Crest factor

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The crest factor or peak-to-average ratio (PAR) or peak-to-average power ratio (PAPR) is a measurement of a waveform equal to the peak amplitude of a waveform divided by the RMS (time-averaged) value of the waveform.

C = {|x|_\mathrm{peak} \over x_\mathrm{rms}}

It is therefore a dimensionless quantity. While this quotient is most simply expressed by a positive rational number, as shown below, in commercial products it is also commonly stated as the ratio of two whole numbers, e.g., 2:1.

Contents

[edit] Examples

DC voltages have a crest factor of 1 since the RMS and the peak amplitude are equal, and it is the same for a square wave (of 50% duty cycle).

This table provides values for some other normalized waveforms:

Wave type Waveform Mean magnitude (rectified) Waveform factor RMS value Crest factor Crest factor (dB)
DC 1 1 1 0 dB
Sine wave {2 \over \pi} \approx 0.637 {\pi \over 2 \sqrt{2}} \approx 1.11 {1 \over \sqrt{2}} \approx 0.707 \sqrt{2} \approx 1.414 3.01 dB
Full-wave rectified sine {2 \over \pi} \approx 0.637 {\pi \over 2 \sqrt{2}} \approx 1.11 {1 \over \sqrt{2}} \approx 0.707 \sqrt{2} \approx 1.414 3.01 dB
Half-wave rectified sine {1 \over \pi} \approx 0.318 {\pi \over 2} \approx 1.571 {1 \over 2} = 0.5 2 \, 6.02 dB
Triangle wave {1 \over 2} = 0.5 {2 \over \sqrt{3}} \approx 1.155 {1 \over \sqrt{3}} \approx 0.577 \sqrt{3} \approx 1.732 4.77 dB
Square wave 1 \, 1 \, 1 \, 1 \, 0 dB
QPSK 3.5 - 4 dB
64QAM 7.7 dB
128QAM 8.2 dB
WCDMA downlink carrier 10.6 dB

Notes: 1. crest factors specified for QPSK, QAM, WCDMA are typical factors needed for reliable communication, not the theoretical crest factors which can be larger.

2. Waveform factor is the ratio of DC average to RMS and is used to scale resistors for measurements with DC or AC meters. The waveform factor for the half wave rectified sine wave should be 2.22 as the DC average is VP/Pi.

[edit] Digital multimeters

Crest factor is an important parameter to understand when trying to take accurate measurements of low frequency signals. For example, given a certain digital multimeter with an AC accuracy of 0.03 % (always specified for sine waves) with an additional error of 0.2 % for crest factors between 1.414 and 5, then the total error for measuring a triangular wave (crest factor = 1.73) is 0.03 % + 0.2 % = 0.23 %. In acoustics, crest factor is usually expressed in decibels. For example, for a sine wave the 1.414 ratio is 20 log(1.414) or 3 dB. Most ambient noise has a crest factor of around 10 dB while impulsive sounds such as gunshots can have crest factors of over 30 dB. (Note the waveform factor of the half wave sine wave rectified signal should be 2.22 not 1.11)

[edit] Applications

[edit] References

  1. ^ What Is The “Crest Factor” And Why Is It Used?
  2. ^ Crest factor analysis for complex signal processing
  3. ^ Crest factor definition — Rane Pro Audio Reference
  4. ^ Level Practices in Digital Audio
  5. ^ Gain Structure — Setting the System Levels, Mackie Mixer Tips
  6. ^ Setting sound system level controls: The most expensive system set up wrong never performs as well as an inexpensive system set up correctly.
  7. ^ Palatal snoring identified by acoustic crest factor analysis

[edit] External links

  • Definition of peak-to-average ratio - ATIS (Alliance for Telecommunications Industry Solutions) Telecom Glossary 2K
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