Crest factor

Crest Factor

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Crest factor

The crest factor or peak-to-average ratio (PAR) or peak-to-average power ratio (PAPR) is a measurement of a waveform

Waveform

Waveform means the shape and form of a signal such as a wave moving in a solid, liquid or gaseous medium.In many cases the medium in which the wave is being propagated does not permit a direct visual image of the form....
, calculated from the peak amplitude of the waveform divided by the RMS

Root mean square

In mathematics, the root mean square , also known as the quadratic mean, is a statistics measure of the magnitude of a varying quantity. It is especially useful when variates are positive and negative, e.g., sinusoids....
value of the waveform.

It is therefore a dimensionless quantity

Dimensionless quantity

In dimensional analysis, a dimensionless quantity is a quantity without any physical units and thus a pure number. Such a number is typically defined as a product or ratio of quantity which do have units, in such a way that all the units cancel out....
. While this quotient is most simply expressed by a positive rational number

Rational number

In mathematics, a rational number is a number which can be expressed as a quotient of two integers. Non-integer rational numbers are usually written as the vulgar fraction , where b is not 0 ....
, as shown below, in commercial products it is also commonly stated as the ratio of two whole numbers, e.g., 2:1.

The minimum possible crest factor is 1.

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Encyclopedia

The crest factor or peak-to-average ratio (PAR) or peak-to-average power ratio (PAPR) is a measurement of a waveform

Waveform

Root mean square

Dimensionless quantity

Rational number

Examples

Direct current

Direct current is the unidirectional flow of electric charge. Direct current is produced by such sources as battery , thermocouples, solar cells, and commutator-type electric machines of the dynamo type....
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

Square wave

A square wave is a kind of non-sinusoidal waveform, most typically encountered in electronics and signal processing. An ideal square wave alternates regularly and instantaneously between two levels....
(irrespective of duty cycle

Duty cycle

In telecommunications and electronics, the duty cycle is the fraction of time that a system is in an "active" state. In particular, it is used in the following contexts:...
).

This table provides values for some other normalized

Normalization

Broadly, normalization is any process that makes something more normal, which typically means conforming to some regularity or rule, or returning from some state of abnormality....
waveform

Waveform

Wave type	Mean Mean In statistics, mean has two related meanings:* the arithmetic mean .* the expected value of a random variable, which is also called the population mean.... magnitude Magnitude (mathematics) The magnitude of a mathematical object is its size: a property by which it can be larger or smaller than other objects of the same kind; in technical terms, an ordering of the class of objects to which it belongs.... (rectified)	RMS Root mean square In mathematics, the root mean square , also known as the quadratic mean, is a statistics measure of the magnitude of a varying quantity. It is especially useful when variates are positive and negative, e.g., sinusoids.... value	Crest factor	Crest factor (dB Decibel The decibel is a logarithmic units of measurement that expresses the magnitude of a physical quantity relative to a specified or implied reference level.... )
DC Direct current Direct current is the unidirectional flow of electric charge. Direct current is produced by such sources as battery , thermocouples, solar cells, and commutator-type electric machines of the dynamo type....	1	1	1	0.0 dB
Sine wave Sine wave The sine wave or sinusoid is a function that occurs often in mathematics, physics, signal processing, hearing , electrical engineering, and many other fields....				3.01 dB
Full-wave rectified Rectifier A rectifier is an electrical device that converts alternating current to direct current , a process known as rectification. Rectifiers have many uses including as components of power supply and as detector s of radio signals.... sine				3.01 dB
Half-wave rectified Rectifier A rectifier is an electrical device that converts alternating current to direct current , a process known as rectification. Rectifiers have many uses including as components of power supply and as detector s of radio signals.... sine				6.02 dB
Triangle wave Triangle wave A triangle wave is a non-sinusoidal waveform named for its triangular shape.Like a square wave, the triangle wave contains only odd harmonics....				4.77 dB
Square wave Square wave A square wave is a kind of non-sinusoidal waveform, most typically encountered in electronics and signal processing. An ideal square wave alternates regularly and instantaneously between two levels....				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.

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 decibel

Decibel

The decibel is a logarithmic units of measurement that expresses the magnitude of a physical quantity relative to a specified or implied reference level....
s. 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)

Peak-to-average ratio (PAR) meter

A peak-to-average ratio meter (Par meter) is a device used to measure the ratio of the peak power

Power (physics)

In physics, power is the rate at which mechanical work is performed or energy is transmitted, or the amount of energy required or expended for a given unit of time....
level to the time

Time

Time is a component of the measurement used to sequence events, to compare the durations of events and the intervals between them, and to quantify the motions of objects....
-averaged power level in an electrical circuit. This quantity is known as the peak-to-average ratio (p/a r or PAR). Such meters are used as a quick means to identify degraded telephone

Telephone

The telephone is a telecommunications device that is used to transmitter and receive electronically or digitally encoded sound between two or more people conversing....
channels.

Par meters are very sensitive to envelope delay distortion. They may also be used for idle channel

Channel (communications)

Channel, in communications , refers to the :wikt:medium used to information transfer information from a sender to a receiver ....
noise

Noise

In common use, the word noise means unwanted sound or noise pollution. In electronics noise can refer to the electronic signal corresponding to acoustic noise or the electronic signal corresponding to the noise commonly seen as 'Noise ' on a degraded television or video image....
, nonlinear distortion

Nonlinear distortion

Nonlinear distortion is a term used to describe the phenomenon of a non-linear relationship between the "input" and "output" signals of - for example - an electronic device....
, and amplitude-distortion measurements.

The peak-to-average ratio can be determined for many signal parameters, such as voltage, current, power, frequency

Frequency

Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency....
, and phase

Phase (waves)

The phase of an oscillation or wave is the fraction of a complete cycle corresponding to an offset in the displacement from a specified reference point at time t = 0....
.

Applications

Electrical engineering
Electrical engineering

Electrical engineering, sometimes referred to as electrical and electronic engineering, is a field of engineering that deals with the study and application of electricity, electronics and electromagnetism....
— for describing the quality of an AC power waveform
Vibration
Oscillation

Oscillation is the repetitive variation, typically in time, of some measure about a central value or between two or more different states. Familiar examples include a swinging pendulum and Alternating current power....
analysis — for estimating the amount of impact wear
Wear

In materials science, wear is the erosion of material from a solid surface by the action of another substance. The study of the processes of wear is part of the discipline of tribology....
in a bearing
Bearing

Bearing may refer to:* Bearing , a term for direction* Bearing , a component that separates moving parts and takes a load...
Radio
Radio

Radio is the transmission of signals, by modulation of electromagnetic radiation with frequency below those of visible light.Electromagnetic radiation radio propagation by means of oscillating electromagnetic fields that pass through the air and the vacuum of space....
and audio
Audio frequency

An audio frequency , or audible frequency is characterized as a periodic vibration whose frequency is audible to the average human. While the range of frequencies that any individual can hear is largely related to environmental factors, the generally accepted standard range of audible frequencies is 20 to 20,000 hertz....
electronics — for estimating the headroom
Headroom

In digital and analog sound reproduction, headroom is the amount by which the signal capabilities of an audio system exceed a designated level, known as Permitted Maximum Level ....
required in a signal chain

Music
Music

Music is an art form whose media is sound organized in time. Common elements of music are pitch , rhythm , dynamics , and the sonic qualities of timbre and texture ....
has a widely-varying crest factor. Typical values for a processed mix are around 4–8 (which corresponds to 12–18 dB
Decibel

The decibel is a logarithmic units of measurement that expresses the magnitude of a physical quantity relative to a specified or implied reference level....
of headroom, usually involving audio level compression
Audio level compression

Dynamic range compression, also called DRC or simply compression, is a process that reduces the dynamic range of an audio signal. Compression is used during sound recording, live sound reinforcement, and broadcasting to control the level of audio....
), and 8–10 for an unprocessed recording (18–20 dB).

Physiology
Physiology

Physiology is the study of the mechanical, physical, and biochemical functions of living organisms. Physiology has traditionally been divided between plant physiology and animal and all living things physiology but the principles of physiology are universal, no matter what particular organism is being studied....
— for analysing the sound of snoring
Snoring

Snoring is the vibration of respiratory structures and the resulting sound, due to obstructed air movement during breathing while sleeping. In some cases the sound may be soft, but in other cases, it can be rather loud and quite unpleasant....

External links

Definition of - ATIS (Alliance for Telecommunications Industry Solutions) Telecom Glossary 2K