Zero-Voltage Switching Resonant Converters

1. Principles of Zero-Voltage Switching

1.1 Principles of Zero-Voltage Switching

Fundamental Concept

Zero-Voltage Switching (ZVS) is a resonant transition technique where a power semiconductor device is turned on or off only when the voltage across it is zero. This eliminates capacitive switching losses, which dominate at high frequencies in conventional hard-switched converters. The mechanism relies on the interaction between parasitic capacitances (e.g., MOSFET output capacitance Coss) and circuit inductance to create a resonant transition interval.

Mechanism of ZVS Operation

For ZVS to occur, the following conditions must be satisfied:

$$ \frac{1}{2} L_r I_p^2 \geq \frac{1}{2} C_{oss} V_{in}^2 $$

where Lr is the resonant inductance, Ip is the peak inductor current, and Vin is the input voltage.

Resonant Tank Dynamics

The ZVS process is governed by an LC resonant circuit formed by:

The characteristic resonant frequency and impedance are:

$$ f_r = \frac{1}{2\pi\sqrt{L_r C_{eq}}} $$ $$ Z_r = \sqrt{\frac{L_r}{C_{eq}}} $$

Implementation Topologies

Common ZVS-enabled converter topologies include:

Practical Design Considerations

Key parameters affecting ZVS performance:

$$ t_{dead} > \pi\sqrt{L_r C_{eq}} $$

Loss Analysis

ZVS eliminates dominant loss components:

Remaining losses are primarily conduction losses and gate drive losses.

ZVS Resonant Transition Waveforms Time-aligned waveforms showing switch voltage (Vds), inductor current (IL), gate drive signal, and resonant capacitor voltage during pre-ZVS, resonant transition, and post-ZVS phases. 0 Time Vds Zero-crossing IL Ip Gate Dead Time Pre-ZVS Resonant Transition Post-ZVS Resonant Frequency (fr)
Diagram Description: The section describes resonant transitions and timing relationships that are inherently visual, particularly the interaction between voltage/current waveforms and dead time alignment.

Advantages of ZVS in Power Converters

Zero-Voltage Switching (ZVS) resonant converters offer significant performance improvements over traditional hard-switching converters. The primary advantage stems from the elimination of switching losses, which dominate at high frequencies. When a power semiconductor transitions states (ON/OFF) under ZVS conditions, the voltage across the device is zero, ensuring minimal energy dissipation during the switching interval. This results in higher efficiency, especially in high-frequency applications where switching losses would otherwise be prohibitive.

Reduction in Switching Losses

The switching loss in a conventional hard-switched converter can be approximated by:

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

where Vds is the drain-source voltage, Ids is the drain current, tr and tf are the rise and fall times, and fsw is the switching frequency. Under ZVS, Vds is near zero during the transition, reducing Psw to negligible levels. This allows converters to operate at higher frequencies without excessive thermal stress, enabling smaller passive components and higher power density.

Electromagnetic Interference (EMI) Mitigation

Hard-switching generates high dv/dt and di/dt transients, which are primary sources of conducted and radiated EMI. ZVS minimizes these abrupt transitions by ensuring smooth voltage and current waveforms. The resonant tank in ZVS converters shapes the switching edges, reducing high-frequency harmonics. This simplifies EMI filter design and compliance with regulatory standards such as CISPR 32 and FCC Part 15.

Improved Reliability and Thermal Management

Since ZVS reduces switching losses, the junction temperature of power devices decreases significantly. This extends the lifetime of semiconductors, as thermal cycling and stress-related failures are mitigated. For example, a MOSFET operating under ZVS at 500 kHz may exhibit a junction temperature 20–30°C lower than its hard-switched counterpart, directly improving mean time between failures (MTBF).

Higher Frequency Operation

The absence of switching losses enables resonant converters to operate at frequencies beyond 1 MHz, which is impractical with hard-switching. Higher frequencies permit the use of smaller magnetics and capacitors, reducing the overall size and weight of the converter. This is particularly advantageous in aerospace, automotive, and portable electronics, where power density is critical.

Soft Recovery of Body Diodes

In hard-switched converters, the reverse recovery of MOSFET body diodes induces high peak currents and voltage spikes. ZVS ensures that the body diode conducts only under zero-voltage conditions, eliminating reverse recovery losses. This is especially beneficial in bridge topologies (e.g., LLC, phase-shifted full-bridge), where diode recovery can cause significant inefficiencies.

Practical Applications

ZVS resonant converters are widely adopted in:

The following diagram illustrates the voltage and current waveforms during ZVS transition:

Time I_ds V_ds
ZVS Transition Waveforms Waveform diagram showing drain-source voltage (V_ds) and drain current (I_ds) during zero-voltage switching transition, with labeled axes and zero-crossing points. Time Voltage/Current V_ds I_ds Zero crossing Zero crossing 0 t0
Diagram Description: The section includes a detailed discussion of voltage and current waveforms during ZVS transition, which is inherently visual and time-domain behavior.

1.3 Key Challenges in Implementing ZVS

Parasitic Capacitance and Inductance Effects

The non-ideal behavior of power semiconductor devices introduces parasitic capacitances (Coss, Cgd) and inductances (Ls), which disrupt the intended zero-voltage switching conditions. The resonant transition time tr must satisfy:

$$ t_r \geq \frac{1}{2} \sqrt{L_r C_{eq}} $$

where Lr is the resonant inductance and Ceq represents the equivalent parasitic capacitance. Misalignment between these parameters leads to hard switching losses, particularly at high frequencies (>1 MHz).

Dead-Time Optimization

Precise dead-time control is critical to prevent shoot-through currents while ensuring complete charge removal from the MOSFET output capacitance. The optimal dead-time td depends on:

$$ t_d = \frac{Q_g}{I_{peak}} + \Delta t_{margin} $$

where Qg is the total gate charge and Ipeak is the resonant current magnitude. Industrial implementations often require adaptive dead-time control circuits to compensate for temperature and load variations.

Load Dependency

ZVS operation degrades significantly under light-load conditions (<20% rated power) due to insufficient energy for capacitive discharge. The minimum current requirement for ZVS is:

$$ I_{min} = V_{in} \sqrt{\frac{C_{eq}}{L_r}} $$

This necessitates either burst-mode operation or auxiliary circuits in applications with wide load ranges, such as server power supplies or wireless charging systems.

Magnetic Component Design

Transformer leakage inductance (Llk) must be carefully controlled—too low prevents ZVS, while excessive values increase conduction losses. The critical coupling coefficient kcrit is:

$$ k_{crit} = 1 - \frac{4L_r}{N^2 L_m} $$

where Lm is the magnetizing inductance and N is the turns ratio. Planar magnetics with interleaved windings are often employed to achieve repeatable Llk values in mass production.

Thermal Management

The resonant tank components experience high RMS currents, leading to I2R losses that scale with frequency. For GaN FETs operating at 5 MHz, the skin depth δ in copper windings becomes a limiting factor:

$$ \delta = \sqrt{\frac{\rho}{\pi \mu_0 f}} $$

This demands advanced cooling techniques like embedded heat pipes or liquid cooling in high-density converters exceeding 100 W/cm3.

EMI Considerations

The high di/dt (>100 A/μs) during resonant transitions generates significant electromagnetic interference. The spectral content of the switching noise voltage Vn(f) follows:

$$ V_n(f) = \frac{2V_{in} t_r}{\pi^2 t_r^2 f^2 + 1} $$

Effective shielding and layout techniques, such as coaxial transformer designs and symmetric PCB stackups, are essential to meet CISPR 32 Class B emissions standards.

Control Loop Stability

The variable switching frequency in LLC converters creates a nonlinear control-to-output transfer function. The small-signal model reveals a right-half-plane zero at:

$$ f_{z,RHP} = \frac{R_{load}}{2\pi L_r} $$

Digital controllers with predictive algorithms (e.g., least-mean-square adaptive filters) are increasingly adopted to maintain stability across the entire operating range while preserving ZVS conditions.

ZVS Implementation Challenges Overview Multi-panel diagram showing equivalent circuit with parasitics, timing diagram of gate signals and resonant transitions, load-dependent waveforms, and thermal/EMI hotspots in zero-voltage switching resonant converters. 1. Equivalent Circuit with Parasitics C_oss L_s L_lk 2. Timing Diagram Time V/I V_GS1 V_GS2 I_res t_d t_r 3. Load-Dependent Waveforms Light Load Heavy Load I_min 4. Thermal/EMI Hotspots V_n(f) δ f_z,RHP
Diagram Description: The section discusses complex relationships between parasitic elements, resonant transitions, and timing constraints that are inherently spatial and temporal.

2. Basic Topologies of Resonant Converters

2.1 Basic Topologies of Resonant Converters

Resonant converters achieve zero-voltage switching (ZVS) or zero-current switching (ZCS) by incorporating resonant tanks—comprising inductors (L) and capacitors (C)—into their power stages. The three fundamental topologies are the series resonant converter (SRC), parallel resonant converter (PRC), and series-parallel resonant converter (SPRC), each distinguished by the arrangement of the resonant elements relative to the load.

Series Resonant Converter (SRC)

The SRC places the resonant tank in series with the load. The resonant current flows directly through the load, making it suitable for high-voltage applications. The equivalent circuit consists of an AC voltage source (Vin), a series L-C network, and a resistive load (RL). The resonant frequency (fr) is given by:

$$ f_r = \frac{1}{2\pi\sqrt{LC}} $$

ZVS occurs when the switching frequency (fs) exceeds fr, ensuring the converter operates in the inductive region. The normalized output voltage (Vo/Vin) is governed by the quality factor (Q) and frequency ratio (F = fs/fr):

$$ \frac{V_o}{V_{in}} = \frac{1}{\sqrt{1 + Q^2(F - 1/F)^2}} $$

Parallel Resonant Converter (PRC)

In the PRC, the resonant capacitor is parallel to the load. This topology inherently limits the output current, making it ideal for high-current applications like induction heating. The resonant frequency remains identical to the SRC, but the output voltage exhibits a second-order response:

$$ \frac{V_o}{V_{in}} = \frac{1}{\sqrt{(1 - F^2)^2 + (F/Q)^2}} $$

ZCS is achievable when fs < fr, as the tank impedance becomes capacitive. PRCs are less sensitive to load variations but require precise dead-time control to prevent shoot-through currents.

Series-Parallel Resonant Converter (SPRC)

The SPRC combines series and parallel resonant elements, offering a hybrid response. A common configuration is the LLC resonant converter, which uses an additional inductor (Lm) to enable ZVS across a wide load range. The resonant frequencies are:

$$ f_r = \frac{1}{2\pi\sqrt{L_rC_r}}, \quad f_m = \frac{1}{2\pi\sqrt{(L_r + L_m)C_r}} $$

where Lr is the resonant inductor and Cr the resonant capacitor. The LLC converter's gain characteristic is:

$$ \frac{V_o}{V_{in}} = \frac{1}{\sqrt{\left(1 + \frac{L_r}{L_m} - \frac{F^2}{F_r^2}\right)^2 + Q^2\left(F - \frac{1}{F}\right)^2}} $$

This topology dominates modern power supplies (e.g., server PSUs) due to its high efficiency and load adaptability.

Practical Considerations

SRC PRC SPRC

2.2 Series vs. Parallel Resonant Converters

Resonant converters are broadly classified into series and parallel topologies, each exhibiting distinct operational characteristics. The choice between them depends on load conditions, efficiency requirements, and voltage/current stress management.

Series Resonant Converters (SRC)

In a series resonant converter, the resonant inductor (Lr) and capacitor (Cr) are connected in series with the load. The tank current flows through both components and the load, making the output current highly load-dependent. The resonant frequency fr is given by:

$$ f_r = \frac{1}{2\pi\sqrt{L_r C_r}} $$

Key properties of SRCs include:

Parallel Resonant Converters (PRC)

In a parallel resonant converter, the resonant tank is connected in parallel with the load. The resonant capacitor (Cr) maintains a nearly constant voltage across the load, making the output voltage less sensitive to load variations. The resonant frequency remains identical to the SRC case, but the impedance characteristics differ:

$$ Z_r = \sqrt{\frac{L_r}{C_r}} $$

Key properties of PRCs include:

Comparative Analysis

The following table summarizes the critical differences:

Parameter Series Resonant Converter Parallel Resonant Converter
Voltage Gain Load-dependent Load-independent
Current Stress Higher Lower
Voltage Stress Lower Higher
Efficiency at Light Load Poor Better

Practical Design Considerations

When selecting between SRC and PRC topologies, engineers must consider:

2.3 Role of Resonant Components in ZVS

The resonant inductor (Lr) and capacitor (Cr) form the core of ZVS operation by shaping the converter's switching transitions. Their interaction determines the resonant tank's natural frequency (fr), which must be carefully tuned relative to the switching frequency (fsw) to achieve zero-voltage switching conditions.

Resonant Tank Dynamics

The resonant frequency is given by:

$$ f_r = \frac{1}{2\pi \sqrt{L_r C_r}} $$

For ZVS operation, fsw must be slightly higher than fr to ensure inductive operation. This creates a phase lag between the voltage and current, allowing the switch's parasitic capacitance to discharge before turn-on. The characteristic impedance (Z0) of the tank:

$$ Z_0 = \sqrt{\frac{L_r}{C_r}} $$

directly influences the peak resonant current and voltage stress on components. Higher Z0 reduces circulating current but increases voltage stress.

Critical Timing Parameters

The dead time (td) between switch transitions must satisfy:

$$ t_d > \frac{C_{oss} V_{in}}{I_{pk}} $$

where Coss is the switch output capacitance, Vin is the input voltage, and Ipk is the peak resonant current. The resonant components must provide sufficient energy to:

Component Selection Tradeoffs

Practical design considerations for Lr and Cr include:

Non-Ideal Effects

Real-world implementations must compensate for:

$$ Q = \frac{1}{R}\sqrt{\frac{L_r}{C_r}} $$

where R represents equivalent series resistance. High Q factors (>5) improve efficiency but narrow the ZVS operating range. Temperature-dependent parameter drift in components can require adaptive control in precision applications.

V_DS I_DS Time Switch Voltage Resonant Current
ZVS Resonant Waveforms and Timing Waveform diagram showing switch voltage (V_DS) and resonant current (I_DS) with timing annotations for Zero-Voltage Switching (ZVS) transitions. Time V/I V_DS I_DS t_d t_d Zero-Crossing Zero-Crossing f_r
Diagram Description: The section describes resonant waveforms and timing relationships that are inherently visual, showing how switch voltage and resonant current interact during ZVS transitions.

3. Selection of Resonant Components

3.1 Selection of Resonant Components

The design of a zero-voltage switching (ZVS) resonant converter hinges on the proper selection of resonant components—primarily the inductor (Lr) and capacitor (Cr)—to achieve optimal efficiency and soft-switching characteristics. The resonant tank's behavior is governed by the natural frequency (ωr) and characteristic impedance (Zr), which must be carefully matched to the converter's operational requirements.

Resonant Frequency and Impedance

The resonant frequency (fr) is determined by the LC tank's components:

$$ f_r = \frac{1}{2\pi \sqrt{L_r C_r}} $$

Meanwhile, the characteristic impedance (Zr) defines the peak current and voltage stresses across the resonant elements:

$$ Z_r = \sqrt{\frac{L_r}{C_r}} $$

For ZVS operation, the converter must operate above the resonant frequency (fsw > fr) to ensure inductive impedance, allowing the switches to turn on at zero voltage.

Component Trade-offs and Practical Considerations

The selection of Lr and Cr involves trade-offs between:

Practical implementations often use lossless snubber capacitors (Coss) of MOSFETs as part of Cr, leveraging their nonlinear characteristics for better ZVS performance.

Design Procedure

A step-by-step approach for selecting resonant components:

  1. Define the desired resonant frequency (fr) based on switching frequency requirements.
  2. Choose Zr to limit peak current while maintaining acceptable voltage stress.
  3. Calculate Lr and Cr using:
    $$ L_r = \frac{Z_r}{2\pi f_r}, \quad C_r = \frac{1}{2\pi f_r Z_r} $$
  4. Verify ZVS conditions through simulation or analytical modeling.

Non-Ideal Effects

Real-world factors such as:

must be incorporated into the design. For example, ferrite cores with low permeability (<μr ≈ 100) are preferred for Lr to minimize core losses at high frequencies.

Case Study: 1 MHz LLC Resonant Converter

For a 1 MHz converter with Zr = 20Ω:

$$ L_r = \frac{20}{2\pi \times 1 \times 10^6} \approx 3.18 \mu H $$ $$ C_r = \frac{1}{2\pi \times 1 \times 10^6 \times 20} \approx 7.96 nF $$

Practical implementations might use Lr = 3.3μH (±5%) and Cr = 8.2nF, accounting for parasitics.

Resonant Tank Component Relationships Diagram showing the relationship between resonant frequency, impedance, and component values in a resonant tank circuit, illustrating how Lr and Cr interact to achieve ZVS conditions. Lr Cr fᵣ = 1/(2π√(Lr·Cr)) Zᵣ = √(Lr/Cr) fsw > fᵣ for ZVS Frequency (f) Impedance (Z) fᵣ ZVS Region fsw > fᵣ
Diagram Description: The diagram would show the relationship between resonant frequency, impedance, and component values in a resonant tank circuit, illustrating how Lr and Cr interact to achieve ZVS conditions.

3.2 Switching Frequency and Dead-Time Optimization

Resonant Tank Dynamics and Switching Frequency

The switching frequency (fsw) in a zero-voltage switching (ZVS) resonant converter must be carefully selected to ensure soft-switching operation while minimizing conduction losses. The resonant frequency (fr) of the tank circuit, determined by the inductor (Lr) and capacitor (Cr), is given by:

$$ f_r = \frac{1}{2\pi \sqrt{L_r C_r}} $$

For ZVS operation, fsw must be higher than fr to ensure inductive behavior, allowing the current to lag the voltage. However, excessive fsw increases switching losses due to parasitic capacitance discharge. The optimal range is typically:

$$ 1.2f_r \leq f_{sw} \leq 2f_r $$

Dead-Time Optimization

Dead-time (td) is the interval between turning off one switch and turning on its complementary switch. Insufficient dead-time causes shoot-through currents, while excessive dead-time increases body diode conduction losses. The minimum dead-time is derived from the resonant current (Ir) and output capacitance (Coss) of the switches:

$$ t_d \geq \frac{2C_{oss}V_{in}}{I_r} $$

where Vin is the input voltage. Practical implementations often include a safety margin of 10–20% to account for component tolerances.

Trade-offs in Frequency and Dead-Time Selection

Practical Implementation Considerations

In high-power applications, gate driver propagation delays and MOSFET turn-off times must be accounted for. Adaptive dead-time control circuits, often implemented using digital signal processors (DSPs) or field-programmable gate arrays (FPGAs), dynamically adjust td based on load conditions. For example, in a 1 kW LLC converter, dead-time may vary from 50 ns at full load to 200 ns at light load.

Case Study: Industrial LLC Resonant Converter

A 500 kHz, 3.3 kW LLC converter with GaN FETs demonstrated a peak efficiency of 98.2% by optimizing fsw at 1.5fr (450 kHz) and dynamically adjusting dead-time between 30 ns and 100 ns. The design avoided hard switching across 20–100% load range.

Dead-time (t_d)
ZVS Transition and Dead-Time Waveforms Waveform diagram showing high-side and low-side switch voltages, resonant current, and dead-time intervals for Zero-Voltage Switching (ZVS) resonant converters. Amplitude Time V_GS1 V_GS2 I_r t_d t_d ZVS region ZVS region
Diagram Description: The section discusses dead-time intervals and ZVS transitions, which are best visualized with voltage/current waveforms to show timing relationships.

3.3 Thermal Management in ZVS Converters

Thermal management in zero-voltage switching (ZVS) resonant converters is critical due to the high-frequency operation and power densities involved. Although ZVS reduces switching losses, conduction losses and parasitic resistances still generate significant heat, necessitating efficient thermal design to ensure reliability and longevity.

Heat Generation Mechanisms

The primary sources of heat in ZVS converters include:

The total power dissipation (Pdiss) in a MOSFET can be approximated by:

$$ P_{diss} = I_{rms}^2 R_{DS(on)} + \frac{1}{2} C_{oss} V_{DS}^2 f_{sw} $$

where Irms is the RMS current, Coss is the output capacitance, VDS is the drain-source voltage, and fsw is the switching frequency.

Thermal Resistance and Heat Sinking

The junction-to-ambient thermal resistance (θJA) determines the temperature rise of a component:

$$ T_j = T_a + P_{diss} \theta_{JA} $$

where Tj is the junction temperature and Ta is the ambient temperature. To minimize Tj, heat sinks with low thermal resistance (θHS) are often employed. The effective thermal resistance becomes:

$$ \theta_{JA} = \theta_{JC} + \theta_{CS} + \theta_{HS} $$

where θJC is the junction-to-case resistance and θCS is the case-to-sink resistance (including thermal interface material effects).

Advanced Cooling Techniques

For high-power ZVS converters, passive cooling may be insufficient. Active cooling methods include:

In multi-kilowatt designs, cold plates with circulating coolant can maintain junction temperatures below 100°C even at power densities exceeding 50 W/cm².

Practical Design Considerations

Effective thermal management requires:

Experimental validation using infrared thermography or embedded temperature sensors (e.g., NTC thermistors) is essential to verify thermal performance under load.

4. High-Efficiency Power Supplies

4.1 High-Efficiency Power Supplies

Zero-voltage switching (ZVS) resonant converters achieve high efficiency by minimizing switching losses through soft-switching techniques. These converters operate by ensuring that the voltage across the switching device is zero at the instant of turn-on, eliminating capacitive discharge losses. The resonant tank, typically comprising an inductor (Lr) and capacitor (Cr), shapes the current and voltage waveforms to enable ZVS conditions.

Resonant Tank Dynamics

The resonant frequency (fr) of the tank circuit is given by:

$$ f_r = \frac{1}{2\pi \sqrt{L_r C_r}} $$

For ZVS to occur, the switching frequency (fsw) must be slightly higher than fr, ensuring inductive operation. This phase lag allows the anti-parallel diode of the switch to conduct before the device turns on, clamping the voltage to zero.

Mathematical Analysis of ZVS Conditions

The critical condition for ZVS is derived from the energy balance between the resonant inductor and the switch output capacitance (Coss). The energy stored in Lr must exceed the energy required to discharge Coss:

$$ \frac{1}{2} L_r I_p^2 \geq \frac{1}{2} C_{oss} V_{in}^2 $$

where Ip is the peak resonant current and Vin is the input voltage. Rearranging yields the minimum current for ZVS:

$$ I_p \geq V_{in} \sqrt{\frac{C_{oss}}{L_r}} $$

Topology Variations

Common ZVS resonant converter topologies include:

Practical Design Considerations

Key parameters for optimizing efficiency:

Real-World Applications

ZVS resonant converters are dominant in:

ZVS Waveforms VDS ID
ZVS Resonant Converter Waveforms and Topology Schematic and time-aligned waveforms of an LLC resonant converter showing zero-voltage switching conditions with labeled resonant tank components and switching characteristics. V_in S1 S2 C_r L_r Load LLC Resonant Converter f_sw V_DS I_D Resonant Waveforms (f_r) ZVS Region
Diagram Description: The section discusses resonant tank dynamics and ZVS conditions with mathematical relationships, where waveforms and component interactions are central to understanding.

4.2 Wireless Power Transfer Systems

Wireless power transfer (WPT) systems leverage resonant inductive coupling to achieve efficient energy transmission across an air gap. The core principle relies on magnetically coupled coils operating at resonance, where zero-voltage switching (ZVS) minimizes switching losses and enhances efficiency. The resonant frequency fr is determined by the primary and secondary coil inductances (Lp, Ls) and their respective capacitances (Cp, Cs):

$$ f_r = \frac{1}{2\pi \sqrt{L_p C_p}} = \frac{1}{2\pi \sqrt{L_s C_s}} $$

Resonant Tank Design

The quality factor (Q) of the resonant tank governs the system's bandwidth and efficiency. For optimal ZVS, the resonant network must satisfy:

$$ Q = \frac{\omega_r L_p}{R_{ac}} = \frac{1}{\omega_r C_p R_{ac}} $$

where Rac is the equivalent AC resistance. High Q (>10) ensures sharp resonance, while excessive Q reduces tolerance to misalignment.

Coupling Coefficient and Efficiency

The coupling coefficient k quantifies magnetic linkage between coils:

$$ k = \frac{M}{\sqrt{L_p L_s}} $$

where M is mutual inductance. Efficiency η peaks when the load resistance RL matches the reflected impedance:

$$ \eta = \frac{k^2 Q_p Q_s}{1 + k^2 Q_p Q_s} \times 100\% $$

Practical considerations: Ferrite shielding mitigates flux leakage, while Litz wire reduces skin effect losses at high frequencies (e.g., 6.78 MHz for A4WP standard).

ZVS Implementation in WPT

To achieve ZVS in a Class-E inverter:

  1. The switching device (e.g., MOSFET) turns on when its drain-source voltage VDS reaches zero.
  2. The resonant tank's inductive current ensures VDS discharges before turn-on.

The ZVS condition requires:

$$ \frac{I_p \cdot t_{dead}}{C_{oss}} \geq V_{DC} $$

where Ip is peak tank current, tdead is dead time, and Coss is MOSFET output capacitance.

Primary (Lp) Secondary (Ls) k = 0.4–0.7 (typical)

Real-World Applications

Misalignment tolerance remains a key challenge, addressed through adaptive frequency tracking or multi-coil designs.

Resonant Inductive Coupling and ZVS Timing A combined schematic and timing diagram showing resonant inductive coupling between primary and secondary coils, along with synchronized voltage and current waveforms during Zero-Voltage Switching transition. L_p L_s M C_r Q1 V_DS Time V_DS I_p t_dead 1/f_r
Diagram Description: The section involves resonant inductive coupling, which is inherently spatial, and the ZVS implementation in a Class-E inverter would benefit from a visual representation of voltage/current timing.

4.3 Electric Vehicle Charging Applications

Challenges in High-Power EV Charging

The demand for fast-charging electric vehicle (EV) infrastructure necessitates high-efficiency power conversion systems capable of handling power levels exceeding 350 kW. Traditional hard-switching converters suffer from significant switching losses at these power levels, leading to thermal management challenges and reduced reliability. Zero-voltage switching (ZVS) resonant converters address these issues by ensuring that the power semiconductor devices switch only when the voltage across them is zero, minimizing switching losses and enabling higher operating frequencies.

Topology Selection for EV Chargers

The LLC resonant converter has emerged as the dominant topology for high-power EV charging due to its ability to maintain ZVS across a wide load range. The converter consists of a resonant tank formed by an inductor (Lr), a capacitor (Cr), and a magnetizing inductor (Lm). The voltage gain characteristic of the LLC converter is given by:

$$ M(f_n) = \frac{1}{\sqrt{\left[1 + \frac{1}{k}\left(1 - \frac{1}{f_n^2}\right)\right]^2 + \left(\frac{f_n - \frac{1}{f_n}}{Q}\right)^2}} $$

where fn is the normalized switching frequency (fsw/fr), k is the inductance ratio (Lm/Lr), and Q is the quality factor of the resonant tank. This equation demonstrates the converter's ability to regulate output voltage through frequency modulation while maintaining ZVS.

Bidirectional Power Flow Implementation

Vehicle-to-grid (V2G) compatibility requires bidirectional power flow capability. A dual-active-bridge (DAB) converter with ZVS is often employed in cascaded configurations with the LLC stage. The DAB converter's phase-shift modulation enables bidirectional power transfer according to:

$$ P = \frac{nV_1V_2}{2f_sL} \phi \left(1 - \frac{|\phi|}{\pi}\right) $$

where n is the transformer turns ratio, V1 and V2 are the primary and secondary voltages, fs is the switching frequency, L is the leakage inductance, and φ is the phase shift angle between bridges. This configuration maintains ZVS across the entire operating range when properly designed.

Thermal and Efficiency Considerations

At 350 kW charging levels, even a 1% improvement in efficiency translates to 3.5 kW of reduced heat dissipation. ZVS resonant converters typically achieve peak efficiencies of 97-98% in EV charging applications. The reduction in switching losses allows for:

Practical Implementation Challenges

While ZVS offers significant advantages, several design challenges must be addressed:

$$ t_d = \frac{C_{oss}V_{dc}}{I_{m,peak}} $$

where Coss is the output capacitance of the switching devices, Vdc is the DC bus voltage, and Im,peak is the peak magnetizing current.

Case Study: 350 kW CCS Charger

A commercial 350 kW Combined Charging System (CCS) implementation uses a three-stage architecture:

  1. PFC stage (three-phase Vienna rectifier)
  2. Isolated DC-DC stage (LLC resonant converter with ZVS)
  3. Output stage (bidirectional current control)

The LLC stage operates at 250 kHz with silicon carbide (SiC) MOSFETs, achieving 98.2% peak efficiency at 400V output. The converter maintains ZVS from 20% to 100% load through precise frequency control and adaptive dead-time adjustment.

EV Charger Power Stages with ZVS Converters Block diagram showing three-stage architecture of an EV charger with Vienna rectifier, LLC resonant converter, and bidirectional output stage, highlighting ZVS switching paths and resonant tank components. PFC Stage Vienna Rectifier LLC Converter Lr Cr Lm DAB Converter (Bidirectional) SiC MOSFETs 350 kW CCS V2G Power Flow ZVS Path
Diagram Description: The section describes complex converter topologies (LLC and DAB) with multiple interacting components and bidirectional power flow, which are inherently spatial concepts.

5. Key Research Papers on ZVS

5.1 Key Research Papers on ZVS

5.2 Recommended Books on Resonant Converters

5.3 Online Resources and Tutorials