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 $V_{DC}=\frac{\omega }{T}{\int }_0^T{V}_m\sin \omega tdt$.

So $V_{DC}=\frac{2V_m}{\pi }=0.636V_m$.  Root-mean-square (RMS) value is $RMS=\sqrt{\frac{1}{T}{\int }_0^T{v^2}_L\left(t\right)dt}=\sqrt{\sqrt{\frac{\omega }{\pi }{\int }_0^{\pi }{\left(V_m\sin \omega t\right)}^{2}dt}}$

and $V_L=\frac{V_m}{\sqrt{2}}=0.707V_m$.

The average value of load current $I_{dc}=\frac{V_{dc}}{R}=\frac{0.636V_{dc}}{R}$. And the RMS value of load current is $I_L=\frac{0.707V_m}{R}$.

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 $I_S=\frac{0.707V_m}{R}$ .

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.