UNIT 2: POWER SEMICONDUCTOR DEVICES & CONVERTERS
I. POWER SEMICONDUCTOR DEVICES
Thyristor (SCR)
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Structure: Four-layer (p-n-p-n), three-junction (J1, J2, J3), three-terminal device.
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Two-Transistor Analogy: Equivalent to a pnp (Q1) and npn (Q2) transistor in positive feedback.
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$$\displaystyle I_A = I_{G} + I_{C2} $$ (Anode current)
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Turn-on condition: $$\displaystyle I_A > I_{H} $$ (Holding current) after gate trigger.
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Turn-On Methods:
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Thermal: Excess temperature increases carrier generation.
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Light (LASCR): Photons generate carriers in junction J2.
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dv/dt: High $$\displaystyle \frac{dv}{dt} $$ across J2 causes capacitive current $$\displaystyle I_C = C \frac{dv}{dt} $$, triggering if $$\displaystyle I_C > I_{H} $$.
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Gate Triggering: Most common. Positive gate current $$\displaystyle I_G $$ injects carriers, reducing $$\displaystyle V_{BO} $$.
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Ratings & Protection:
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dv/dt rating: Max allowable $$\displaystyle \frac{dv}{dt} $$ without false triggering. Exceeding causes unintended turn-on.
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di/dt rating: Max allowable $$\displaystyle \frac{di}{dt} $$ during turn-on. Exceeding causes local hot-spots and damage due to non-uniform current spread.
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Protection:
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Over-current: Fuses, circuit breakers, current-limiting reactors.
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Over-voltage: Snubber circuits (RC, RCD), varistors, lightning arrestors.
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dv/dt protection: RC snubber across anode-cathode.
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di/dt protection: Series inductor.
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Series & Parallel Operation:
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Series: For high voltage. Need static (shunt resistor) and dynamic (shunt capacitor) equalization due to unequal leakage currents and switching times.
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Parallel: For high current. Need derating factor (typically 0.1-0.2) and small series resistors for current sharing.
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Equalizing Circuit Derivation:
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Static (Resistor R): Balances steady-state voltage. For n SCRs, $$\displaystyle R \leq \frac{V_{TM} - V_{DM}}{I_{RM} - I_{DM}} $$ (where TM = max leakage, DM = min leakage).
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Dynamic (Capacitor C): Balances transient voltage during switching. $$\displaystyle C \geq \frac{\Delta I_{sc} \cdot t_q}{\Delta V_{max}} $$ (where $$\displaystyle \Delta I_{sc} $$ = difference in switching currents, $$\displaystyle t_q $$ = turn-off time, $$\displaystyle \Delta V_{max} $$ = max allowable voltage imbalance).
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Gate Turn-Off Thyristor (GTO)
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Structure: Similar to SCR but with highly doped p+ layer near cathode for efficient hole extraction.
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Switching: Turn-on by positive gate pulse (like SCR). Turn-off by high-density negative gate current pulse ($$\displaystyle I_{G(off)} $$), typically 1/3 to 1/5 of anode current.
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V-I Characteristics: Similar to SCR but with specified turn-off time and negative gate voltage capability.
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Applications: High-power choppers, inverters, motor drives (replaces SCR in forced commutation circuits).
Triac
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Structure: Two SCRs in inverse parallel with common gate. Three terminals (MT1, MT2, G).
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Modes of Operation (with $$\displaystyle I_+ $$ = positive gate current, $$\displaystyle I_- $$ = negative gate current):
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Mode I (MT2+, G+): $$\displaystyle I_+ $$ triggers p-n-p-n-p structure in MT1→MT2 direction. Equivalent to SCR.
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Mode II (MT2+, G-): $$\displaystyle I_- $$ triggers n-p-n-p-n structure in MT1→MT2 direction.
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Mode III (MT2-, G-): $$\displaystyle I_- $$ triggers p-n-p-n-p structure in MT2→MT1 direction.
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Mode IV (MT2-, G+): $$\displaystyle I_+ $$ triggers n-p-n-p-n structure in MT2→MT1 direction.
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Applications: Light dimmers, fan speed control, AC motor control.
Power MOSFET
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n-channel Conduction: Apply $$\displaystyle V_{GS} > V_{th} $$. Inversion layer forms channel, electrons flow from source to drain.
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V-I Characteristics: Ohmic region (linear), saturation region. Low on-resistance $$\displaystyle R_{DS(on)} $$, voltage-controlled.
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Switching: Very fast (ns), majority carrier device. No minority carrier storage.
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Applications: Low-voltage (<200V), high-frequency DC-DC converters, switch-mode power supplies.
Insulated Gate Bipolar Transistor (IGBT)
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Structure: MOS gate controlling a bipolar pnp transistor. Combines MOSFET input with BJT output.
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Operation: $$\displaystyle V_{GE} > V_{th} $$ forms MOSFET channel, injecting electrons into pnp base, turning on BJT.
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V-I Characteristics: Similar to BJT but voltage-controlled. Has "tail current" during turn-off.
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Switching: Faster than BJT, slower than MOSFET. Low $$\displaystyle V_{CE(sat)} $$.
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Applications: Medium-power (600V-3.3kV) inverters, AC drives, UPS.
Other Devices
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DIAC: Two-terminal, bidirectional trigger diode. Conducts when $$\displaystyle |V_{AK}| > V_{BO} $$ (breakover voltage). Used to trigger TRIACs.
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LASCR (Light Activated SCR): SCR triggered by light (photodiode integrated). Used in optical isolation, high-voltage switching.
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UJT (Unijunction Transistor): Single p-n junction device. Used in relaxation oscillator circuits for SCR firing (generates sharp pulse).
II. PHASE CONTROLLED RECTIFIERS
Single-Phase Converters
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Half-Wave Controlled (R Load): $$\displaystyle V_o = \frac{V_m}{2\pi}(1 + \cos\alpha) $$, $$\displaystyle I_o = V_o/R $$. $\alpha$ = firing angle.
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Full-Wave Semi-Controlled (Diode + SCR): Bridge with two SCRs, two diodes. $$\displaystyle V_o = \frac{2V_m}{\pi}\cos\alpha $$ (R load). Freewheeling diode conducts during $$\displaystyle \alpha < \omega t < \pi+\alpha $$.
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Full-Wave Fully Controlled Bridge:
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R Load: $$\displaystyle V_o = \frac{2V_m}{\pi}\cos\alpha $$.
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RL Load (Continuous Current): $$\displaystyle V_o = \frac{2V_m}{\pi}\cos\alpha $$. Current continuous for $\alpha \leq \omega t \leq \pi+\alpha$.
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RLE Load: $$\displaystyle V_o = \frac{2V_m}{\pi}\cos\alpha - E $$ (if $$\displaystyle I_o $$ continuous). Firing angle limit: $$\displaystyle \alpha \leq \cos^{-1}\left(\frac{E}{V_m}\right) $$ for continuous conduction.
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Effect of Freewheeling Diode:
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Prevents negative voltage on load (improves load voltage waveform).
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Improves input power factor by making input current unidirectional and in phase with voltage during freewheeling.
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Rectification vs. Inversion Mode:
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Rectification: $$\displaystyle 0 \leq \alpha \leq 90^\circ $$, $$\displaystyle V_o > 0 $$, power flows AC→DC.
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Inversion: $$\displaystyle 90^\circ < \alpha \leq 180^\circ $$, $$\displaystyle V_o < 0 $$, power flows DC→AC (requires DC source E).
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Effect of Source Impedance (Overlap):
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Source inductance $$\displaystyle L_s $$ causes overlap angle $\mu$. During $\mu$, two SCRs conduct.
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Output voltage drop: $$\displaystyle V_o = \frac{2V_m}{\pi}\cos(\alpha + \frac{\mu}{2}) $$.
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$\mu$ calculated from: $$\displaystyle V_L = L_s \frac{di}{dt} \approx \frac{\sqrt{2}V_m}{\omega L_s}(\cos\alpha - \cos(\alpha+\mu)) $$.
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Three-Phase Converters
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Full-Wave Bridge (No Source Inductance): $$\displaystyle V_o = \frac{3\sqrt{6}}{\pi}V_{LL} \cos\alpha = 1.654 V_{LL} \cos\alpha $$.
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With Source Inductance (Overlap):
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Overlap angle $\mu$: $$\displaystyle V_o = \frac{3\sqrt{6}}{\pi}V_{LL} \cos(\alpha + \frac{\mu}{2}) $$.
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$\mu$ given by: $$\displaystyle \cos\alpha - \cos(\alpha+\mu) = \frac{\omega L_s I_o}{\sqrt{6} V_{LL}} $$.
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For given $\alpha$, $\mu$, $$\displaystyle V_o = \frac{3\sqrt{6}}{\pi}V_{LL} \cos(\alpha + \frac{\mu}{2}) $$.
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III. AC VOLTAGE CONTROLLERS
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Principle: Phase angle control by delaying SCR firing angle $\alpha$ within each half-cycle.
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Single-Phase Half-Wave (R Load):
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$$\displaystyle V_{rms} = V_s \sqrt{\frac{1}{2\pi}(2\pi - \alpha + \sin\alpha\cos\alpha)} $$.
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$$\displaystyle P_o = \frac{V_{rms}^2}{R} $$, Input PF = $\cos\alpha$ (for R load).
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Single-Phase Full-Wave (Anti-parallel SCRs, R Load):
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$$\displaystyle V_{rms} = V_s \sqrt{\frac{1}{\pi}(2\pi - 2\alpha + \sin2\alpha)} $$.
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$$\displaystyle P_o = \frac{V_{rms}^2}{R} $$.
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Full-Wave with RL Load:
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Current may be discontinuous. Two-stage sequence control used for better control:
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First Stage: Firing angle $\alpha$ varied from $$\displaystyle 0^\circ $$ to $$\displaystyle 90^\circ $$.
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Second Stage: $\alpha$ fixed at $$\displaystyle 90^\circ $$, conduction angle $\beta$ varied by skipping cycles.
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Firing Angle for Given Load Power (R Load): From $$\displaystyle P_o = \frac{V_s^2}{R} \cdot \frac{1}{\pi}(2\pi - 2\alpha + \sin2\alpha) $$, solve for $\alpha$.
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Input Power Factor: $$\displaystyle PF = \frac{P_o}{V_s I_{rms}} $$. For RL load, $$\displaystyle I_{rms} $$ depends on $\alpha$ and load angle $\phi$.
IV. INVERTERS
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VSI vs. CSI:
| VSI | CSI | | :--- | :--- | | DC voltage source input | DC current source input | | Output voltage ~ square wave | Output current ~ square wave | | Needs feedback diodes | No feedback diodes needed | | Load commutation possible | Forced commutation required |
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Three-Phase VSI - 180° Conduction:
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Each SCR conducts for 180°. Switching sequence: T1→T2→T3→T4→T5→T6.
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Line Voltages: $$\displaystyle V_{ab} = \frac{2}{3}V_d $$ for $$\displaystyle 0 < \omega t < 60^\circ $$, etc. Six-step waveform.
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Phase Voltages (Star Load): $$\displaystyle V_{AN} = \frac{V_d}{3} $$ for $$\displaystyle 0 < \omega t < 120^\circ $$, etc.
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Three-Phase VSI - 120° Conduction:
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Each SCR conducts for 120°. Only two SCRs on at a time (one from each leg).
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RMS Load Current (Star, R/phase): $$\displaystyle I_{rms} = \frac{V_d}{3R} $$ (for 120° mode).
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Load Power: $$\displaystyle P = \frac{V_d^2}{3R} $$.
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Square-Wave Inverter (RL Load):
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Load current: $$\displaystyle i_o(t) = \frac{V_d}{Z}\left[\sin(\omega t - \theta) - e^{-t/\tau}\sin(-\theta)\right] $$ (for first quarter cycle), where $$\displaystyle Z=\sqrt{R^2+(\omega L)^2} $$, $$\displaystyle \theta = \tan^{-1}(\omega L/R) $$, $$\displaystyle \tau = L/R $$.
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RMS Load Current: $$\displaystyle I_{rms} = \frac{V_d}{Z} \sqrt{\frac{1}{2} + \frac{\tau}{T} e^{-T/(2\tau)} \cos\theta} $$.
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Average Source Current: $$\displaystyle I_{d(avg)} = \frac{1}{T}\int_0^T i_o(t) dt $$ (depends on load phase shift).
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Self-Commutated Inverters: Use devices that can be turned off by gate signal (GTO, IGBT, MOSFET). No external commutation circuit needed.
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McMurray-Bedford Inverter: Uses auxiliary SCRs and capacitors for forced commutation. Capacitor C charged to $$\displaystyle V_d $$ is discharged across conducting SCR to turn it off.
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Single Pulse Modulation: Apply a single gating pulse of width $\gamma$ at $$\displaystyle \omega t = \pi $$. Output fundamental voltage $$\displaystyle V_1 = \frac{4V_d}{\pi}\sin\frac{\gamma}{2} $$.
V. DC-DC CONVERTERS (CHOPPERS)
Type-A: Step-Down (Buck)
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Circuit: Switch (SCR/MOSFET) in series with load, diode across load.
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Operation: Switch ON ($$\displaystyle T_{on} $$): $$\displaystyle V_s $$ applied to load. Switch OFF ($$\displaystyle T_{off} $$): Diode freewheels load current.
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Average Output Voltage: $$\displaystyle V_o = \alpha V_s $$ (ideal), where $$\displaystyle \alpha = T_{on}/T $$ (duty cycle).
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Continuity Condition: Critical Inductance $$\displaystyle L_{cr} = \frac{(1-\alpha)R}{\alpha f} $$ for R load. If $$\displaystyle L > L_{cr} $$, continuous conduction.
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Given Problem (Jun 2025):
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$$\displaystyle V_s = 220V $$, $$\displaystyle T = 2000\mu s $$, $$\displaystyle T_{on} = 600\mu s $$, $$\displaystyle R=1\Omega $$, $$\displaystyle L=5mH $$, $$\displaystyle E=24V $$.
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$$\displaystyle \alpha = 0.3 $$, $$\displaystyle f = 1/T = 500 Hz $$.
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i) Continuity Check: $$\displaystyle L_{cr} = \frac{(1-0.3) \times 1}{0.3 \times 500} = 4.67 mH $$. Since $$\displaystyle L=5mH > L_{cr} $$, continuous.
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ii) Avg Output Current: $$\displaystyle I_o = \frac{V_o - E}{R} = \frac{\alpha V_s - E}{R} = \frac{66 - 24}{1} = 42 A $$.
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iii) Max/Min Current:
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$$\displaystyle \Delta I = \frac{V_s - E}{L} T_{on} = \frac{196}{5 \times 10^{-3}} \times 600 \times 10^{-6} = 23.52 A $$.
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$$\displaystyle I_{max} = I_o + \frac{\Delta I}{2} = 42 + 11.76 = 53.76 A $$.
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$$\displaystyle I_{min} = I_o - \frac{\Delta I}{2} = 42 - 11.76 = 30.24 A $$.
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Type-B: Step-Up (Boost)
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Circuit: Switch in series with source, inductor. Diode from inductor to load.
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Operation: Switch ON: $$\displaystyle V_s $$ applied to L, current ramps up. Switch OFF: L energy transfers to load via diode.
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Derivation:
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ON: $$\displaystyle V_s = L \frac{di}{dt} $$ → $$\displaystyle \Delta i_{on} = \frac{V_s}{L} T_{on} $$.
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OFF: $$\displaystyle V_o = V_s + L \frac{di}{dt} $$ → $$\displaystyle \Delta i_{off} = \frac{V_o - V_s}{L} T_{off} $$.
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Steady-state: $$\displaystyle \Delta i_{on} = \Delta i_{off} \Rightarrow \frac{V_s}{L} T_{on} = \frac{V_o - V_s}{L} T_{off} $$.
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$$\displaystyle \boxed{V_o = \frac{V_s}{1-\alpha}} $$.
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Type-C: Reversible Chopper
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Circuit: Two switches (T1, T2) in parallel with opposite polarity diodes. Load can be motoring or regenerative.
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Motoring (Forward): T1 ON → $$\displaystyle V_s $$ applied, current $$\displaystyle I_o $$ positive.
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Regeneration (Reverse): T2 ON → load back-EMF $E$ drives current opposite, energy fed back to source via D1.
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Voltage/Current: $$\displaystyle V_o = \alpha_1 V_s - \alpha_2 V_s $$ (where $$\displaystyle \alpha_1 $$, $$\displaystyle \alpha_2 $$ are duties of T1, T2). Reversible by changing $$\displaystyle \alpha_1 $$, $$\displaystyle \alpha_2 $$.
Special Choppers
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Morgan Chopper: Uses auxiliary commutating capacitor. Main switch (SCR) turns on, capacitor charges. To turn off SCR, auxiliary SCR fires, discharging capacitor through main SCR, forcing current to zero.
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Jones Chopper: Uses two main SCRs (T1, T2) and two commutating SCRs (T3, T4) with capacitor C. T1 on, C charges via T3. To turn off T1, fire T4, C discharges through T1 & T4, turning off T1.
Control Technique
- Current Limit Control: Switch ON until $$\displaystyle I_o $$ reaches $$\displaystyle I_{max} $$, then OFF until $$\displaystyle I_o $$ drops to $$\displaystyle I_{min} $$. Maintains current within band. Frequency varies.
VI. AC-AC CONVERTERS (CYCLOCONVERTERS)
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Principle: Direct AC-AC frequency conversion. Output frequency $$\displaystyle f_o < f_i $$ (typically). Uses phase-controlled SCRs in bridge configuration.
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Single-Phase Mid-Point:
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Two SCRs in series across each half of center-tapped transformer.
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Positive Group: SCRs conduct for positive output half-cycle.
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Negative Group: SCRs conduct for negative output half-cycle.
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Waveform: For $$\displaystyle \alpha=0^\circ $$, $$\displaystyle f_o = f_i/2 $$ for resistive load (each SCR conducts for $$\displaystyle 180^\circ $$ at input frequency).
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Single-Phase Bridge:
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Four SCRs in bridge. Two SCRs conduct at a time (one from each half of bridge).
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Output polarity determined by which pair conducts.
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Step-Up Cycloconverter: Output frequency $$\displaystyle f_o > f_i $$. Requires complex control, less common.
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Three-Phase to Single-Phase:
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Uses six SCRs (three for positive, three for negative group).
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Each group acts as a three-phase full-wave converter.
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Output frequency typically $$\displaystyle f_o = f_i/3 $$ or $$\displaystyle f_i/6 $$ for simple cases.
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VII. FIRING AND COMMUTATION CIRCUITS
SCR Firing Circuits
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RC Firing: Resistor R and capacitor C from gate to cathode. Provides delayed pulse. Firing angle $$\displaystyle \alpha = \sin^{-1}\left(\frac{V_{GT}}{V_m}\right) $$ approx.
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RLC Firing: Adds inductor L to RC. Improves pulse shape and provides negative gate voltage during off-period.
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UJT Firing:
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UJT with capacitor C charging through R. When $$\displaystyle V_{UB} = V_P $$ (peak point), UJT fires, capacitor discharges through pulse transformer to SCR gate.
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Firing angle $$\displaystyle \alpha = \cos^{-1}\left(1 - \frac{V_P}{V_s}\right) $$.
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Forced Commutation Techniques
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Class A: Self-commutation using LC circuit (e.g., in inverter legs).
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Class B: Commutation by preceding SCR (e.g., in choppers).
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Class C: Uses auxiliary SCR to discharge capacitor into main SCR.
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Class D: Uses two auxiliary SCRs to transfer current from main SCR to load.
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Class E: Resonant commutation using LC circuit.
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Applications: Inverters (Class A, B), choppers (Class C, D).
VIII. PROTECTION & EQUALIZATION
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Over-Current Protection:
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Fuses: Fast-blow semiconductor fuses.
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Circuit Breers: Magnetic/thermal.
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Current Limiting Reactors: Series inductor limits di/dt.
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Over-Voltage Protection:
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Snubbers: RC (limits dv/dt), RCD (clamps voltage).
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Varistors (MOV): Voltage-dependent resistor, clamps transients.
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Lightning Arrestors: For high-energy surges.
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Series/Parallel Equalization:
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Need: Unequal leakage currents (series), unequal switching times (parallel).
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Static Equalization: Shunt resistors across each SCR. Derive R from voltage imbalance condition.
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Dynamic Equalization: Shunt capacitors across each SCR. Derive C from charge balance during switching transient.
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IX. PERFORMANCE ANALYSIS & HARMONICS
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Key Derivations:
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Single-Phase Full Converter (RLE): $$\displaystyle V_o = \frac{2V_m}{\pi}\cos\alpha - E $$ (continuous $$\displaystyle I_o $$).
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Single-Phase Full-Wave AC Controller (R Load): $$\displaystyle V_{rms} = V_s \sqrt{\frac{1}{\pi}(2\pi - 2\alpha + \sin2\alpha)} $$.
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Step-Up Chopper: $$\displaystyle V_o = \frac{V_s}{1-\alpha} $$.
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RMS/Average/Power:
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For any periodic waveform: $$\displaystyle V_{rms} = \sqrt{\frac{1}{T}\int_0^T v^2 dt} $$, $$\displaystyle V_{avg} = \frac{1}{T}\int_0^T v dt $$.
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Power factor: $$\displaystyle PF = \frac{P}{V_{rms} I_{rms}} $$.
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Harmonics:
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Sources: Non-sinusoidal currents from phase-controlled converters, inverters (square-wave), AC controllers.
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Reduction:
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PWM: Spreads harmonic spectrum.
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Multipulse Converters (12-pulse, 18-pulse): Cancels low-order harmonics.
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Filters: LC tuned filters for specific harmonics.
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Increasing Pulse Number in inverters.
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[!TIP] EXAM FOCUS
- SCR: Two-transistor analogy, dv/dt & di/dt, equalization (R & C derivation) are very frequent.
- Converters: Derive $$\displaystyle V_o $$ for single-phase full converter with RLE load. Effect of freewheeling diode & source inductance (overlap).
- AC Controllers: RMS voltage derivation for full-wave bridge. Two-stage control for RL. Power factor calculation.
- Inverters: 120° vs 180° conduction modes (waveforms, currents). Square-wave inverter RL load analysis.
- Choppers: Type-A continuity check & current ripple (Jun 2025 pattern). Type-B voltage derivation. Type-C operation.
- Cycloconverter: Bridge configuration waveform for $$\displaystyle f_o = f_i/2 $$.
- Numericals: Always check continuity condition first in chopper problems. For AC controllers, use $$\displaystyle P_o = V_{rms}^2/R $$ to find $\alpha$.