How to Calculate Modified Sine Waveform

I am sure you might have often wondered how to accomplish the correct way of optimizing and calculating a modified square wave such that it produced almost an identical replication of a sine wave when used in an inverter application.

本文讨论的计算将帮助您了解经过改进的方波电路，可以将改进的方波电路变成SineWave等效的技术。让我们了解程序。

The first criterion to accomplish this is to match the RMS value of the modified square with the sinewave counterpart in a way that the result replicates the sinusoidal waveform as closely as possible.

What is RMS (Root Mean Square)

我们知道我们的家庭AC正弦波形电压的RMS通过解决以下关系来确定：

V顶峰= √2 Vrms.

Where V顶峰is the maximum limit or the peak limit of the sine waveform cycle, while the mean magnitude of the each cycle of the waveform is shown as the Vrms.

The√2in the formula helps us to find the平均值or the net value of an AC cycle which changes its voltage exponentially with time. Because the sinusoidal voltage value varies with time and is a function of time, it cannot be calculated by employing the basic average formula, instead we depend on the above formula.

或者，AC RMS可以被理解为相当于直流电流（DC）的值，该值在横跨电阻负载连接时产生相同的平均功率耗散。

OK, so now we know the formula for calculating the RMS of a sinewave cycle with reference to its peak voltage value.

This can be applied for evaluating the peak and the RMS for our home 50 Hz AC too. By solving this we get the RMS as 220V and peak as 310V for all 220V based mains AC systems.

计算修改的方波rms和峰值

Now let's see how this relationship could be applied in modified square wave inverters for setting up the right waveform cycles for a 220V system, which would correspond to a 220V AC sinusoidal equivalent.

我们已经知道，AC RMS相当于DC波形的平均功率。这给了我们这个简单的表达：

V顶峰= V.rms.

但我们也希望方波的峰值在310V，因此似乎上面的等式不会保持良好，不能用于目的。

对于每个方波周期，标准是具有310V峰值以及220V的平均值或平均值。

To solve this correctly we take the help of the ON/OFF time of the square waves, or the duty cycle percentage as explained below:

50 Hz AC波形的每个半周期的持续时间为10毫秒（MS）。

A modified half wave cycle in its most crude form must look like as shown in the following image:

我们可以看到每个循环从零或空白间隙开始，然后拍摄高达310V峰值脉冲，并再次以0V间隙结束，然后对其他半周期重复该过程。

为了实现所需的220V rms，我们必须计算和优化峰值和零间隙部分或循环的开/关周期，使得平均值产生所需的220V。

The grey line represents the 50% period of the cycle, which is 10 ms.

现在我们需要找出平均220V的开/关时间的比例。我们以这种方式这样做：

220 / 310 x 100 = 71 % approximately

这表明310 v峰值在上面的改变了d cycle should occupy 71% of the 10 ms period, while the two zero gaps should be 29% combined, or 14.5% each.

因此在一个10 len女士gth, the first zero section should be 1.4 ms, followed by the 310 V peak for 7 ms, and finally the last zero gap of another 1.4 ms.

一旦完成这一点，我们可以期望来自逆变器的输出来产生正弦波形的合理复制。

Despite of all these you may find that the output is not quite an ideal replication of the sine wave, because the discussed modified square wave is in its most basic form or a crude type. If we want the output to match the sine wave with maximum precision, then we have to go for anSPWM approach.

我希望上面的讨论可能已经启发了你如何计算和优化修改正方形来复制Sinewave输出的修改方。

For practical verification, the readers can try applying the above technique to this简单的改装逆变电路。

这是另一个classic example of an optimized modified waveform用于在变压器的次级获取一个良好的正弦波。