# Formula to calculate output power

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#### martinbls

Hi everybody!

I have a small solid state power amp, handmade about 25 years ago (not by myself), and I don't know any of the specifications for this amp. However, it delivers a lovely sound and I'm thinking about upgrading the toroid transformer to a larger one. Currently there is a 50VA transformer with 2x15Vac secondaries, delivering (measured) +-21,5Vdc for both channels.

Is there a simple formula to calculate the maximum constant output power at 4 and 8 ohms, only by the given power supply voltage?

Thank you!
Martin

Yes.

#### martinbls

;-)
Thanks Andrew, very enlightening!

By the way, here are a few pics.

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#### AndrewT

Joke over.
Yes, the PSU supply determines in part the maximum output voltage from the amplifier.
One must subtract the PSU voltage sag when trying to deliver a short term or longer term output current.
Then one must subtract the voltage lost through the amplifier and any resistances before you reach the output terminals.

For a +-21.5Vdc supply expect ~43/3V into high impedance loads, i.e. low current transients
For lower impedance loads requiring maximum current capability of the PSU and amplifier expect Vpk ~ Vpsu-5V. i.e. ~16Vpk into 8ohm and maybe ~14Vinto 4ohm.

Maximum average output power is given by applying the Formulae:

P = I^2 * R
P = V^2 / R
P = V * I
strictly these only apply to DC operation.

For AC one must add in ac for both Voltage and current. i.e Vac or Vrms and Iac or Irms must be used for AC calculation.
One can also use the peak voltage and peak current (obtained from an oscilloscope as an example) by modifying the formulae slightly.

P = Ipk^2 * R / 2
P = Vpk^2 /R / 2
P = Vpk * Ipk / 2

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#### Nico Ras

I see 2A written on the transformer so probably 60VA. If it uses transistors in the output stage I would say that the output would be around 24 watts sine wave into an 8 ohm load per channel. To audibly detect a reasonable difference you will need to double the power, is it worth the effort?

#### east electronics

alps blue line ...relay selector neat and nice construction dontr know who made it and when ...but trust me the man knew exactly what he was doing ...

hei Nico good to see you !!! i hope you are doing just fine

#### martinbls

Hey Andrew, thanks a lot!!

Hi Nico,

well, I always thought a 50VA transformer for a stereo amp might be a little bit on thin ice when it comes to short peaks in current delivery from the ps. The "2A" you read on the transformer is just the suggested secondary fuse. It is a Monacor International RKTM 5015, so it's definitely a 50VA type.

I heaven't calculated the output power by Andrews formula yet, but if you are even close with your estimation of around 24W sine wave per channel at 8 ohms, then a 50VA tranformer is DEFINITELY too small, given the average effeciency of around 60% for transistors!

Regards!
Martin

#### AndrewT

I would estimate 16W into 8r0 and 25W into 4r0.
Since this is a 2channel amplifier, then when 8ohm speakers are used the total output power is ~32W. A transformer rated from 32VA to 64VA will work properly. A transformer outside that range will still allow the amplifier to work.

If you use 4ohm speakers then expect a 50VA to 100VA to work properly and again a transformer outside this range will allow the amplifier to work.

I see nothing wrong with 50VA for a 25+25W domestic use amplifier.

You would have to check the temperature de-rated SOAR for the load impedance of your speakers for that single pair output stage, before considering modifying your amplifier.
It maybe that the designer uses the low VA of the transformer and the low smoothing capacitance to let the output and driver devices survive abuse without needing to use current limiting nor fuses in the secondary side.

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#### martinbls

Hi Andrew,

again: Thanks a lot! I did a few calculations and a bit of research and my estimate of about 17W into 8r0 and 27W into 4r0 comes close to your values.

Some time ago I had the opportunity to talk to the constructor and the reson why the transformer is that small is mainly because he wanted to put all the goods of this small stereo amp with integrated passive pre and source selection into this enclosure of just 44mm hight (37,5mm inside).

I was planning to rebuild the amp as a power amp without the volume pot and the source selection, because I want to build a remote controlled passive pre. This is why I thought about using a larger enclosure (same type, but 88mm hight) and use the empty space for a larger transformer of 120VA, just to add some more headroom for peak power. Smoothing capacitance is now 2x4700uF and could be increased to 2x10.000uF (I already have some of these lying around, brand new ones.)

Regards!
Martin

#### AndrewT

CHECK the SOAR before considering modifications!

#### nigelwright7557

Hey Andrew, thanks a lot!!
given the average effeciency of around 60% for transistors!

Regards!
Martin

In a class AB amp 40% is lost in heat in the heatsink.

Unless it is class D when you can usually get better than 80-90% efficiency.

#### martinbls

Yes, that's the point! So I thought, ok, 2x15W at 8r0 is 30W continuous output power in total, so, with a 50VA transformer I would have exactly the 20VA headroom for this losses. At 4r0 and 25W per channel the 50VA is equal to the total output power and so there is no headroom for heat losses. That's why I thought to get a bigger transformer for the baby!
But then, I know that many diy'er say the transformer rating can be the same as the maximum output power without stressing the transformer. So I guess 50VA just might be enough...

Thanks!
Martin

#### AKSA

Martin,

A simple formula.

You measure the peak to peak undistorted (that is, unclipped) output on a CRO at 1KHz.

With 21V rails, you'd probably get within about 3V of each rail, gving you 18 x 2 = 36Vpp.

Square this voltage and divide by 64 for 8R loads, 32 for 4R loads.

In this instance we have 36exp2/64 = 20.25 watts.

Agree with Nico and Sakis, beautifully made amp, really very professional.

Hugh

#### martinbls

Hello Hugh!

Thanks a lot for this simple formula! I also calculated to something in that range first, but 2x20W in 8r0 and 2x40W into 4r0 seemed just to be a bit too much, so I substracted a few watts to get a perhaps more realistic result.
But if you're right with your calculations, then this 50VA transformer is indeed way too small for undistorted maximum power output into 4r0 load.

One more thing: Andrew, in your third post you wrote: "It maybe that the designer uses the low VA of the transformer and the low smoothing capacitance to let the output and driver devices survive abuse without needing to use current limiting nor fuses in the secondary side."
That's a very good point! But then there are fuses on the pcb, 4 of them, for each rail. I checked their values and these are T2A-types (time delay).

Well, this is getting quite difficult. Of course I do really like this small enclosure, and I can tell you something: With my Reference 3a speakers (2-way, crossoverless 8" Midbass, 90dB sensitivity) in my quite small listening room, this tiny thing really rocks! It's unbelievable when I open my eyes after listening to some really hard and fast rock music and see this little thing...

#### east electronics

this is comon practice for many comercial products ....NAD comes in mind ( had to replace a load of trafos )

transformer is marginal and that will mean that the outpout of your amp doesnt have enough power to create damage ... but that also mean that the amp[lifier will play good enough for the 50-60% of the rated power ....

In your case i think that the constructor had in mind a performer !!! a sweet litle thing that will produce noisless quality while power was a secondary target ...

beyond fine tuning ...few checks with capacitors ( if still are ok ) may some small upgarde ( nothing more than a few relativelly exotic caps ) i would do nothing more with this machine ....keep it as is

#### AndrewT

........... in my quite small listening room, this tiny thing really rocks! It's unbelievable when I open my eyes after listening to some really hard and fast rock music and see this little thing...
build a new amp and leave your little amp as is.
When your new amps can better the little fellow then is the time to retire it or move it to the snug or bedroom or kitchen.

Whatever, don't modify it until you have something comparable to let you hear what you have achieved.

#### martinbls

build a new amp and leave your little amp as is.
When your new amps can better the little fellow then is the time to retire it or move it to the snug or bedroom or kitchen.

Whatever, don't modify it until you have something comparable to let you hear what you have achieved.

Hi Andrew,

well, trust me, I did! But after serveral amps I build it's still hard to achieve this special kind of character this small thing has. It's sound is fluid, musical, detailed, very airy and fast! And the lower frequency response is more powerful and prominent that with most of the much larger amps I build!

By the way, many years ago the man who build this amp sent me over a circuit diagram of another amp, basically the same design, but for a slightly higher rail voltage. I think there are many similarities with the small one, except the small amp has BD239 and BD240 as output devices. But I am not that deep into amplifier topology, so perhaps one of you can share a few thoughts about this diagram:

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#### AndrewT

BD as output stage.
You really must check the SOAR before mods.

#### macboy

Hello Hugh!

Thanks a lot for this simple formula! I also calculated to something in that range first, but 2x20W in 8r0 and 2x40W into 4r0 seemed just to be a bit too much, so I substracted a few watts to get a perhaps more realistic result.
But if you're right with your calculations, then this 50VA transformer is indeed way too small for undistorted maximum power output into 4r0 load.
No it is probably just fine. Keep in mind that music has a very high crest factor (if you want to call it that). This means that the peaks are very high compared to the average or RMS value. So when the amp is amplifying music (not a one-tone sine wave from your signal generator), it may have only 2 or 3 W of average output power even when driven hard enough to clip or be close to clipping on peaks of the signal. With highly compressed pop music, you can expect the average level to be higher, but for real music I usually estimate average power at about 1/10 peak power. Efficiency of the amp is poor at low output power, but it will still consume much less than the 50 VA that the transformer can supply... even when driven near clipping, with music.

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