 Crest factor

The crest factor or peaktoaverage ratio (PAR) or peaktoaverage power ratio (PAPR) is a measurement of a waveform, calculated from the peak amplitude of the waveform divided by the RMS value of the waveform.
It is therefore a dimensionless quantity. While this quotient is most simply expressed by a positive rational number, in commercial products it is also commonly stated as the ratio of two whole numbers, e.g., 2:1. In signal processing applications it is often expressed in decibels (dB).
The minimum possible crest factor is 1, 1:1 or 0 dB.
Contents
Examples
This table provides values for some normalized waveforms:
Wave type Waveform Peak magnitude (normalized) RMS value Crest factor Crest factor (dB) DC 1 1 1 0.0 dB Sine wave 1 ^{[1]} 3.01 dB Fullwave rectified sine 1 ^{[1]} 3.01 dB Halfwave rectified sine 1 ^{[1]} 6.02 dB Triangle wave 1 4.77 dB Square wave 1 1 1 0 dB PWMSignal 1 ^{[1]} dB
QPSK 1 1 1 0 dB^{[citation needed]} 8VSB 6.5–8.1 dB ^{[2]} 64QAM 1 3.7 dB^{[citation needed]} QAM 1 4.8 dB^{[citation needed]} WCDMA downlink carrier 10.6 dB OFDM ~12 dB GMSK 1 1 1 0 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.
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)
Peaktoaverage ratio (PAR) meter
A peaktoaverage ratio meter (Par meter) is a device used to measure the ratio of the peak power level to the timeaveraged power level in an electrical circuit. This quantity is known as the peaktoaverage ratio (p/a r or PAR). Such meters are used as a quick means to identify degraded telephone channels.
Par meters are very sensitive to envelope delay distortion. They may also be used for idle channel noise, nonlinear distortion, and amplitudedistortion measurements.
The peaktoaverage ratio can be determined for many signal parameters, such as voltage, current, power, frequency, and phase.
Applications
 Electrical engineering — for describing the quality of an AC power waveform
 Vibration analysis — for estimating the amount of impact wear in a bearing ^{[3]}
 Radio and audio electronics — for estimating the headroom required in a signal chain ^{[4]}
 Music has a widelyvarying crest factor. Typical values for a processed mix are around 4–8 (which corresponds to 12–18 dB of headroom, usually involving audio level compression), and 8–10 for an unprocessed recording (18–20 dB).^{[5]}^{[6]}^{[7]}^{[8]}
 Physiology — for analysing the sound of snoring ^{[9]}
References
 ^ ^{a} ^{b} ^{c} ^{d} "RMS and Average Values for Typical Waveforms". Archived from the original on 20100721. http://www.webcitation.org/5rPH2bywi.
 ^ http://broadcastengineering.com/mag/broadcasting_transitioning_transmitters_cofdm/
 ^ What Is The “Crest Factor” And Why Is It Used?
 ^ Crest factor analysis for complex signal processing
 ^ Crest factor definition — Rane Pro Audio Reference
 ^ Level Practices in Digital Audio
 ^ Gain Structure — Setting the System Levels, Mackie Mixer Tips
 ^ Setting sound system level controls: The most expensive system set up wrong never performs as well as an inexpensive system set up correctly.
 ^ Palatal snoring identified by acoustic crest factor analysis
This article incorporates public domain material from the General Services Administration document "Federal Standard 1037C" (in support of MILSTD188).
External links
 Definition of peaktoaverage ratio – ATIS (Alliance for Telecommunications Industry Solutions) Telecom Glossary 2K
 Definition of crest factor – ATIS (Alliance for Telecommunications Industry Solutions) Telecom Glossary 2K
Categories: Electronics terms
 Microwave technology
 Audio engineering
 Amplifiers
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