Crest factor

The crest factor or crest factor ( English crest factor in the) describes electrical engineering , the ratio of peak to rms value of an alternating quantity and is always greater than or equal to one. It is used in the areas of electrical measurement technology , communications technology , sound technology and acoustics .

Like the form factor or the distortion factor, it serves as a characteristic value for roughly describing the curve shape of an alternating quantity.

The square of the crest factor is defined as English peak-to-average power ratio ( PAPR hereinafter) and expresses the ratio of peak power to the average power of a signal. The PAPR is usually given as a logarithmic measure in decibels . Among other things, it is used in radio receivers to obtain a control signal for automatic gain control (AGC).

definition

The crest factor of size is defined as: ${\ displaystyle X}$

{\ displaystyle k_ {s} = {\ frac {| X | _ {\ mathrm {max}}} {X _ {\ mathrm {eff}}}}}

Example: If a sinusoidal AC voltage has an effective value of 230 V , the peak value is approx. 325 V. In this case, the crest factor is . ${\ displaystyle k_ {s}}$ ${\ displaystyle {\ sqrt {2}} \ approx 1 {,} 414}$

Practical meaning

Measuring devices for alternating current and voltage with effective value measurement must be able to process instantaneous values around the peak value of the measurement signal sufficiently quickly. Simple electronic electricity meters and ammeters therefore often work imprecisely at high peak factors, because they either have too little dynamic range and / or a sampling rate that is too low .

High peak factors of the current consumed by mains-operated devices mean a high proportion of harmonics in the mains, and due to the internal resistance of the mains, this also results in distortions of the sinusoidal voltage. Consumers with high crest factors for power consumption cause high distortion reactive power . Typical examples are switched-mode power supplies , converters and frequency converters without power factor correction . The effective current is higher than the current to be expected for the power consumed. Despite symmetrical loading with single-phase consumers with distorted power consumption, the neutral conductor in the three-phase network can carry a greatly increased current, which overloads it even though there is no overcurrent in the outer conductors. High crest factors are therefore undesirable. They are avoided by the power factor correction.

Also, power transformers are connected rectifier and filter capacitors charged far higher than a resistive load, as the current for recharging the capacitor only during the current flow angle is flowing.

Thyristor controllers and dimmers have a strongly distorted, pulse-shaped power consumption in partial load operation. The current consumed by them sometimes has a very high crest factor of up to over 10.

In acoustics and sound engineering , high crest factors of the signal and the envelope are typical and determine the required modulation of amplifiers , loudspeakers, microphones and sound carriers. Level indicators take this into account through the so-called true peak meter , which enables the sound engineer to reduce the level to prevent distortion. Good sound engineering must be able to process high crest factors without overdriving . Dynamic compression can also avoid this, but leads to a loss of information or to reduced music quality.

PAPR

The ratio of peak power to the average power of a signal, English Peak-to-Average Power Ratio and abbreviated PAPR, is:

{\ displaystyle \ mathrm {PAPR} = k_ {s} ^ {2} = {\ frac {| X | _ {\ mathrm {max}} ^ {2}} {X _ {\ mathrm {eff}} ^ {2 }}}}

Expressed logarithmically this is:

{\ displaystyle \ mathrm {PAPR} _ {\ mathrm {dB}} = k_ {s \ \ mathrm {dB}} ^ {2} = 10 \ \ lg {\ frac {| X | _ {\ mathrm {max} } ^ {2}} {X _ {\ mathrm {eff}} ^ {2}}} \ \ mathrm {dB}}

Crest factor values (examples)

The following table shows the crest factors and PAPR for various simple signal forms and some modulation methods commonly used in communications engineering . With the modulation methods listed (modulated RF signals), the crest factor is related to the most powerful symbol . A frequency-modulated signal, for example, has a constant envelope and thus a crest factor of 1.

Properties of different waveforms
Vibration type	Average amount through peak value	Form factor = average amount by effective value	Crest factor = peak value divided by effective value	PAPR ${\ displaystyle _ {\ mathbf {dB}}}$
Sine wave	${\ displaystyle {\ frac {2} {\ pi}} \ approx 0 {,} 637}$	${\ displaystyle {\ frac {\ pi} {2 {\ sqrt {2}}}} \ approx 1 {,} 11}$	${\ displaystyle {\ sqrt {2}} \ approx 1 {,} 414}$	${\ displaystyle 3 {,} 01 \ \ mathrm {dB}}$
Full oscillation of rectified sine	${\ displaystyle {\ frac {2} {\ pi}} \ approx 0 {,} 637}$	${\ displaystyle {\ frac {\ pi} {2 {\ sqrt {2}}}} \ approx 1 {,} 11}$	${\ displaystyle {\ sqrt {2}} \ approx 1 {,} 414}$	${\ displaystyle 3 {,} 01 \ \ mathrm {dB}}$
Half -wave rectified sine	${\ displaystyle {\ frac {1} {\ pi}} \ approx 0 {,} 318}$	${\ displaystyle {\ frac {\ pi} {2}} \ approx 1 {,} 571}$	${\ displaystyle 2 \,}$	${\ displaystyle 6 {,} 02 \ \ mathrm {dB}}$
Triangular oscillation	${\ displaystyle {\ frac {1} {2}} = 0 {,} 5}$	${\ displaystyle {\ frac {2} {\ sqrt {3}}} \ approx 1 {,} 155}$	${\ displaystyle {\ sqrt {3}} \ approx 1 {,} 732}$	${\ displaystyle 4 {,} 77 \ \ mathrm {dB}}$
Symmetrical square wave	${\ displaystyle 1 \,}$	${\ displaystyle 1 \,}$	${\ displaystyle 1 \,}$	${\ displaystyle 0 \ \ mathrm {dB}}$
Asymmetrical square wave ( PWM signal)	${\ displaystyle {\ frac {t_ {1}} {T}}}$	${\ displaystyle {\ sqrt {\ frac {T} {t_ {1}}}}}$	${\ displaystyle {\ sqrt {\ frac {T} {t_ {1}}}}}$	${\ displaystyle 10 \ \ lg {\ frac {T} {t_ {1}}} \ \ mathrm {dB}}$
Frequency or phase modulation, e.g. B. GMSK or QPSK			${\ displaystyle 1}$	${\ displaystyle 0 \ \ mathrm {dB}}$
4-bit quadrature amplitude modulation ( 16-QAM )			${\ displaystyle {\ sqrt {\ frac {9} {5}}}}$	${\ displaystyle 2 {,} 6 \ \ mathrm {dB}}$
6-bit quadrature amplitude modulation ( 64-QAM )			${\ displaystyle {\ sqrt {\ frac {7} {3}}}}$	${\ displaystyle 3 {,} 7 \ \ mathrm {dB}}$

literature

Rene Flosdorff, Günther Hilgarth: Electrical energy distribution . Teubner, 2003, ISBN 3-519-26424-2 .
Tony J. Rouphael: RF and Digital Signal Processing for Software-Defined Radio . 1st edition. Newnes, 2008, ISBN 978-0-7506-8210-7 .
Jürgen Nitsch, Uwe Knauff, Mathias Magdowski: Introduction to electrical engineering . 2nd Edition. Shaker, 2011, ISBN 978-3-8322-7684-3 .

Individual evidence

↑ IEC 60050, see DKE : German online edition of the International Electrotechnical Dictionary .
↑ ^a ^b ^c R. Wolf, F. Ellinger, R. Eickhoff: Mobile Lightweight Wireless Systems: Second International ICST Conference, Mobilight 2010, May 10-12, 2010, Barcelona, Spain, Revised Selected Papers . Ed .: Periklis Chatzimisios, Christos Verikoukis, Ignacio Santamaria, Massimiliano Laddomada, Oliver Hoffmann. Springer Science & Business Media, 2010, ISBN 978-3-642-16643-3 , p. 164 (English, limited preview in Google Book Search).

[1] IEC 60050, see DKE : German online edition of the International Electrotechnical Dictionary .

[ChatzimisiosVerikoukis2011-2] R. Wolf, F. Ellinger, R. Eickhoff: Mobile Lightweight Wireless Systems: Second International ICST Conference, Mobilight 2010, May 10-12, 2010, Barcelona, Spain, Revised Selected Papers . Ed .: Periklis Chatzimisios, Christos Verikoukis, Ignacio Santamaria, Massimiliano Laddomada, Oliver Hoffmann. Springer Science & Business Media, 2010, ISBN 978-3-642-16643-3 , p. 164 (English, limited preview in Google Book Search).