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本帖最后由 1109 于 2013-10-19 13:44 编辑
说来惭愧，搞了2年多开关电源竟然一直都没有搞清楚正弦波的有效值（RMS），峰峰值（Peak-Peak）及平均值（Avg）之间的关系，只知道：有效值=最大值/√2.....................
昨天上午正在看一份資料，里面写道“有效值=最大值/√2”，当时也不知道发什么神经想去自己推算一下这个关系式，结果悲剧了。发现自己整整上午都没有推出来 。到下午上班的时候就放狗去搜，结果搜到的资料里面没有一份有计算步骤的！我很生气了，于是扩大搜索范围，到樯外面去逛了一圈，很幸运的找到了一份不错的资料，不敢独享，遂转过来分享给坛子里面可爱的兄弟们，顺便感谢一下美利坚国际友人！
PS:本人英语也是个大菜鸟，所以就不能帮各位翻译了，如果有不认识的请找词霸帮忙！
原帖转自：http://www.rfcafe.com/references/electrical/sinewave-voltage-conversion.htm
A sinewave is defined by the trigonometric sine function. When plotted as voltage (V) as a function of phase (θ), it looks similar to the figure to the right. The waveform repeats every 2p radians (360°), and is symmetrical about the voltage axis (when no DC offset is present). Voltage and current exhibiting cyclic behavior is referred to as alternating; i.e., alternating current (AC). One full cycle is shown here. The basic equation for a sinewave is as follows:
There are a number of ways in which the amplitude of a sinewave is referenced, usually as peak voltage (Vpk or Vp), peak-to-peak voltage (Vpp or Vp-p or Vpkpk or Vpk-pk), average voltage (Vav or Vavg), and root-mean-square voltage (Vrms). Peak voltage and peak-to-peak voltage are apparent by looking at the above plot. Root-mean-square and average voltage are not so apparent.
Root-Mean-Square Voltage (Vrms)：
As the name implies, Vrms is calculated by taking the square root of the mean average of the square of the voltage in an appropriately chosen interval. In the case of symmetrical waveforms like the sinewave, a quarter cycle faithfully represents all four quarter cycles of the waveform. Therefore, it is acceptable to choose the first quarter cycle, which goes from 0 radians (0°) through p/2 radians (90°).
Vrms is the value indicated by the vast majority of AC voltmeters. It is the value that, when applied across a resistance, produces that same amount of heat that a direct current (DC) voltage of the same magnitude would produce. For example, 1 V applied across a 1 Ω resistor produces 1 W of heat. A 1 Vrms sinewave applied across a 1 Ω resistor also produces 1 W of heat. That 1 Vrms sinewave has a peak voltage of √2 V (≈1.414 V), and a peak-to-peak voltage of 2√2 V (≈2.828 V).
Since finding a full derivation of the formulas for root-mean-square (Vrms) voltage is difficult, it is done here for you.
So,
Average Voltage (Vavg)：
As the name implies, Vavg is calculated by taking the average of the voltage in an appropriately chosen interval. In the case of symmetrical waveforms like the sinewave, a quarter cycle faithfully represents all four quarter cycles of the waveform. Therefore, it is acceptable to choose the first quarter cycle, which goes from 0 radians (0°) through p/2 radians (90°).
So,
As with the Vrms formula, a full derivation for the Vavg formula is given here as well.
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阿莫论坛20周年了！感谢大家的支持与爱护！！
如果天空是黑暗的，那就摸黑生存;
如果发出声音是危险的，那就保持沉默;
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也不要为自己的苟且而得意；
不要嘲讽那些比自己更勇敢的人。
我们可以卑微如尘土，但不可扭曲如蛆虫。
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发表于 2013-10-19 13:30:35
楼主
话说我现在一直搞不懂交流电怎么算