the voltage for all three phases are plotted on the right.

no law of physics are broken, as the waveforms are completely contained within 0% and 100% PWM range

now, let's decompose each of these waveforms back onto its fundamental sinewave plus third harmonic sinewave

the fundamental sinewave (the ones that are too big for the bus voltage) are easily distinguishable for each phase and can be seen poking out the top and bottom limits of 0% and 100% PWM

but do you notice anything interesting about the third harmonic waveforms for each phase?

they are all exactly the same waveform

all three third harmonic waveforms are plotted to the right, which share the same black waveform

in other words, the third harmonic (black) waveform is a common-mode waveform to all three phase

Since the black waveform is common on all three phases of the motor, that means that every point in the motor is going up and down at a third harmonic rate with respect to the DC bus.

The motor center node (neutral) is of particular interest, and also has this third harmonic waveform on it with respect to the DC bus.

The question now becomes, “what is the phase-to-neutral voltage waveform across each winding?”

In other words, if we take an oscilloscope probe, attach the ground clip to the motor's center node, and then attach the probe tip to each phase voltage, what would the waveforms look like?

Recall that the phase voltages consist of a big sinewave plus a third harmonic sinewave added together. The scope will display the phase voltage minus the center node voltage.

So doing a little verbal mathematics, the scope will see a big sinewave plus the third harmonic sinewave (at the probe tip) minus the third harmonic sinewave (at the probe ground).

In other words, the third harmonic term goes away! (Press spacebar to see what the scope will see).

Presto! We have now created phase-to- neutral sinewaves on the motor windings whose peak-to-peak amplitudes exceed the DC bus voltage!

And we did it perfectly legal, without breaking any laws of physics.

Is that cool or what! We can accomplish this feat of magic by allowing the motor's center node voltage to move around with respect to the DC bus.

所有三相的電壓都繪製在右側。

沒有違反物理定律，因為波形完全包含在 0% 和 100% PWM 範圍內

現在，讓我們將每個波形分解回其基波正弦波加上三次諧波正弦波

每個相位的基本正弦波（對於總線電壓來說太大的正弦波）很容易區分，並且可以看到突出了 0% 和 100% PWM 的上限和下限

但是您是否注意到每相的三次諧波波形有什麼有趣的地方？

它們的波形完全相同

所有三個三次諧波波形都繪製在右側，它們共享相同的黑色波形

換句話說，三次諧波（黑色）波形是所有三相的共模波形

由於黑色波形在馬達的所有三相上都很常見，這意味著馬達中的每個點都以相對於直流母線的三次諧波速率上升和下降。

馬達中心節點（中性點）特別令人感興趣，並且其上也具有相對於直流母線的三次諧波波形。

現在的問題是：“每個繞組上的相電壓波形是多少？”換句話說，如果我們使用示波器探頭，將接地夾連接到馬達的中心節點，然後將探頭尖端連接到每相電壓，波形會是什麼樣子？

回想一下，相電壓由一個大正弦波加上一個三次諧波正弦波組成。

示波器將顯示相電壓減去中心節點電壓。

因此，進行一些口頭數學計算，示波器將看到一個大正弦波加上三次諧波正弦波（在探頭尖端）減去三次諧波正弦波（在探頭接地）。換句話說，三次諧波項消失了！ （按空白鍵可查看示波器將看到的內容）。

急！我們現在已經在馬達繞組上創建了相到中性正弦波，其峰峰值幅度超過了直流母線電壓！

我們的做法完全合法，沒有違反任何物理定律。

這很酷還是什麼！

我們可以透過允許馬達的中心節點電壓相對於直流總線移動來實現這一神奇壯舉。

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