Form factor (electronics): Difference between revisions

Revision as of 17:18, 28 August 2015

Revision as of 07:13, 29 August 2015

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It will always be at least as large as <math>X_\mathrm{arv}</math>, which only measures the absolute distance from said average. The form factor thus cannot be smaller than 1 (a square wave where all momentary values are equally far above or below the average value; see below), and has no theoretical upper limit for functions with sufficient deviation.

<math>\mathrm{RMS}_\mathrm{total} = \sqrt{{{\mathrm{RMS}_1}^2} + {{\mathrm{RMS}_2}^2} + ... + {{\mathrm{RMS}_n}^2}}</math>

can be used for combining signals of different frequencies (for example, for harmonics<ref name=Dusza />), while for the same frequency, <math>\mathrm{RMS}_\mathrm{total} = \mathrm{RMS}_1 + \mathrm{RMS}_2 + ... + \mathrm{RMS}_n</math>.

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As ARV's on the same ___domain can be summed as

<math>\mathrm{ARV}_\mathrm{total} = \mathrm{ARV}_1 + \mathrm{ARV}_2 + ... + \mathrm{ARV}_n</math>,

the form factor of a complex wave composed of multiple waves of the same frequency can sometimes be calculated as

<math>k_{\mathrm{f}_\mathrm{tot}} = \frac{\mathrm{RMS}_\mathrm{tot}}{\mathrm{ARV}_\mathrm{tot}} = \frac{\mathrm{RMS}_1 + ... + \mathrm{RMS}_n}{\mathrm{ARV}_1 + ... + \mathrm{ARV}_n}</math>.

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<math>a</math> represents the amplitude of the function, and any other coefficients applied in the vertical dimension. For example, <math>8 \sin(t)</math> can be analyzed as <math>f(t) = a \sin(t),\ a = 8</math>. As both RMS and ARV are directly proportional to it, it has no effect on the form factor, and can be replaced with a normalized 1 for calculating that value.

<math>D = \frac{\tau}{T}</math> is the [[duty cycle]], the ratio of the "pulse" time <math>\tau</math> (when the function's value is not zero) to the full wave [[Periodic function|period]] <math>T</math>. Most basic wave functions only achieve 0 for infinitely short instants, and can thus be considered as having <math>\tau = T, D = 1</math>. However, any of the non-pulsing functions below can be appended with <math>\frac{\sqrt{D}}{D} = \frac{1}{\sqrt{D}} = \sqrt{\frac{T}{\tau}}</math>

to allow pulsing. This is illustrated with the half-rectified sine wave, which can be considered a pulsed full-rectified sine wave with <math>D = \frac{1}{2}</math>, and has <math>k_\mathrm{f} = k_{\mathrm{f}_\mathrm{frs}}\sqrt{2}</math>.

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| [[Sine wave]] || [[File:Simple sine wave.svg|100px]] || <math>\frac{a}{\sqrt{2}}</math><ref name=Dusza /> || <math>a\frac{2}{\pi}</math><ref name=Dusza /> || <math>\frac{\pi}{2\sqrt{2}} \approx 1.11072073</math><ref name="Jędrzejewski" />

|-

| [[Rectifier#Half-wave_rectificationwave rectification|Half-wave rectified sine]] || [[File:Simple half-wave rectified sine.svg|100px]] || <math>\frac{a}{2}</math> || <math>\frac{a}{\pi}</math> || <math>\frac{\pi}{2} \approx 1.5707963</math>

|-

| [[Rectifier#Full-wave_rectificationwave rectification|Full-wave rectified sine]] || [[File:Simple full-wave rectified sine.svg|100px]] || <math>\frac{a}{\sqrt{2}}</math> || <math>a\frac{2}{\pi}</math>|| <math>\frac{\pi}{2\sqrt{2}}</math>

|-

| [[Square wave]], constant value || [[File:Square wave.svg|100px]] || <math>a</math> || <math>a</math> || <math>\frac{a}{a} = 1</math>

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| [[AWGN|Gaussian white noise]] ''U''(-1,1) || || <math>\frac{1}{\sqrt{3}}</math>{{citation needed|date=May 2014}} || <math>\frac{1}{2}</math>{{citation needed|date=May 2014}} || <math>\frac{2}{\sqrt{3}}</math>

|}

==References==

{{Reflist}}

{{DEFAULTSORT:Form Factor (Electronics)}}

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