1. Single-Phase Half-Wave Rectifier
ECE 442 Power Electronics

2. Waveforms
ECE 442 Power Electronics

3. Single-Phase Half-Wave Rectifier
ECE 442 Power Electronics

4. Performance Parameters
Average value of the output voltage, Vdc
Average value of the output current, Idc
Output dc power, Pdc
Pdc = VdcIdc
rms value of the output voltage, Vrms
Output ac power, Pac
Pac = VrmsIrms
ECE 442 Power Electronics

5. Performance Parameters (continued)
Efficiency, η
η = Pdc/Pac
Effective (rms) value of the ac component of the output voltage, Vac
Vac = Vrms2 – Vdc2
Form factor, FF
FF = Vrms/Vdc
Ripple factor, RF
RF = Vac/Vdc
ECE 442 Power Electronics

6. Performance Parameters (continued)
Alternate form for ripple factor
Transformer utilization factor, TUF
TUF = Pdc/VsIs
Vs, Is are rms voltage and current of the transformer secondary
ECE 442 Power Electronics

7. Input Voltage and Current
ECE 442 Power Electronics

8. Performance Parameters (continued)
Displacement angle, Φ
Displacement Factor, DF
DF = cos(Φ)
Harmonic Factor, HF
ECE 442 Power Electronics

9. Performance Parameters (continued)
Power Factor, PF
ECE 442 Power Electronics

10. Performance Parameters (continued)
Crest Factor, CF
ECE 442 Power Electronics

11. Example 3.1
Determine η, FF, RF, TUF, PIV of the diode, CF of the input current, input PF.
ECE 442 Power Electronics

12. Determine the Average Voltage, Vdc
ECE 442 Power Electronics

13. ECE 442 Power Electronics

14. Determine the rms Voltage, Vrms
ECE 442 Power Electronics

15. Determine Pdc, Pac, and η
ECE 442 Power Electronics

16. Determine FF and RF
ECE 442 Power Electronics

17. Determine the TUF
ECE 442 Power Electronics

18. Determine the PIV
PIV is the maximum (peak) voltage that appears across the diode when reverse biased. Here, PIV = Vm. - -
PIV + +
ECE 442 Power Electronics

19. Determine CF
ECE 442 Power Electronics

20. Determine PF
ECE 442 Power Electronics

21. Summary – Half-Wave Rectifier
RF=121% High
Efficiency = 40.5 Low
TUF = Low
1/TUF = 3.496
transformer must be times larger than when using a pure ac voltage source
ECE 442 Power Electronics

22. Half-Wave Rectifier with R-L Load
ECE 442 Power Electronics

23. Waveforms of Current and Voltage
Conduction period of D1 extends beyond ωt = π
ECE 442 Power Electronics

24. Average Output Voltage
Increase average voltage and current by making σ = 0
ECE 442 Power Electronics

25. Waveforms with Dm installed
ECE 442 Power Electronics

26. Application as a Battery Charger
Diode conducts for vs > E, starting when Vmsinα = E
ECE 442 Power Electronics

27. Waveforms for the Battery Charger
Diode turns off when vs < E (at β = π – α)
Charging current io = (vs – E)/R
io = (Vmsinωt – E)/R for α < ωt < β
ECE 442 Power Electronics

28. Single-Phase Full-Wave Rectifier
Center-Tapped Transformer
ECE 442 Power Electronics

29. Waveforms for the Full-Wave Rectifier
ECE 442 Power Electronics

30. Single-Phase Full-Wave Rectifier
PIV = 2Vm
ECE 442 Power Electronics

31. Full-Wave Bridge Rectifier
ECE 442 Power Electronics

32. Waveforms for the Full-Wave Bridge
ECE 442 Power Electronics

33. Full-Wave Bridge with Waveforms
Conduction pattern
D1 – D D3 – D4
PIV = Vm
ECE 442 Power Electronics