# Peak Envelope Power (PEP) Calculator (with Examples)

The Peak Envelope Power of a signal is measured in a resistive load, and the formula for it is

PEP = (Vpeak2/2)* (1/R)

or

PEP = VRMS2/R

In the calculator below, enter

• Peak voltage or the RMS voltage
• Resistance

The tool will calculate the Peak Envelope Power

## Background

### What is a signal envelope?

In electrical engineering the envelope of a time varying signal is the smooth curve that tracks its extremes. It is shown below for a sine wave. There are two envelopes – the upper and lower. Upper tracks the maximum values while lower tracks the minimum values.

Peak envelope power of an RF modulated waveform is the largest value of the power measurement during a single cycle or time interval.

As shown in the picture above the PEP is power at the crest (or peak) of modulation.

PEP is an important number for radio amateurs as it represents restrictions on transmit power levels in various frequency bands.

### Peak Envelope Power for Sine Waves

PEP (as the name suggests) utilizes the peak voltage in the formula

PEP = (Vpeak2/2)* (1/R)

VRMS = Vpp/(2âˆš2)

and this is the basis for the formula

PEP = VRMS2/R

### What is PEP for Non Sinusoidal Signals?

The ITU defines PEP as

The average power supplied to the antenna transmission line by a transmitter during one radio frequency cycle at the crest of the modulation envelope taken under normal operating conditions.

Note that there is no mention of a sine wave in the definition.

One method to practically calculate PEP is with the use of a digital oscilloscope such as the one below that is able to capture and display a recorded signal. The signal could be non-continuous, pulse or burst type signal.

It’s important to ensure that the circuit that is being measured doesn’t have an output level that exceeds the input range of the oscilloscope. Use the dBm to Volt calculator to ensure that it does not.

Why is PEP an important number?

The peak envelope power is a measure of the signal strength. In order that wireless signals do not interfere with one another, regulatory bodies place limits on signals by way of their PEP specification. The PEP is generally higher than average power and a more meaningful measure of the max transmitted power.

As well, Crest Factor or Peak to Average Power Ratio defined as the ratio of PEP to Average power as:

CF = PEP/Pavg

is used in conjunction with the Error Vector Magnitude (EVM) to compute the required Signal-to-Noise ratio for different waveforms.

### Example Calculation

For Vpeak = 100 volt into a 50 ohm load, the RMS voltage is Vrms = 70.7 volt. The resulting Peak envelope power is 100 Watt.

## Demonstration

In the video below, Tom demonstrates the concept of PEP in his microwave lab.

A digital storage scope has many advantages over older analog oscilloscopes and making measurements like the one above is one.