MOSFET as a Switch

1. Structure and Symbol of MOSFET

Structure and Symbol of MOSFET

The Metal-Oxide-Semiconductor Field-Effect Transistor (MOSFET) is a four-terminal device consisting of a gate (G), drain (D), source (S), and body (B) terminal. Its operation relies on the modulation of charge carriers in a channel formed between the drain and source via an electric field generated by the gate voltage.

Physical Structure

The MOSFET is fabricated on a semiconductor substrate (typically silicon) with the following layered structure:

Gate (G) Source (S) Drain (D) Body (B)

Circuit Symbols

MOSFETs are represented in circuit diagrams with standardized symbols that distinguish between:

G D S N-channel Enhancement G D S P-channel Enhancement

Key Structural Parameters

The switching characteristics are governed by physical dimensions and material properties:

$$ C_{ox} = \frac{\epsilon_{ox}}{t_{ox}} $$

Where:

$$ I_D = \mu_n C_{ox} \frac{W}{L} \left[ (V_{GS} - V_{th})V_{DS} - \frac{V_{DS}^2}{2} \right] $$

This equation describes the drain current in the linear region, where:

Practical Considerations

Modern power MOSFETs incorporate advanced features to optimize switching performance:

MOSFET Structure and Symbols A side-by-side comparison of MOSFET physical structure (cross-section) and standard circuit symbols for N-channel and P-channel types, with labeled components. Substrate (B) Oxide Layer Gate (G) Source (S) Drain (D) Channel N-Channel MOSFET Structure G S D N-Channel G S D P-Channel MOSFET Circuit Symbols Enhancement Mode: Arrow points away from channel (N) or toward channel (P) Depletion Mode: Dashed channel line MOSFET Structure and Symbols
Diagram Description: The section describes the physical structure and circuit symbols of MOSFETs, which are inherently spatial concepts best shown visually.

1.2 Working Principles of MOSFET

Basic Structure and Operation

The Metal-Oxide-Semiconductor Field-Effect Transistor (MOSFET) operates as a voltage-controlled switch, leveraging the modulation of charge carriers in a semiconductor channel. The primary components are:

When a sufficient gate-to-source voltage (VGS) is applied, an inversion layer forms beneath the oxide, creating a conductive path between the source and drain.

Modes of Operation

MOSFETs exhibit three primary operational regions:

Mathematical Derivation of Drain Current

The drain current (ID) in the triode and saturation regions is derived from the gradual channel approximation:

$$ I_D = \mu_n C_{ox} \frac{W}{L} \left( (V_{GS} - V_{th})V_{DS} - \frac{V_{DS}^2}{2} \right) \quad \text{(Triode)} $$
$$ I_D = \frac{1}{2} \mu_n C_{ox} \frac{W}{L} (V_{GS} - V_{th})^2 \quad \text{(Saturation)} $$

where μn is electron mobility, Cox is oxide capacitance per unit area, and W/L is the aspect ratio.

Switching Characteristics

As a switch, the MOSFET transitions between cutoff (OFF) and triode (ON) regions. Key parameters include:

Practical Considerations

In power electronics, MOSFETs are often driven in the saturation region to minimize conduction losses. However, parasitic capacitances (Cgs, Cgd, Cds) and the Miller effect can delay switching transitions. Advanced gate drivers and zero-voltage switching (ZVS) techniques mitigate these issues.

MOSFET Cross-Section Gate (G) Source (S) Drain (D)
MOSFET Cross-Section with Inversion Layer A vertical cross-section of a MOSFET showing the gate, oxide layer, source, drain, body, and inversion layer formation when biased. B (Body) S (Source) D (Drain) SiO₂ G (Gate) Inversion Layer V_GS
Diagram Description: The diagram would physically show the cross-sectional structure of a MOSFET with labeled components (Gate, Source, Drain, Body) and the inversion layer formation.

1.3 Regions of Operation: Cutoff, Triode, and Saturation

Fundamental Operating Modes

A MOSFET operates in three distinct regions depending on the bias conditions applied to its terminals. These regions—cutoff, triode (linear), and saturation—dictate the device's current-voltage characteristics and its suitability for switching or amplification.

1. Cutoff Region

In the cutoff region, the gate-source voltage VGS is below the threshold voltage VTH, preventing the formation of an inversion layer. The drain current ID is effectively zero, making the MOSFET behave as an open switch. The condition for cutoff is:

$$ V_{GS} < V_{TH} $$

This region is critical for digital logic circuits where the MOSFET must completely block current in the OFF state. Leakage currents (subthreshold conduction) become significant in nanometer-scale devices but are often negligible in power applications.

2. Triode (Linear) Region

When VGS exceeds VTH and VDS is small, the MOSFET enters the triode region. Here, the channel acts as a voltage-controlled resistor. The drain current is given by:

$$ I_D = \mu_n C_{ox} \frac{W}{L} \left[ (V_{GS} - V_{TH})V_{DS} - \frac{V_{DS}^2}{2} \right] $$

Where:

For small VDS, the quadratic term becomes negligible, simplifying to a linear relationship. This region is exploited in analog switches and voltage-controlled resistors.

3. Saturation Region

The saturation region occurs when VDS ≥ VGS - VTH, causing channel pinch-off at the drain end. The current becomes independent of VDS and is modeled by:

$$ I_D = \frac{1}{2} \mu_n C_{ox} \frac{W}{L} (V_{GS} - V_{TH})^2 (1 + \lambda V_{DS}) $$

Where λ is the channel-length modulation parameter. This region is essential for amplification, where the MOSFET provides high output impedance. For switching applications, the device transitions rapidly through saturation during switching transients.

Boundary Conditions and Transition Behavior

The boundary between triode and saturation is defined by:

$$ V_{DS(sat)} = V_{GS} - V_{TH} $$

In power electronics, minimizing time spent in saturation reduces switching losses. Modern MOSFETs achieve nanosecond-scale transitions by optimizing gate drive circuits and reducing parasitic capacitances (Cgd, Cgs).

Practical Implications for Switching

For optimal switching performance:

Advanced gate driver ICs use adaptive timing to accelerate transitions through saturation, critical in high-frequency DC-DC converters (>1 MHz).

MOSFET Operating Regions I-V Characteristics A graph showing the I-V characteristics of a MOSFET, illustrating the cutoff, triode, and saturation regions with labeled curves and boundaries. V_DS I_D V_TH V_DS(sat) 3V I_D1 I_D2 I_D3 V_GS1 V_GS2 V_GS3 Pinch-off V_TH Cutoff Triode Saturation
Diagram Description: The diagram would show the three distinct operating regions (cutoff, triode, saturation) on a MOSFET's I-V characteristic curve with labeled boundaries and key voltage thresholds.

2. Switching Characteristics of MOSFET

Switching Characteristics of MOSFET

The switching behavior of a MOSFET is governed by its transient response when transitioning between the cut-off and saturation regions. Key parameters include turn-on delay (td(on)), rise time (tr), turn-off delay (td(off)), and fall time (tf). These metrics are critical in high-frequency applications, where switching losses dominate.

Gate Charge Dynamics

The gate-to-source voltage (VGS) must exceed the threshold voltage (Vth) to initiate conduction. The gate charge (QG) comprises three components:

$$ Q_G = Q_{GS} + Q_{GD} + Q_{G(OV)} $$

Switching Time Derivation

The rise time (tr) depends on the gate resistance (RG) and input capacitance (Ciss):

$$ t_r \approx 2.2 R_G C_{iss} $$

where Ciss = CGS + CGD (Miller effect neglected during initial turn-on).

Miller Plateau Effect

During switching, VGS exhibits a plateau phase while discharging CGD. The duration (tplateau) is:

$$ t_{plateau} = \frac{Q_{GD}}{I_{G}} $$

where IG is the gate driver current. This phase directly impacts switching losses.

Power Dissipation

Total switching losses (Psw) combine turn-on and turn-off energy:

$$ P_{sw} = \frac{1}{2} V_{DS} I_D (t_r + t_f) f_{sw} $$

where fsw is the switching frequency. High dV/dt and di/dt during transitions may induce voltage spikes or ringing.

Practical Considerations

V_GS (Gate-Source Voltage) I_D (Drain Current) Turn-on Turn-off
MOSFET Switching Waveforms and Miller Plateau Time-domain plots of V_GS (top) and I_D (bottom) waveforms showing the Miller plateau effect during MOSFET switching. Time V_GS V_th I_D Miller Plateau Q_GD t_d(on) t_r t_plateau t_d(off) t_f I_G
Diagram Description: The section describes time-domain switching behavior with voltage/current waveforms and the Miller plateau effect, which are inherently visual concepts.

2.2 Gate-Source Voltage (VGS) and Threshold Voltage (Vth)

The operation of a MOSFET as a switch hinges critically on the relationship between the gate-source voltage (VGS) and the threshold voltage (Vth). When VGS exceeds Vth, the MOSFET enters the on-state, allowing significant drain current (ID) to flow. Below Vth, the device remains in cutoff, acting as an open switch.

Threshold Voltage (Vth): Definition and Physics

The threshold voltage is the minimum VGS required to form an inversion layer (conductive channel) between the source and drain. For an n-channel MOSFET, it is derived from the electrostatic balance at the oxide-semiconductor interface:

$$ V_{th} = V_{FB} + 2\phi_B + \frac{\sqrt{2q \epsilon_s N_A (2\phi_B)}}{C_{ox}} $$

where:

Gate-Source Voltage (VGS) and Channel Formation

When VGS > Vth, the surface potential attracts minority carriers (electrons in nMOS), forming an inversion layer. The overdrive voltage (VOV = VGS - Vth) determines the inversion charge density (Qinv):

$$ Q_{inv} = -C_{ox} (V_{GS} - V_{th}) $$

In saturation, the drain current (ID) follows the square-law model:

$$ I_D = \frac{1}{2} \mu_n C_{ox} \frac{W}{L} (V_{GS} - V_{th})^2 (1 + \lambda V_{DS}) $$

Practical Implications for Switching

For robust switching:

Real-World Considerations

In high-frequency switching applications, the Miller effect introduces a delay as VGS must first charge the gate-drain capacitance (CGD) before overcoming Vth. This is mitigated by:

MOSFET Transfer Characteristics (ID vs VGS) Vth Cutoff Region Saturation Region

2.3 On-State Resistance (RDS(on)) and Its Impact

Definition and Physical Origin

The on-state resistance (RDS(on)) of a MOSFET represents the total resistance between the drain and source terminals when the device is fully turned on. It arises from the combined contributions of the channel resistance, drift region resistance, and parasitic resistances in the source, drain, and metallization layers. In modern power MOSFETs, RDS(on) is dominated by the epitaxial layer resistance, which is designed to sustain the blocking voltage in the off-state.

Mathematical Derivation

The channel resistance component can be derived from the MOSFET's I-V characteristics in the linear region. For a gate voltage VGS significantly above the threshold voltage Vth, the drain current ID is given by:

$$ I_D = \mu_n C_{ox} \frac{W}{L} \left( (V_{GS} - V_{th})V_{DS} - \frac{V_{DS}^2}{2} \right) $$

For small VDS, the quadratic term becomes negligible, and the expression simplifies to:

$$ I_D \approx \mu_n C_{ox} \frac{W}{L} (V_{GS} - V_{th})V_{DS} $$

The channel resistance Rch is then obtained as:

$$ R_{ch} = \frac{V_{DS}}{I_D} = \frac{1}{\mu_n C_{ox} \frac{W}{L} (V_{GS} - V_{th})} $$

The total RDS(on) includes additional resistances:

$$ R_{DS(on)} = R_{ch} + R_{drift} + R_{source} + R_{drain} $$

Temperature Dependence

RDS(on) exhibits a strong positive temperature coefficient due to the mobility degradation of charge carriers with increasing temperature. The relationship is approximately linear for silicon MOSFETs:

$$ R_{DS(on)}(T) = R_{DS(on)}(25^\circ C) \times [1 + \alpha (T - 25)] $$

where α typically ranges from 0.6% to 1.0% per °C for modern devices. This characteristic enables natural current sharing in parallel-connected MOSFETs but also leads to higher conduction losses at elevated temperatures.

Impact on Switching Performance

The RDS(on) directly determines the conduction losses in switching applications:

$$ P_{cond} = I_{RMS}^2 R_{DS(on)} $$

For high-frequency switching circuits, the trade-off between RDS(on) and gate charge (QG) becomes critical. Devices optimized for lower RDS(on) typically exhibit higher gate capacitance, increasing switching losses. The figure of merit (FOM) for this trade-off is:

$$ FOM = R_{DS(on)} \times Q_G $$

Advanced Device Structures

Modern power MOSFET technologies employ various techniques to minimize RDS(on):

Wide-bandgap devices like GaN and SiC MOSFETs achieve significantly lower RDS(on) values compared to silicon counterparts due to their higher critical electric field strength, enabling thinner drift regions.

Measurement Considerations

Accurate RDS(on) measurement requires:

Modern curve tracers and power device analyzers implement pulsed measurement techniques to prevent self-heating during characterization.

MOSFET Structure and RDS(on) Components A vertical cross-section of a MOSFET showing the structure and labeled resistance components (Rch, Rdrift, Rsource, Rdrain) contributing to RDS(on). Rch Rdrift Rsource Rdrain Epitaxial Layer Gate Drain Source Legend Channel (Rch) Drift (Rdrift) Source (Rsource) Drain (Rdrain)
Diagram Description: The section explains the physical origin of RDS(on) and its components, which would benefit from a visual breakdown of the MOSFET structure and resistance contributions.

3. Driving the MOSFET: Gate Drivers and Bootstrap Circuits

Driving the MOSFET: Gate Drivers and Bootstrap Circuits

Gate Drive Requirements

MOSFET switching speed and conduction losses are heavily influenced by the gate drive characteristics. The gate-source capacitance (CGS) and gate-drain capacitance (CGD, or Miller capacitance) must be charged and discharged rapidly to minimize transition times. The required gate charge (QG) is derived from the integral of the gate current:

$$ Q_G = \int_{0}^{t} I_G \, dt $$

For fast switching, the gate driver must supply sufficient peak current (IG) to overcome the capacitive load:

$$ I_G = \frac{V_{DRIVE} - V_{TH}}{R_G + R_{G(int)}} $$

where VDRIVE is the gate driver output voltage, VTH is the MOSFET threshold voltage, RG is the external gate resistor, and RG(int) is the internal gate resistance.

Gate Driver ICs

Dedicated gate driver ICs are essential for high-frequency or high-power applications. Key specifications include:

Modern drivers integrate features like:

Bootstrap Circuit Design

In high-side configurations, a bootstrap circuit maintains gate drive voltage above the source potential. The bootstrap capacitor (CBOOT) must store enough charge to keep the high-side MOSFET on during the entire conduction period:

$$ C_{BOOT} \geq \frac{Q_G + I_{BS(leak)} \cdot t_{ON}}{\Delta V_{BOOT}} $$

where IBS(leak) is the bootstrap diode leakage current, tON is the maximum on-time, and ΔVBOOT is the allowable voltage droop (typically ≤10% of VDRIVE).

The bootstrap diode must withstand the full supply voltage and have fast recovery to prevent reverse charge leakage. Schottky diodes are commonly used for their low forward voltage and negligible recovery time.

Practical Considerations

Gate Driver MOSFET VCC CBOOT

3.2 Switching Speed and Switching Losses

Switching Speed Fundamentals

The switching speed of a MOSFET is determined by how quickly the device transitions between the cut-off and saturation regions. This speed is primarily governed by the time required to charge or discharge the gate capacitance (CGS and CGD). The total switching time (tsw) consists of two phases:

$$ t_{sw} = t_{d(on)} + t_r + t_{d(off)} + t_f $$

Gate Drive and Switching Speed

The switching speed is heavily influenced by the gate driver's current capability. A higher gate drive current (IG) reduces the RC time constant of the gate circuit, speeding up the transition:

$$ t_r \approx \frac{Q_g}{I_G} $$

where Qg is the total gate charge. However, excessively fast switching can lead to voltage overshoot and ringing due to parasitic inductances in the circuit.

Switching Losses

Switching losses occur during the transient periods when the MOSFET is neither fully on nor off, resulting in simultaneous high voltage and current. The energy dissipated per switching cycle (Esw) is given by:

$$ E_{sw} = \frac{1}{2} V_{DS} \cdot I_D \cdot (t_r + t_f) \cdot f_{sw} $$

where fsw is the switching frequency. Total power loss (Psw) scales linearly with frequency:

$$ P_{sw} = E_{sw} \cdot f_{sw} $$

Impact of Parasitic Elements

Parasitic capacitances (Coss, Crss) and inductances (Ls, Ld) in the MOSFET and PCB layout contribute to switching losses. The Miller effect (due to CGD) further slows down switching by effectively increasing the input capacitance during the VDS transition.

Optimizing Switching Performance

To minimize losses while maintaining acceptable switching speed:

Trade-offs in High-Frequency Applications

At high frequencies (fsw > 1 MHz), switching losses dominate over conduction losses. Designers must balance:

Advanced techniques like zero-voltage switching (ZVS) or zero-current switching (ZCS) can eliminate switching losses but require resonant topologies.

3.3 Heat Dissipation and Thermal Management

When a MOSFET operates as a switch, power dissipation occurs primarily in two modes: conduction losses (I²R) and switching losses. The total power dissipated (Pdiss) is the sum of these components:

$$ P_{diss} = I_{D}^2 R_{DS(on)} + \frac{1}{2} V_{DS} I_D (t_r + t_f) f_{sw} $$

where ID is the drain current, RDS(on) is the on-state resistance, VDS is the drain-source voltage during switching, tr and tf are the rise and fall times, and fsw is the switching frequency.

Thermal Resistance and Junction Temperature

The MOSFET's junction temperature (TJ) must be kept within safe limits to prevent thermal runaway or device failure. The thermal path from junction to ambient is characterized by thermal resistances:

$$ T_J = T_A + P_{diss} \cdot (R_{θJC} + R_{θCS} + R_{θSA}) $$

where:

Practical Thermal Management Techniques

Effective heat dissipation requires optimizing multiple factors:

1. Heatsink Selection

The heatsink's thermal resistance must be low enough to maintain TJ below the maximum rated value (typically 150–175°C for silicon MOSFETs). Forced air cooling can reduce RθSA by 30–50% compared to natural convection.

2. Thermal Interface Materials (TIMs)

Thermal grease, pads, or phase-change materials fill microscopic gaps between the MOSFET case and heatsink, minimizing RθCS. Typical values range from 0.3°C/W (high-performance grease) to 1.5°C/W (silicone pads).

3. PCB Layout Considerations

For surface-mount devices, thermal vias and copper pours act as extended heatsinks. A 2 oz/ft² copper plane with multiple vias can achieve RθJA as low as 20°C/W without external heatsinks.

Transient Thermal Analysis

Under pulsed operation, the thermal time constant (τth) of the package determines how quickly heat spreads:

$$ \tau_{th} = R_{θJA} C_{th} $$

where Cth is the thermal capacitance. For short pulses (tpulse << τth), the effective thermal resistance is reduced:

$$ R_{θJA(eff)} = R_{θJA} \cdot \frac{t_{pulse}}{\tau_{th}} $$

This explains why MOSFETs can handle higher peak currents in pulsed applications compared to DC operation.

Advanced Cooling Methods

For high-power applications (>500W), liquid cooling or heat pipes may be necessary. These can achieve RθSA values below 0.1°C/W, enabling power densities exceeding 100W/cm².

MOSFET Thermal Resistance Network Thermal equivalent circuit diagram showing heat flow from the MOSFET junction to ambient through labeled thermal resistances. T_J T_C T_S T_A RθJC RθCS RθSA P_diss Heat Flow
Diagram Description: The thermal resistance network and power dissipation components would benefit from a visual representation of the thermal path and energy flow.

4. Power Supply Switching

4.1 Power Supply Switching

MOSFETs are widely employed in power supply switching due to their low on-resistance (RDS(on)), fast switching speeds, and high efficiency. When operating as a switch, a MOSFET transitions between the cutoff and saturation regions, effectively controlling the flow of current in a power circuit. The gate-source voltage (VGS) determines the conduction state, with the threshold voltage (Vth) serving as the critical switching point.

Switching Dynamics and Power Dissipation

The total power dissipation in a MOSFET during switching consists of conduction losses (Pcond) and switching losses (Psw). Conduction losses occur when the device is fully on and are given by:

$$ P_{cond} = I_D^2 R_{DS(on)} $$

Switching losses arise during the transient periods when the MOSFET is neither fully on nor off. These losses depend on the switching frequency (fsw), drain-source voltage (VDS), drain current (ID), and the rise (tr) and fall (tf) times:

$$ P_{sw} = \frac{1}{2} V_{DS} I_D (t_r + t_f) f_{sw} $$

Gate Drive Considerations

Efficient switching requires careful gate drive design. The gate charge (QG) must be fully delivered to ensure the MOSFET reaches the desired VGS. The gate driver must supply sufficient current (IG) to charge the input capacitance (Ciss) quickly:

$$ I_G = \frac{Q_G}{t_r} $$

In high-frequency applications, parasitic inductances and capacitances can lead to ringing and increased losses. Proper PCB layout, including minimized gate loop inductance and use of low-resistance gate resistors, is critical.

Thermal Management

Power dissipation raises the junction temperature (TJ), which must be kept within safe limits. The thermal resistance from junction to ambient (RθJA) determines the temperature rise for a given power dissipation:

$$ T_J = T_A + P_{total} R_{θJA} $$

Heat sinks or forced air cooling may be necessary for high-power applications to maintain reliable operation.

Practical Applications

MOSFETs are extensively used in DC-DC converters, motor drives, and switched-mode power supplies (SMPS). For example, in a buck converter, the MOSFET switches at high frequency to regulate the output voltage. The choice of MOSFET depends on voltage rating, current handling, and switching speed requirements.

Advanced designs often incorporate synchronous rectification, where a second MOSFET replaces the freewheeling diode to reduce conduction losses further. This technique is prevalent in modern power supplies aiming for efficiencies above 90%.

MOSFET Switching Waveforms and Power Dissipation Oscilloscope-style waveforms showing gate-source voltage (V_GS), drain current (I_D), and drain-source voltage (V_DS) during MOSFET switching transitions, with labeled rise/fall times and power dissipation regions. Time (t) V_GS V_th t_r I_D t_f V_DS P_sw P_cond R_DS(on) V_GS: Gate-Source Voltage I_D: Drain Current V_DS: Drain-Source Voltage
Diagram Description: The section discusses switching dynamics with mathematical relationships between time-domain parameters (rise/fall times) and power losses, which are best visualized with waveforms.

4.2 Motor Control Circuits

MOSFET-based motor control circuits leverage the transistor's fast switching capabilities and low on-resistance to efficiently regulate the speed and direction of DC motors. The fundamental topology consists of a MOSFET in series with the motor, driven by a gate signal that switches between saturation and cutoff regions.

Basic PWM Motor Drive Circuit

The most common approach uses pulse-width modulation (PWM) to control average motor current. When the MOSFET is in saturation (VGS > VTH), the motor sees the full supply voltage. During the off-state (VGS = 0), the motor's inductive kickback must be managed through a freewheeling diode. The duty cycle D of the PWM signal directly controls the motor's effective voltage:

$$ V_{eff} = D \cdot V_{DD} $$

where D = ton/T (with T being the PWM period). The resulting average motor current is:

$$ I_{avg} = \frac{V_{eff} - EMF}{R_{wind}} $$

where EMF is the back-electromotive force and Rwind is the motor winding resistance.

Gate Drive Considerations

Motor control requires careful gate drive design due to:

The required gate drive current IG is determined by:

$$ I_G = \frac{Q_g}{t_r} $$

where Qg is the total gate charge from the datasheet and tr is the desired rise time. For motors drawing >1A, dedicated gate driver ICs (e.g., TC4427) are typically employed.

Thermal Design

Power dissipation in the MOSFET comes from two primary sources:

  1. Conduction losses: Pcond = IRMS2 \cdot RDS(on)
  2. Switching losses: Psw = \frac{1}{2} V_{DS} I_D (t_r + t_f) f_{PWM}

The junction temperature can be estimated using the thermal impedance RθJA:

$$ T_J = T_A + (P_{cond} + P_{sw}) \cdot R_{θJA} $$

Protection Circuits

Essential protection mechanisms include:

For bidirectional control, H-bridge configurations using four MOSFETs (arranged as two complementary pairs) allow both speed and direction control while maintaining proper shoot-through protection through dead-time insertion in the gate drive signals.

MOSFET Motor Control Circuit Topologies A diagram illustrating PWM motor control circuits and H-bridge configurations with MOSFETs, freewheeling diodes, and timing waveforms. PWM Gate Driver V_GS Motor Freewheel Diode V_DS I_D Basic PWM Motor Control Motor H-Bridge Configuration Q1 Q2 Q3 Q4 Time V PWM Waveform Dead Time Dead Time
Diagram Description: The section describes PWM motor control circuits and H-bridge configurations, which are spatial arrangements of components with critical signal timing relationships.

4.3 PWM (Pulse Width Modulation) Applications

Fundamentals of PWM Switching

Pulse Width Modulation (PWM) is a technique where the duty cycle of a square wave is modulated to control the average power delivered to a load. When a MOSFET operates as a switch in PWM applications, it transitions rapidly between cutoff and saturation regions, minimizing power dissipation during switching. The average output voltage Vavg is given by:

$$ V_{avg} = D \cdot V_{DD} $$

where D is the duty cycle (0 ≤ D ≤ 1) and VDD is the supply voltage. The switching frequency fsw must be high enough to avoid visible flicker in lighting applications or audible noise in motor control, typically ranging from 20 kHz to several MHz.

MOSFET Switching Losses in PWM

Power dissipation in a PWM-driven MOSFET consists of conduction losses (Pcond) and switching losses (Psw):

$$ P_{cond} = I_{RMS}^2 \cdot R_{DS(on)} \cdot D $$
$$ P_{sw} = \frac{1}{2} V_{DD} I_D (t_r + t_f) f_{sw} $$

where tr and tf are the rise and fall times, respectively. For high-efficiency designs, fsw is optimized to balance between switching losses and ripple current.

Gate Drive Considerations

Fast switching requires low-impedance gate drive circuits to minimize transition times. The required gate drive current IG is:

$$ I_G = \frac{Q_g}{t_r} $$

where Qg is the total gate charge specified in the MOSFET datasheet. Insufficient drive current leads to excessive switching losses due to prolonged transition through the linear region.

Practical Applications

Motor Speed Control

In brushed DC motors, PWM regulates speed by varying the average voltage while maintaining torque. The back-EMF (Vemf) of the motor acts as a natural low-pass filter, smoothing the current ripple:

$$ V_{emf} = k_e \omega $$

where ke is the back-EMF constant and ω is the angular velocity.

LED Dimming

PWM dimming preserves LED chromaticity by operating at either zero or nominal current, avoiding the spectral shift associated with analog dimming. A typical LED driver circuit uses a high-side MOSFET switch with a freewheeling diode for inductive kickback protection.

Switch-Mode Power Supplies

Buck and boost converters rely on PWM to regulate output voltage. The duty cycle controls the energy transfer to the output capacitor and load. For a buck converter in continuous conduction mode (CCM), the output voltage is:

$$ V_{out} = D \cdot V_{in} $$

Critical design parameters include inductor selection (L > Lcrit) to maintain CCM and output capacitor sizing to limit voltage ripple.

Dead-Time Insertion

In half-bridge or full-bridge configurations, dead-time (tdead) prevents shoot-through current during MOSFET switching transitions. The dead-time must exceed the sum of the turn-off delay (td(off)) and the turn-on delay (td(on)) of the complementary MOSFETs:

$$ t_{dead} > t_{d(off)} - t_{d(on)} $$

Modern gate drivers integrate programmable dead-time generators to optimize this parameter dynamically.

PWM MOSFET Switching Waveforms and Applications A diagram illustrating PWM waveforms, MOSFET switching transitions, and application circuits for motor control and LED dimming. PWM Signal V_H 0 Time (t) D 1-D f_sw MOSFET Switching V_GS I_D Time (t) t_r t_f dead-time region Applications M MOSFET D V_emf LED MOSFET D V_avg
Diagram Description: The section covers PWM waveforms, MOSFET switching transitions, and practical applications like motor control and LED dimming, which are highly visual concepts.

5. Recommended Books and Papers

5.1 Recommended Books and Papers

5.2 Online Resources and Datasheets

5.3 Advanced Topics and Research Directions