Vrms = 0.5 Vmax for Half Wave Rectifier: Proof

In summary, the conversation discusses how to prove that Vrms = 0.5 Vmax for a half-wave rectifier. It is explained that the graph of a half-wave rectifier is just the upper or lower part of a sinusoidal wave, and that voltage can be defined as a piecewise function of time. The RMS value of the function is then calculated to prove the statement.
  • #1
songoku
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Homework Statement


How to prove that Vrms = 0.5 Vmax for half wave rectifier


Homework Equations





The Attempt at a Solution


I know the graph of half wave rectifier is just the upper part or lower part of sinusoidal wave. But I don't have clue to prove it..

Thanks
 
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  • #2
So that means that for a half-wave rectifier you can define voltage as a piecewise function of time:
[tex]
V(t) = \left\{ \begin{array}{cc}V_{max}sin({\omega}t),&\mbox{ if } 0 \leq t \leq \frac{T}{2}\\0,&\mbox{ if } \frac{T}{2} < t \leq T\end{array}\right.
[/tex]

And it's a fairly straightforward calculation to find the RMS value of the function:
[tex]
\sqrt{\frac{1}{T}\int_{0}^{T}[V(t)]^2dt[/tex]
 
  • #3
I get it now

Thanks a lot, JaWiB ! :smile:
 

1. What is a half wave rectifier?

A half wave rectifier is an electronic device that converts an alternating current (AC) input signal into a direct current (DC) output signal. It does this by allowing only half of the AC waveform to pass through, resulting in a pulsating DC output.

2. How does a half wave rectifier work?

A half wave rectifier works by using a diode, which acts as a one-way valve for electrical current. The AC input signal is applied to one end of the diode, and the output is taken from the other end. When the AC waveform is positive, the diode allows current to flow through, but when the waveform is negative, the diode blocks current from passing through.

3. What is the purpose of a half wave rectifier?

The purpose of a half wave rectifier is to convert an AC signal into a DC signal. This is useful in many electronic applications, such as power supplies, where a steady DC voltage is needed for devices to operate properly.

4. What are the advantages of using a half wave rectifier?

One advantage of using a half wave rectifier is its simplicity. It only requires one diode and a few other components, making it a cost-effective option. It also has a relatively high efficiency, meaning it can convert a large portion of the AC input signal into DC output.

5. What are the limitations of a half wave rectifier?

One limitation of a half wave rectifier is that it produces a pulsating DC output, meaning the voltage is not constant and may not be suitable for some sensitive electronic devices. It also only utilizes half of the AC input signal, resulting in a lower average output voltage compared to a full wave rectifier.

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