查看“︁峰值因數”︁的源代码

'''峰值因數'''又稱'''波峰因數'''（'''crest factor'''，簡寫 '''CF'''，又稱'''peak-to-average ratio'''，簡稱'''PAR'''）是和[[波形]]有關的[[無因次量]]，為波形的[[振幅]]再除以波形[[平方平均數|RMS]] （time-averaged）所得到的值。
:<math>
C = {|x|_\mathrm{peak} \over x_\mathrm{rms}}
</math>

'''峰均功率比'''（'''peak-to-average power ratio'''，簡稱'''PAPR'''）是另一個相關的無因次量，定義為振幅平方（表示峰值功率）除以RMS平方（表示平均功率）的比值<ref>{{cite web |title=Wireless 101: Peak to average power ratio (PAPR) |url=http://www.eetimes.com/design/microwave-rf-design/4017754/Wireless-101-Peak-to-average-power-ratio-PAPR- |access-date=2013-03-17 |archive-url=https://web.archive.org/web/20130221042545/http://eetimes.com/design/microwave-rf-design/4017754/Wireless-101-Peak-to-average-power-ratio-PAPR- |archive-date=2013-02-21 |dead-url=yes }}</ref>：
:<math>
\mathit{PAPR} = {{|x|_\mathrm{peak}}^2 \over {x_\mathrm{rms}}^2} = C^2
</math>

因一波形的振幅恆大於等於RMS值，因此峰值因數及峰均功率比的最小可能數值均為1，即峰均功率比 1:1 或 0dB。

== 常見波形的峰值因數 ==
下表列出了常見[[波形]]的峰值因數。所有範例中的峰值都統一為 1。
{| class="wikitable" style="text-align:center;"
! 波形名稱
! 波形圖
! [[均方根|RMS]] 值
! 峰值因數
! 峰均功率比 (dB)
|-
| [[直流]] ||  || 1 || 1 || 0.0 dB
|-
| [[正弦波]] || [[Image:Simple sine wave.svg|100px]] || <math>{1 \over \sqrt{2}} \approx 0.707</math><ref name=ness>{{cite web|title=RMS and Average Values for Typical Waveforms |url=http://www.nessengr.com/techdata/rms/rms.html |archive-url=https://web.archive.org/web/20100123085330/http://www.nessengr.com/techdata/rms/rms.html |archive-date=2010-01-23 |url-status=dead }}</ref> || <math>\sqrt{2} \approx 1.414</math> || 3.01 dB
|-
| 正弦波經全波整流後 || [[Image:Simple full-wave rectified sine.svg|100px]] || <math>{1 \over \sqrt{2}} \approx 0.707</math><ref name=ness/> || <math>\sqrt{2} \approx 1.414</math> || 3.01 dB
|-
| 正弦波經半波整流後 || [[Image:Simple half-wave rectified sine.svg|100px]] || <math>{1 \over 2 } = 0.5</math><ref name=ness/> || <math>2 \,</math> || 6.02 dB
|-
| [[三角波]] || [[Image:Triangle wave.svg|100px]] || <math>{1 \over \sqrt{3}} \approx 0.577</math> || <math>\sqrt{3} \approx 1.732</math> || 4.77 dB
|-
| [[方波]] || [[Image:Square wave.svg|100px]] || 1 || 1 || 0 dB
|-
| [[脈衝寬度調變|PWM]] 訊號 <br/>V(t) ≥ 0.0&nbsp;V|| [[Image:Pulse wide wave.svg|100px]] || <math>\sqrt{ \frac{t_1}{T}}</math><ref name=ness/> || <math>\sqrt{\frac{T}{t_1}}</math> || 
<math>20\log\mathord\left(\frac{T}{t_1}\right)</math>&nbsp;dB
|-
| [[QPSK]] || || 1 || 1 || 1.761 dB<ref>{{Cite book|url=http://kilyos.ee.bilkent.edu.tr/~signal/defevent/papers/cr1037.pdf|title=POWER RATIO DEFINITIONS AND ANALYSIS IN SINGLE CARRIER MODULATIONS|last1=Palicot|first1=Jacques|last2=Louët|first2=Yves|publisher=IETR/Supélec - Campus de Rennes|pages=2}}</ref>
|-
| [[8PSK]] || || || || 3.3 dB<ref name=modulation>{{Cite web | url=http://www.readbag.com/ece-ucsb-yuegroup-teaching-ece594bb-lectures-steer-rf-chapter1 | title=Read steer_rf_chapter1.pdf | access-date=2014-12-11 | archive-date=2016-03-22 | archive-url=https://web.archive.org/web/20160322185955/http://www.readbag.com/ece-ucsb-yuegroup-teaching-ece594bb-lectures-steer-rf-chapter1 | url-status=dead }}</ref>

|-
| [[Phase-shift keying#π/4-QPSK|{{frac|π|4}}-DQPSK]] || || || || 3.0 dB<ref name=modulation />
|-
| [[OQPSK]] || || || || 3.3 dB<ref name=modulation />
|-
| [[8VSB]] || || || || 6.5–8.1 dB<ref>{{cite web |url=http://broadcastengineering.com/mag/broadcasting_transitioning_transmitters_cofdm/ |title=Transitioning transmitters to COFDM |access-date=2009-06-17 |url-status=dead |archive-url=https://web.archive.org/web/20090821020320/http://broadcastengineering.com/mag/broadcasting_transitioning_transmitters_cofdm/ |archive-date=2009-08-21 }}</ref>
|-
| [[QAM|64QAM]] || || <math>\sqrt{ \frac{3}{7} }</math> || <math>\sqrt{ \frac{7}{3} } \approx 1.528</math> || 3.7 dB<ref name="ChatzimisiosVerikoukis2011">{{cite book|url=https://books.google.com/books?id=tSwKZxtx82gC|title=Mobile Lightweight Wireless Systems: Second International ICST Conference, Mobilight 2010, May 10-12, 2010, Barcelona, Spain, Revised Selected Papers|author1=R. Wolf|author2=F. Ellinger|author3=R.Eickhoff|author4=Massimiliano Laddomada|author5=Oliver Hoffmann|date=14 July 2011|publisher=Springer|isbn=978-3-642-16643-3|editor=Periklis Chatzimisios|page=164|access-date=13 December 2012}}</ref>
|-
| <math>\infty</math>-QAM || || <math>{1 \over \sqrt{3}} \approx 0.577</math> || <math>\sqrt{3} \approx 1.732</math> || 4.8 dB<ref name="ChatzimisiosVerikoukis2011"/>
|-
| [[WCDMA]] 下行載波 || || || || 10.6 dB
|-
| [[OFDM]] || || || 4 || ~12 dB
|-
| [[GMSK]] || || 1 || 1 || 0 dB
|-
| [[高斯噪声]] || || [[standard deviation|<math>\sigma</math>]]<ref>[http://www.ti.com/lit/ml/sloa082/sloa082.pdf Op Amp Noise Theory and Applications] {{webarchive|url=https://web.archive.org/web/20141130224524/http://www.ti.com/lit/ml/sloa082/sloa082.pdf |date=2014-11-30 }} - 10.2.1 rms versus P-P Noise</ref><ref>[http://users.ece.gatech.edu/mleach/ece6416/Labs/exp01.pdf Chapter 1 First-Order Low-Pass Filtered Noise] - "The standard deviation of a Gaussian noise voltage is the root-mean-square or rms value of the voltage."</ref> || <math>\infty</math><ref>[http://noisewave.com/faq.pdf Noise: Frequently Asked Questions] - "Noise theoretically has an unbounded distribution so that it should have an infinite crest factor"</ref><ref>Telecommunications Measurements, Analysis, and Instrumentation, Kamilo Feher, section 7.2.3 Finite Crest Factor Noise</ref>  || <math>\infty</math> dB
|-
| 週期性[[啁啾|啁啾(Chirp)]] || || <math>{1 \over \sqrt{2}} \approx 0.707</math> || <math>\sqrt{2} \approx 1.414</math> || 3.01 dB
|}

附註:
# 表中 QPSK, QAM, WCDMA 的峰值因數是進行可靠通訊時的典型數值，並非理論上的峰值因數數值，後者可能較高。

== 相關條目 ==
* [[波形因數|波形因數 (Form Factor)]]

==參考資料==
{{reflist}}

{{數學小作品}}

[[Category:放大器]]