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Power Electronics Circuits

Learn with multiple-choice questions, including calculations: single-phase and three-phase rectifiers, the average value of full-wave rectification, smoothing capacitors and ripple, thyristor phase control and the firing angle, line commutation, the power factor of distorted currents, the conversion ratios of buck, boost and buck-boost converters, volt-second balance, inductor ripple current, continuous and discontinuous conduction modes, output voltage ripple, synchronous rectification and dead time, switching loss, light-load efficiency, flyback and forward converters, half-bridge and full-bridge inverters, sinusoidal PWM and the modulation index, the line voltage of three-phase inverters, overmodulation, carrier frequency, bootstrap circuits, power factor correction, the synchronous speed and slip of induction motors, V/f control, the back EMF of DC motors, brushless DC motors, regeneration and the turns ratio of transformers.

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Power Electronics Circuits: key points

New to this topic? Start with: What Is an Inverter? DC to AC for Air Conditioners and EVs / How AC Adapters and Chargers Work: From Wall Outlet to 5 V

Power semiconductor devices cannot convert power on their own. Diodes, thyristors, MOSFETs and IGBTs are combined with inductors, capacitors and transformers into circuits and switched at the right moments to turn AC into DC, DC into DC at another voltage, and DC into AC. This topic covers the basics of these power conversion circuits and of the motors they drive.

It starts with single-phase and three-phase rectifiers, the average value of full-wave rectification, estimating the ripple with a smoothing capacitor, thyristor phase control and the firing angle, line commutation and the power factor of distorted currents. It then derives the conversion ratios of buck, boost and buck-boost converters from the volt-second balance of the inductor and works through the inductor ripple current, the boundary between continuous and discontinuous conduction modes, output voltage ripple, the current path during dead time with synchronous rectification, switching loss and light-load efficiency, with calculations. Isolated converters are introduced only at the level of how flyback and forward converters operate. The second half covers half-bridge and full-bridge inverters, sinusoidal PWM and the modulation index, the line voltage of three-phase inverters, overmodulation, choosing the carrier frequency, the voltage error caused by dead time, sizing the bootstrap capacitor and boost-type power factor correction, and ends with the synchronous speed and slip of induction motors, V/f control, the back EMF and torque of DC motors, brushless DC motors, regeneration during deceleration and the current ratio of an ideal transformer. It can serve as an introduction to the power electronics and electric machines parts of electrical licensing exams such as Japan's Electric Chief Engineer exam (third class) and Korea's Electrical Engineer exam. The values in the calculation questions, including those of the wrong choices, have been checked by computing them in Python (NumPy). The structure and characteristics of devices such as MOSFETs, IGBTs, SiC and GaN, gate drivers, snubber circuits and soft switching are covered in "Power semiconductors"; the comparison of LDOs and switching regulators in "Analog and electronic circuits"; AC circuits, three-phase AC, transformer voltage ratios and impedance transformation in "Circuit and electromagnetism basics"; the control loops of DC-DC converters and cascade control of motors in "Control Engineering Basics"; PWM and duty cycle in "Embedded Systems & Firmware"; and electric-vehicle inverters in "Automotive Semiconductors and Functional Safety".

All Power Electronics Circuits questions (40)
  1. When AC is applied to a single-phase bridge rectifier made of four diodes, which of the following correctly describes the path of the current during one half cycle?
  2. Which of the following correctly describes the output of a three-phase full-wave rectifier that rectifies three-phase AC with a bridge of six diodes?
  3. A sinusoidal AC voltage of 100 V RMS is full-wave rectified with an ideal diode bridge. Without a smoothing capacitor, which of the following is closest to the average output voltage?
  4. Estimate on the assumption that the capacitor supplies all of the load current for one full ripple period. When 50 Hz AC is full-wave rectified, smoothed with a 10,000 µF capacitor, and a constant 2 A flows to the load, which of the following is the approximate peak-to-peak output voltage ripple?
  5. In phase control with an AC supply and thyristors, which of the following correctly describes how the average output voltage changes when the firing angle (control angle) α is increased?
  6. A 200 V RMS single-phase AC supply feeds a resistive load through a single-phase full-wave rectifier using thyristors, with phase control. Which of the following is closest to the average output voltage at a firing angle of 60°?
  7. In a thyristor phase-control circuit connected to an AC supply, which of the following correctly explains why the thyristor turns off without any action to turn it off from the gate?
  8. In a power supply whose input current is not sinusoidal but contains many harmonics, which of the following correctly explains why the power factor is not 1 even if the fundamental of the current is in phase with the voltage?
  9. In a step-down chopper (buck converter), which of the following correctly describes the path of the inductor current while the switch is off?
  10. For an ideal step-up chopper (boost converter) with an input voltage of 5 V and a switch duty cycle of 0.6, which of the following is the output voltage in continuous conduction mode?
  11. For an ideal buck-boost chopper (inverting buck-boost converter) with an input voltage of 12 V and a duty cycle of 0.6, which of the following is the magnitude of the output voltage in continuous conduction mode?
  12. Which of the following is the correct basis for deriving the ideal output voltage Vout = D × Vin of a buck converter?
  13. For an ideal buck converter with an input voltage of 12 V, an output voltage of 3 V, an inductance of 15 µH and a switching frequency of 300 kHz, which of the following is the peak-to-peak inductor ripple current in continuous conduction mode?
  14. Which of the following correctly describes continuous conduction mode (CCM) of a DC-DC converter?
  15. In an ideal buck converter (freewheeling through a diode) with an input voltage of 12 V, an output voltage of 3 V, an inductance of 15 µH and a switching frequency of 300 kHz, the load current is gradually reduced. Which of the following is the minimum output current that keeps continuous conduction mode (the boundary with discontinuous conduction mode)?
  16. Assume that the entire AC component of the inductor ripple current (0.6 A peak to peak) flows into the output capacitor of a buck converter. With a switching frequency of 300 kHz and an output capacitance of 25 µF (ignore the ESR), which of the following is the peak-to-peak output voltage ripple?
  17. In a DC-DC converter with a low output voltage, which of the following is the main purpose of synchronous rectification, which uses a MOSFET in place of the freewheeling diode?
  18. In a synchronous buck converter, which of the following correctly describes the path of the inductor current during the dead time when both the upper and lower MOSFETs are off?
  19. Assume that the power lost during a transition is, on average, half of voltage × current. For a power device switching 400 V and 10 A with turn-on and turn-off transition times of 50 ns each and a switching frequency of 100 kHz, which of the following is closest to the switching loss?
  20. In a DC-DC converter, which of the following correctly combines the main reason efficiency drops sharply at very small load currents with a countermeasure?
  21. In a power supply that makes DC from the AC mains, which of the following is the main reason isolated converters, which isolate input from output with a transformer, are used?
  22. Which of the following correctly describes the operation of a flyback converter?
  23. In a forward converter, which of the following correctly explains why a transformer reset winding (or a clamp circuit) is needed?
  24. In sinusoidal PWM for an inverter, which of the following correctly describes how the switches are turned on and off?
  25. For inverters that make single-phase AC from a DC voltage E, which of the following correctly compares the output voltage of a half bridge (two switches) and a full bridge (four switches)?
  26. An inverter leg on a 600 V DC supply is operated with sinusoidal PWM at a modulation index of 0.8. Which of the following is the amplitude (peak) of the fundamental of the leg output voltage with respect to the midpoint of the DC supply?
  27. A three-phase inverter on a 400 V DC supply is operated with sinusoidal PWM at a modulation index of 1. Which of the following is closest to the RMS value of the fundamental of the output line-to-line voltage?
  28. In a sinusoidal PWM inverter, which of the following correctly describes what happens when the modulation index is made larger than 1 (overmodulation)?
  29. In a PWM inverter driving a motor, which of the following correctly describes the effect of raising the carrier frequency?
  30. In a voltage-source PWM inverter, which of the following correctly describes the effect of the dead time on the output voltage?
  31. The gate drive voltage is 10 V, and currents other than the gate charge are ignored. When a high-side MOSFET with a gate charge of 100 nC is driven by a bootstrap circuit, which of the following is the minimum capacitance that keeps the drop in the bootstrap capacitor voltage at one turn-on to 0.5 V or less?
  32. In a boost-type power factor correction circuit (PFC circuit) for a power supply that works from 100 to 240 V AC, which of the following correctly explains why the DC output voltage is often set to about 380 to 400 V?
  33. Which of the following is the synchronous speed of a four-pole induction motor operated from three-phase AC at 50 Hz?
  34. A four-pole induction motor operating at 60 Hz is running with a slip of 0.05. Which of the following is the rotor speed?
  35. Which of the following correctly explains why an induction motor cannot run at exactly the synchronous speed while operating as a motor?
  36. When the speed of an induction motor is varied with an inverter, which of the following is the main reason the voltage-to-frequency ratio (V/f) is kept roughly constant?
  37. A voltage of 24 V is applied to a DC motor with an armature resistance of 0.5 Ω and a back-EMF constant of 0.1 V/(rad/s), and the armature current is 8 A. Which of the following is the angular speed of rotation at this point?
  38. Which of the following correctly describes a brushless DC motor?
  39. Which of the following correctly combines what can happen when an induction motor driven by an inverter is decelerated quickly by lowering the frequency with the countermeasure?
  40. When an ideal transformer converts the primary voltage into a lower secondary voltage, which of the following correctly describes the relationship between the primary and secondary currents?

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