Need for DC Motor Speed Control
Speed Control of DC Motors
Fundamental Speed Equation
\[\omega_m = \frac{V_a - I_a R_a}{K\phi}\] where \(V_a\) is armature voltage, \(I_a\) is armature current, \(R_a\) is armature resistance, \(K\) is machine constant, and \(\phi\) is field flux.
Speed Control Methods:
- Armature voltage control (\(V_a\))
- Field flux control (\(\phi\))
- Armature resistance control (\(R_a\))
Industrial Applications
DC Motor Drives are Essential in:
- Electric vehicles & traction systems
- Cranes and hoists
- Conveyor systems
- CNC machine tools
- Battery-powered equipment
- Renewable energy systems
- Solar pumping applications
- MPPT-based drives
Key Requirement
Modern applications demand efficient, precise, and responsive speed control with minimal energy losses.
Classical Speed Control Approaches
Traditional Methods:
-
Rheostatic (resistance) control
- Variable resistance in series with armature
- Simple but inefficient
-
Motor-Generator (Ward-Leonard) set
- AC motor drives DC generator
- Variable voltage output
-
Phase-controlled rectifiers (SCR)
- AC to controlled DC conversion
- Thyristor-based control
Conventional Speed Control Techniques
Conventional Methods and Limitations
Comparative Analysis of Speed Control Methods
| Parameter | Rheostatic | M-G Set | SCR Rectifier | Chopper |
|---|---|---|---|---|
| Efficiency | Very poor (\(<50\%\)) | Moderate (60–75%) | Good (80–90%) | Excellent (\(>95\%\)) |
| Response time | Fast | Slow | Moderate | Very fast (ms) |
| Size/Weight | Compact | Very bulky | Compact | Compact |
| Maintenance | Minimal | High | Low | Minimal |
| DC source usable | Yes | No | No | Yes |
| Power factor | N/A | Good | Poor | N/A |
| Harmonics | None | None | Significant | Low |
Limitations of Classical Methods
Rheostatic Control
Disadvantages:
- Very poor efficiency (\(<50\%\))
- Energy wasted as heat in resistors
- Speed regulation poor under load
- Limited speed range
Ward-Leonard Set
Disadvantages:
- Very bulky and heavy
- High initial cost
- Slow dynamic response
- High maintenance (rotating machines)
Phase-Controlled Rectifier
Disadvantages:
- Poor power factor (especially at low speeds)
- Significant harmonic content
- Requires AC source (not suitable for battery/solar)
- Complex filtering needed
Modern Solution
DC choppers overcome all these limitations with high efficiency, fast response, and DC source compatibility.
Why Chopper Drives?
Motivation for DC Chopper Drives
Modern drive applications demand: high efficiency, fast dynamic response, DC-source compatibility, compact form factor, and low maintenance.
Choppers deliver all five requirements.
Key Advantages
- Efficiency \(> 95\%\)
- Fast dynamic response (millisecond range)
- Compact and lightweight design
- Compatible with DC sources (batteries, solar panels)
- Low maintenance (no moving parts)
Application Domains
- Electric and hybrid vehicles
- Battery-powered equipment
- Solar PV pumping systems
- Traction systems
- Industrial servo drives
DC Chopper: Operating Principle
What is a DC Chopper?
Definition
A DC chopper is a static power electronic device that converts a fixed-voltage DC source into a variable-voltage DC output through high-frequency switching of a power semiconductor device (MOSFET, IGBT, GTO, etc.).
DC Transformer Analogy
A DC chopper is analogous to an AC transformer with a continuously variable turns ratio, but it operates on DC voltage and achieves step-up or step-down conversion with high efficiency (\(>95\%\)).
Key Principle:
- Energy transfer through switching (not resistive dissipation)
- Output voltage controlled by duty cycle
- No moving parts \(\Rightarrow\) high reliability
Basic Chopper Circuit
Components:
- \(Q\): Power switch (MOSFET/IGBT)
- \(D_m\): Freewheeling diode
- \(L_a\): Armature inductance
- \(V_s\): DC source voltage
Operation
When \(Q\) is ON: motor connected to source
When \(Q\) is OFF: current freewheels through \(D_m\)
Chopper Operating Modes
Two Switching States:
State 1: Switch ON (\(t_{\text{ON}}\))
- Current path: \(V_s \to Q \to\) Motor
- Motor voltage: \(v_a = V_s\)
- Energy supplied from source
- Armature current increases
State 2: Switch OFF (\(t_{\text{OFF}}\))
-
>
- Current path: Motor \(\to D_m\)
- Motor voltage: \(v_a \approx 0\)
- Energy stored in inductance
- Armature current decreases
Average Output Voltage
\[V_a = \frac{t_{\text{ON}}}{T} V_s = k \cdot V_s\] where \(k\) is the duty cycle: \(k = \dfrac{t_{\text{ON}}}{T}\), \(0 \le k \le 1\)
Duty Cycle and Voltage Control
Duty Cycle Definition
\[k = \frac{t_{\text{ON}}}{T} = \frac{t_{\text{ON}}}{t_{\text{ON}} + t_{\text{OFF}}}\] where \(T\) is the chopping period and \(f = 1/T\) is the chopping frequency.
Voltage Relationships:
- \(k = 0\): \(V_a = 0\) (motor stopped)
- \(k = 0.5\): \(V_a = 0.5 V_s\)
- \(k = 1\): \(V_a = V_s\) (full speed)
Speed control achieved by varying \(k\) from 0 to 1.
Typical Parameters:
- Chopping frequency: 1–20 kHz
- Duty cycle range: 0–100%
- Linear voltage control
- Continuous current mode preferred
Step-Down Chopper Analysis
Step-Down (Buck) Chopper: Circuit and Waveforms
Characteristics:
- Also called Buck chopper
- Output voltage: \(V_a = k V_s\)
- \(0 \le k \le 1\)
- Power flow: source \(\to\) load
Applications:
- DC motor speed control
- Battery charging
- Voltage regulators
Step-Down Chopper: Current Analysis
Current Ripple
During ON period (\(0 < t < t_{\text{ON}}\)): \[V_s = E + L_a \frac{di_a}{dt} + i_a R_a\]
During OFF period (\(t_{\text{ON}} < t < T\)): \[0 = E + L_a \frac{di_a}{dt} + i_a R_a\]
Current Ripple Magnitude: \[\Delta I = \frac{V_s - E}{L_a} \cdot t_{\text{ON}} = \frac{E}{L_a} \cdot t_{\text{OFF}}\]
Design Consideration
Higher chopping frequency \(\Rightarrow\) Lower current ripple \(\Rightarrow\) Smoother motor operation
Continuous vs. Discontinuous Conduction
Continuous Conduction Mode (CCM)
- Current never falls to zero
- \(I_{\min} > 0\)
- Better for motor control
- Requires: \(L_a > L_{\text{critical}}\)
Condition: \[L_a > \frac{(V_s - E) R_a (1-k)}{2 f V_s}\]
Discontinuous Conduction Mode (DCM)
- Current falls to zero during OFF period
- \(I_{\min} = 0\)
- Higher current ripple
- Occurs at light loads or low \(L_a\)
Effect:
- Non-linear control
- Higher torque ripple
- Generally avoided in motor drives
Average Output Voltage and Current
Average Armature Voltage
\[V_a = \frac{1}{T} \int_0^T v_a(t) \, dt = \frac{1}{T} \left( V_s \cdot t_{\text{ON}} + 0 \cdot t_{\text{OFF}} \right) = k V_s\]
Average Armature Current (Steady State)
\[I_a = \frac{V_a - E}{R_a} = \frac{k V_s - E}{R_a}\] where \(E\) is the back-EMF of the motor.
Power Relationships:
- Input power: \(P_{\text{in}} = V_s I_s\)
- Output power: \(P_{\text{out}} = V_a I_a = k V_s I_a\)
- Efficiency: \(\eta = \dfrac{P_{\text{out}}}{P_{\text{in}}} > 95\%\) (typical)
Step-Up Chopper Analysis
Step-Up (Boost) Chopper: Circuit
Characteristics:
- Also called Boost chopper
- Output voltage: \(V_a = \dfrac{V_s}{1-k}\)
- \(V_a > V_s\) (voltage boost)
- \(0 \le k < 1\)
Operating Principle:
- When \(Q\) ON: Energy stored in \(L\)
- When \(Q\) OFF: \(L\) releases energy
- Voltage across \(L\) adds to \(V_s\)
- Diode prevents reverse flow
Application
Used for regenerative braking in DC motor drives
Step-Up Chopper: Voltage Analysis
Voltage Boost Relationship
Average output voltage: \[V_a = \frac{V_s}{1-k}\] where \(k\) is the duty cycle.
Examples:
- \(k = 0.5\): \(V_a = 2 V_s\) (voltage doubled)
- \(k = 0.75\): \(V_a = 4 V_s\) (four times boost)
- \(k \to 1\): \(V_a \to \infty\) (theoretical limit)
Practical Limitation
In practice, \(k\) is limited to 0.8–0.9 due to switching losses and component limitations. Typical boost ratio: 2–5 times.
Step-Up Chopper: Regenerative Braking
Braking Operation:
- Motor acts as generator
- Back-EMF \(E > V_s\)
- Energy returned to source
- Current flows from motor to source
Power Flow
During regeneration: \[P_{\text{regen}} = E \cdot I_a - I_a^2 R_a\] Energy recovered in battery/capacitor
Applications:
- Electric vehicles (downhill braking)
- Cranes (lowering loads)
- Elevators (descending)
- Traction systems
Efficiency Benefit
Regenerative braking can recover 60–70% of kinetic energy, significantly improving overall system efficiency.
PWM Control Techniques
Pulse Width Modulation (PWM)
PWM Principle
PWM controls the average output voltage by varying the width of pulses at a fixed frequency. \[V_a = k V_s = \frac{t_{\text{ON}}}{T} V_s\]
Advantages:
- Constant switching frequency
- Linear voltage control
- Low harmonic content
- Easy digital implementation
- Predictable filtering requirements
Parameters:
- Carrier frequency: \(f_c\) (1–20 kHz)
- Modulation index: \(m = V_{\text{control}}/V_{\text{carrier}}\)
- Duty cycle: \(k = m\)
- Output voltage: \(V_a = m V_s\)
PWM Generation Methods
Analog PWM
- Compare control signal with triangular carrier
- Op-amp based comparator
- Continuous modulation
- Simple hardware
Control Law: \[k = \frac{V_{\text{control}}}{V_{\text{carrier}}}\]
Digital PWM
- Microcontroller/DSP based
- Timer/counter implementation
- Programmable frequency and duty cycle
- Flexible and precise
Implementation: \[t_{\text{ON}} = k \cdot T_{\text{PWM}}\] Update \(k\) based on feedback control
Modern Practice
Digital PWM is the industry standard due to flexibility, programmability, and integration with control algorithms.
Frequency vs. Variable Frequency Control
Constant Frequency (PWM)
Features:
- Fixed period \(T\)
- Variable \(t_{\text{ON}}\)
- Duty cycle: \(k = t_{\text{ON}}/T\)
Advantages:
- Predictable harmonics
- Easy filtering
- Linear control
- Preferred method
Variable Frequency
Features:
- Fixed \(t_{\text{ON}}\) or \(t_{\text{OFF}}\)
- Variable period \(T\)
- Frequency modulation
Disadvantages:
- Variable harmonics
- Complex filtering
- Non-linear control
- Rarely used in motor drives
PWM Frequency Selection
Trade-offs in Choosing Switching Frequency:
Higher Frequency (>10 kHz)
Advantages:
- Lower current ripple
- Smoother torque
- Smaller filter components
- Quieter operation (above audible range)
Disadvantages:
- Higher switching losses
- Increased EMI
- More expensive switches
Lower Frequency (1–5 kHz)
Advantages:
- Lower switching losses
- Higher efficiency
- Less EMI
- Lower cost switches
Disadvantages:
- Higher current ripple
- Larger inductors needed
- Audible noise
- Greater torque ripple
Typical Range: 2–20 kHz depending on power level and application
Current Ripple and Inductance Design
Current Ripple Analysis
Peak-to-Peak Current Ripple
For a step-down chopper in CCM: \[\Delta I = \frac{V_s - E}{L_a} \cdot t_{\text{ON}} = \frac{V_s (1-k)}{L_a f}\] where \(f = 1/T\) is the switching frequency.
Maximum Ripple Condition:
- Maximum ripple occurs at \(k = 0.5\) (50% duty cycle)
- At this point: \(\Delta I_{\max} = \dfrac{V_s}{4 f L_a}\)
Design Implication
Inductance \(L_a\) must be sized for worst-case ripple at \(k = 0.5\) to ensure CCM throughout the operating range.
Minimum Inductance for CCM
Critical Inductance
To ensure continuous conduction mode (CCM) at all duty cycles: \[L_{\min} = \frac{(1-k) R_a}{2f}\] where the maximum value occurs at \(k = 0.5\).
Alternative Design Criterion (Ripple-Based): \[L_a \ge \frac{V_s}{4 f \Delta I_{\max}}\] where \(\Delta I_{\max}\) is the maximum allowable current ripple.
Typical Design Rule:
- Limit ripple to 10–20% of rated current
- Example: For \(I_{\text{rated}} = 10\) A, choose \(\Delta I_{\max} = 1\)–2 A
- Calculate \(L_a\) accordingly
Inductor Design Example
Given Data:
- Source voltage: \(V_s = 200\) V
- Switching frequency: \(f = 10\) kHz
- Rated current: \(I_{\text{rated}} = 20\) A
- Desired ripple: \(\Delta I_{\max} = 2\) A (10% of rated)
Solution: \[L_{\min} = \frac{V_s}{4 f \Delta I_{\max}} = \frac{200}{4 \times 10{,}000 \times 2} = \frac{200}{80{,}000} = 2.5 \text{ mH}\]
Design Choice:
- Select standard value: \(L_a = 3\) mH
- Add 20% safety margin
- Verify thermal and saturation ratings
Input Filter Design
Need for Input Filtering
Why Input Filters are Required:
Problems Without Filtering
- Pulsating input current
- High-frequency ripple
- EMI to source and other equipment
- Voltage spikes
- Source voltage variations
Filter Benefits
- Smooth DC input current
- Reduced EMI
- Protection of source
- Improved power quality
- Compliance with EMC standards
Standard Practice
An LC input filter is essential for all chopper drives, especially when powered from batteries or sensitive DC sources.
LC Input Filter Design
Filter Components:
- \(L_f\): Series inductor
- \(C_f\): Shunt capacitor
- Forms low-pass filter
Design Criteria
Cutoff frequency must be much lower than switching frequency: \[f_c = \frac{1}{2\pi\sqrt{L_f C_f}} \ll f_s\]
Typical Rule: \[f_c \le \frac{f_s}{10}\]
Additional Consideration:
- Damping resistor may be needed
- Prevents resonance oscillations
Filter Component Selection
Design Equations
For desired cutoff frequency \(f_c\): \[L_f C_f = \frac{1}{(2\pi f_c)^2}\]
Practical Design Steps:
- Choose \(f_c = f_s/10\) to \(f_s/20\)
- Select capacitor \(C_f\) based on voltage ripple requirement: \[C_f \ge \frac{I_{\text{rated}}}{2 \pi f_c \Delta V_{\text{ripple}}}\]
- Calculate inductor: \(L_f = \dfrac{1}{(2\pi f_c)^2 C_f}\)
- Verify inductor current rating \(\ge I_{\text{rated}}\)
- Add damping if needed to control resonance
Chopper Drive Classifications
Classification of DC Choppers
Choppers are classified based on quadrant of operation:
| Class | Configuration | Quadrants | Application |
|---|---|---|---|
| A | Step-down (Buck) | Q1 (Forward motoring) | Basic speed control |
| B | Step-up (Boost) | Q2 (Forward braking) | Regenerative braking |
| C | Two-quadrant (A+B) | Q1, Q2 | Motoring + braking |
| D | Two-quadrant | Q1, Q4 | Bidirectional current |
| E | Four-quadrant (H-bridge) | Q1, Q2, Q3, Q4 | Full reversibility |
Selection Criteria
Choose chopper class based on application requirements: unidirectional vs. bidirectional operation, regenerative braking capability, and reversing requirements.
Class A: Single-Quadrant (Step-Down)
Operating Characteristics:
- Quadrant 1 only (Q1)
- \(v_a > 0\), \(i_a > 0\)
- Forward motoring only
- No braking capability
Voltage Control
\[V_a = k V_s, \quad 0 \le k \le 1\] where \(k\) is the duty cycle.
Applications:
- Simple DC motor drives
- Fan speed control
- Pump drives
- Unidirectional conveyors
Limitation: Cannot provide braking; motor coasts to stop when power is removed.
Class B: Single-Quadrant (Step-Up)
Operating Characteristics:
- Quadrant 2 only (Q2)
- \(v_a > 0\), \(i_a < 0\)
- Regenerative braking only
- Power flows: motor \(\to\) source
Voltage Boost
\[V_a = \frac{V_s}{1-k}, \quad k < 1\] Back-EMF \(E > V_s\) required for regeneration.
Applications:
- Regenerative braking systems
- Energy recovery in EVs
- Hoist lowering operations
- Downhill traction
Note: Always used in combination with Class A for complete drive functionality.
Class C: Two-Quadrant (Forward Direction)
Structure:
- Combines Class A (\(Q_1\), \(D_1\)) and Class B (\(Q_2\), \(D_2\))
- Two power switches
- Bidirectional current capability
Operating Modes
Motoring (Q1): \(Q_1\) modulated, \(Q_2\) OFF \[V_a = k V_s\]
Braking (Q2): \(Q_2\) modulated, \(Q_1\) OFF \[V_a = \frac{V_s}{1-k}\]
Applications:
- Electric vehicles
- Traction systems
- Hoist drives
Class D: Two-Quadrant Chopper
Operating Quadrants:
- Q1: Forward motoring (\(v_a > 0\), \(i_a > 0\))
- Q4: Reverse braking (\(v_a < 0\), \(i_a > 0\))
Voltage Reversal Capability
- Can reverse voltage polarity
- Current remains positive
- Enables field weakening
- Useful for special applications
Control Strategy:
- \(Q_1\) ON: \(v_a = +V_s\)
- \(Q_4\) ON: \(v_a = -V_s\)
- PWM modulation of \(Q_1\) and \(Q_4\)
Application: Specialized drives requiring voltage polarity reversal.
Class D: Operating Modes
Mode 1: Forward Operation (\(\alpha > 0.5\))
- Switch \(Q_1\) ON for time \(t_a\)
- Switch \(Q_4\) ON for time \(T_p - t_a\)
- Average voltage:
\[\bar{v}_a = \frac{2t_a - T_p}{T_p} V_s\]
For \(t_a > T_p/2\): \(\bar{v}_a > 0\) (motoring)
Duty cycle: \(\alpha = t_a/T_p\)
Mode 2: Reverse Operation (\(\alpha < 0.5\))
- Same switching pattern
- Different average voltage polarity
For \(t_a < T_p/2\): \(\bar{v}_a < 0\) (braking)
Transition Point
At \(\alpha = 0.5\) (i.e., \(t_a = T_p/2\)): \[\bar{v}_a = 0\] Current continues to flow, but average voltage is zero.
Class D: Voltage Gain
Converter Voltage Gain
The rate of change of average output voltage with respect to ON-time: \[k_v = \left|\frac{d\bar{v}_a}{dt_a}\right| = \frac{2V_s}{T_p} \quad [\text{V/s}]\]
Operating Regions:
- \(\alpha > 0.5\): \(\bar{v}_a > 0\)
- Power flow: source \(\to\) load
- Motoring operation
- \(\alpha = 0.5\): \(\bar{v}_a = 0\)
- Zero average voltage
- Current can be non-zero
- \(\alpha < 0.5\): \(\bar{v}_a < 0\)
- Power flow: load \(\to\) source
- Braking operation
Note
Current direction remains positive in both modes; only average voltage (and power flow) reverses.
Class E: Four-Quadrant Chopper Drive
Class E: Four-Quadrant H-Bridge Drive
Structure:
- H-bridge configuration
- Four switches: \(Q_1\)–\(Q_4\)
- Four anti-parallel diodes: \(D_1\)–\(D_4\)
| Quadrant | \(v_L\) | \(i_L\) |
|---|---|---|
| Q1 (Fwd motoring) | \(+\) | \(+\) |
| Q2 (Fwd braking) | \(+\) | \(-\) |
| Q3 (Rev motoring) | \(-\) | \(-\) |
| Q4 (Rev braking) | \(-\) | \(+\) |
Class E: Operating Configurations
Configuration Flexibility:
- \(Q_4\) ON continuously \(\Rightarrow\) Class C behavior
- \(Q_1\), \(Q_2\) modulate for motoring/braking
- \(Q_1\) ON continuously \(\Rightarrow\) Class D behavior
- \(Q_3\), \(Q_4\) modulate for voltage reversal
Unified Topology
Class E subsumes Classes C and D by appropriate switching strategies. It is the most general and versatile topology.
Safety Constraints:
- \(Q_1\) and \(Q_2\) must never be ON simultaneously
- Causes shoot-through (short circuit)
- \(Q_3\) and \(Q_4\) must never be ON simultaneously
- Causes shoot-through
- Dead-time insertion: typically 1–5 \(\mu\)s
- Ensures safe commutation
- Prevents overlap
Class E: Full Drive Flexibility
Complete Quadrant Coverage
Class E provides access to all four quadrants, enabling:
- Forward and reverse motoring
- Regenerative braking in both directions
- Seamless transitions between modes
Applications Requiring Four-Quadrant Operation:
- Reversible machine tools and CNC equipment
- Servo drives with bidirectional positioning
- Electric vehicle traction (forward/reverse with regeneration)
- Elevator drives (up/down with energy recovery)
- Rolling mill drives
- Test stands and dynamometers
Control Complexity
Four-quadrant operation requires sophisticated control algorithms to manage transitions and ensure stability across all operating modes.
Power Semiconductor Devices
Power Switching Devices for Choppers
| Device | Power Range | Freq. Range | Commutation | Typical Use |
|---|---|---|---|---|
| MOSFET | \(< 10\) kW | 20–100 kHz | Self-commutated | Low-power, high-freq |
| IGBT | 10–500 kW | 5–20 kHz | Self-commutated | Industrial standard |
| GTO | 100–5000 kW | 1–5 kHz | Self-commutated | High-power traction |
| Thyristor (SCR) | \(> 500\) kW | \(< 1\) kHz | Forced commutation | Legacy/very high power |
Selection Criteria:
- Power level of application
- Required switching frequency
- Voltage and current ratings
- Gate drive complexity
- Cost and availability
Self vs. Forced Commutation
Self-Commutated Devices
Examples: MOSFET, IGBT, GTO
Characteristics:
- Turn ON and OFF controlled by gate signal
- No auxiliary circuit needed for turn-off
- Fast switching capability
- Simpler drive circuits
- Higher reliability
Status:
- Preferred for all modern drives
- Dominant in industrial applications
Forced-Commutated Devices
Example: Thyristor (SCR)
Characteristics:
- Gate controls only turn-ON
- External circuit required for turn-off
- Complex commutation circuits
- Adds cost and components
- Lower switching frequency
Status:
- Legacy technology
- Limited to very high power (\(>500\) kW)
- Being phased out
IGBT: Industry Standard for Choppers
Why IGBT?
IGBT (Insulated Gate Bipolar Transistor) is the dominant device for industrial DC chopper drives in the 10–500 kW power range.
IGBT Advantages:
- High voltage capability (up to 6.5 kV)
- High current capability (up to 3600 A)
- Moderate switching frequency (5–20 kHz)
- Low on-state voltage drop
- Simple gate drive (voltage-controlled)
- Excellent safe operating area (SOA)
- Good thermal characteristics
Comparison with Alternatives:
- vs. MOSFET: Higher power capability
- vs. GTO: Simpler gate drive, higher frequency
- vs. SCR: Self-commutated, no turn-off circuit
Typical Ratings:
- Voltage: 600 V to 6.5 kV
- Current: 10 A to 3600 A
- Switching frequency: 1–20 kHz
Summary
Summary: Motivation and Core Relations
Why Choppers?
Classical Methods Limitations:
- Rheostatic: Poor efficiency (\(<50\%\))
- M-G set: Bulky, slow, expensive
- SCR rectifier: Poor PF, AC source required
Chopper Advantages:
- Efficiency \(> 95\%\)
- Fast response (ms range)
- Compact, lightweight
- DC-source compatible
Core Relations
Step-down: \[V_a = k V_s, \quad 0 \le k \le 1\]
Step-up: \[V_a = \frac{V_s}{1-k}, \quad k < 1\]
Max ripple (at \(k=0.5\)): \[\Delta I_{\max} = \frac{V_s}{4fL_a}\]
Min inductance: \[L_{\min} = \frac{V_s}{4f\,\Delta I_{\max}}\]
Summary: Drive Classes and Devices
Chopper Classes
- Class A: Step-down, Q1 motoring
- Class B: Step-up, Q2 braking
- Class C: Q1+Q2, motoring/braking (EV, traction)
- Class D: Two-quadrant (Q1+Q4), voltage reversal
- Class E: Four-quadrant H-bridge, fully reversible
Control & Devices
PWM Control:
- Constant frequency preferred
- Variable duty cycle: \(k = V_{\text{cr}}/V_r\)
- Linear voltage control
Key Design Points:
- Higher \(f_s\) \(\Rightarrow\) lower ripple, higher loss
- Input LC filter essential
- IGBT: standard for 10–500 kW drives