Articles : Measuring Power


“Naw man, it’s louder because they’re tube watts!” This article discusses some common misconceptions about amplifier power ratings, explains the differences between peak and RMS, and provides the method Noble uses to measure amplifier output power.


History

Power is measured in watts, named after James Watt, a Scottish inventor and engineer who made fundamental improvements to the design of the steam engine, which in many ways opened the doors for the Industrial Revolution. Watt also developed the units of horsepower.

One watt is equal to one joule of energy per second. In electrical terms one watt is one volt times one amp (1W = 1V * 1A; volts and amps are also units named after famous people, the scientists Volta and Ampère).


Volume vs Wattage

Regarding amplifiers, it is commonly assumed that higher wattage amplifiers will be louder. This is generally true (given identical speakers), but not to the extent most people think. Because the ear is logarithmic, doubling the power does not double the perceived volume. Rather, doubling the volume requires ten times more power! The difference between 20W and 30W is slight; the difference between 20W and 200W is noticeable. In comparing two different amplifiers, the lower wattage amp will break up and distort first, where the higher power amp will remain cleaner at higher volumes.

In 1974 the FTC instituted a ruling requiring audio power and distortion ratings for home audio equipment to be measured in a defined manner with power stated in RMS terms. Currently there is not a similar ruling specifying how power should be reported for musical instrument amplifiers. There are differences between solid state and tube amplifiers as well - solid state amps distort rapidly and harshly when pushed beyond their clean power limit, and so are rarely used near this limit, whereas tube amplifiers distort much more smoothly and gradually, and are frequently pushed beyond their clean power limit for power amp break up.

Nevertheless, we at Noble feel that instrument amplifiers should follow the hi-fi market and report clean amplifier power in RMS terms. However many amplifier makers do not report clean RMS power, so be aware that the stated power output of a tube amplifier is somewhat objective and usually can’t be directly compared between different manufacturers. It is also a poor indicator of how a given amplifier will sound or perform in actual use. Usually the efficiency of the speaker has more of an effect on the “loudness” of an amp (see Choosing Speakers on the Articles page).


RMS vs Peak

RMS stands for Root Mean Square - the square root of the average of the squares of a set of numbers. Also known as the "quadratic mean", RMS is a statistical measure of the magnitude of a varying quantity. Don’t worry, there’s really not a lot of math required to use the term correctly, just think of it as an average. RMS is the proper way to average the type of signals musical amplifiers process.

This waveform shows RMS and Peak values for a sine wave: RMS is less than Peak, because it is an average. It is easy to convert back and forth between the RMS and Peak values. For a sine wave the conversion factor is 1.414 (the square root of 2). To convert from Peak to RMS, divide by 1.414; to go from RMS to Peak, multiply by 1.414.

For example, 50W Peak = 35W RMS. (50/1.414 = 35)


Measuring Output Power

To remove the effects of the speaker, amplifier manufacturers use a pure resistive load attached to the output of the amplifier when measuring power. Unlike this resistive load, the impedance of a speaker varies with frequency. Speakers are referred to by their “nominal” impedance, usually 4, 8, or 16 ohms for guitar amp speakers. Amp makers must also select a single frequency to measure power at, since the response of the amp varies with frequency. The generally accepted frequency to measure the power of a guitar amplifier is 1kHz, a round number and roughly in the middle of the amplifier’s response (100Hz to 10kHz - 1kHz is in the middle logarithmically).

Here is the procedure Noble uses to measure the output power of the amplifiers we build and service:

  1. Connect an 8Ω resistive load to the output of the amplifier (Ω is the symbol for ohms)
  2. Apply 1kHz test tone to the input of the power amp
  3. Adjust the input voltage so the power amp is just prior to break up
  4. Measure the output voltage across the resistive load with an RMS meter
  5. Compute the RMS power by squaring the measured voltage and dividing by 8Ω