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Choppers, Inverters, PWM & Induction Motor Drives

DC-DC converter topologies, V/f control, PWM synthesis and the induction motor speed-control story that anchors every EEE drive interview.

ABBSiemensTata MotorsBHEL

Key formulas

Vout = Vin / (1 − δ)
Boost converter output: Continuous-conduction, ideal switches; real designs cap δ ≲ 0.85 because losses explode as δ → 1.
Ns = 120f/P, s = (Ns − N)/Ns
Synchronous speed & slip: Torque is produced only while s ≠ 0; at rated slip (2–5%) the motor runs just below synchronous speed.

▸Chopper duty cycle δ = Ton/(Ton+Toff): buck Vout = δ·Vin, boost Vout = Vin/(1−δ), buck-boost = −δ·Vin/(1−δ).
▸Class A chopper = step-down/motoring only; Class B = regenerative; Class C = A+B (two-quadrant); Class D = two-quadrant with reversible voltage; Class E = four-quadrant.
▸VSI vs CSI: VSI needs a stiff DC voltage source with feedback diodes and is standard for drives; CSI needs a current source (large inductor) and suits very high power.
▸V/f control keeps flux (Φ ∝ V/f) constant: below base speed = constant-torque region; above base speed, field weakening at constant power.
▸PWM: sinusoidal PWM compares a sine reference with a triangular carrier; modulation index m = Vref/Vcarrier controls output fundamental.
▸Slip s = (Ns − N)/Ns; Ns = 120f/P. Induction motor speed control options: V/f (stator voltage+frequency), rotor resistance (wound rotor), slip-power recovery (Kramer/Scherbius), pole changing.
▸Space Vector PWM gives better DC-bus utilisation (~15% more fundamental than SPWM) and lower harmonics — standard in modern VFDs.

Method	How it works	Typical use
V/f (scalar)	Varies both voltage and frequency, flux held constant	General-purpose VFDs, fans, pumps
Vector (FOC)	Decouples torque and flux via Park/Clarke transforms	Cranes, EV traction, high dynamic drives
Rotor resistance	External rotor resistance (wound rotor only)	Cranes/hoists, simple torque control
Slip-power recovery	Kramer/Scherbius returns slip power to the line	Large pumps/fans (MW-scale)
Pole changing	Reconnects stator winding for different pole count	Two-speed motors (2:1 ratio)

1. A boost chopper with duty cycle 0.6 and 100 V input gives an output of about…

2. V/f control maintains constant…

3. A four-quadrant DC drive needs a chopper of class…

4. Space Vector PWM improves DC-bus utilisation by roughly…

5. An induction motor with 4 poles on 50 Hz has synchronous speed…