Crest factor
Wave type RMS value Crest factor PAPR ( dB )
DC 1 1 0.0 dB
Sine wave 1 2 ≈ 0.707 { \displaystyle { 1 \over { \sqrt { 2 } } } \approx 0.707 } 2 ≈ 1.414 { \displaystyle { \sqrt { 2 } } \approx 1.414 } 3.01 dB
N superimposed sine waves ( same amplitudes , different frequencies ) N 2 { \displaystyle { \sqrt { \frac { N } { 2 } } } } 2 N { \displaystyle { \sqrt { 2N } } } 10 log ⁡ 2 N { \displaystyle 10\log 2N } dB
Full-wave rectified sine 1 2 ≈ 0.707 { \displaystyle { 1 \over { \sqrt { 2 } } } \approx 0.707 } 2 ≈ 1.414 { \displaystyle { \sqrt { 2 } } \approx 1.414 } 3.01 dB
Half-wave rectified sine 1 2 = 0.5 { \displaystyle { 1 \over 2 } =0.5 } 2 { \displaystyle 2\ , } 6.02 dB
Triangle wave 1 3 ≈ 0.577 { \displaystyle { 1 \over { \sqrt { 3 } } } \approx 0.577 } 3 ≈ 1.732 { \displaystyle { \sqrt { 3 } } \approx 1.732 } 4.77 dB
Square wave 1 1 0 dB
PWM Signal V ( t ) ≥ { \displaystyle \geq } 0.0 V t 1 T { \displaystyle { \sqrt { \frac { t_ { 1 } } { T } } } } T t 1 { \displaystyle { \sqrt { \frac { T } { t_ { 1 } } } } } 10 log ⁡ T t 1 { \displaystyle 10\log { \frac { T } { t_ { 1 } } } } dB
QPSK 1 1 1.761 dB
8PSK 3.3 dB
π/4DQPSK 3.0 dB
OQPSK 3.3 dB
8VSB 6.5-8.1 dB
64QAM 3 7 { \displaystyle { \sqrt { \frac { 3 } { 7 } } } } 7 3 ≈ 1.542 { \displaystyle { \sqrt { \frac { 7 } { 3 } } } \approx 1.542 } 3.7 dB
∞ { \displaystyle \infty } -QAM 1 3 ≈ 0.577 { \displaystyle { 1 \over { \sqrt { 3 } } } \approx 0.577 } 3 ≈ 1.732 { \displaystyle { \sqrt { 3 } } \approx 1.732 } 4.8 dB
WCDMA downlink carrier 10.6 dB
OFDM 4 ~12 dB
GMSK 1 1 0 dB
Gaussian noise σ { \displaystyle \sigma } ∞ { \displaystyle \infty } ∞ { \displaystyle \infty } dB
Examples
This table provides values for some normalized waveforms . All peak magnitudes have been normalized to 1 .
Crest factor is a parameter of a waveform, such as alternating current or sound, showing the ratio of peak values to the effective value. In other words, crest factor indicates how extreme the peaks are in a waveform. Crest factor 1 indicates no peaks, such as direct current or a square wave. Higher crest factors indicate peaks, for example sound waves tend to have high crest factors. Crest factor is the peak amplitude of the waveform divided by the RMS value of the waveform. This is equivalent to the ratio of the L norm to the L norm of the function of the waveform:
The peak-to-average power ratio (PAPR) is the peak amplitude squared (giving the peak power) divided by the RMS value squared (giving the average power). It is the square of the crest factor:
formula_5 dB
formula_15 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.