The Effect of Phase on Switching Rectifiers

In the previous post, we examined some of the most basic switch based rectifying circuits and saw that the switch could be replaced with a passive diode. Here, we will explore what happens when the switch is no longer in phase with the input. Let us consider a different way to operate the switch.

The very basic circuit used in the first example.

Using the same circuit as the previous example, we instead turn on the switch whenever $V_{ac} > V_{peak/s}$, and turn it off one half cycle later. The input and output voltage waveforms are shown below. The input has $ = 0$ and $V_{RMS} = V_{peak}/\sqrt{2}$. The switch turns on as the input waveform crosses the line $V_{peak}/2$, $30^o$ after the zero crossing point.

Output waveform from the simple switched AC source with 30 degree phase shift.

\begin{aligned} v_{out} &= \frac{1}{2\pi} V_{peak} \int_{\pi/3}^{2\pi/3} cos \theta d\theta\\ &= \frac{\sqrt{3}}{2\pi}V_{peak}\\ &= 0.2757 V_{peak} \end{aligned}

which is only 87% of the previous DC value. The RMS voltage is still $V_{peak}/2$.

In the last example, a diode cannot be used to perform the requested conversion. The circuit still performs rectification, but some more general switch will be needed to permit the necessary control. The rectifier example shows how a switch can be used to obtain a conversion function. From the examples, rectifier operation can be adjusted by manipulating switching timing or the load properties. The DC output depends on when the switch is turned on or off. For example, for a 90 degree phase shift, the switch turns on during the maximum of the AC cycle and remains on until the minimum. In this case it is clear that the output will average to zero over time. Similarly, a 180 degree phase shift means the switch is only on during the negative portions of the AC cycle, resulting in a negative polarity rectifier. This can be seen directly in the math above by shifting the limits of integration.

However, the output so far is not a clean DC waveform and very useful yet. We need filtering to recover the DC value. Any type of low-pass filter could, in principle, allow recovery of the DC output. Filters are one way in which energy storage elements are applied in power electronics. We will explore adding filtering elements to out basic switched circuit in the next post.