Editing Rectifier (section)

== Quantification of rectifiers ==
{{missing information|section|conversion ratios for at least three-phase half-wave and full-wave rectification, since these rectifiers have their own sections in this article.|date=October 2017}}
Several ratios are used to quantify the function and performance of rectifiers or their output, including transformer utilization factor (TUF), conversion ratio (<big>''η''</big>), ripple factor, form factor, and peak factor.  The two primary measures are DC voltage (or offset) and peak-peak ripple voltage, which are constituent components of the output voltage.

=== Conversion ratio ===
Conversion ratio (also called "rectification ratio", and confusingly, "efficiency") <big>''η''</big> is defined as the ratio of DC output power to the input power from the AC supply.  Even with ideal rectifiers, the ratio is less than 100% because some of the output power is AC power rather than DC which manifests as ripple superimposed on the DC waveform.  The ratio can be improved with the use of smoothing circuits which reduce the ripple and hence reduce the AC content of the output. Conversion ratio is reduced by losses in transformer windings and power dissipation in the rectifier element itself. This ratio is of little practical significance because a rectifier is almost always followed by a filter to increase DC voltage and reduce ripple.  In some three-phase and multi-phase applications the conversion ratio is high enough that smoothing circuitry is unnecessary.<ref>Wendy Middleton, Mac E. Van Valkenburg (eds), ''Reference Data for Engineers: Radio, Electronics, Computer, and Communications'', p. 14. 13, Newnes, 2002 {{ISBN|0-7506-7291-9}}.</ref>
In other circuits, like filament heater circuits in vacuum tube electronics where the load is almost entirely resistive, smoothing circuitry may be omitted because resistors dissipate both AC and DC power, so no power is lost.

For a half-wave rectifier the ratio is very modest.

: <math>P_\mathrm {AC} = {V_\mathrm{peak} \over 2} \cdot {I_\mathrm {peak} \over 2}</math>    (the divisors are 2 rather than {{radic|2}} because no power is delivered on the negative half-cycle)

: <math>P_\mathrm {DC} = {V_\mathrm{peak} \over \pi} \cdot {I_\mathrm {peak} \over \pi}</math>

Thus maximum conversion ratio for a half-wave rectifier is,

: <math>\eta = {P_\mathrm {DC} \over P_\mathrm {AC}} \approx 40.5\% </math>

Similarly, for a full-wave rectifier,

: <math>P_\mathrm {AC} = {V_\mathrm{peak} \over \sqrt 2} \cdot {I_\mathrm {peak} \over \sqrt 2}</math>

: <math>P_\mathrm {DC} = {2 \cdot V_\mathrm{peak} \over \pi} \cdot {2 \cdot I_\mathrm {peak} \over \pi}</math>

: <math>\eta = {P_\mathrm {DC} \over P_\mathrm {AC}} \approx 81.0\% </math>

Three-phase rectifiers, especially three-phase full-wave rectifiers, have much greater conversion ratios because the ripple is intrinsically smaller.

For a three-phase half-wave rectifier,

: <math>P_\mathrm {AC} = 3 \cdot {V_\mathrm{peak} \over 2} \cdot {I_\mathrm {peak} \over 2}</math>

: <math>P_\mathrm {DC} = \frac{3\sqrt{3} \cdot V_\mathrm{peak}}{2 \pi} \cdot \frac{3\sqrt3 \cdot I_\mathrm{peak}}{2 \pi}</math>

For a three-phase full-wave rectifier,

: <math>P_\mathrm {AC} = 3 \cdot {V_\mathrm{peak} \over \sqrt 2} \cdot {I_\mathrm {peak} \over \sqrt 2}</math>

: <math>P_\mathrm {DC} = \frac{3\sqrt3 \cdot V_\mathrm{peak}} \pi \cdot \frac{3\sqrt3 \cdot I_\mathrm{peak}} \pi</math>

=== Transformer utilization ratio ===
The transformer utilization factor (TUF) of a rectifier circuit is defined as the ratio of the DC power available at the input resistor to the AC rating of the output coil of a transformer.<ref name="Rashid2011">{{cite book|url=https://books.google.com/books?id=eS1z95mzi28C&pg=PA153|title=POWER ELECTRONICS HANDBOOK|last=Rashid|first=Muhammad|date=2011-01-13|publisher=Elsevier|isbn=9780123820372|page=153}}</ref><ref name="A.P.Godse2008">{{cite book|url=https://books.google.com/books?id=1uP2oVwXEZAC&pg=SA8-PA16|title=Elements of Electronics Engineering|last1=Atul P.Godse|last2=U. A. Bakshi|date=2008-01-01|publisher=Technical Publications|isbn=9788184312928|page=8}}</ref>

: <math>
\text{T.U.F} = \frac{P_\text{odc}}{\text{VA rating of transformer}}
</math>

The <math>VA</math> rating of the transformer can be defined as: <math>
VA = V_{\mathrm{rms}} \dot I_{\mathrm{rms}} (\text{For secondary coil.})
</math>