Sources and References

• Mohan, Undeland, and Robbins, Power Electronics: Converters, Applications, and Design, 3rd ed., Wiley.
• Rashid, Power Electronics: Circuits, Devices, and Applications, 4th ed., Pearson.
• Krishnan, Electric Motor Drives: Modeling, Analysis, and Control, Prentice Hall.
• Erickson and Maksimović, Fundamentals of Power Electronics, 3rd ed., Springer.
• Fitzgerald, Kingsley, and Umans, Electric Machinery, 7th ed., McGraw-Hill.

Chapter 1: Power Electronic Switches and Building Blocks

Power electronics enables controlled conversion of electrical energy between forms: AC to DC, DC to DC, DC to AC, and AC to AC at a different frequency. The heart of every converter is a semiconductor switch operated in saturation or cutoff; losses occur during the finite switching interval and as ohmic conduction in the on state. Efficient converters use fast devices and clever topologies to minimize both contributions.

1.1 Semiconductor Switches

Diodes conduct when forward-biased; they commutate naturally when current drops to zero. Thyristors (SCRs) latch on with a gate pulse and hold until current falls below holding current; they are fundamentally line-commutated. Fully controllable switches — bipolar junction transistors, power MOSFETs, IGBTs, and wide-bandgap SiC and GaN devices — turn on and off on command, enabling pulse-width-modulated converters at frequencies from line to hundreds of kilohertz.

The MOSFET has low on-state resistance (voltage drop proportional to current), is ideal for low-voltage, high-frequency DC–DC converters. The IGBT combines MOSFET gate drive with bipolar conduction, producing a nearly flat forward voltage drop; it dominates medium-voltage (600–6500 V) applications such as motor drives. SiC MOSFETs and GaN HEMTs push switching frequencies and efficiency beyond what silicon can offer.

1.2 Driving and Protection

Gate drivers source and sink substantial transient current to switch a power device in tens of nanoseconds. Isolated drivers protect low-voltage control circuitry; desaturation detection and active Miller clamping manage abnormal events. Snubbers, clamps, and active protection limit overvoltage, overcurrent, and thermal stresses.

1.3 Loss and Thermal Management

Conduction loss is approximated as \( I^2 R_{DS(on)} \) for MOSFETs or \( I V_{CE(sat)} \) for IGBTs. Switching loss per transition scales with device stored charge and with \( V I t_{sw} \). Total loss equals the sum times the switching frequency. Heat sinks and thermal-interface materials are sized to keep junction temperature below derated limits; the thermal model stacks junction-to-case, case-to-sink, and sink-to-ambient resistances.

Chapter 2: DC–DC Converters

2.1 Buck, Boost, and Buck–Boost

The buck converter steps down voltage; for continuous conduction mode, \( V_{out} = D V_{in} \) where \( D \) is duty cycle. The boost converter steps up: \( V_{out} = V_{in}/(1-D) \). The buck–boost and its Ćuk, SEPIC, and Zeta relatives invert, isolate, or smooth current in one or both ports.

2.2 Averaged Models and Small-Signal Analysis

Averaging over a switching period eliminates high-frequency detail and produces continuous models suitable for control. The state-space average of a buck converter gives a second-order plant between duty cycle and output voltage; adding the inductor current gives the current-mode control plant. Cross-over frequency, phase margin, and ripple are all set within this framework.

2.3 Isolated Converters

Flyback, forward, push–pull, half-bridge, and full-bridge isolated converters use transformers to achieve galvanic isolation. They appear in off-line supplies, where safety standards demand isolation from the mains. Transformer design — core material, turns ratio, leakage inductance — is the central element of these topologies.

Chapter 3: AC–DC and DC–AC Conversion

3.1 Rectifiers

A half-wave rectifier passes a single polarity of line voltage; a full-wave rectifier uses a bridge of diodes. With capacitive filter, output voltage ripples at line or twice-line frequency. Harmonic current drawn from the line is significant; international regulations (IEC 61000-3-2) limit harmonic injection, motivating power-factor-corrected front ends.

3.2 Active Power-Factor Correction

A boost PFC converter draws sinusoidal current in phase with line voltage by programming inductor current with a control loop. The result is near-unity power factor and tightly regulated DC bus voltage. Critical-conduction, continuous-conduction, and average-current modes trade EMI, switch stress, and loss.

3.3 Inverters

A half-bridge or full-bridge inverter synthesizes an AC output from a DC bus using pulse-width modulation. Sinusoidal PWM compares a sinusoidal reference to a high-frequency triangular carrier; the resulting pulse train’s fundamental component reproduces the reference, and the switching harmonics lie around the carrier frequency for easy filtering. Space-vector PWM exploits the three-phase geometry to extend the linear modulation range and reduce switching losses.

Chapter 4: DC and Specialty Machines

4.1 DC Motor Fundamentals

A DC machine has a stationary field (permanent magnets or a shunt field winding) and a rotating armature. EMF induced in the armature is \( e = k_e \omega \); torque produced is \( T = k_t i \), with \( k_e = k_t \) in SI units. Electrical dynamics couple to mechanical dynamics via

Brushless DC (BLDC) and permanent-magnet synchronous motors (PMSM) move the commutation to electronic switches; they dominate modern variable-speed applications.

4.2 Stepper and Switched Reluctance Motors

Stepper motors advance by discrete rotor increments with each input pulse; they are open-loop precise but prone to loss of synchronization under overload. Switched-reluctance motors use salient poles and sequential phase excitation; they are rugged, inexpensive, but noisier and require more sophisticated control.

4.3 Linear and Voice-Coil Motors

Linear motors produce linear motion directly, avoiding gearboxes and backlash; voice-coil actuators are miniature, high-bandwidth linear motors used in disk drives and precision stages. The same \( F = Bil \) force relation governs all of these.

Chapter 5: Motor Drive Control

5.1 DC Motor Drives

Speed control of a permanent-magnet DC motor is direct: apply \( V_a = k_e \omega + R_a I_a \); at steady state, \( \omega \approx V_a/k_e \) for light loads. A four-quadrant chopper provides forward/reverse operation with regenerative braking. A cascade control structure — outer position/speed loop, inner current loop — is standard.

5.2 BLDC and PMSM Field-Oriented Control

The PMSM is modelled in a rotor-oriented dq frame where stator flux and torque decouple. Field-oriented control (FOC) transforms measured three-phase currents to dq using the rotor-angle estimate; a PI controller drives \( i_d \) to zero (pure torque production, no field weakening) and \( i_q \) to the torque reference. The dq voltage commands are transformed back to three-phase references fed to a sinusoidal or space-vector PWM modulator.

Rotor position is obtained from a resolver, encoder, or Hall sensors; sensorless schemes estimate it from back-EMF (at speed) or high-frequency injection (at low speed). Field-weakening extends the constant-power speed range by injecting negative \( i_d \) at high speed, trading torque for voltage headroom.

5.3 Induction Motor Drives

Induction motors are ubiquitous in industry. Scalar (V/f) control keeps flux roughly constant; vector and direct-torque control provide full dynamic capability at the cost of rotor-parameter identification. Indirect field-oriented control uses rotor-flux-oriented dq frame similar to PMSM but with rotor-flux angle derived from slip calculation.

5.4 Specialty Drives

Stepper drives use full-step, half-step, or microstepping patterns, optionally with current-regulated chopper control to smooth torque. Switched-reluctance drives require phase-current profiling synchronized to rotor position. Linear motor drives use the same FOC machinery with the translation from linear position to electrical angle set by pole pitch.

Power electronics and motor drives form the backbone of modern mechatronic actuation. Efficient, compact, and precisely controllable electrical machines make possible everything from electric vehicles to industrial robots to household appliances, and the power-electronics engineer sits squarely on the critical path of each of these designs.