UNIT 3: POWER ELECTRONICS, CONTROL SYSTEMS & DEVICES
I. POWER SUPPLIES & RECTIFIERS
A. Rectifier Fundamentals
1. Single-phase Half-Wave Rectifier (R & RL Load)
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Circuit: Single diode in series with load (R or RL).
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Waveforms (R Load): Output follows positive half-cycle of input sine wave; zero during negative half-cycle.
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Waveforms (RL Load - Discontinuous Conduction): Due to inductance, current continues beyond π radians until it naturally decays to zero. Output voltage is zero when diode is reverse-biased, even if load current is flowing.
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Average Output Voltage (R Load):
$$V_{dc} = \frac{V_m}{\pi} \approx 0.318 V_m$$
where $$\displaystyle V_m $$ = peak input voltage.
\boxed{V_{dc} = \frac{V_m}{\pi}}
- Average Output Voltage (RL Load - Discontinuous):
$$V_{dc} = \frac{V_m}{2\pi} (1 + \cos\alpha)$$
where $\alpha$ = firing/commutation angle (angle at which current becomes zero).
\boxed{V_{dc} = \frac{V_m}{2\pi} (1 + \cos\alpha)}
[!TIP] Exam Focus: Distinguish between continuous (R load) and discontinuous (RL load) conduction by waveform shape and derivation. Discontinuous conduction reduces average output voltage.
2. Single-phase Full-Wave Rectifiers
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Centre-Tapped (CT) Transformer:
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Uses two diodes and a centre-tapped transformer.
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Each diode conducts for half the cycle (180°).
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$$\displaystyle V_{dc} = \frac{2V_m}{\pi} $$ (for R load, ideal diodes).
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PIV per diode = $$\displaystyle 2V_m $$.
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Bridge Rectifier:
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Uses four diodes in bridge configuration.
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All diodes conduct for half the cycle (180°).
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$$\displaystyle V_{dc} = \frac{2V_m}{\pi} $$ (same as CT).
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PIV per diode = $$\displaystyle V_m $$.
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Comparative Analysis (Power Supply Applications):
| Feature | Centre-Tapped | Bridge | | :--- | :--- | :--- | | Diodes Required | 2 | 4 | | Transformer | Requires CT (costlier, bulky) | No CT needed (simpler) | | PIV per Diode | $$\displaystyle 2V_m $$ | $$\displaystyle V_m $$ | | Utilization | Lower (CT utilization) | Higher (full secondary used) | | Common Use | Less common | Most common for low-voltage supplies |
[!TIP] Common Pitfall: Remember PIV (Peak Inverse Voltage) ratings differ significantly. Bridge rectifier is preferred for low-voltage, high-current applications due to lower PIV requirement.
B. Voltage Regulators & SMPS
1. Linear Voltage Regulators
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Series Regulator: Pass transistor in series with load. Error amplifier compares sample of output with reference. Controls transistor to maintain constant $$\displaystyle V_{out} $$.
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Shunt Regulator: Zener diode or transistor shunt across load. Simple but inefficient for high current.
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Key Drawback: Low efficiency ($$\displaystyle \eta \propto \frac{V_{out}}{V_{in}} $$) due to continuous power dissipation in series element.
2. Switched-Mode Power Supplies (SMPS)
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Block Diagram & Working Principle:
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Input Rectifier & Filter: AC to raw DC.
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Switch (Transistor): High-frequency (20kHz-1MHz) ON/OFF switching. Key: Switch operates in saturation/cutoff (low loss), not active region.
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Power Transformer: Smaller/cheaper due to high frequency.
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Output Rectifier & Filter: High-frequency AC to smooth DC.
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Feedback Loop: Opto-coupler isolates feedback. Compares output with reference, controls switch duty cycle ($$\displaystyle D = T_{on}/T $$).
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Types (Derived from Buck):
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Buck (Step-Down): $$\displaystyle V_{out} = D \cdot V_{in} $$. Switch in series, diode across load.
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Boost (Step-Up): $$\displaystyle V_{out} = \frac{V_{in}}{1-D} $$. Inductor before switch, diode to output.
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Buck-Boost: $$\displaystyle V_{out} = -\frac{D}{1-D} V_{in} $$. Inverts polarity.
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Full-Bridge (from Buck): Uses four switches in bridge. For high power, provides isolation and bidirectional voltage/current handling. Essentially two buck converters in push-pull.
\boxed{V_{out} = D \cdot V_{in} \text{ (Buck)}}
\boxed{V_{out} = \frac{V_{in}}{1-D} \text{ (Boost)}}
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3. Uninterruptible Power Supply (UPS) - On-Line
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Block Diagram & Function:
AC Mains → Rectifier → DC Bus → Inverter → AC Output → Load ↑ ↑ Battery Static Switch-
Rectifier: Converts AC to DC to charge battery and feed inverter.
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Battery: Provides backup during mains failure.
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Inverter: Always active. Converts DC (from rectifier or battery) to clean, regulated AC.
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Static Switch: Fast solid-state switch (thyristors/IGBTs). Bypasses inverter during maintenance or failure; connects mains directly to load.
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Active Power Line Conditioning: Uses PWM inverter to correct input voltage sags, surges, harmonics, and provide clean sine wave output. Core concept: Inverter acts as a controlled voltage source in series with the line.
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II. POWER SEMICONDUCTOR DEVICES (SCR, MOSFET, IGBT)
A. Silicon Controlled Rectifier (SCR)
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Construction: Four-layer (PNPN), three terminals (Anode A, Cathode K, Gate G).
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VI Characteristics:
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Forward Blocking: $$\displaystyle V_{AK} > 0 $$, $$\displaystyle I_G = 0 $$. Small leakage current until $$\displaystyle V = V_{BO} $$ (breakover voltage).
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Forward Conducting: Triggered by gate pulse or $$\displaystyle V > V_{BO} $$. Latching current $$\displaystyle I_L $$ must be exceeded to maintain conduction after gate removal. Holding current $$\displaystyle I_H $$ is minimum current to keep SCR ON.
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Reverse Blocking: Acts like a diode.
\boxed{I_L > I_H}
[!TIP] Critical Distinction: Latching Current ($$\displaystyle I_L $$): Minimum current to turn ON and sustain conduction after gate signal removed. Holding Current ($$\displaystyle I_H $$): Minimum current to keep SCR ON. $$\displaystyle I_L > I_H $$.
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Transistor Model (Two-Transistor Analogy):
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SCR = NPN ($$\displaystyle Q_1 $$) + PNP ($$\displaystyle Q_2 $$) transistor coupled.
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Anode current $$\displaystyle I_A = \alpha_1 I_A + I_{CBO1} + \alpha_2 I_K + I_{CBO2} $$.
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Solving: $$\displaystyle I_A = \frac{I_{CBO1} + I_{CBO2}}{1 - (\alpha_1 + \alpha_2)} $$.
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Turn-ON Condition: $$\displaystyle \alpha_1 + \alpha_2 \geq 1 $$. Gate current increases $$\displaystyle \alpha_1 $$.
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Turn-On Methods:
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Forward Voltage Triggering: Apply $$\displaystyle V_{AK} > V_{BO} $$ (undesirable, damages device).
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dV/dt Triggering: High dV/dt causes charge flow like gate current (requires snubber).
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Gate Triggering: Standard method. Positive gate current pulse.
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Turn-Off (Commutation) Methods:
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Natural (Line) Commutation: AC circuit. Current goes to zero naturally, SCR turns off.
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Forced Commutation: DC circuit. Use external circuitry to force current to zero.
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Self-Commutated: Use another SCR/switch in parallel with main SCR (e.g., Class B).
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Auxiliary Commutated: Use separate commutating capacitor/inductor (e.g., Class C, D).
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Resonant Commutation: Use LC circuit to create oscillating current (e.g., Class E).
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Protection Circuits:
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Overvoltage: Snubber Circuit (R-C across SCR) limits dV/dt and absorbs transient voltage. Varistor (non-linear resistor) clamps high-voltage surges.
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Overcurrent: Electronic Crowbar (fast-acting thyristor across supply) shorts output to protect SCR from fault current.
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Other: Heat sink for thermal protection.
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Causes of Damage: Overvoltage (transients), overcurrent (faults), high dV/dt, high dI/dt, thermal runaway, gate overvoltage.
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Applications: Controlled rectifiers (phase control), AC/DC motor speed control, power switching, inverters, overvoltage protection (crowbar).
B. Power MOSFET
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Construction (VDMOS): Vertical structure. N⁺ source, P-body, N⁻ drift region, N⁺ drain. Gate oxide isolates gate. Vertical for high voltage/current.
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Principle of Operation: Voltage-controlled device. $$\displaystyle V_{GS} > V_{th} $$ creates inversion layer (channel) between source and drain. Drain current $$\displaystyle I_D $$ flows.
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Characteristics:
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$$\displaystyle I_D $$-$$\displaystyle V_{DS} $$: Ohmic region (linear), saturation region (constant $$\displaystyle I_D $$).
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Transfer ($$\displaystyle I_D $$-$$\displaystyle V_{GS} $$): Threshold voltage $$\displaystyle V_{th} $$. Above $$\displaystyle V_{th} $$, $$\displaystyle I_D \propto (V_{GS} - V_{th})^2 $$ (quadratic in saturation).
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Advantages: Voltage-driven (high input impedance), fast switching (ns), no minority carrier storage, simple drive.
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Limitations: On-resistance $$\displaystyle R_{DS(on)} $$ increases with voltage rating (higher conduction loss at high voltage).
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Applications: Switch-mode power supplies (low-voltage, high-frequency), DC-DC converters, motor drives (low power), amplifiers.
C. Insulated Gate Bipolar Transistor (IGBT)
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Construction: MOSFET gate structure (N⁺ source, P-body, gate oxide) + BJT output (P⁺ collector, N⁻ drift, P-body/N⁺ emitter). Combines MOSFET input with BJT output.
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Principle of Operation: $$\displaystyle V_{GE} > V_{th} $$ creates MOSFET channel, injects electrons into N⁻ drift region. These electrons forward-bias P-N junction (collector-body), turning on the PNP BJT. High current gain from BJT action.
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Transistor Model: Equivalent to MOSFET driving a BJT (PNP). Base current of BJT = MOSFET drain current.
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Characteristics:
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Output ($$\displaystyle I_C $$-$$\displaystyle V_{CE} $$): Similar to BJT but with higher saturation voltage $$\displaystyle V_{CE(sat)} $$ than MOSFET's $$\displaystyle V_{DS(on)} $$.
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Transfer ($$\displaystyle I_C $$-$$\displaystyle V_{GE} $$): Threshold $$\displaystyle V_{GE(th)} $$. Above threshold, $$\displaystyle I_C $$ rises sharply.
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Features vs. MOSFET & BJT:
| Feature | IGBT | MOSFET | BJT | | :--- | :--- | :--- | :--- | | Drive | Voltage (like MOSFET) | Voltage | Current | | Switching Speed | Medium (µs) | Fast (ns) | Medium | | On-State Voltage | Moderate | Low (at low V) | Low | | Voltage Rating | High (up to 6.5kV) | Low-Medium | Medium | | Current Rating | High | Medium | High |
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Applications: Medium to high-power AC/DC motor drives, inverters (UPS, traction), welding, induction heating.
D. Comparative Study (SCR, MOSFET, IGBT)
| Parameter | SCR | MOSFET | IGBT |
|---|---|---|---|
| Type | Thyristor (bipolar) | Unipolar | Mixed (MOSFET+BJT) |
| Control | Current (gate) | Voltage | Voltage |
| Switching Speed | Slow (µs) | Fast (ns) | Medium (µs) |
| Voltage Handling | Very High | Low-Medium | High |
| Current Handling | Very High | Medium | High |
| Drive Circuit | Complex (needs commutation) | Simple | Simple |
| Conduction Loss | Low (at high I) | Low (at low V) | Moderate |
| Key App | AC power control, high-power rectifiers | Low-V, high-freq switching | Medium-high power AC drives |
III. OPERATIONAL AMPLIFIERS (OP-AMPs) & APPLICATIONS
A. Basic OP-AMP Characteristics & Configurations
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Ideal OP-AMP Characteristics:
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$$\displaystyle A_{OL} \to \infty $$ (Open-loop gain)
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$$\displaystyle Z_{in} \to \infty $$ (Input impedance)
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$$\displaystyle Z_{out} = 0 $$ (Output impedance)
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BW $\to \infty$, CMRR $\to \infty$, Slew Rate $\to \infty$, Offset $$\displaystyle V_{io}, I_{io} = 0 $$.
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Inverting Amplifier:
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$$\displaystyle V_{out} = -\frac{R_f}{R_{in}} V_{in} $$
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Virtual ground at inverting input.
\boxed{A_v = -\frac{R_f}{R_{in}}
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Non-Inverting Amplifier:
- $$\displaystyle V_{out} = \left(1 + \frac{R_f}{R_{in}}\right) V_{in} $$
\boxed{A_v = 1 + \frac{R_f}{R_{in}}
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Key Parameters:
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CMRR (Common-Mode Rejection Ratio): $$\displaystyle CMRR = \frac{A_d}{A_{cm}} $$ (dB). Rejects noise common to both inputs.
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Slew Rate (SR): Max rate of change of $$\displaystyle V_{out} $$ (V/µs). Limits max freq for large signals: $$\displaystyle f_{max} = \frac{SR}{2\pi V_{p}} $$.
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Gain-Bandwidth Product (GBW): Constant for a given op-amp. $$\displaystyle A_v \times BW = constant $$.
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B. OP-AMP as Comparator
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Basic Comparator: No feedback. Compares $$\displaystyle V_+ $$ and $$\displaystyle V_- $$. Output saturates to $$\displaystyle +V_{sat} $$ or $$\displaystyle -V_{sat} $$.
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$$\displaystyle V_{out} = +V_{sat} $$ if $$\displaystyle V_+ > V_- $$
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$$\displaystyle V_{out} = -V_{sat} $$ if $$\displaystyle V_+ < V_- $$
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Window Comparator: Two comparators (upper $$\displaystyle V_{UT} $$, lower $$\displaystyle V_{LT} $$) + logic gate. Output high when $$\displaystyle V_{in} $$ is between $$\displaystyle V_{LT} $$ and $$\displaystyle V_{UT} $$.
C. OP-AMP in Filters & Oscillators
1. Low-Pass Filter (First-Order):
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Circuit: Inverting config with capacitor $C$ in parallel with $$\displaystyle R_f $$.
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Transfer Function: $$\displaystyle H(s) = \frac{V_{out}}{V_{in}} = -\frac{R_f}{R_{in}} \cdot \frac{1}{1 + sR_f C} $$
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Cutoff Frequency: $$\displaystyle f_c = \frac{1}{2\pi R_f C} $$
2. Wien Bridge Oscillator:
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Circuit: Non-inverting op-amp with positive feedback through Wien network (series R-C and parallel R-C).
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Barkhausen Criterion: Loop gain $$\displaystyle |A\beta| = 1 $$ and phase shift = 0°.
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Condition for Oscillation: $$\displaystyle R_f = 2 R_1 $$ (for ideal op-amp).
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Frequency of Oscillation:
\boxed{f_o = \frac{1}{2\pi RC}}
3. Relaxation Oscillator (Astable Multivibrator):
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Circuit: Inverting op-amp with positive feedback through $$\displaystyle R_1 $$ and RC charging from $$\displaystyle V_{out} $$ to inverting input via $$\displaystyle R_2 $$, $C$.
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Operation: Capacitor $C$ charges/discharges between two threshold voltages set by feedback. Output switches between $$\displaystyle +V_{sat} $$ and $$\displaystyle -V_{sat} $$.
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Frequency: $$\displaystyle f_o \approx \frac{1}{2RC \ln\left(\frac{1+\beta}{1-\beta}\right)} $$, where $$\displaystyle \beta = \frac{R_3}{R_3 + R_4} $$ (feedback ratio).
D. Other Applications
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Function Generator: Uses integrator (converts square to triangle) and comparator with hysteresis (Schmitt trigger, converts triangle to square) in feedback loop.
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Summing Amplifier: Inverting config with multiple inputs. $$\displaystyle V_{out} = -R_f \left(\frac{V_1}{R_1} + \frac{V_2}{R_2} + ...\right) $$.
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Instrumentation Amplifier: Three-op-amp design for high CMRR, high $$\displaystyle Z_{in} $$, differential gain. $$\displaystyle V_{out} = \left(1 + \frac{2R_1}{R_{gain}}\right) \frac{R_3}{R_2} (V_2 - V_1) $$.
IV. PROGRAMMABLE LOGIC CONTROLLERS (PLCs)
A. Fundamentals & Architecture
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Definition: Industrial digital computer, ruggedized, for control of manufacturing processes.
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Functional Block Diagram:
Power Supply → CPU (Processor) ↔ Memory (Program/Data) ↓ ↑ I/O Modules ←→ Programming Device ↓ Field Devices (Sensors, Actuators) -
Comparison with Relay Logic:
| Feature | Relay Logic | PLC | | :--- | :--- | :--- | | Flexibility | Hardwired, changes require rewiring | Software program, easy modification | | Reliability | Mechanical contacts wear | Solid-state, high MTBF | | Space | Bulky, many components | Compact | | Cost | Low for simple, high for complex | Economical for complex logic | | Troubleshooting | Difficult, physical tracing | Easy (diagnostics, LEDs) | | Disadvantages | Inflexible, noisy, high maintenance | Requires programming skill, initial cost |
B. PLC Programming & Languages
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Ladder Logic (LD) - Primary Language:
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Symbols:
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Contacts:
--| |--(Normally Open),--|/|--(Normally Closed). -
Coils:
--( )--(Output). -
Timers:
TON(On-delay),TOF(Off-delay). -
Counters:
CTU(Up),CTD(Down).
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Rules: Power flows left to right, top to bottom. Each rung must end with an output (coil).
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Example: Motor Start-Stop (Seal-in):
|--[ I1 (Start) ]--[ I2 (Stop) ]--[ M1 (Seal) ]--( O1 (Motor) )--|I1= Start pushbutton (NO),I2= Stop pushbutton (NC),M1= auxiliary contact of motor (NO),O1= motor contactor coil.
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Other IEC 61131-3 Languages (Brief):
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Instruction List (IL): Text-based, like assembly.
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Function Block Diagram (FBD): Graphical blocks (like logic gates, timers).
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Structured Text (ST): High-level text (like Pascal/C).
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C. PLC Operation Modes & Communication
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Operation Modes:
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Program Mode: Download/modify program. I/O disabled.
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Run Mode: Execute program, control process.
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Test Mode: Monitor/force I/O while program runs.
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Standard PLC Communication Protocols:
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Modbus: Simple master-slave (RTU/ASCII/TCP). Widely used.
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Profibus: Fast, deterministic (DP for devices, PA for process).
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DeviceNet: CAN-based, device-level network (sensors, actuators).
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Interfacing PLC with Power Electronics:
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PLC provides low-power logic control (digital outputs).
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Drives/contactors/solid-state relays (SSRs) act as interface/power stage.
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PLC digital outputs → SSR/contactor coil → Power circuit (SCR/IGBT bridge).
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Feedback (current, voltage, temp) from power circuit → PLC analog inputs → control algorithm.
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D. Event-Driven Devices
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Concept: Devices that generate an interrupt signal upon a specific event (e.g., high-speed counter reaching value, encoder pulse, fault condition).
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PLC Handling: PLC scans I/O, but event-driven modules can trigger immediate attention (interrupt subroutine) for time-critical tasks, bypassing normal scan cycle.
V. SPECIAL TOPICS & SHORT NOTE CATEGORIES
A. Power Electronic Circuits & Systems
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Commutation Methods:
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Natural (Line): AC source. Current zero crossing turns off SCR.
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Forced:
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Class A (Self): Load commutation (load is resonant LC).
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Class B (Auxiliary): Auxiliary SCR discharges capacitor into main SCR.
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Class C (Auxiliary): Auxiliary SCR in parallel with main SCR.
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Class D (Resonant): Switches operate with resonant load (zero-current/voltage switching).
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Losses in Semiconductor Devices:
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Conduction Loss: $$\displaystyle P_{cond} = I_{rms}^2 \cdot R_{on} $$ (MOSFET/IGBT) or $$\displaystyle V_{TM} \cdot I_{avg} $$ (SCR). ON-state loss.
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Switching Loss: $$\displaystyle P_{sw} = \frac{1}{2} V \cdot I \cdot (t_{on} + t_{off}) \cdot f_{sw} $$. Occurs during transitions.
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Total Loss: $$\displaystyle P_{total} = P_{cond} + P_{sw} $$.
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B. Oscillators & Waveforms
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Wien Bridge Oscillator (Detailed):
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Circuit: Non-inverting op-amp. Feedback network: Series RC (Z1) and Parallel RC (Z2).
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Analysis: At $$\displaystyle f_o = 1/(2\pi RC) $$, phase shift of network = 0°, gain = 1/3.
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Oscillation Condition: $$\displaystyle |A_v| \geq 3 $$ (usually $$\displaystyle R_f = 2R_1 $$ for $$\displaystyle A_v=3 $$). Amplitude stabilized by non-linear elements (lamp, diodes, FET).
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C. Protection & Safety
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SCR Protection:
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Overvoltage: Snubber (R-C across SCR) limits dV/dt. Varistor (MOV) clamps transients.
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Overcurrent: Fast-blow fuse, semiconductor fuse, electronic crowbar (detect overcurrent → fire SCR across supply).
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Electronic Crowbar for Power Transistors:
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Circuit: Current sense resistor → comparator → gate driver → SCR/thyristor across DC bus.
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Operation: Overcurrent detected → comparator output triggers SCR → SCR shorts supply → blows fuse/disconnects. Fastest protection.
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D. System Integration
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PLC Interfaced with Power Electronics Drives:
PLC (Ladder Logic) → Digital Output Card → SSRs/Contactors → Drive (SCR/IGBT Bridge) → Motor ↑ ↑ Analog Input Card ← Sensors (Current, Voltage, Temp)-
PLC sends start/stop, speed reference (via analog output or digital pulses).
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Drive handles power switching and closed-loop control (current, speed).
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Feedback signals return to PLC for monitoring/interlocks.
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Role of PLCs in Process vs. Discrete Control:
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Discrete (Machine/Assembly): On/off states (solenoids, motors). Ladder logic ideal.
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Process (Continuous): Variables (temp, pressure, flow). Uses PID control blocks in PLC, analog I/O, setpoint control.
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[!TIP] Exam Strategy: For 7-mark questions, always include diagram + explanation + key equations + applications. For 5-mark short notes, be concise: definition, key features, one application. Past papers frequently ask for comparisons (rectifiers, devices) and detailed operation (SCR turn-on/off, OP-AMP apps).