**Circuit Configuration (Figure a)**Grounded center tap on secondary winding

Equivalent to two half-wave rectifiers

Each rectifier receives half the secondary voltage

**Operation****Diode D1**: Conducts on positive half-cycle**Diode D2**: Conducts on negative half-cycleRectified load current flows during both half-cycles

**Positive Half-Cycle (Figure b)**D1 is forward biased

Positive load voltage across load resistor

**Negative Half-Cycle (Figure c)**D2 is forward biased

Positive load voltage

**Output Characteristics**Same load voltage polarity during both half-cycles

Load current direction remains constant

Converts AC input to pulsating DC output (Figure d)

DC or Average Value

Full-wave rectifier average value: \[V_{\mathrm{dc}} = \frac{2 V_p}{\pi}\]

Approximate form: \[V_{\mathrm{dc}} \approx 0.636 V_p\]

Example:

Peak voltage, \(V_p = 100\text{ V}\)

DC voltage: \(V_{\mathrm{dc}} \approx 63.6\text{ V}\)

Output Frequency

Half-wave rectifier: Output frequency = Input frequency

Full-wave rectifier: Output frequency is double the input frequency

Input frequency: \(f_{\text{in}} = 60\text{ Hz}\)

Input period: \[T_{\text{in}} = \frac{1}{f_{\text{in}}} = \frac{1}{60\text{ Hz}} = 16.7\text{ ms}\]

Output period: \[T_{\text{out}} = 0.5 \times T_{\text{in}} = 8.33\text{ ms}\]

Output frequency: \[f_{\text{out}} = \frac{1}{T_{\text{out}}} = 120\text{ Hz}\]

General relation: \[f_{\text{out}} = 2 f_{\text{in}}\]

Full-wave rectifier \(\approx\) Two back-to-back half-wave rectifiers

Approximate peak output voltage: \[V_{\text{peak,approx}} = V_p - 0.7\text{ V}\]

Example to illustrate the idea.

\[\begin{aligned} V_m & = \sqrt{2} \cdot V_{rms} = \sqrt{2} \times 120 = 170 \mathrm{~V} \\ V_{p(2)} &=\frac{V_{p(1)}}{N_1 / N_2}=\frac{170 \mathrm{~V}}{10}=17 \mathrm{~V}\\ V_{p(\mathrm{in})} & =0.5(17 \mathrm{~V})=8.5 \mathrm{~V} \\ V_{p(\text { out })} & =8.5 \mathrm{~V}\\ V_{p(\text { out })} & =8.5 \mathrm{~V}-0.7 \mathrm{~V}=7.8 \mathrm{~V} \end{aligned}\]

**Bridge Rectifier Circuit**Produces a full-wave output voltage

Diodes D1 and D2 conduct on positive half-cycle

Diodes D3 and D4 conduct on negative half-cycle

Rectified load current flows during both half-cycles

**Positive Half-Cycle**D1 and D2 are forward biased

Produces positive load voltage

Visualize D2 shorted: Circuit resembles half-wave rectifier

**Negative Half-Cycle**D3 and D4 are forward biased

Produces positive load voltage

Visualize D3 shorted: Circuit resembles half-wave rectifier

**Output Characteristics**Same load voltage polarity during both half-cycles

Load current direction remains constant

Converts AC input to pulsating DC output

Advantage: Uses entire secondary voltage

**Average Value:**\[V_{\mathrm{dc}} = \frac{2 V_p}{\pi}\]63.6% of peak value

Example: \(V_{\mathrm{dc}} = 63.6\text{ V}\) for \(V_p = 100\text{ V}\)

**Output Frequency:**\[f_{\mathrm{out}} = 2 f_{\mathrm{in}}\]Example: \(f_{\mathrm{out}} = 120\text{ Hz}\) for \(f_{\mathrm{in}} = 60\text{ Hz}\)

**Advantage:**Uses entire secondary voltage

Twice as much peak voltage and DC voltage compared to center-tap full-wave rectifier

**Terminology:**Full-wave rectifier may refer to:

Conventional full-wave rectifier

Two-diode full-wave rectifier

Center-tapped full-wave rectifier

**Peak Output Voltage:**\[V_{p(\text{out})} = V_{p(\text{in})} - 1.4\text{ V}\]Subtract 1.4 V (two diode drops) for accurate peak load voltage

**Summary Table:**