# What is RF Peak Envelope Power (PEP)

## Definition of Power

Power is the rate of doing work or the rate of flow of energy.

## Power in a DC circuit

In a DC circuit, power is given by Joules first law and Ohms law as V*I.

## Power in an AC circuit

In an AC circuit with steady sinusoidal excitation, voltage and current vary with time and the instantaneous power (p(t)=v(t)*i(t)) varies with time. The power in an AC circuit is usually taken as the power averaged over a whole AC cycle.

The figure above shows v(theta) and i(theta) in an AC circuit (theta=ω*t or theta=2*π*f*t). Also plotted is the instantaneous power p(theta) and the power averaged over a whole cycle, Pav.

The notation is that V is the amplitude of the wave, and v(theta) is the instantaneous voltage as a function of theta.

In the simple case where the load is purely resistive, the current is in-phase with the voltage, and it can be shown that Pav=V2/2/R or I2/2*R.

In fact, in this case, the average power is the average (or mean) of the sum of v(theta)2/R for all values of theta over one cycle, which can be expressed as the the mean of the squares of v(theta), divided by R. An equivalent DC voltage which would develop the power in R would therefore be the square root of the the mean of the squares of v(theta), and it is known as the RMS voltage. Power would be VRMS2/R, and for a sine wave, it can be seen that VRMS=0.707*V.

## Peak Envelope Power

An RF waveform under any form of amplitude modulation is not a steady sine wave, and a common measure is of the power at the crest of modulation.

The ITU Radio Regulations define the terms Peak Envelope Power as:

Peak Envelope Power ‘pX’ (s1.157) means the average power supplied to the antenna transmission line by a transmitter during one radiofrequency cycle at the crest of the modulation envelope taken under normal operating conditions.

This is not very different to the method of determining average power in an AC circuit, except that for the purpose of determining Peak Envelope Power, the power is averaged over a cycle at the crest of the modulation envelope.

Peak Envelope Power is usually measured in a resistive load, and in that case it is simply given by PEP=V2/2/R (where V is the peak RF voltage) or PEP=VRMS2/R.

The challenge in measurement of PEP of waves like SSB telephony is to design an instrument that captures the very short crests of modulation and holds the sample for display. For more information, see Peak amplifier for an RF wattmeter.

## An example

Above is a CRO display of an AM transmitter modulated by a single sine wave and connected to a 50 ohm dummy load with a 50 ohm transmission line.

• I have an oscilloscope connected to a -40dB sampling port on the dummy load.
• The oscilloscope has a 10:1 probe and the Y input sensitivity is set to 20mV/cm.
• The crest of the modulated envelope measures 8cm peak to peak, the valley measures 2cm peak to peak (don’t read from the graticule in the picture, use the values stated in this text).

What is the PEP (ITU pX)?

For the answer, see RF Power Terms.