# Measuring average or mean power of a complex radio frequency wave

You will often hear people refer the the 'average power' or 'mean power' of a transmitter producing a complex radio frequency wave, eg SSB, AM etc.

## Average or mean power

Firstly, lets visit the meaning of 'average' or (arithmetic) 'mean'. In the mathematical or statistical sense, the average or mean is one of several measures of the central tendency of a data set. It is calculated as the sum of the values of observations in the data set, divided by the number of observations. So the average or mean of the data set {5,7,6,5,8} is (5+7+6+5+8)/5=6.2.

In the case of average or mean power, it is the average rate of flow of energy over time. It can be calculated as the average of a sufficient number of values of instantaneous power sampled at equal intervals, the more samples over a given time, the more accurate the average or mean power. The choice of the time over which power is averaged is very important to the result.

The ITU defines Mean Power as the average power supplied to the antenna transmission line by a transmitter during an interval of time sufficiently long compared with the lowest frequency encountered in the modulation taken under normal operating conditions.

So for a wave such as continuous A1 Morse Telegraphy, an integration time long enough to capture ten words might be a good basis for average or mean power. For a transmission such as continuous speech on SSB or AM, perhaps many tens of seconds would be necessary, and for half duplex telephony, perhaps several minutes.

## Measuring mean power

What type of instrument could perform this averaging over such a long period?

Well, a classic approach was that of a calorimeter. One type of calorimeter would comprise a load that was placed in an insulated container of known quantity of water. The complex wave was applied for a measured period, and the temperature rise of the stirred water was measured, and the change of energy calculated. Average power is calculated as the total change in energy divided by the integration time.

There are other methods, some enabled by newer tecnologies which allow digital sampling of power and calculation of average or mean power by averaging over a sufficient integration time.

## Does a common directional wattmeter measure mean power?

The common directional wattmeter such as a Bird 43 has a quasi peak response to voltage or current or the square root of power. This quasi peak square root of power drives a moving coil meter, where the average torque and hence deflection is proportional to the average of its coil current. So the outcome is deflection proportional to the average of the quasi peak of the square root of power. This is not average power as can be demonstrated with the following simple test.

• Take an A1 Morse code transmitter and key it with an autmatic Morse keyer making dits with 50% Mark:Space ratio. Observe the indicated power on an inline wattmeter when the dit speed is varied from very slow to very fast. If the meter does not read exactly 50% of the key down constant carrier power at all keying speeds, it is not indicating the average power.

Average power of a complex wave such as voice modulated AM or SSB cannot be measured with a typical inexpensive inline directional power meter.

## Conclusions

Average or mean power of a complex wave can be measured, and the measurement techique must suit the characteristics of the wave.

Whilst measuring Peak Envelope Power of an SSB or AM telephony wave might seem a challenge, measuring mean power is usually much more difficult.