Full-Wave Rectifiers: Center-Tapped Transformer vs. Bridge Rectifier

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-cycle
- Rectified 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

\[V_{\mathrm{dc}} = \frac{2 V_p}{\pi}\]
Full-wave rectifier average value:
\[V_{\mathrm{dc}} \approx 0.636 V_p\]
Approximate form:
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: \(f_{\text{in}} = 60\text{ Hz}\)
\[T_{\text{in}} = \frac{1}{f_{\text{in}}} = \frac{1}{60\text{ Hz}} = 16.7\text{ ms}\]
Input period:
\[T_{\text{out}} = 0.5 \times T_{\text{in}} = 8.33\text{ ms}\]
Output period:
\[f_{\text{out}} = \frac{1}{T_{\text{out}}} = 120\text{ Hz}\]
Output frequency:
\[f_{\text{out}} = 2 f_{\text{in}}\]
General relation:

Second Approximation

Full-wave rectifier \(\approx\) Two back-to-back half-wave rectifiers
\[V_{\text{peak,approx}} = V_p - 0.7\text{ V}\]
Approximate peak output voltage:
Example to illustrate the idea.

LAB example of full-wave rectifier

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

Bridge Rectifier

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:
- 63.6% of peak value
- Example: \(V_{\mathrm{dc}} = 63.6\text{ V}\) for \(V_p = 100\text{ V}\)

\[V_{\mathrm{dc}} = \frac{2 V_p}{\pi}\]

Output Frequency:
- Example: \(f_{\mathrm{out}} = 120\text{ Hz}\) for \(f_{\mathrm{in}} = 60\text{ Hz}\)

\[f_{\mathrm{out}} = 2 f_{\mathrm{in}}\]

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:
- Subtract 1.4 V (two diode drops) for accurate peak load voltage

\[V_{p(\text{out})} = V_{p(\text{in})} - 1.4\text{ V}\]

Summary Table: