# 波形因數

## 計算

$X_{rms} = \sqrt {{1 \over {T}} {\int_{t_0}^{t_0+T} {[f(t)]}^2\, dt}}$

$X_{arv} = {1 \over {T}} {\int_{t_0}^{t_0+T} {|x(t)|\, dt}}$

$k_f = \frac{RMS}{ARV} = \frac{\sqrt {{1 \over {T}} {\int_{t_0}^{t_0+T} {[f(t)]}^2\, dt}}}{{1 \over {T}} {\int_{t_0}^{t_0+T} {|x(t)|\, dt}}} = \frac{\sqrt{T\int_{t_0}^{t_0+T}{{[f(t)]}^2\, dt}}}{\int_{t_0}^{t_0+T} {|x(t)|\, dt}}$

## 性質

• 峰值因數$k_a = \frac{X_{max}}{X_{rms}}$，最大值和均方根值的比值。
• 平均因數：$k_{av} = \frac{X_{max}}{X_{arv}}$，最大值和整流平均值的比值，較少用到。

$k_{av} \ge k_a \ge k_f$[2]

$k_{av} = k_ak_f$,[2]

$k_f = \frac{k_a}{k_{av}}$.

## 參考資料

1. ^ Stutz, Michael. Measurement of AC Magnitude. BASIC AC THEORY. [30 May 2012].
2. ^ 2.0 2.1 2.2 2.3 2.4 Dusza, Jacek; Grażyna Gortat, Antoni Leśniewski. Podstawy Miernictwa (Foundations of Measurement). Warszawa: Wydawnictwo Politechniki Warszawskiej. 2002: 136–142, 197–203, 323. ISBN 83-7207-344-9 （Polish）.
3. ^ 3.0 3.1 3.2 Jędrzejewski, Kazimierz. Laboratorium Podstaw Pomiarow. Warsaw: Wydawnictwo Politechniki Warszawskiej. 2007: 86–87. ISBN 978-83-7207-4 （Polish）.
4. ^ Tanuwijaya, Franky. True RMS vs AC Average Rectified Multimeter Readings when a Phase Cutting Speed Control is Used. Esco Micro Pte Ltd. [2012-12-13].
5. ^ 5.0 5.1 Nastase, Adrian. How to Derive the RMS Value of Pulse and Square Waveforms. [9 June 2012].