Rectification (Converting AC to DC): Difference between revisions

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===A Mathematical Model===
===A Mathematical Model===


What are the mathematical equations that allow us to model this topic.  For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.
For the half-wave rectifier, only one half of the wave is passed, so the output voltage is lower:
 
<math>\begin{align}
V_\mathrm {rms} &= \frac{V_\mathrm {peak}}{2}\\
V_\mathrm {dc} &= \frac{V_\mathrm {peak}}{\pi}
\end{align}</math>
 
''V''<sub>rms</sub>: the root-mean-square value of output voltage
 
 
For a full-wave rectifier, the following voltages are:
 
<math>\begin{align}
V_\mathrm {dc}=V_\mathrm {av}&=\frac{2V_\mathrm {peak}}{\pi}\\
V_\mathrm {rms}&=\frac {V_\mathrm {peak}}{\sqrt 2}
\end{align}</math>
====Efficiency====
The power efficiency for rectifiers is defined as the ratio of input power (AC) to output power (DC). Energy is lost from the conversion creating ripples, but can be maximized through the use of capacitors and smoothing.
 
:<math>P_\mathrm {in} = {V_\mathrm {peak} \over 2} \cdot {I_\mathrm {peak} \over 2}</math>
 
(the divisors are 2 rather than √2 because no power is delivered on the negative half-cycle)
 
:<math>P_\mathrm {out} = {V_\mathrm {peak} \over \pi} \cdot {I_\mathrm {peak} \over \pi}</math>
 
Thus maximum efficiency for a half-wave rectifier is,
 
<math>\eta = {P_\mathrm {out} \over P_\mathrm {in}} = \frac{4}{\pi^2} = 40.6% </math>
 
Similarly, for a full-wave rectifier,
 
<math>\eta = {P_\mathrm {out} \over P_\mathrm {in}} = \frac{8}{\pi^2} = 81.1% </math> 


===A Computational Model===
===A Computational Model===

Revision as of 22:09, 5 December 2015

Rectification is the conversion of alternating current (AC) to direct current (DC). This is performed by a device that only allows one-way flow of electrons (a rectifier).

The Main Idea

Rectification is the conversion of alternating current to direct current. Rectification is performed by a diode that allows current to flow in one direction but not in the opposite direction. Direct current that has only been rectified, however, has various changes in voltage lingering from the alternating current. Capacitors are used to smooth the current and make it even.

The simplest kind of rectifier circuit is the half-wave rectifier. Only one half of an AC waveform to pass through to the load.

To rectify AC power to obtain the full use of both half-cycles of the sine wave, a different rectifier circuit configuration may be used. Such a circuit is called a full-wave rectifier.

A Mathematical Model

For the half-wave rectifier, only one half of the wave is passed, so the output voltage is lower:

[math]\displaystyle{ \begin{align} V_\mathrm {rms} &= \frac{V_\mathrm {peak}}{2}\\ V_\mathrm {dc} &= \frac{V_\mathrm {peak}}{\pi} \end{align} }[/math]

Vrms: the root-mean-square value of output voltage


For a full-wave rectifier, the following voltages are:

[math]\displaystyle{ \begin{align} V_\mathrm {dc}=V_\mathrm {av}&=\frac{2V_\mathrm {peak}}{\pi}\\ V_\mathrm {rms}&=\frac {V_\mathrm {peak}}{\sqrt 2} \end{align} }[/math]

Efficiency

The power efficiency for rectifiers is defined as the ratio of input power (AC) to output power (DC). Energy is lost from the conversion creating ripples, but can be maximized through the use of capacitors and smoothing.

[math]\displaystyle{ P_\mathrm {in} = {V_\mathrm {peak} \over 2} \cdot {I_\mathrm {peak} \over 2} }[/math]

(the divisors are 2 rather than √2 because no power is delivered on the negative half-cycle)

[math]\displaystyle{ P_\mathrm {out} = {V_\mathrm {peak} \over \pi} \cdot {I_\mathrm {peak} \over \pi} }[/math]

Thus maximum efficiency for a half-wave rectifier is,

[math]\displaystyle{ \eta = {P_\mathrm {out} \over P_\mathrm {in}} = \frac{4}{\pi^2} = 40.6% }[/math]

Similarly, for a full-wave rectifier,

[math]\displaystyle{ \eta = {P_\mathrm {out} \over P_\mathrm {in}} = \frac{8}{\pi^2} = 81.1% }[/math]

A Computational Model

How do we visualize or predict using this topic. Consider embedding some vpython code here Teach hands-on with GlowScript

Examples

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External links

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References

http://www.allaboutcircuits.com/textbook/semiconductors/chpt-3/rectifier-circuits/

http://www.global.tdk.com/news_center/publications/power_electronics_world/pdf/aaa60607.pdf

http://www3.nd.edu/~lemmon/courses/ee224/web-manual/web-manual/lab8b/node6.html

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