# 波形因數

## 計算

${\displaystyle X_{rms}={\sqrt {{1 \over {T}}{\int _{t_{0}}^{t_{0}+T}{[f(t)]}^{2}\,dt}}}}$

${\displaystyle X_{arv}={1 \over {T}}{\int _{t_{0}}^{t_{0}+T}{|x(t)|\,dt}}}$

${\displaystyle k_{f}={\frac {RMS}{ARV}}={\frac {\sqrt {{1 \over {T}}{\int _{t_{0}}^{t_{0}+T}{[f(t)]}^{2}\,dt}}}{{1 \over {T}}{\int _{t_{0}}^{t_{0}+T}{|x(t)|\,dt}}}}={\frac {\sqrt {T\int _{t_{0}}^{t_{0}+T}{{[f(t)]}^{2}\,dt}}}{\int _{t_{0}}^{t_{0}+T}{|x(t)|\,dt}}}}$

## 性質

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

${\displaystyle k_{av}\geq k_{a}\geq k_{f}}$[2]

${\displaystyle k_{av}=k_{a}k_{f}}$,[2]

${\displaystyle k_{f}={\frac {k_{av}}{k_{a}}}}$.

## 參考資料

1. ^ Stutz, Michael. Measurement of AC Magnitude. BASIC AC THEORY. [30 May 2012].
2. 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 （波兰语）.
3. Jędrzejewski, Kazimierz. Laboratorium Podstaw Pomiarow. Warsaw: Wydawnictwo Politechniki Warszawskiej. 2007: 86–87. ISBN 978-83-7207-4 （波兰语）.
4. ^ Tanuwijaya, Franky. True RMS vs AC Average Rectified Multimeter Readings when a Phase Cutting Speed Control is Used (PDF). Esco Micro Pte Ltd. [2012-12-13]. 引用错误：带有name属性“true_rms”的<ref>标签用不同内容定义了多次 引用错误：带有name属性“true_rms”的<ref>标签用不同内容定义了多次
5. Nastase, Adrian. How to Derive the RMS Value of Pulse and Square Waveforms. [9 June 2012].