Matching power amps to pre-amps - does anyone know the maths?!

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I would love to understand this better.

There are several explanations and formulas on the internet, but I can't find one that works exactly as I like, is there anyone that can explain it to me, I am sure it would be useful for several of us. Something to do with logarithms / ohms law ?? o_O

What I am after, is something along the lines of...

1 volt input into a power amp which has 29db gain, driving 8 ohm speakers = how much power output (in watts)?

What happens if 1 volt goes up to 1.1 volts, or 1.2 volts etc

What happens if the gain is 26db, or 31db?

What if the speakers are 6 ohms or 4 ohms?

What is the relationship between a power amps input sensitivity and gain?
 
No-one knows?

I have started to try and figure some things out using these two calculators:



So if we take a 1 volt output from the pre-amp, as a starter, and apply it to a power amp with 29db of gain, that power amp will multiply that volt by a factor of 28.183829

The next calculator uses Resistance in ohms (speaker) and the voltage that we got from the previous calculator, plus current of 3.52297862 amps (what is this, is it electric power?) to output power in watts.

If I am correct, then so far we have this:

1 volt into a power amp with a gain of 26db, and speakers of 8 ohms = power output of 49 watts

1 volt into a power amp with a gain of 29db, and speakers of 8 ohms = power output of 99 watts

1 volt into a power amp with a gain of 31db, and speakers of 8 ohms = power output of 157 watts

That sounds like it might be correct.

Let's try the same with 1.2 volts:

1.2 volts into a power amp with a gain of 26db, and speakers of 8 ohms = power output of 71 watts

1.2 volts into a power amp with a gain of 29db, and speakers of 8 ohms = power output of 143 watts

1.2 volts into a power amp with a gain of 31db, and speakers of 8 ohms = power output of 226 watts

Interesting, so where does input sensitivity fit in, and also impedance?
 
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The only usual problems with pre and power matching are usually relating to input impedance which practically is matching valve to sold state, gain is less of an issue unless the input sensitivity is dramatically different than the output - you are just adjusting volume, you can consider noise floors but in reality you are unlikely to have a problem, even clipping wont be an issue unless you are overdriving the power amp and that would be turning up to 11 so to speak !

If you have low impedance speakers, particularly at lower frequency, then the current required will be higher and some amps can't cope with that. A perfect amp should double the wattage as the impedance halves. So when you see 100W into 8 ohms and 180W into 4 Ohm (very few will actually manage to double) this would be a gutsy amp with a lot of drive for difficult loads, some amps will manage to drive speakers that dip into 2 ohms, some do.
 
The other way round is to look at what db levels yo are looking for, particularly peaks, most speakers will have a max db level which will be based on the drivers, cabinet volume, efficient etc, this max will have a wattage and current power level, they will usually tolerate more and be okay with dynamic peaks. Amplifier distortion is more likely to damage speaker than clean power if you follow

I think you are more questioning what power amp you might need rather than pre and power matching ? as this will dictate the dbL produced in combination with the speakers

Both have gain but given most digital sources have similar voltages on their outputs to pre amps often the pre amp will reduce the voltage on the output and just have a role in processing and switching and perhaps D-A
 
Great, thanks for your input.

Yes, speaker impedance, I think I am clear on. Ouput impedance of a pre-amp and input impedance of a power amp, not so clear.

Interesting that you use the term current here:

If you have low impedance speakers, particularly at lower frequency, then the current required will be higher and some amps can't cope with that.

Does that mean electrical power that is flowing through the power amplifier? If so, how is it different to power in watts, or is it the same thing, but just a different way of describing it?
 
I think the terms gain and input sensitivity are basically interchangeable.

I wouldn't worry too much about about input and output impedance. Most line driving stages will have a source impedance of around 600 Ohms or less, while unless you have a quite an esoteric power amplifier, it will have an input impedance of 40K Ohms or more.

To answer your question regarding reducing speaker impedance and power, halving impedance doubles the potential output power - at least in theory. In reality, once you get below a certain value the power will no longer increase - or the increase will be less than the theoretical maximum.

Power in Watts = Volts x Amps.
Current in Amps = Volts divided by Resistance, so as the resistance (Impedance in this case as we are talking AC circuits) reduces, current increases and the power supply rail (Voltage) should remain unchanged.
 
I think the terms gain and input sensitivity are basically interchangeable.

I wouldn't worry too much about about input and output impedance. Most line driving stages will have a source impedance of around 600 Ohms or less, while unless you have a quite an esoteric power amplifier, it will have an input impedance of 40K Ohms or more.

To answer your question regarding reducing speaker impedance and power, halving impedance doubles the potential output power - at least in theory. In reality, once you get below a certain value the power will no longer increase - or the increase will be less than the theoretical maximum.

Power in Watts = Volts x Amps.
Current in Amps = Volts divided by Resistance, so as the resistance (Impedance in this case as we are talking AC circuits) reduces, current increases and the power supply rail (Voltage) should remain unchanged.
Brilliant, thanks, I think I actually understand that :smashin:

So, do my numbers above look in the right ball park, do you think?
 
Speaker impedance has no relevance to pre amp and power amp matching afaik.

Only factors are pre amps max voltage capability, and impedance, with the power amplifier voltage input for full power, and amplifier gain.

Speaker sensitivity also comes to it.

I've never really put much thought into it, I don't think I've bought a power amplifier and thought "hmm will this work with my pre amp and speakers"

But I suppose if I had a pre amp with non standard ultra low pre out level ie 500mv, I'd put some thought into the power amps.

The pres and powers I use shouldn't be a problem together, audiolab and lexicon pre, with audiolab and ATI power amps
 
One way to look at it is the power supply in the amp feeds the power amplifier and the and the power amplifier is driving the speaker, the power quoted in watts is usually at 8 Ohms, as most speakers average 8 ohms across their frequency range, a number will have varying impedence with frequency and sometimes lower impedance at lower frequency which can mean the amplifier needs to provide a lot of current. This is were some amps show weakness, unable to supply the current demanded by a significant low frequency kick for example. They might sound a bit soft and a little flat and less dynamic. Well regarded amps have this in hand and are designed with real life demands of real speakers and real soundtracks in mind

My naim 135’s have huge power supplies for their deminutive 70w per channel, they deliver 135w into 4 Ohms, hence the name and have incredible current delivery capable of driving 2 ohm loads at constant high power. This over engineering allows them to sound incredibly powerful, much more so than a NAD M25 I had and an ArcamP7. Both on paper being more powerful
 
One way to look at it is the power supply in the amp feeds the power amplifier and the and the power amplifier is driving the speaker, the power quoted in watts is usually at 8 Ohms, as most speakers average 8 ohms across their frequency range, a number will have varying impedence with frequency and sometimes lower impedance at lower frequency which can mean the amplifier needs to provide a lot of current. This is were some amps show weakness, unable to supply the current demanded by a significant low frequency kick for example. They might sound a bit soft and a little flat and less dynamic. Well regarded amps have this in hand and are designed with real life demands of real speakers and real soundtracks in mind

My naim 135’s have huge power supplies for their deminutive 70w per channel, they deliver 135w into 4 Ohms, hence the name and have incredible current delivery capable of driving 2 ohm loads at constant high power. This over engineering allows them to sound incredibly powerful, much more so than a NAD M25 I had and an ArcamP7. Both on paper being more powerful
Thanks again. I'm really focussing on trying to understand the science of it in this thread.

Where you refer to current, which I understand is measured in amps, is that the same as power, measured in watts, but just a different description, or are they two different things entirely?
 
Thanks again. I'm really focussing on trying to understand the science of it in this thread.

Where you refer to current, which I understand is measured in amps, is that the same as power, measured in watts, but just a different description, or are they two different things entirely?

Those questions are to do with the amp, speakers and expected SPL/room in question, not pre and power matching.

Typically 100w will provide around 100-105db in usual distances, that's for two speakers.
 
Power is the product of amps and volts.
Watts = volts x amps.
Right, yes, you said that before didn't you. So, voltage in from the pre-amp, multiplied by the gain that the power amp applies equals current in amps. That process creates power to the speakers or load, which is measured in watts. Is that it?
 
Those questions are to do with the amp, speakers and expected SPL/room in question, not pre and power matching.

Typically 100w will provide around 100-105db in usual distances, that's for two speakers.
Yes, I'm happy with that bit, it's the bit before we get the 100 watts to the speakers that I am referring to. Where does that 100 watts come from?
 
Watts Out = (Vin * 2 ^ ( gain db / 6.02 ) ) ^ 2 / ohms
 
I just chose a good round round number where I feel is the "ideal" power required for loud levels, in typical room.ie you can have more power but probably not worth it, and half of that 100w probably a little low for loudest scenes. Of course that's with speakers around 90db, if you use some at very low 85db need a lot more power

 
In the above, if an Arcam AVR550 can only output 1.3v from its pre-outs before clipping going into an Emotiva XPA with 29 dB sensitivity / gain driving 6 ohm speakers, you’ll get a theoretical 223 watts before the Arcam starts to clip, presuming the amp can deliver it without clipping itself and the speakers can accept that amount of power before distorting.
 
Would give hitchhiker guides "disaster area" a run for their money
 

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In the above, if an Arcam AVR550 can only output 1.3v from its pre-outs before clipping going into an Emotiva XPA with 29 dB sensitivity / gain driving 6 ohm speakers, you’ll get a theoretical 223 watts before the Arcam starts to clip, presuming the amp can deliver it without clipping itself and the speakers can accept that amount of power before distorting.
Watts Out = (Vin * 2 ^ ( gain db / 6.02 ) ) ^ 2 / ohms
Yes, I had googled that but it's not very user friendly - I guess you are not doing those sums long hand are you? Are you using an online calculator like the one I linked to above?

That gives me this:

1.2 volts into a power amp with a gain of 29db, and speakers of 8 ohms = power output of 143 watts

1.2 volts into a power amp with a gain of 31db, and speakers of 8 ohms = power output of 226 watts

Do you get the same numbers?
 
Normally the voltage rail will be a fixed value - around 30-50V normally. Although there is voltage gain within the power amplifier, the majority of the power comes from the increase in current.

Think of it this way, a pre-amp may output 2V and have a tiny current driving capability, but the power amp might output 40V and 6A - or about 240W.

As others have said, the voltage gain is of less importance, as the pre-amp will accommodate quite large changes - maybe 500mV (Some of the older Quad equipment) up to 2V or more. This is for the nominal 0DB level, with peaks possibly reaching 15V before clipping.

Matching domestic amplifiers to speakers is very easy in most cases. The difference between 30W and 300W is not actually that much in terms of level and the chances of needing that amount of power from a single speaker in a domestic environment quite low - sub woofers excepted.

Think more about functionality, amplifier design - class A, AB, D etc. These do sound different and you may prefer one over the other.

Unless you are specifying a complex PA system - I spent a while speccing PAs for oil rigs, you do not need to worry about power output and input sensitivity on the whole. Domestic equipment generally works very well together and it really is possible to over think this :)
 
@rccarguy Hi, thanks for the input, we are talking about different things. Your bit deserves a thread of it's own, as in how much power do you need, and what level of SPL will you get in your room with that power and your speakers etc...

I am talking about the bit before the power hits the speakers. So the journey from the voltage being generated and output from the pre-amp, until it hits the speakers as power in watts.
 
No I typed the Calc into a spreadsheet to calc it but yes get the same figures
 
=($A3*2^(B$2/$E$1))^2/$C$1
A3= Volts In
B2= Gain db
E1= 6.02
C1= ohms
 
There’s no easy online calc for this, but there are separate ones for gain dB to volt gain and then from volt out to watts is another
 
@rccarguy Hi, thanks for the input, we are talking about different things. Your bit deserves a thread of it's own, as in how much power do you need, and what level of SPL will you get in your room with that power and your speakers etc...

I am talking about the bit before the power hits the speakers. So the journey from the voltage being generated and output from the pre-amp, until it hits the speakers as power in watts.

It's simply what the pre amp voltage can reach, at low thd, to match the power amp input level.ie most power amps are around 1.6v for full power (29db gain)
 

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