# ADISimRF - Crest Factor Calculation

Hello,

I would like to know why the crest factor calculation fir a sine wave is to  be set to 0...

The crest factor that I calculate is about 3dB... XL

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• This is a tricky issue. A few years ago I did some peak-to-peak voltage measurements on a modulated carrier and got what I thought were surprising results. For simplicity, lets say the carrier was 0 dBm rms (or 0.2236 Vrms). The Rohde & Schwarz Signal generator display said that the "Peak Envelop Power" was 12 dBm (it was a Wideband CDMA carrier but that is not important here). I assumed that the peak voltage level would be 0.8944 Vpeak (i.e. the 12 dB delta corresponds to a voltage ratio of 4x between Vrms and Vpeak). However, the voltage level I observed was 3 dB higher at 1.26 Vpeak (I did these measurements on an oscilloscope and a spectrum analyzer; I set the carrier frequency to 100 MHz so that I could easily observe the carrier in the time domain without needing a fancy RF sampling oscilloscope; I used a peak-hold function in the scope to capture the peaks).

So why is the peak voltage 3 dB higher than expected.  Here is how I have rationalized this observation. If the carrier has a "Peak Envelop Power" of 12 dBm, this means that the carrier occasionally achieves a power level of 12 dBm. If we imagine that the carrier becomes a 12 dB CW for a short period of time (say 10 cycles), then the peak voltage during that time would be 1.265Vpeak.

If you apply this logic to an un-modulated Sinewave, you conclude that its RMS power level is equal to its Peak Envelope Power level because the envelope is not changing.  So the PEP-to-RMS ratio is 0 dB.

So when we were defining all of this in ADIsimRF, it presented a dilemma because everyone thinks of a Sine Wave having a crest factor or peak-to-average ratio of 1.4142x or 3dB.  The best we could do was to talk about and focus on Peak Envelope Power and PEP-to-RMS ratio. This ensures that the tool correctly calculates the peak voltage levels of modulated carriers. It's still a bit confusing that is the best we can do.