# Watts P.M.P.O. and audio equipment power

I am a beginner in electrical engineering, and to begin learning I decided to look into audio amplifiers.

I have seen that the power of audio amplifiers is often described in the units of watts, watts RMS, and watts PMPO.
So far, the only one of those units that I think I understand is watts.

For instance, I just recently made my own audio amplifier circuit. If I think: "What is the power of my amplifier supposed to be?", then my thought process goes like this:

The transistors I used are the TIP120, which have a maximum rated power of 65W. Then, I decide that 60W is a safer maximum which would be reached if my amplifier runs 19V through one of my 6Ω speakers.
Therefore, the power of my amplifier is 2x60W.

Then, I look at the datasheets of audio amplifier ICs, like the TPA3116 that says: "50W into a 4Ω load at 21V", which makes me conclude that in that setting it'll output 14V maximum into the speaker, which I think makes sense.
But then, I look at the datasheet of the TDA7294, and they talk about "RMS Power" and "RMS Music Power", units which I couldn't find clear information about.

Then, I look at home audio systems, like a Panasonic Stereo System I have which has "9500 Watts P.M.P.O." written on the front.
9500W? That sounds stupidly high to me, but then I look again and it has 300W written on the back of it.
If I'm correct, maybe a 1kW home stereo system could make sense, but a 2kW or greater one would not exist.

So...
Are my conclusions about my audio amplifier circuit and the TPA3116 correct?
Are my conclusions about audio equipment power correct?
Are WattsPMPO, WattsRMS and RMSmusicpower, real useful units?

• These numbers are pure marketing BS figures. The only valid figure is average power which is the average of the instantaneous power $p(t)=i(t)v(t)$ over a period. It is valid regardless of the shape or phase of the waveforms. If you multiply rms current and rms voltage, you obtain apparent power in VA. What can exist is peak power in the sense that the amplifier is sized to permanently (read thermally safe) deliver 100 W for instance but in presence of large transients, can deliver 150 or 200 W before clipping. If this lasts too long, then a thermal protection may trip. – Verbal Kint Jan 16 at 8:24
• Thank you everyone for all the useful information. I'll be forgetting about all of this "Power" nonsense and start looking into the VA unit. – user271600 Jan 16 at 16:29
• Lemmy would have said "You should be looking for mega-watts mate!" : ) – Verbal Kint Jan 16 at 16:31

Audio has tons of "specifications" which really are marketing bullshit.

To specify the output power of an amp is more subtle than it looks.

• Max output voltage: gives you an idea of the peak output power.

• Max output voltage into 4/8 ohms resistive load: same as above, but it will be a bit lower since it takes into account the output current capability of the output stage into a resistive load.

• "RMS power"

Note "RMS volts" has a meaning, which is Root of Mean of Square of voltage, ie $$\ \sqrt{ \int v^2 dt } \$$.

RMS volts (or amps) have a specific, well defined physical meaning: no matter the signal shape, if you know the RMS value you can calculate power into a resistive load by a simple $$\ V^2/R \$$. So you can run a heater on 230VDC or 230VAC RMS, you'll get exactly the same power. Note the RMS value of a DC voltage is the DC voltage.

But "RMS power" is misleading. It does not mean $$\ \sqrt{ \int p^2 dt } \$$ (with p as power). Calculating the RMS value of power would give a number, but it wouldn't mean anything useful. What "RMS power" usually means in audio jargon is "Average apparent power delivered to load of specified impedance over a specific time without overheating." But there is no agreed upon standard about load impedance, duration of test, etc.

Still, "RMS power" is useful. Say an amp has a peak output power of 100W into 8 ohms resistive load, this means its maximum "RMS" power would be 50W. But if the spec sheet says 25W instead, then you know it will deliver a burst of peak power, but not for very long. Maybe the power supply caps or the transformer or the heat sinks were "cost-optimized", and it can output 50W "RMS" for 100ms but not for a minute.

Because transformers, heat sinks, big caps, and chunky power transistors cost money, and money is expensive, you get "music power" which basically means "hey if you want 100W we will deliver that for 1 second but the power supply will give up soon and if you insist the amp will overheat but we can print a nice number on the brochure".

This is basically marketing bullshit. Take everything that looks like a watt inside the device, add it all up, round up an order of magnitude or two, and you got a number. An intern from marketing will add a zero or two. Basically, any mention of "PMPO" on the box means it contains garbage and the specs are so ridiculous they have to wing it in order to sell it. Engineering-wise, it is about as useful as saying a Tesla can reach Mach 2 if you shoot it into space with a rocket and watch it do atmospheric reentry.

"What is the power of my amplifier supposed to be?"

In a resistive load, that's simple. Maximum current comes at max output voltage, so when you know how much voltage the output transistors drop at max current then you get the peak output voltage and you get output power from that.

With a real loudspeaker, that's a rather complicated question because the impedance curve is wiggly: a "8 ohms" speaker will go from 6 to 16-20 ohms over the frequency range. So for a known output voltage, current and power will depend on speaker impedance and thus on frequency. Besides, these are reactive loads, so current is out of phase with voltage. Resistive loads are easy because as output voltage and current increase, voltage drop over the power transistor decreases. Thus maximum dissipation in the output transistors is easy to calculate, and max current occurs at minimum voltage drop across the transistor.

But when current is out of phase with voltage, output transistor instantaneous dissipation can be much higher. For example if current lags voltage by 90° then a transistor can have the full supply voltage and max output current at the same time, which is much worse. This means Safe Operating Area is an important thing to consider (look at your transistor datasheets).

If I'm correct, maybe a 1kW home stereo system could make sense

No, it does not...

If you want to design an amp, the first thing to do is to stick a 0.1R resistor in series with your speaker, and measure current and voltage with a scope while playing music at your favorite levels. Then calculate average and peak power from the scope measurements. Most likely, if your speakers are reasonably efficient, you'll measure about 1W average and 10-50W peaks. Then you know it isn't necessary to have a kilowatt amp.

Curves on the left show collector current labeled Ic(Q2), voltage Vce(Q2), and instantaneous power Pd(Q2) in the upper power transistor with resistive load and inductive load. I set the inductance to a high enough value to add a substantial phase lag.

Ic(Q2) shows two different current curves with inductive load and without. Note the current peak is lower in this example with the inductor, due to extra impedance.

Pd(Q2) shows instantaneous power, for resistive load Ic peak occurs at minimum Vce but for inductive load it does not, and peak power dissipated in the transistor with inductive load is much higher because it is Ic*Vce and the Ic peak no longer occurs at minimum Vce.

Plotting Ic and Vce on top of the datasheet SOA graph shows we're on the edge of what is allowed:

Pd(Q2)

• Thank you for all the information. You said: "For example if current lags voltage by 90° then a transistor can have the full supply voltage and max output current at the same time"; doesn't that only happen when the current are voltage are in sync? I know I do not want a 1kW amplifier, I'm completely happy with the one I made. What I meant with 1kW making sense is that maybe it actually exists and is being sold. "RMS power" still looks to me like it is too cumbersome and inaccurate to be useful, I think it is only still worth it to look at voltage and current delivery during normal operation. – user271600 Jan 16 at 15:55
• When output current and voltage are in sync (resistive load) then max current and max voltage in the load happen at the same point on the waveform. But Vce of the output transistor is the difference between output voltage and power supply, so max output voltage corresponds to minimum Vce. I've added plots to the answer. – bobflux Jan 16 at 17:10
• Thank you. I understand now. (W = Ic * Vce) is crucial information I had somehow not learned about yet. I can't find clear information about whether or not any typical speaker's inductance ever gets above 1mH. Sadly, I don't have a scope to do any real world testing. – user271600 Jan 17 at 4:57

'Watts RMS' is the maximum continuous 'undistorted' output power delivered to the specified load when playing a sine wave. It is called 'RMS' to distinguish it from non-sine, peak, or instantaneous power. You may think this is the only proper way to specify audio amplifier power output, but it's not - for several reasons:-

1. Music is a complex waveform that rarely consists of a sine wave at maximum volume. The crest factor is typically much higher, requiring higher instantaneous output power to reproduce.

2. Modern amplifiers have low distortion right up to the point of overload, then clip the signal harshly. To avoid this clipping the amp needs 'overhead' to ensure that short peaks do not get clipped. The average power output of music at maximum volume is usually much lower than the possible 'RMS' output with a pure sine wave.

3. Audio Power amps often run off unregulated power supplies. When forced to output a pure sine wave at maximum volume the power supply voltage may sag significantly and have increased ripple, reducing the achievable output power.

4. Continuous output power may be limited by dissipation and resulting temperature rise.

5. Speakers have varying impedances and efficiencies. Ultimately the important thing is how much sound is produced, not the amplifier's electrical power output.

'Music power' and 'PMPO' are attempts to produce a figure that more closely represents the perceived power output when playing music.

'RMS Music power' refers to the sine wave power that can be delivered for a short time before the power supply voltage sags or components overheat. In many designs this is more relevant than continuous power output.

PMPO (Peak Music Power Output) is based on the theory that short peaks in the signal may reach instantaneous power levels many times higher than the typical continuous output. Since the amp and speakers have to handle this peak power without distortion, the theory is that it is a better measure of real-world performance. However this figure has been abused to the point of being meaningless marketing speak. How they calculate it is anybody's guess.

Are my conclusions about my audio amplifier circuit and the TPA3116 correct?

When the TPA3116 datasheet says: "50W into a 4Ω load at 21V" it probably means that is the maximum continuous sinewave power output into a 4 Ω resistive load with the specified voltage and adequate cooling. The peak-to-peak voltage required to do this is 40 V, which it achieves using a 'bridge' output that puts out up to +-21 V across the speaker.

Your design would be able to put +-19 V peak across 6 Ω for 30 W sine wave 'RMS power' - except that your op amps and Darlington transistors have a voltage loss of ~2.7 V per side, so the actual peak speaker voltage is probably only about +-16.3 V and actual power output is ~22 W. That may seem like a huge loss, but it is only 1.35 dB less which is barely noticeable.

• RMS power is also marketing hype/BS. Power is the average of v x i or, power can be Vrms x Irms (cos phi). Power produced is an average value and we should not encourage anyone to believe that RMS watts are meaningful. – Andy aka Jan 16 at 10:13
• I concur with Andy's comment, rms power does not exist per se. If you multiply rms voltage and current, you have apparent power in VA which equals average power for a resistive load (no parasitics). It is well detailed in this Wikipedia page. – Verbal Kint Jan 16 at 10:23
• Yes, I know that 'RMS' power is just average power. Nevertheless that's what it is commonly called in the hi-fi world. – Bruce Abbott Jan 16 at 11:10
• @G36, I did not say anything different: "rms power does not exist per se" otherwise stated, it is wrong to use the term : ) – Verbal Kint Jan 16 at 11:18
• @BruceAbbott Thank you for all the information. I left "how much sound is produced" and the efficiencies of speakers out of the question because I think that always comes separate from the amplifier itself and what it is designed to be capable of handling. Are you sure about your explanation on the TPA3116? I don't think it can deliver a peak-to-peak of 40V, maybe I'm wrong. I know about the transistor loss in my design, I was actually thinking about running the circuit at just slightly below 24V, with the option of 30V being overkill. – user271600 Jan 16 at 16:28