Power Electronics

# Single-phase full-wave diode rectifier

### Single-phase full-wave diode rectifier

Single-phase diode rectifier, converting ac signal into a dc voltage, exist in two types – half-wave and full-wave one. Half-wave diode rectifier was mentioned before.

Full-wave diode rectifier can be two types as well – with a centre-tapped transformer and bridge rectifier. Both of them are depicted on the figure below.

In the case of center-tapped transformer, we have two half-wave rectifiers, combined. The DC currents of these half-wave transformers are equal but opposite. Each diode conducts in corresponding half-cycle of transformer. Below you can see the current and voltage wave-forms for this rectifier.

Bridge rectifier circuit is depicted below. Here we have four diodes instead of two. So in each half-cycle of transformer we have two conducting diodes. Below you can see voltage and current wave-forms for this rectifier.

The average voltage is ${V}_{DC}=\frac{\omega }{T}{\int }_{0}^{T}{V}_{m}\mathrm{sin}\omega tdt$.

So ${V}_{DC}=\frac{2{V}_{m}}{\pi }=0.636{V}_{m}$.  Root-mean-square (RMS) value is $RMS=\sqrt{\frac{1}{T}{\int }_{0}^{T}{{v}^{2}}_{L}\left(t\right)dt}=\sqrt{\sqrt{\frac{\omega }{\pi }{\int }_{0}^{\pi }{\left({V}_{m}\mathrm{sin}\omega t\right)}^{2}dt}}$

and ${V}_{L}=\frac{{V}_{m}}{\sqrt{2}}=0.707{V}_{m}$.

The average value of load current ${I}_{dc}=\frac{{V}_{dc}}{R}=\frac{0.636{V}_{dc}}{R}$. And the RMS value of load current is ${I}_{L}=\frac{0.707{V}_{m}}{R}$.

The rectification ratio (RF), measures of rectification effectiveness  $\sigma =\frac{{P}_{dc}}{{P}_{L}}=0.81$.

Form factor (FF) is a ratio of root-mean-square value of voltage or current to it’s average value. $FF=\frac{{V}_{L}}{{V}_{dc}}$ and $FF=\frac{{I}_{L}}{{I}_{dc}}$. For full-wave rectifier $FF=1.1$.

Ripple factor (RF)  is the measure of ripple $RF=\frac{{V}_{ac}}{{V}_{dc}}$, where ${V}_{ac}=\sqrt{{{V}^{2}}_{L}+{{V}^{2}}_{dc}}$. Making several mathematical simplifications $RF=\sqrt{{\left(\frac{{V}_{L}}{{V}_{dc}}\right)}^{2}–1}=\sqrt{F{F}^{2}–1}=0.482$.

Transformer utilisation factor (TUF) is a transformer merit measure $TUM=\frac{{V}_{dc}{I}_{dc}}{{V}_{S}{I}_{S}}$ where ${V}_{S}$ and ${I}_{S}$ are rms voltage and rms current ratings of secondary transformer. Where for full-wave transformer ${I}_{S}=\frac{0.707{V}_{m}}{R}$ .

Reader must note that only half-wave rectifier with resistive load produce harmonic currents in their transformers.

Datasheets of industrial single-phase full-wave diode rectifiers contain following important parameters:

• Peak repetitive reverse voltage ${V}_{RRM}$;
• Ripple factor;
• RMS input voltage per transformer leg ${V}_{S}$;
• Diode average current ${I}_{F\left(AV\right)}$;
• Rectification ratio;
• Output ripple frequency ${f}_{r}$;
• Peak repetitive forward current ${I}_{FRM}$;
• Transformer rating primary VA;
• Diode RMS current ${I}_{F\left(RMS\right)}$ ;
• Form factor;
• Transformer rating secondary VA;
• Form factor of diode current $\frac{{I}_{F\left(RMS\right)}}{{I}_{F\left(AV\right)}}$.

For instance, Digi-Key Electronics offers great range of single-phase full-wave and bridge rectifiers.