A. Machine types and applications
Foundations (B-H, iron losses, EMF, rotating field) → DC machines → induction machines → synchronous machines → special machines (BLDC, PMSM, SRM, steppers, servos).
Lessons
B-H curve & hysteresis
Magnetic basics, virgin curve and saturation, the hysteresis loop with B_r / H_c / B_sat, soft vs hard materials, Steinmetz hysteresis-loss model P_h = K_h·f·B_max^n.
Iron losses — hysteresis + eddy current
Total core loss = P_h (∝f) + P_e (∝f²·t²·σ). Loss separation by plotting P/f vs f. Mitigation via thin laminations, silicon alloying, CRGO grain orientation, amorphous metal, ferrite cores.
How EMF is generated
Faraday + Lenz from the ground up: motional EMF, transformer EMF, and the 4.44·f·N·Φ result.
The rotating magnetic field
Three pulsating MMFs 120° apart in space and time add up to one constant-magnitude rotating wave.
The commutator in action
A purely mechanical inverter/rectifier — AC inside the coil, DC at the brushes. The single most elegant trick in machine design.
DC: generated EMF and torque
E_a = K_a·Φ·ω, T = K_a·Φ·I_a — one machine constant, two equations, four numbers in lockstep.
DC excitation: shunt vs series vs compound
Three field arrangements, three personalities — constant-speed shunt, high-torque series, balanced compound.
DC armature reaction and commutation
Cross-magnetising distortion, MNA shift, and how interpoles + compensating windings cancel them automatically.
DC motor speed control — the three knobs
V_t below base speed, field weakening above base speed, armature resistance for starting. Modern 4Q drives integrate all three.
DC generator external characteristics
V_t vs I_L curves: linear droop (sepex), regenerative droop (shunt), rising (series), over/flat/under-compound.
Cross-field DC machines (Amplidyne, Metadyne)
Rotary power amplifiers using shorted q-axis brushes for 2-stage cross-field amplification. Gain 10⁴-10⁵. WWII radar / naval gun / elevator / mill servos. Replaced by power electronics — Bimbhra / GATE syllabus.
How an induction motor turns
Stator's rotating field → induced rotor EMFs → bar currents → F = i × B → torque. Slip is what makes it work.
Slip and rotor frequency
s, f_r = s·f, E_2s = s·E_2 — three numbers that move together across every induction-machine operating region.
Induction motor equivalent circuit
Treat the rotor as a transformer secondary; the R_2/s trick reveals mechanical power as a fictitious resistor.
Torque-slip characteristic
The T-s curve, breakdown torque at s_m = R₂/X₂, and why T_max is independent of R₂ (rotor-resistance starting).
No-load + blocked-rotor tests
Two bench tests — the direct parallel of transformer OC/SC — that pin down every equivalent-circuit parameter.
Circle diagram construction
One geometric figure built from NL + BR tests gives stator current, PF, torque, power, and efficiency at every operating point.
Induction generator (s < 0)
Drive the rotor above n_s and the same machine generates power. Grid-connected, SEIG, and the DFIG for variable-speed wind.
Double-cage and deep-bar induction motors
Breaking the single-cage R_2 trade-off: outer (high R, low X) and inner (low R, high X) cages give high starting torque AND high run efficiency. Deep-bar via skin effect. NEMA Designs A/B/C/D.
Cogging & crawling in induction motors
Slot-harmonic parasitic phenomena. Cogging = locks at start when S=R. Crawling = stuck at n_s/7 from 7th space-harmonic torque. Universal cure: skew rotor bars one stator slot pitch.
Single-phase induction motors
Double-revolving-field theory (1-φ field = forward + backward). Starter families: split-phase, capacitor-start, PSC, cap-start-cap-run, shaded-pole. ECMs increasingly replacing them in residential / small commercial.
Rotor-resistance speed control (slip-ring IM)
Wound-rotor IM with external R_ext via slip rings. Shifts T-s curve right: s_max ∝ R_2, T_max unchanged. Slip-power penalty = s·P_input. Modern variants: Kramer / Scherbius / DFIG wind turbines.
Alternator armature reaction
How the load's power factor sets the angle between F_a and F_f — magnetising, demagnetising, or cross-magnetising.
Synchronous equivalent circuit
E_f = V_t + I_a(R_a + jX_s) — one source, one resistance, one reactance, and the phasor diagram that tells you everything.
Power-angle equation and stability
P = (E_f·V_t / X_s)·sin δ — the heartbeat of synchronous-machine analysis, with pull-out at δ = 90°.
Synchronous motor V-curves
I_a vs I_f at constant load — the operator's chart for choosing field current and power factor at any operating point.
Generator capability curve (P-Q chart)
Five constraints — armature, field, prime-mover, stability, under-excitation — bounding the safe operating envelope.
Synchronising onto a grid
Four matching conditions, three-dark-lamp method, two-bright-one-dark, synchroscope, and modern auto-synchroniser.
Salient-pole two-reaction theory
Blondel's d/q decomposition + reluctance-power term explains hydro alternators and the reluctance motor.
Methods to determine synchronous reactance — OCC, SCC, ZPF, slip test
EMF method (air-gap line ÷ SCC), Potier construction for X_L vs X_ar, and the slip test for X_d / X_q in salient-pole machines. Saturated vs unsaturated Z_s.
Hunting & damper (amortisseur) windings
Synchronous-machine swing equation J·δ̈ + D·δ̇ + K_s·δ = 0. Damper bars in pole faces suppress hunting via induction-motor action. Other roles: line-starting synchronous motors, NSC absorption.
Synchronous-machine excitation systems
DC exciter (legacy), brushless AC (rotating diodes), static thyristor (<100 ms, 3-4× ceiling). AVR closed-loop with OEL/UEL/V-Hz limiters. PSS for rotor-swing damping. IEEE 421.5 standardized models.
Synchronous condenser
Synchronous machine with no shaft load, smooth variable Q via field control. Provides INERTIA + FAULT MVA that capacitors / SVC / STATCOM cannot. Modern comeback for low-inertia high-renewable grids and HVDC support.
Stepper motors — VR, PM, hybrid + drive modes
Discrete-angle motion per pulse. Variable-reluctance vs permanent-magnet vs hybrid (1.8° 200-step/rev). Full / half / micro-step drives. Pull-in vs pull-out torque-speed envelope and missed-step risk.
Brushless DC (BLDC) motors
Inverted DC: stator 3-φ windings + rotor PM. Trapezoidal back-EMF (vs PMSM sinusoidal), 6-step commutation via 3 Hall sensors, T = k_t·I torque law. Drones, EVs, HDDs, power tools.
Permanent-magnet synchronous motors (PMSM)
Sinusoidal back-EMF, SPM vs IPM saliency, dq-axis torque equation, field-oriented control with MTPA and field weakening. The dominant EV traction motor (Prius, Tesla Model 3) and industrial servo.
Switched-reluctance motor (SRM)
Pure reluctance torque, T = ½·i²·dL/dθ. Salient rotor of laminated steel only — no windings, no magnets. Asymmetric half-bridge per phase. Rising interest as a rare-earth-free EV traction alternative.
Linear induction motor (LIM)
Rotary IM unrolled into a flat plane. v_s = 2·τ·f. Slip + thrust analogs of rotary. End-effect efficiency penalty (60-80%). Applications: maglev (Transrapid, JR-Maglev), urban transit, EMALS, roller coasters.
Synchronous reluctance motor (SynRM)
Salient steel rotor + sinusoidal 3-φ supply. Pure reluctance torque T = (3/2)(P/2)(L_d − L_q)·i_d·i_q. NO magnets, NO windings on rotor. FOC same as PMSM. Modern rare-earth-free PMSM alternative (ABB, Siemens, Bosch).
Hysteresis synchronous motor
Smooth hard-magnetic-material rotor. Constant T from rest to sync (flat T-s). Locks at exact n_s. Very smooth and quiet. Classic uses: precision clocks, audio capstans, gyroscope rotors. Low η (5-30%) — niche today.
Universal motor + AC commutator motors
Series-wound DC motor that runs on AC (T = K·I² → unidirectional). High RPM, high power density, droopy curve — drives nearly every corded power tool. Plus repulsion, compensated series, and AC traction motor history.
Servo motors — DC and AC servo systems
Closed-loop position/velocity control. DC servos (PM + encoder + PI). AC servos = PMSM + high-res encoder + FOC drive. Cascaded current/velocity/position loops. CNC, robots, fab equipment.
Synchros and resolvers
Small electrical machines for angular position transmission. CG/CX/CT/CDX three-letter codes. Classic CX→CT servo loop. Resolver = 2-φ variant with V·sinθ + V·cosθ outputs. Brushless via rotary transformer. Aerospace + military legacy.
Schrage motor
3-φ AC commutator motor with variable speed (50-150% n_s) by brush shifting + simultaneous PF control. Rotor carries primary 3-φ winding + auxiliary commutator winding. Industrial workhorse 1920s-60s; Bimbhra / GATE EE / PSU exam syllabus.