BIOMEDICAL ELECTRONICS (EC-604 (B)) - Unit 3 Short Notes

UNIT 3: BIOMEDICAL INSTRUMENTATION, EMBEDDED SYSTEMS & POWER ELECTRONICS

I. BIOMEDICAL FUNDAMENTALS & TRANSDUCERS

A. Physiology & Cell Biology

• Cell Structure: Basic unit of life. Key parts:

  • Nucleus: Contains genetic material (DNA).

  • Cytoplasm: Gel-like substance containing organelles.

  • Cell Membrane: Selectively permeable barrier controlling entry/exit.

• Resting Potential (~ -70 mV): Voltage difference across membrane of excitable cells (neurons, muscle) at rest. Maintained by Na⁺/K⁺ pump (active transport) and differential ion permeability.

• Action Potential: Rapid, transient change in membrane potential.

  • Depolarization: Membrane potential becomes less negative (reaches threshold ~ -55 mV), Na⁺ channels open.

  • Repolarization: K⁺ channels open, K⁺ efflux restores negative potential.

  • Propagation: Wave of depolarization travels along axon/muscle fiber.

  [!TIP] Exam Focus: Action potential phases (depolarization, repolarization) and ion movements (Na⁺ in, K⁺ out) are frequently asked.

B. Transducers & Sensors

• Definition: Device that converts a non-electrical physical quantity (e.g., pressure, temperature) into a proportional electrical signal.

• Selection Criteria: Accuracy, sensitivity, linearity, frequency response, size, biocompatibility, cost.

• Piezoelectric Transducers:

  • Principle: Certain crystals (Quartz, PZT) generate voltage (direct effect) when mechanically stressed, or deform (converse effect) when voltage applied.

  • Applications: Ultrasound transducers (both emitter & receiver), pressure sensors (catheter-tip), accelerometers.

• Temperature Sensors (Biomedical):

  • Thermistors: Semiconductor beads. Resistance ↓ with temperature ↑ (NTC). High sensitivity, non-linear.

  • RTDs (Resistance Temperature Detectors): Pure metals (Platinum). Resistance ↑ linearly with temperature ↑. High accuracy & stability.

  • Thermocouples: Two dissimilar metals joined. Seebeck effect: Temperature difference → voltage. Wide range, no excitation needed.

• Optical Sensors - Photoplethysmography (PPG):

  • Principle: Beer-Lambert Law. Light (LED) transmitted/reflected through tissue. Blood volume changes modulate detected light intensity (photodiode).

  • Applications: Pulse oximetry (SpO₂), heart rate monitoring, blood flow.

• Electrode Theory:

  • Half-Cell Potential: Voltage developed at metal-electrolyte interface due to ion exchange. Source of DC offset.

  • Polarization: Build-up of reaction products at electrode surface altering potential. Minimized with Ag/AgCl electrodes.

  • Electrode-Skin Interface: Major source of noise/impedance. Skin preparation (cleaning, abrasion) and conductive gel reduce impedance.

  • Types:

    • Surface: ECG, EEG (Ag/AgCl).

    • Needle: EMG, deeper signals.

    • Micro: Intracellular, single-unit recordings.

C. Biopotential Amplifiers

• Purpose: Amplify tiny biopotentials (ECG: 1-5 mV, EEG: 10-100 µV) while rejecting noise (50/60 Hz mains, motion artifact).

• Key Characteristics:

  1. High CMRR (>100 dB): Rejects common-mode voltage (e.g., potential between two electrodes).

  2. High Input Impedance (>100 MΩ): Prevents loading the source (body).

  3. Low Noise: Crucial for microvolt signals.

  4. Safety (Isolation): Patient protection from mains faults. Optical or transformer isolation.

  5. Right-Leg Drive (RLD) Circuit: Feedback to reduce common-mode voltage on patient.

  [!TIP] Common Pitfall: CMRR is for common-mode signals, not differential signal gain. High input impedance is to avoid loading the biopotential source.

II. DIAGNOSTIC & MONITORING SYSTEMS

A. Cardiovascular System Measurements

• Electrocardiography (ECG):

  • Generation: Cardiac depolarization/repolarization creates time-varying dipole → body surface potentials.

  • Standard Leads (Einthoven): I (LA-RA), II (LL-RA), III (LL-LA). Augmented (aVR, aVL, aVF), Chest (V1-V6).

  • Waveform Components:

    • P: Atrial depolarization.

    • QRS: Ventricular depolarization (dominant, sharp).

    • T: Ventricular repolarization.

    • U: Possible late repolarization (not always visible).

  • Block Diagram: Electrodes → Biopotential Amp (with RLD) → Filters (HPF: baseline wander, LPF: high-freq noise, 50/60 Hz Notch) → ADC/Display/Recorder.

• Blood Pressure Measurement:

  • Direct (Invasive): Arterial catheter with pressure transducer. Continuous, real-time, accurate. Used in surgery/ICU.

  • Indirect (Non-invasive):

    • Korotkoff Sounds: Stethoscope over brachial artery during cuff deflation. First sound = Systolic, disappearance = Diastolic.

    • Oscillometric: Cuff pressure oscillations detected. Max oscillation amplitude ≈ Mean Arterial Pressure (MAP). Algorithm determines Sys/Dia.

• Heart Sounds (Phonocardiogram):

  • S1 ("Lub"): AV valves close. Start of systole.

  • S2 ("Dub"): Semilunar valves close. Start of diastole.

  • S3: Ventricular filling (normal in children, pathological in adults).

  • S4: Atrial kick (pathological, stiff ventricle).

• Pulse Oximetry (Finger-Tip):

  • Principle: Spectrophotometry. Two wavelengths (Red ~660nm, IR ~940nm). Oxygenated Hb (HbO₂) and Deoxygenated Hb (Hb) have different absorption spectra.

  • Beer-Lambert Law: $$\displaystyle I = I_0 e^{-\epsilon c l} $$. Ratio of pulsatile (AC) to DC components at both wavelengths gives SpO₂.

  • Calculation: $$\displaystyle \text{SpO}_2 = \frac{\text{Ratio}_{\text{ac/red}} - \text{Constant}}{\text{Slope} \times (\text{Ratio}_{\text{ac/IR}} - \text{Constant})} $$ (Calibrated empirically).

  [!TIP] Key Formula: SpO₂ derived from AC/DC ratios at two wavelengths, not absolute absorption.

B. Respiratory System Measurements

• Spirometry:

  • Parameters:

    • VC (Vital Capacity): Max air exhaled after max inhalation.

    • FVC (Forced VC): Max air exhaled forcefully after max inhalation.

    • FEV1 (Forced Expiratory Volume in 1s): Volume exhaled in first second of FVC. FEV1/FVC ratio < 70% indicates obstruction (COPD, asthma).

  • Photo Spirometer: Light beam interruption. Paddle attached to moving bellows interrupts a light beam. Frequency of interruption → flow rate. Integration → volume.

C. Neurological Measurements

• Electroencephalography (EEG):

  • Frequency Bands & States:

    | Band | Frequency (Hz) | Associated State/Condition | | :--- | :--- | :--- | | Delta | 0.5 - 4 | Deep sleep (infants), brain injury | | Theta | 4 - 8 | Drowsiness, early sleep, meditation | | Alpha | 8 - 13 | Relaxed, eyes closed (occipital) | | Beta | 13 - 30 | Alert, active thinking, anxiety | | Gamma | >30 | High-level cognitive processing |

  • Electrode Placement: 10-20 System. Based on skull measurements (nasion-inion, preauricular points).

  • Block Diagram: Electrodes → High-gain Amp (1MΩ input, CMRR >120dB) → Filters (0.05-70 Hz) → Isolation Amp → ADC/Display.

D. Blood Gas & Chemical Analysis

• Partial Pressure of Oxygen (PO₂) - Clark Electrode:

  • Principle: Polarography. Cathode (Pt) and Anode (Ag/AgCl) in KCl electrolyte, covered by O₂-permeable Teflon membrane.

  • Operation: O₂ diffuses through membrane → reduced at cathode: $$\displaystyle O_2 + 2H_2O + 4e^- \rightarrow 4OH^- $$. Current ∝ PO₂ (amperometric).

  • Use: Continuous intra-arterial or transcutaneous monitoring.

E. Medical Imaging

• Magnetic Resonance Imaging (MRI):

  • Principle: Nuclear Magnetic Resonance (NMR). Strong static B₀ field aligns H⁺ proton spins. RF pulse at Larmor frequency tips magnetization. Signal emitted as spins relax (T1, T2) → spatially encoded using gradient fields → reconstructed into image.

  • Advantages: Excellent soft-tissue contrast, no ionizing radiation.

• Endoscopy:

  • Fiber-Optic Principle: Total Internal Reflection in glass fibers. Components:

    • Light Source: Illuminates cavity.

    • Objective Lens: Forms image at fiber bundle tip.

    • Image Guide: Coherent fiber bundle transmits image.

    • Eyepiece/Camera: View/record image.

  • Applications: GI tract, bronchoscopy, laparoscopy.

• Thermography:

  • Principle: Infrared (IR) radiation emitted by body (7-14 µm) detected by microbolometer or thermopile array.

  • Applications: Detect inflammation (arthritis), tumors (breast), vascular disorders, fever screening.

F. Biometric Systems

• Definition: Automated recognition of individuals based on unique biological/behavioral traits.

• Types & Biomedical Link:

  • Fingerprint: Ridge patterns. Patient ID, access control.

  • Iris: Complex patterns. Highly accurate ID.

  • Facial Recognition: Geometry of face. Security, patient tracking.

  • Vein Pattern: Sub-dermal vein map (near-IR). High security, hygienic.

  [!TIP] Exam Context: Biometrics in biomedical context primarily for patient identification, security, and access control in hospitals.

III. THERAPEUTIC EQUIPMENT & LIFE SUPPORT

A. Cardiac Therapy

• Pacemakers:

  • Types:

    • Fixed-Rate: Regular pulses, ignores intrinsic activity.

    • Demand (VVI, DDD): Senses intrinsic beat; inhibits/triggers pacing. Prevents competition.

    • Dual-Mode: Can sense & pace both atrium & ventricle (DDD).

  • Block Diagram: Sense Amp → Pulse Generator (microcontroller) → Output Circuit (capacitor discharge) → Electrode.

• Defibrillators:

  • Classification:

    • DC Defibrillator: High-energy (200-360J) capacitor discharge. Manual or Automated External (AED).

    • Implantable Cardioverter-Defibrillator (ICD): Monitors heart, delivers therapy (pacing, cardioversion, defibrillation).

  • Waveform: Monophasic (older, more myocardial damage) vs. Biphasic (modern, lower energy, more effective).

  • Principle: Capacitor charged to high voltage, discharged across heart via paddles/patches to depolarize all cells simultaneously, allowing natural pacemaker to regain control.

B. Cardiopulmonary Bypass (Heart-Lung Machine)

• Purpose: Temporarily take over heart & lung function during surgery.

• Components:

  1. Pump: Roller or centrifugal. Propels blood.

  2. Oxygenator: Bubble (direct gas-blood contact, old) or Membrane (semi-permeable, gas exchange via diffusion, modern).

  3. Heat Exchanger: Controls blood temperature (hypothermia).

  4. Arterial Filter: Removes emboli, debris.

  5. Reservoir: Collects venous return.

C. Renal Therapy

• Hemodialysis & Dialyzer (Artificial Kidney):

  • Principle: Diffusion (solutes move down concentration gradient across semi-permeable membrane) and Ultrafiltration (hydrostatic pressure gradient removes fluid).

  • Dialyzer Structure: Thousands of hollow capillary fibers (synthetic membrane). Blood flows inside, dialysate flows outside (counter-current).

  • Removes: Urea, creatinine, excess K⁺, fluid. Retains proteins, blood cells.

IV. DATA TRANSMISSION & BIO-TELEMETRY

A. Bio-Telemetry Systems

• Block Diagram:

  Sensors → Signal Conditioning → Modulator → Transmitter (Patient Unit)

  → Receiver → Demodulator → Display/Recorder

• Types:

  • Wireless: Radio (ISM bands), Ultrasonic (short-range).

  • Wired: Ambulatory systems (Holter monitor).

• Advantages: Patient mobility, continuous monitoring, remote areas.

• Disadvantages: Noise susceptibility, battery life, security/privacy, size/weight constraints.

B. Communication Interfaces

• RS-232 Serial Communication:

  • Role: Standard for short-distance serial data communication (PC to device).

  • Signal Levels: Voltage-based (Logic 1: -3 to -15V, Logic 0: +3 to +15V). Not TTL compatible.

  • Key Handshaking Signals:

    • RTS (Request To Send): DTE → DCE, "I have data to send."

    • CTS (Clear To Send): DCE → DTE, "You may send."

    • DTR (Data Terminal Ready): DTE ready.

    • DSR (Data Set Ready): DCE ready.

  • Pin Config (DB9/25): Pin 2: RxD, Pin 3: TxD.

• 8051 Serial Port Modes:

  | Mode | Description | Baud Rate Source | | :--- | :--- | :--- | | 0 | Shift Register (8-bit UART sync) | f_osc / 12 | | 1 | 8-bit UART, variable baud | Timer 1 overflow | | 2 | 9-bit UART, fixed baud | f_osc / 32 or /64 | | 3 | 9-bit UART, variable baud | Timer 1 overflow |

  [!TIP] Mode 1 vs Mode 3: Both use Timer 1 for baud rate. Mode 1 is 8-bit, Mode 3 is 9-bit (allows address/data framing).

C. Real-Time Clock (RTC)

• Purpose: Provides time-stamping for logged biomedical data (e.g., ECG episodes, glucose readings). Independent timekeeping even when main system is off (battery-backed).

• Common IC: DS1307 (I²C interface). Stores seconds, minutes, hours, date, month, year.

V. EMBEDDED SYSTEMS FOR BIOMEDICAL APPLICATIONS

A. Fundamentals

• Definition: Specialized computer system designed for specific control functions within a larger mechanical/electrical system, often with real-time constraints.

• vs. General-Purpose Computing: Dedicated function, resource-constrained (cost, power, size), real-time operation, high reliability, often no user interface.

• Characteristics: Single-function, low-cost, low-power, real-time, high reliability, small form-factor.

• Quality Attributes: Performance, power, cost, size/weight, reliability, safety, security.

• Design Metrics: Trade-offs (e.g., speed vs. power, cost vs. performance).

B. Classification of Embedded Processors

C. Processor Architectures

• Von Neumann: Single memory for data & instructions, shared bus. Bottleneck: Cannot fetch instruction & data simultaneously.

• Harvard: Separate memory & buses for instructions & data. Advantage: Parallel access, faster.

• RISC vs. CISC:

  | Feature | RISC (ARM, MIPS) | CISC (x86, 8051) | | :--- | :--- | :--- | | Instructions | Fixed length, simple | Variable length, complex | | Operations | Load-store (memory access only via load/store) | Memory-to-memory allowed | | Registers | Many (16-32) general-purpose | Few (4-8) specialized | | Pipelining | Easy, single-cycle execution | Difficult, multi-cycle | | Goal | Execute simple instructions fast | Execute complex instructions in fewer steps |

D. Microcontroller Deep Dive: 8051 & 8096

• 8051 Microcontroller:

  • Architecture: 8-bit. ALU, Registers (A, B, PSW, DPTR), 4 I/O ports, 2 Timers/Counters (Timer 0,1), Full-duplex Serial Port.

  • Timer/Counter Modes:

    • Mode 0: 13-bit timer/counter.

    • Mode 1: 16-bit timer/counter (THx, TLx). Application: Precise time delay or square wave generation.

    • Mode 2: 8-bit auto-reload.

    • Mode 3: Timer 0 split into two 8-bit timers; Timer 1 stopped.

  • Square Wave Generation (Mode 1): For 1kHz @ 11.0592MHz:

    • Timer reload value = $$\displaystyle 65536 - \frac{f_{osc}}{12 \times 2 \times f_{desired}} = 65536 - \frac{11.0592e6}{12 \times 2000} = 65536 - 460.8 \approx 65075 $$ (0xFE3B).

    • Load TH0=0xFE, TL0=0x3B. Toggle P2.3 in ISR.

  • DAC Interfacing (Parallel): Connect PORT P1 to DAC's data lines. Use Timer for update rate.

  • Serial Comm (Mode 1): Set SCON=0x50 (8-bit UART, REN=1). Baud rate from Timer1 overflow. Use SBUF for transmit/receive.

  • 8051-based DAQ: Sensor → Signal Conditioning (Amplifier, Filter) → ADC → 8051 (Read, Process) → Display/RS-232/SD Card.

• 8096 Microcontroller (Superior to 8051):

  • Superiority: 16-bit architecture, on-chip ADC (10-bit), PWM output, high-speed I/O, more timers (3), watchdog, better interrupt system.

  • Functional Block Diagram: CPU (16-bit) ↔ Internal RAM (232B) ↔ Internal ROM (8KB) ↔ I/O Ports (H/L modes) ↔ A/D Converter ↔ PWM ↔ Timers/Counters (3) ↔ Watchdog Timer ↔ Serial Port ↔ External Bus Interface.

  • Hardware Features:

    • I/O Ports: Port 0 (H/L), Port 1 (H/L), Port 2 (H/L).

    • A/D Converter: 10-bit, 8/16 channel, successive approximation.

    • PWM: 8-bit resolution, fixed frequency (1.5kHz).

    • Watchdog Timer (WDT): Separate timer, overflow resets chip.

  • Registers & Addressing Modes:

    • Control/Status: WDTR (Watchdog Timer Reset), AD_COMMAND (ADC control), P1MODE, P2MODE.

    • Addressing Modes (with examples):

      1. Immediate: LD R1, #05H ; R1 ← 05H

      2. Direct: LD R1, 0200H ; R1 ← [0200H]

      3. Indirect: LD R1, @R2 ; R1 ← [R2] (R2 holds address)

      4. Register: LD R1, R2 ; R1 ← R2

      5. Register Indirect: LD R1, @R2 ; R1 ← [R2] (same as Indirect? Context differs)

      6. Immediate to Register: LD R1, #05H (same as Immediate)

    [!TIP] 8096 has no immediate-to-memory direct mode.

  • Instruction Set Classification:

    • Data Transfer: LD, ST, PUSH, POP.

    • Arithmetic/Logic: ADD, SUB, AND, OR, CMP.

    • Branch: JBC, DJNZ, SJMP, LJMP.

    • Control: NOP, EINT, DINT, DISWDT.

    • I/O: ANL/ORL/XRL to port, READA/WRITA for ADC/PWM.

    • Special: MPY (multiply), DIV (divide). Overflow Risk: MPY result in R1:R0 (32-bit). DIV by zero → undefined, overflow flag set.

  • Memory Mapping: Internal ROM (0000H-1FFFH), Internal RAM (0000H-00E7H, 00E8H-00FFH). External memory via ADDR/DATA bus.

E. System Support Components

• Watchdog Timer (WDT):

  • Purpose: Recover from software hangs/glitches. Improves reliability/safety (critical in medical devices).

  • Operation: Software must periodically "kick" (write to WDT register) before timeout. If timeout → reset.

  • Timing Diagram: Kick sequence (write sequence to WDT) must occur within timeout period T_timeout.

• Interrupt Controller:

  • Need: Prioritize multiple interrupt sources, allow nesting (higher priority can interrupt lower).

  • Functional Block: Multiple interrupt request lines → Priority Encoder → Interrupt Service Register (ISR) → CPU.

  • Types: Vectored (jump to fixed address) vs. Non-vectored (common ISR, poll source). Hardware (external pin) vs. Software (INT instruction).

• Keyboard Controller (8279):

  • Modes:

    1. Scanned Keyboard: Scans matrix (N rows x M columns), debounces, stores key code in FIFO.

    2. Scanned Sensor Matrix: Reads sensor array (e.g., proximity).

    3. Display: Drives 7-segment/LED displays (auto-increment address).

  • Operation: Debouncing: Hardware (RC filter) or software (wait, re-scan). Scanning: Drive rows low sequentially, read columns. Key press → row/column address → key code.

• 16-bit PIC & dsPIC:

  • Overview: Modern, high-integration alternatives to 8051/8096.

  • Features: RISC core, many peripherals (ADC, DAC, PWM, CAN, USB), low power, dsPIC adds DSP engine for signal processing. Used in advanced portable monitors, insulin pumps.

VI. POWER ELECTRONICS FOR BIOMEDICAL EQUIPMENT

A. Power Semiconductor Devices

• Power Diodes:

  • Standard: General rectification (50/60 Hz).

  • Fast Recovery: $$\displaystyle t_{rr} < 1\mu s $$. Used in high-frequency switching (SMPS, inverters).

  • Schottky: Low $$\displaystyle V_f $$ (~0.3V), fast, low reverse voltage (<200V). Used in low-voltage, high-frequency DC-DC converters.

• Thyristor (SCR):

  • Structure: 4-layer (PNPN), 3 terminals (Anode, Cathode, Gate).

  • V-I Characteristics:

    • Latching Current ($$\displaystyle I_L $$): Min anode current to maintain conduction after gate pulse removed.

    • Holding Current ($$\displaystyle I_H $$): Min anode current to keep SCR ON. $$\displaystyle I_L > I_H $$.

  • Turning ON: Forward voltage + positive gate current.

  • Turning OFF: Anode current < $$\displaystyle I_H $$ (natural commutation) or forced commutation (external circuit).

  • Static/Dynamic: $$\displaystyle t_{on} \approx 1-5\mu s $$, $$\displaystyle t_{off} \approx 50-100\mu s $$.

• Commutation Techniques:

  • Natural (Line): AC source voltage reverses (for AC circuits).

  • Forced: External circuit forces current to zero.

    • External Pulse: Auxiliary SCR discharges capacitor into main SCR anode.

    • Resonant: LC circuit creates oscillating current.

• Series/Parallel Operation:

  • Series: Unequal voltage sharing due to different leakage currents. Solution: Parallel snubber (RC) across each SCR.

  • Parallel: Unequal current sharing due to different $$\displaystyle V_{TM} $$. Solution: Small magnetic coupling (shared core) or equalizing resistors.

• Power MOSFET:

  • Structure: Vertical, many parallel cells. Voltage-controlled.

  • Transfer Char: $$\displaystyle I_D $$ vs $$\displaystyle V_{GS} $$ (threshold $$\displaystyle V_{th} $$). Output Char: $$\displaystyle I_D $$ vs $$\displaystyle V_{DS} $$ (ohmic region, saturation).

  • Switching: Low gate charge, fast (ns). Used in low voltage (<200V), high frequency (100s kHz) DC-DC converters.

• IGBT:

  • Structure: MOSFET gate + BJT output. MOSFET input (high impedance), BJT output (low saturation voltage).

  • V-I Char: Like MOSFET turn-on, BJT-like saturation. Advantages: High input impedance, low $$\displaystyle V_{CE(sat)} $$ (~2-3V), suitable for medium voltage (600V-3.3kV), medium frequency (10-50kHz) inverters, motor drives.

B. AC-DC Converters (Rectifiers)

• Single-Phase Half-Wave (R Load): $$\displaystyle V_{avg} = \frac{V_m}{\pi} $$, $$\displaystyle V_{rms} = \frac{V_m}{2} $$.

• Single-Phase Full-Wave Bridge:

  • Diode Bridge: $$\displaystyle V_{avg} = \frac{2V_m}{\pi} $$.

  • Fully Controlled Bridge (4 SCRs):

    • RL Load (Continuous Conduction): $$\displaystyle V_{avg} = \frac{2V_m}{\pi} \cos \alpha $$.

    • Waveforms: $$\displaystyle v_o $$ = rectified sine, $$\displaystyle i_o $$ = delayed, continuous (if $$\displaystyle \alpha < \phi $$, $$\displaystyle \phi = \tan^{-1}(\omega L/R) $$).

  • Half-Controlled Bridge (2 SCRs + 2 Diodes): $$\displaystyle V_{avg} = \frac{V_m}{\pi} (1 + \cos \alpha) $$. Unidirectional output current.

• Effect of Source Inductance ($$\displaystyle L_s $$):

  • Causes overlap angle ($\mu$). During commutation, two SCRs conduct.

  • Voltage Drop: $$\displaystyle \Delta V = \frac{V_m}{\pi} \cos \alpha - \frac{V_m}{\pi} \cos(\alpha + \mu) $$.

  • Extinction Angle: $$\displaystyle \beta = \alpha + \mu $$. Must be < $\pi$ for successful commutation.

• Three-Phase Full-Wave Bridge (Fully Controlled):

  • Average Output Voltage: $$\displaystyle V_{avg} = \frac{3\sqrt{6}}{\pi} V_{LL} \cos \alpha = \frac{3\sqrt{2}}{\pi} V_{L} \cos \alpha \approx 2.34 V_{L} \cos \alpha $$.

  • Example: $$\displaystyle V_L = 440V $$, $$\displaystyle \alpha = 60^\circ $$ → $$\displaystyle V_{avg} = 2.34 \times 440 \times \cos 60^\circ = 2.34 \times 440 \times 0.5 = \boxed{514.8\ \text{V}} $$.

  [!TIP] Formula: For 3-phase bridge, $$\displaystyle V_{avg} \approx 2.34 V_{L} \cos \alpha $$ (line-to-line RMS voltage $$\displaystyle V_L $$).

C. DC-AC Converters (Inverters)

• Single-Phase Bridge Inverter:

  • Operation: 4 switches (SCRs/MOSFETs) in H-bridge. T1,T4 ON → $$\displaystyle v_o = V_{dc} $$; T2,T3 ON → $$\displaystyle v_o = -V_{dc} $$.

  • Resistive Load: $$\displaystyle v_o $$ square wave, $$\displaystyle i_o $$ in-phase square wave.

  • Inductive Load (RL): $$\displaystyle i_o $$ sinusoidal (due to inductor), displacement from $$\displaystyle v_o $$. Current lags voltage.

• Pulse Width Modulated (PWM) Inverter:

  • Principle: High-frequency switching (carrier) modulated by sinusoidal reference. Output voltage magnitude controlled by modulation index ($$\displaystyle m_a $$).

  • Advantages: Harmonic reduction (fundamental dominant), input voltage control without changing DC bus.

• Three-Phase Bridge Inverter:

  • 180° Conduction: Each switch conducts 180°. $$\displaystyle v_{AN}, v_{BN}, v_{CN} $$ are 120° shifted square waves. $$\displaystyle v_{AB} $$ = 6-step waveform.

  • 120° Conduction: Each switch conducts 120°. More switches on at a time, lower harmonic content.

• Harmonics in Inverters: Problems: Heating (core/copper), torque pulsation (motors), EMI, filter size.

  • Reduction Techniques:

    1. PWM: Shifts harmonics to high frequency (easier filtering).

    2. Multi-level Inverters: More voltage levels, staircase waveform.

    3. Output Filters: LC filters.

• Resonant Inverters:

  • Series Resonant: Load (R) in series with LC. At resonance ($$\displaystyle \omega_0 = 1/\sqrt{LC} $$), impedance = R (min), current max.

  • Output Current at Resonance: $$\displaystyle I_o = \frac{V_{dc}}{R} $$ (for square-wave input, fundamental component dominates).

D. AC Voltage Controllers

• On-Off Control (Integral Cycle): Switch entire cycles ON/OFF. RMS voltage control: $$\displaystyle V_{rms} = V_s \sqrt{\frac{m}{m+n}} $$ (m cycles on, n cycles off).

• Phase Control (Triac): Delay firing angle ($\alpha$) each half-cycle. RMS output voltage (R load): $$\displaystyle V_{rms} = V_s \sqrt{\frac{1}{2\pi} \int_{\alpha}^{\pi+\alpha} \sin^2 \theta d\theta} = V_s \sqrt{\frac{1}{2\pi} \left( \pi - \alpha + \frac{\sin 2\alpha}{2} \right)} $$.

  • Inductive Load: $$\displaystyle \alpha > \phi $$ (load angle). Current lags voltage. Triac may turn off when current < $$\displaystyle I_H $$ → commutation required.

• Example Calculation (On-Off): $$\displaystyle V_s=230V $$, R=15Ω, 6 cycles on, 4 cycles off (50Hz → cycle=20ms).

  • Total time = 10 cycles = 200ms.

  • $$\displaystyle V_{rms} = 230 \times \sqrt{\frac{6}{10}} = 230 \times \sqrt{0.6} = \boxed{177.9\ \text{V}} $$.

  • Input Power Factor = $$\displaystyle \frac{\text{Real Power}}{V_s I_s} = \frac{V_{rms}^2 / R}{V_s^2 / R} = \left( \frac{V_{rms}}{V_s} \right)^2 = 0.6 $$ (since purely resistive).

E. DC-DC Converters (Choppers)

• Step-Down (Buck):

  • Circuit: Switch (MOSFET) in series with inductor, diode across load.

  • Operation: Switch ON → inductor stores energy ($$\displaystyle i_L $$ ↑). Switch OFF → diode conducts, inductor releases energy ($$\displaystyle i_L $$ ↓).

  • V_out Derivation: $$\displaystyle V_{avg} = \alpha V_{dc} $$ (for continuous conduction), where $\alpha$ = duty cycle ($$\displaystyle T_{on}/T $$).

  • \boxed{V_{out} = \alpha V_{in}}

• Step-Up (Boost):

  • Circuit: Switch in series with inductor, diode to load.

  • Operation: Switch ON → inductor stores energy ($$\displaystyle i_L $$ ↑), diode blocks. Switch OFF → inductor voltage adds to $$\displaystyle V_{in} $$, diode conducts to load.

  • V_out Derivation: $$\displaystyle V_{out} = \frac{V_{in}}{1-\alpha} $$.

  • \boxed{V_{out} = \frac{V_{in}}{1 - \alpha}}

• Buck-Boost:

  • Circuit: Switch, inductor, diode, capacitor (inverting output).

  • Operation: Similar to boost but output polarity reversed.

  • V_out: $$\displaystyle V_{out} = -\frac{\alpha}{1-\alpha} V_{in} $$.

  • When $$\displaystyle V_{in} > V_{out} $$: Use Buck mode ($$\displaystyle \alpha < 0.5 $$). When $$\displaystyle V_{in} < V_{out} $$: Use Boost mode ($$\displaystyle \alpha > 0.5 $$).

F. AC-AC Converters (Cycloconverters)

• Single-Phase to Single-Phase Cycloconverter (Bridge Type):

  • Step-Down Operation: Output frequency $$\displaystyle f_o < f_{in} $$ (e.g., 50Hz → 10Hz).

  • Circuit: Two opposite-connected fully-controlled bridges (positive & negative group).

  • Operation with Resistive Load: Each bridge conducts for half-cycle of output. Phase control of each bridge's firing angle to synthesize low-frequency sine.

  • Waveforms: Output voltage = segments of input sine waves, phase-shifted to create lower frequency.

• Advantages: Direct frequency conversion, regenerative (power can flow back to AC source).

• Limitations: Low input power factor (especially at low $$\displaystyle f_o $$), complex control (firing angles vary), harmonics in input current.

G. Switched-Mode Power Supplies (SMPS)

• Principle vs. Linear: Switch at high frequency (50-500kHz) → smaller transformer/inductor → higher efficiency (80-90% vs. 40-60%). Regulation via duty cycle control.

• Topologies:

  • Flyback Converter (Isolated):

    • Principle: Energy stored in transformer core during switch ON (primary current builds, secondary diode reverse-biased). Energy released to output during switch OFF.

    • Equivalent Circuits:

      • Switch ON: $$\displaystyle V_{in} $$ across $$\displaystyle N_p $$, $$\displaystyle i_p $$ linear ramp ↑. Secondary open.

      • Switch OFF: Transformer acts as current source, $$\displaystyle i_s $$ flows through diode to output capacitor/load.

    • Waveforms: $$\displaystyle V_{DS} $$ (switch) spikes at turn-off (leakage inductance), $$\displaystyle i_D $$ (diode) discontinuous.

  • Forward: Energy transferred directly during switch ON. Requires reset mechanism (tertiary winding or auxiliary switch).

  • Push-Pull/Half/Full Bridge: Use center-tapped or split primary, lower switch stress.

• Feedback Control:

  • Voltage Mode Control: Error amp compares output voltage with reference → controls PWM comparator (sets duty cycle). Simple, good noise immunity.

  • Current Mode Control: Inner current loop (sense switch current) → outer voltage loop. Advantages: inherent over-current protection, easier compensation, better line regulation.

[!TIP] Exam Focus: SMPS topologies (Flyback vs. Forward), feedback control types, and advantages over linear supplies are high-frequency questions. Derive V_out = αV_in for buck and V_out = V_in/(1-α) for boost chopper.