Full-Wave Rectifiers

• 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.

• 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: