AM Sine Wave

Peak Envelope Power

The FCC defines Peak Envelope Power for radio amateurs as, "The average power supplied to the antenna transmission line by a transmitter during one RF cycle at the crest of the modulation envelope taken under normal operating conditions." [47CFR97.3(b)(9)]

The International Telecommunications Union defines it in the same way. [RR1.157]

That definition is confusing, at best. Hopefully, this page will clarify its meaning.

RF signals such as AM and SSB have a constantly changing amplitude during transmission, like the image at the top of the page. For these signals, there will be points where the amplitude is at its greatest (see Figure 1). This is the "one RF cycle at the crest of the modulation envelope" in the definition. Other signals, such as FM, PM (phase modulation) and CW, have a constant amplitude, so every RF cycle is its "peak" cycle.

Peak Envelope Voltage

Figure 1. Peak Envelope Voltage

Once that cycle is identified, we calculate the average power over its complete duration. That's the red area in Figure 2.

Note that we calculate the power in both the positive voltage half-cycle and the negative voltage half-cycle. They don't cancel out because, as shown below, the PEV is squared, making both of them positive.

Peak Envelope Power Sine Wave

Figure 2. Peak Envelope Power Sine Wave

Start by measuring the amplitude of the peak, usually in volts. That is PEV in Figure 1.

Then apply the following formula:

Peak Envelope Power Formula

* PEP is Peak Envelope Power, in watts
* PEV is Peak Envelope Voltage, in volts
* R is resistance, in ohms

In most amateur radio systems, R is approximately 50 ohms.

The part of the formula in the parentheses (PEV x 0.707) converts the PEV to voltsRMS.

This reduces the formula to the familiar Ohms Law for power:

Ohms Law - Power

An example:

If the PEV = 100 volts with a 50 ohm load, then:

Peak Envelope Power Formula Example

(Image sources: ARRL and