doubled?

It still makes sense to me that the output impedance of the amplifier is involved somehow.

Thus, although we connect an external 4 ohm load, the amplifier output impedance means that the output device is actually driving a bit more than 4 ohms when it is providing maximum power.

So, when we double the external 4 ohm load to 8 ohms, we are not exactly doubling the overall load seen by the amplifier. In fact we're adding a bit less than double the overall load, so we obtain a bit more than half the maximum power.

[TimR]

I don't know what the manufacturers use as a 4ohm load. If its a speaker then at a sine wave of 1khz a 4ohm speak is NOT 4ohms. Neither is an 8ohm speaker 8ohms. It'll be different for all speakers. We're also talking about a reactive load so there will be phase differences and all sorts going on. DC theory will only get you so far.

You just have to content yourselves with the knowledge that transistors are NOT linear devices. Look at some current curves. You can-nae break the laws of physics.

[flyfisher]

Fair point about DC theory not being strictly applicable, though it's one way of 'visualising' what's going on - to a very rough approximation anyway.

Given, as you rightly say, all the variability involved with music waveforms and speaker behaviours, it's a wonder we bother worrying as much as we seemingly do with precise 'matching' of speakers and amps.

But I guess describing a speaker as '4 ohms' or '8 ohms' also helps people 'visualise' things - to a very rough approximation.