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Properties of periodic signals table
Table shows properties of common periodic signals (sine, square, triangle etc.) such as absolute mean value, effective value or shape factor.

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Periodic signals

Type of signalGraphAbsolute mean valueRoot Mean Square (RMS)Waveform factorCrest factorTotal Harmonic Distortion h1Total Harmonic Distortion h2
Constant signal (DC)Show source11Show source11Show source11Show source11Show source-Show source-
SineShow source2π0,637\frac{2}{\pi}\approx 0,637Show source120,707\frac{1}{\sqrt{2}}\approx 0,707Show sourceπ221,11\frac{\pi}{2\sqrt{2}}\approx 1,11Show source21,414\sqrt{2}\approx 1,414Show source00Show source00
Sine (full-wave rectification)Show source2π0,637\frac{2}{\pi}\approx 0,637Show source120,707\frac{1}{\sqrt{2}}\approx 0,707Show sourceπ221,11\frac{\pi}{2\sqrt{2}}\approx 1,11Show source21,414\sqrt{2}\approx 1,414Show source0,225\approx 0,225Show source0,219\approx 0,219
Sine (half-wave rectification)Show source1π0,318\frac{1}{\pi}\approx 0,318Show source12=0,5\frac{1}{2} = 0,5Show sourceπ21,571\frac{\pi}{2}\approx 1,571Show source22Show source0,441\approx 0,441Show source0,404\approx 0,404
Triangle symmetricShow source12=0,5\frac{1}{2} = 0,5Show source130,577\frac{1}{\sqrt{3}}\approx 0,577Show source231,155\frac{2}{\sqrt{3}}\approx 1,155Show source31,732\sqrt{3}\approx 1,732Show sourceπ49610,121\sqrt{\frac{\pi^4}{96}-1}\approx 0,121Show source196π40,120\sqrt{1-\frac{96}{\pi^4}}\approx 0,120
Square symmetric (50% fill)Show source11Show source11Show source11Show source11Show sourceπ2810,483\sqrt{\frac{\pi^2}{8}-1}\approx 0,483Show source18π20,435\sqrt{1-\frac{8}{\pi^2}}\approx 0,435
SawtoothShow source12=0,5\frac{1}{2} = 0,5Show source130,577\frac{1}{\sqrt{3}}\approx 0,577Show source231,155\frac{2}{\sqrt{3}}\approx 1,155Show source31,732\sqrt{3}\approx 1,732Show sourceπ2610,803\sqrt{\frac{\pi^2}{6}-1}\approx 0,803Show source16π20,626\sqrt{1-\frac{6}{\pi^2}}\approx 0,626

What is the meaning of each calculator field ?

  • Type of signal - the name of the signal, usually comes from the mathematical function that describes the signal (sinusoidal, square etc.).
  • Graph - graphical representation of the signal in the form of a graph, the graph is normalized to one and shows one period.
  • Absolute mean value - average value of the signal without sign (absolute value):
    ARV=1T0Tx(t)dtARV = \frac{1}{T}\int\limits_0^T{|x(t)|dt}
    where:
    • T - signal period (e.g. 2π2\pi for sine signal),
    • t - time,
    • x(t) - signal value in time t.
  • Root Mean Square (RMS) - The effective value of the alternating current is the value of the direct current, which in the course of time equal to the period of alternating current will cause the same thermal effect as the given AC signal (alternating current). It's statistical value defined as:
    RMS=1T0Tx2(t)dtRMS = \sqrt{\frac{1}{T}\int\limits_{0}^{T}\,x^{2}(t)dt}
    where:
    • T - signal period (e.g. 2π2\pi for sine signal),
    • t - time,
    • x(t) - signal value in time t.
  • Waveform factor - the ratio of the rms value to the mean of the absolute value:
    kf=RMSARVk_f = \frac{RMS}{ARV}
    where:
    • RMSRMS - root mean value (effective value),
    • AVRAVR - mean absolute value.
  • Crest factor - peak (maximum) value to RMS ratio:
    kc=XmaxRMSk_c = \frac{X_{max}}{RMS}
    where:
    • XmaxX_{max} - maximum signal value (peak value),
    • RMSRMS - root mean square (effective value).
  • Total Harmonic Distortion (THD) - a factor determining how much the signal deviates from the sinusoidal signal, defined as:
    h1=n=2Xn2X1h_{1}=\frac{\sqrt{\sum\limits_{n=2}^{\infty}X_{n}^{2}}}{X_{1}}
    or
    h2=n=2Xn2n=1Xn2h_{2}=\frac{\sqrt{\sum\limits_{n=2}^{\infty}X_{n}^{2}}}{\sqrt{\sum\limits_{n=1}^{\infty}X_{n}^{2}}}
    where:
    • X1X_1 - effective value (RMS) of base component,
    • XnX_n - effective value (RMS) of n-th harmonic.

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