# Voltage-multiplying Rectifiers[

Dec 28, 2017

### Voltage-multiplying rectifiers

Main article: Voltage multiplier

Switchable full bridge/voltage doubler.

The simple half-wave rectifier can be built in two electrical configurations with the diodes pointing in opposite directions, one version connects the negative terminal of the output direct to the AC supply and the other connects the positive terminal of the output direct to the AC supply. By combining both of these with separate output smoothing it is possible to get an output voltage of nearly double the peak AC input voltage. This also provides a tap in the middle, which allows use of such a circuit as a split rail power supply.

A variant of this is to use two capacitors in series for the output smoothing on a bridge rectifier then place a switch between the midpoint of those capacitors and one of the AC input terminals. With the switch open, this circuit acts like a normal bridge rectifier. With the switch closed, it act like a voltage doubling rectifier. In other words, this makes it easy to derive a voltage of roughly 320 V (±15%, approx.) DC from any 120 V or 230 V mains supply in the world, this can then be fed into a relatively simple switched-mode power supply. However, for a given desired ripple, the value of both capacitors must be twice the value of the single one required for a normal bridge rectifier; when the switch is closed each one must filter the output of a half-wave rectifier, and when the switch is open the two capacitors are connected in series with an equivalent value of half one of them.

Cockcroft Walton voltage multiplier

Cascaded diode and capacitor stages can be added to make a voltage multiplier (Cockroft-Walton circuit). These circuits are capable of producing a DC output voltage potential up to about ten times the peak AC input voltage, in practice limited by current capacity and voltage regulation issues. Diode voltage multipliers, frequently used as a trailing boost stage or primary high voltage (HV) source, are used in HV laser power supplies, powering devices such as cathode ray tubes (CRT) (like those used in CRT based television, radar and sonar displays), photon amplifying devices found in image intensifying and photo multiplier tubes (PMT), and magnetron based radio frequency (RF) devices used in radar transmitters and microwave ovens. Before the introduction of semiconductor electronics, transformerless vacuum tube receivers powered directly from AC power sometimes used voltage doublers to generate roughly 300 VDC from a 100–120 V power line.

## Quantification of rectifiers

 It has been suggested that Transformer utilization factor be merged into this section. (Discuss) Proposed since November 2017.
 This section is missing information about conversion ratios for at least three-phase half-wave and full-wave rectification, since these rectifiers have their own sections in this article.. Please expand the section to include this information. Further details may exist on the talk page. (October 2017)

Several ratios are used to quantify the function and performance of rectifiers or their output, including transformer utilization factor (TUF), conversion ratio (η), 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.

Conversion ratio (also called "rectification ratio", and confusingly, "efficiency") η 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.[6] 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.

• {\displaystyle P_{\mathrm {AC} }={V_{\mathrm {peak} } \over 2}\cdot {I_{\mathrm {peak} } \over 2}} (the divisors are 2 rather than √2 because no power is delivered on the negative half-cycle)

• {\displaystyle P_{\mathrm {DC} }={V_{\mathrm {peak} } \over \pi }\cdot {I_{\mathrm {peak} } \over \pi }}

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

• {\displaystyle \eta ={P_{\mathrm {DC} } \over P_{\mathrm {AC} }}\approx 40.5\%}

Similarly, for a full-wave rectifier,

• {\displaystyle P_{\mathrm {AC} }={V_{\mathrm {peak} } \over {\sqrt {2}}}\cdot {I_{\mathrm {peak} } \over {\sqrt {2}}}}

• {\displaystyle P_{\mathrm {DC} }={2\cdot V_{\mathrm {peak} } \over \pi }\cdot {2\cdot I_{\mathrm {peak} } \over \pi }}

• {\displaystyle \eta ={P_{\mathrm {DC} } \over P_{\mathrm {AC} }}\approx 81.0\%}

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,

• {\displaystyle P_{\mathrm {AC} }=3\cdot {V_{\mathrm {peak} } \over 2}\cdot {I_{\mathrm {peak} } \over 2}}

• {\displaystyle P_{\mathrm {DC} }={\frac {3\cdot {\sqrt {3}}\cdot V_{\mathrm {peak} }}{2\pi }}\cdot {\frac {3\cdot {\sqrt {3}}\cdot I_{\mathrm {peak} }}{2\pi }}}

For a three-phase full-wave rectifier,

• {\displaystyle P_{\mathrm {AC} }=3\cdot {V_{\mathrm {peak} } \over {\sqrt {2}}}\cdot {I_{\mathrm {peak} } \over {\sqrt {2}}}}

• {\displaystyle P_{\mathrm {DC} }={\frac {3\cdot {\sqrt {3}}\cdot V_{\mathrm {peak} }}{\pi }}\cdot {\frac {3\cdot {\sqrt {3}}\cdot I_{\mathrm {peak} }}{\pi }}}