Full Wave Rectifier

In the previous article, you learned about the half-wave rectifier. It uses only one half of the AC input signal, which results in lower rectification efficiency and high ripple in the output. Due to these drawbacks, it is not suitable for applications requiring a stable and smooth DC output. To overcome these limitations, a full-wave rectifier is used.

In this article, you will clearly understand the working of a centre-tapped full-wave rectifier, its circuit diagram, waveforms, formulas, and performance parameters such as DC value, RMS value, form factor, peak factor, and rectification efficiency.

Full Wave Rectifier

A full-wave rectifier is an electronic circuit that converts an alternating current (AC) signal into pulsating direct current (DC) by utilizing both the positive and negative half-cycles of the AC input waveform.

There are two types of full-wave rectifiers:

  • Centre Tapped Full Wave Rectifier
  • Bridge Rectifier

The diagram below shows a centre-tapped full-wave rectifier circuit, and its input and output waveforms.

Full Wave Rectifier

In this article, we will focus only on the centre-tapped full-wave rectifier; we will cover the bridge rectifier in different posts.

Full Wave Rectifier Circuit

The centre-tapped full-wave rectifier consists of a centre-tapped transformer, two PN junction diodes, and a load resistor (RL).

Center-Tapped Full Wave Rectifier Circuit

The two diodes are connected to each end of the secondary winding of the transformer, and the load resistor is connected between the common cathode (or anode, depending on configuration) point of the diodes and the centre tap of the transformer.

You may find a slightly different circuit diagram of the centre-tapped full-wave rectifier in some books or on the internet, as shown below.

Full Wave Rectifier Circuit

However, if you look closely, you will notice that it represents the same circuit shown above, only drawn in a different orientation. The components and connections remain the same; the diagram is simply arranged differently for clarity.

Working of a Full-Wave Rectifier

To understand the working of a centre-tapped full-wave rectifier, you first need to understand what a centre-tapped transformer is.

A centre-tapped transformer is a transformer whose secondary winding is divided into two equal halves with a centre connection called the centre tap (CT). Each half of the secondary winding produces the same voltage, but their polarities are opposite with respect to the centre tap.

Center-Tapped Transformer

The two outputs of the secondary winding are 180° out of phase. When terminal A is positive with respect to the centre tap (CT), terminal B is negative with respect to CT. Both waveforms exist simultaneously on the same time axis, and their magnitudes are equal.

Centre-Tapped Transformer Output Waveform

Now focus on the rectifier circuit below. The red color in the diagram indicates the active half cycle of the waveform and the portion of the circuit that is currently conducting.

Full Wave Rectifier Working - Positive Half Cycle

During the positive half cycle of the AC input, the upper end of the secondary winding becomes positive with respect to the centre tap. Diode D1 becomes forward-biased, while diode D2 becomes reverse-biased. Current flows through D1 and the load resistor RL, producing an output voltage across the load. The output across RL is a positive half sine wave.

Full Wave Rectifier Working - Negative Half Cycle

During the negative half cycle of the AC input, the lower end of the secondary winding becomes positive with respect to the centre tap. Diode D2 becomes forward biased, while diode D1 becomes reverse biased. Current flows through D2 and the load resistor RL. The direction of current through RL remains the same, so a positive voltage again appears across the load resistor.

Full-wave Rectifier Output Waveform

Full-wave Rectifier Output Waveform

From the waveform diagram, you can see that the input is a sinusoidal AC waveform. The two halves of the secondary winding are 180° out of phase. The output waveform consists of both half-cycles converted into positive pulses. This is why it is called a full-wave rectifier, because it utilizes both halves of the AC input signal.

Since it uses the entire AC waveform, the rectification efficiency increases. However, you can observe that the output voltage still falls to very low values between peaks, which produces significant ripple in the output voltage.

Full-wave Rectifier with Smoothing Capacitor

To reduce the ripple present in the rectified output, a smoothing capacitor (filter capacitor) is used in the circuit. Adding a capacitor significantly improves the quality of DC output and makes the rectifier suitable for real-world applications such as adapters, chargers, and regulated power supplies.

The capacitor is connected directly across the load resistor. A small capacitor results in a large ripple, while a larger capacitor reduces ripple and provides better smoothing, but it increases cost and size. In practical power supplies, electrolytic capacitors typically range from 100 µF to 4700 µF, depending on the load current.

Full Wave Rectifier with Smoothing Capacitor

During the peak of each half cycle, the conducting diode allows current to flow. The capacitor quickly charges up to the peak voltage. Once fully charged, it stores electrical energy.

When the input voltage starts decreasing after the peak, the diode becomes reverse-biased. The capacitor starts discharging slowly through the load resistor. This discharge maintains the output voltage instead of letting it fall to zero. This continuous charging and slow discharging action smoothens the output waveform.

Full Wave Rectifier Formula

The performance of a full-wave rectifier is evaluated using different electrical parameters. These formulas help us understand how effective the rectifier is in converting AC into DC.

DC Output Voltage

The DC output voltage represents the average value of the rectified output waveform. It tells us the usable DC component of the output.

For a centre-tapped full-wave rectifier:

VDC=2VmπV_{DC} = \frac{2V_m}{\pi}

Where:
VmV_m​ = Maximum (peak) value of the secondary voltage

Voltage current relationship.

Vdc=IavRL=2πImaxRL\begin{array}{l}V_{dc}=I_{av}R_{L}=\frac{2}{\pi}I_{max}R_{L}\end{array}

RMS Value

The RMS (Root Mean Square) value represents the effective value of the output voltage. It is useful for calculating the power delivered to the load.

Vrms=Vmax2\begin{array}{l}V_{rms}=\frac{V_{max}}{\sqrt{2}}\end{array}

and,

Irms=Imax2\begin{array}{l}I_{rms}=\frac{I_{max}}{\sqrt{2}}\end{array}

The RMS value helps determine the heating effect and power dissipation in the load resistor.

Form Factor

Form factor is the ratio of the RMS value to the DC value.

Kf=RMSvalueofcurrentAveragevalueofcurrent=IrmsIdc=Imax/22Imax/π=π22=1.11\begin{array}{l}K_{f}=\frac{RMS\,value\,of\,current}{Average\,value\,of\,current}=\frac{I_{rms}}{I_{dc}}=\frac{I_{max}/\sqrt{2}}{2I_{max}/{\pi}}=\frac{\pi }{2\sqrt{2}}=1.11\end{array}

A form factor close to 1 indicates smoother DC output. The full-wave rectifier has a lower form factor than the half-wave rectifier, meaning less ripple.

Peak Factor

Peak factor is the ratio of the maximum value to the RMS value.

Kp=PeakvalueofcurrentRMSvalueofcurrent=ImaxImax/2=2\begin{array}{l}K_{p}=\frac{Peak\,value\,of\,current}{RMS\,value\,of\,current}=\frac{I_{max}}{I_{max}/\sqrt{2}}=\sqrt{2}\end{array}

This value shows how large the peaks are compared to the effective value.

Rectification Efficiency

Rectification efficiency tells us how efficiently the rectifier converts AC input power into DC output power.

η=DCOutputPowerACOutputPower\begin{array}{l}\eta=\frac{DC\,Output\,Power}{AC\,Output\,Power} \end{array}

For a full wave rectifier:η=81.2%\eta = 81.2\%

This is much higher than the half-wave rectifier (40.6%), which makes the full-wave rectifier more efficient and practical.

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