Three-Phase Half-Wave Rectifiers with Resistive Loads

Introduction

• Discussion on three-phase half-wave rectifiers, transitioning from single-phase rectifiers.
• Three-phase half-wave rectifier is the simplest type for a three-phase voltage source.

Reasons for Using Three-Phase Rectifiers

• Common in industrial applications needing DC voltage from three-phase sources.

Characteristics of Three-Phase Voltage Sources

• Typically balanced, with voltages separated by a third of a cycle.
• For a period of 2π:
  • Voltage separation: 2π/3 and 4π/3.

Voltage Equations

• Phase voltages defined as:
  • Va = Vs * sin(ωt)
  • Vb = Vs * sin(ωt - 2π/3)
  • Vc = Vs * sin(ωt + 2π/3)

Phase Voltage Crossings

• Crossings occur at specific points; for example, where Va crosses Vc:
  • Set Va = Vc to find crossing:
    • Results in ωt = π/6
  • The voltage at this crossing is 0.5 Vs.

Output Voltage Behavior

• Output voltage equals the greatest of the three phase voltages at any time.
• Diode behavior based on which phase voltage is greater:
  • D1 on when Va > Vb and Vc
  • D2 on when Vb > Va and Vc
  • D3 on when Vc > Va and Vb

Output Voltage Characteristics

• Output voltage fluctuates between peak voltage (Vs) and minimum voltage (0.5 Vs) based on diode switching.
• The output voltage ripple is defined by these transitions.

Average Output Voltage Calculation

• Average calculated using:
  • [ V_{out} = \frac{1}{T} \int_0^{T} V_{out} d\omega t ]
• Multiple integrals over the waveform, separately calculating for each diode's conduction period.
  • Total average output voltage:
    • Approximately 0.827 Vs or ( \frac{3\sqrt{3}}{2\pi} Vs )

Conclusion

• Three-phase rectifiers provide better output voltage characteristics compared to single-phase rectifiers even without filtering.
• Next topic: Full wave three-phase rectifier with resistive load.