Electronics Guide

Displacement Current and Power Transfer

In a CPT system, power transfers through the displacement current between electrode plates:

The displacement current density is given by:

J-d = epsilon * dE/dt

For sinusoidal excitation, this becomes:

I = omega * C * V

where omega is the angular frequency, C is the coupling capacitance, and V is the voltage across the capacitor. This relationship shows that power transfer capability scales with frequency, capacitance, and voltage. Since coupling capacitance is typically small (picofarads to nanofarads), CPT systems require either high voltages, high frequencies, or both to achieve practical power levels.

Typical CPT systems operate with coupling capacitances of 10 pF to 100 nF depending on electrode size and spacing, voltages from hundreds of volts to several kilovolts, and frequencies from hundreds of kilohertz to tens of megahertz.

Electric Field Distribution

The electric field pattern between CPT electrodes determines both coupling efficiency and emissions characteristics:

Parallel plate configuration: With flat, parallel electrodes of equal size, the field is relatively uniform in the central region but exhibits fringing at the edges. The fringing field extends beyond the electrode footprint and contributes to EMC emissions.

Concentric configuration: Cylindrical or disc-shaped concentric electrodes can create more contained field patterns but may be geometrically constrained.

Asymmetric configurations: When transmitter and receiver electrodes differ in size or shape, the field distribution becomes asymmetric, potentially concentrating field intensity in some regions while reducing it in others.

Unlike magnetic fields in IPT systems that decay as 1/r-cubed at distance, electric fields from finite electrodes also decay rapidly but can have more complex distance dependence based on geometry. The transition from near-field to far-field behavior occurs at distances comparable to electrode dimensions and wavelength.

Comparison with Inductive Systems

CPT and IPT systems have complementary characteristics affecting their EMC profiles:

• Field type: CPT uses electric fields while IPT uses magnetic fields. Electric field shielding is generally easier than magnetic field shielding at low frequencies
• Operating voltage: CPT typically requires higher voltages than IPT for equivalent power, creating insulation and safety challenges
• Operating frequency: CPT often operates at higher frequencies than IPT, placing emissions in different regulatory categories
• Metal tolerance: CPT systems are less affected by nearby metal objects than IPT systems, as metals block electric fields rather than concentrating them
• Coupling structure: CPT electrodes can be thinner and lighter than IPT coils with ferrite backing, enabling different form factors

Fringing Field Control

The fringing electric field at electrode edges is a primary source of emissions:

Edge field concentration: Electric field intensity is typically highest at electrode edges due to geometric field enhancement. This creates localized high-field regions that can dominate far-field emissions.

Guard electrodes: Surrounding the main electrodes with guard electrodes held at controlled potentials can shape the fringing field and reduce emissions. Guard electrodes effectively extend the uniform-field region and reduce edge concentration.

Rounded edges: Smooth, rounded electrode edges reduce field concentration compared to sharp corners. While this may slightly reduce coupling capacitance, it improves both EMC performance and voltage breakdown margins.

Graded dielectric: Using dielectric materials with spatially varying permittivity can shape field distribution to reduce fringing while maintaining coupling efficiency in the central region.

Shielding Approaches

Electric field shielding for CPT systems employs several techniques:

Grounded enclosures: A grounded conductive enclosure around the electrode assembly blocks electric field emission effectively. Unlike magnetic shielding, which requires thickness comparable to skin depth, electric shielding can use thin conductive layers.

Shield electrode configuration: Placing grounded shield electrodes adjacent to the coupling electrodes creates a defined field region. The four-plate CPT configuration, with two coupling electrodes and two shield electrodes, is commonly used to contain fields while enabling power transfer through the gap between coupling plates.

Aperture control: The gap between transmitter and receiver assemblies necessarily allows some field leakage. Minimizing this gap and using conductive gaskets or overlapping shield structures can reduce emissions through this aperture.

Cable shielding: High-voltage cables connecting to the electrodes must be properly shielded to prevent them from becoming secondary emission sources. Coaxial construction with well-grounded shields is essential.

Near-Field versus Far-Field Emissions

CPT emission characteristics differ in the near and far field:

Near-field (reactive) region: Close to the electrodes, the electric field dominates and the wave impedance is high (greater than 377 ohms). Energy is primarily stored rather than radiated. Human exposure assessment often focuses on this region where field intensities are highest.

Far-field (radiating) region: At distances greater than about lambda/(2*pi), the fields transition to plane wave behavior with 377-ohm impedance. EMC emissions testing typically measures far-field radiation, which depends on the effective antenna characteristics of the electrode structure.

The transition distance depends on both electrode size and operating frequency. At 1 MHz, the transition occurs at approximately 50 meters; at 10 MHz, approximately 5 meters. Higher frequency CPT systems may have their near-field extend only a few meters, placing standard EMC test distances (3 or 10 meters) in the far field.

High Voltage Hazards

CPT systems typically operate at voltages from hundreds of volts to several kilovolts:

Direct contact hazard: Contact with energized electrodes can cause electric shock. Even though the current capability may be limited, the high voltage can be dangerous. System design must prevent direct contact through physical barriers, insulation, or interlock systems.

Capacitor discharge: The coupling capacitance and any resonant capacitors store energy that can deliver a shock even after the system is de-energized. Automatic discharge circuits and discharge time specifications are necessary safety features.

Insulation breakdown: High voltages stress insulation materials and can cause breakdown, particularly at elevated temperatures, high humidity, or in contaminated environments. Insulation coordination following appropriate safety standards (such as IEC 62368-1 or IEC 60950-1) is essential.

Corona and arcing: At sufficiently high field strengths, corona discharge or arcing can occur, particularly at sharp points or contaminated surfaces. This creates fire hazards and generates broadband electromagnetic emissions.

Electric Field Exposure

Human exposure to electric fields is governed by different mechanisms than magnetic field exposure:

Body currents: External electric fields induce currents in the human body. At frequencies below about 100 kHz, the primary concern is nerve and muscle stimulation; at higher frequencies, tissue heating becomes the dominant mechanism.

Surface charge effects: At low frequencies, the human body is effectively conductive, and exposure to electric fields causes surface charge redistribution and induced currents. Hair movement and spark discharge can occur at high field strengths.

Exposure limits: ICNIRP and IEEE exposure guidelines specify reference levels for external electric field strength. At 1 MHz, the ICNIRP general public reference level is 87 V/m; at 10 MHz, it reduces to approximately 28 V/m (specific values depend on frequency and whether the 2020 guidelines or earlier versions apply).

Assessment methods: Electric field measurement near CPT systems should use calibrated field probes appropriate for the operating frequency. Numerical simulation with anatomical body models can assess induced currents and SAR for compliance verification.

Safety System Design

Safe CPT system design incorporates multiple protective measures:

• Presence detection: Capacitive or other sensing systems can detect human presence near high-field regions and reduce power or shut down the system
• Physical barriers: Enclosures, guards, and insulation prevent contact with high-voltage components
• Interlock systems: Switches that detect cover removal or intrusion into hazardous areas disable the high-voltage supply
• Discharge circuits: Automatic resistive discharge of stored energy after shutdown
• Voltage limiting: Protection circuits that prevent overvoltage conditions
• Clear labeling: Warning labels indicating high voltage hazards

Coupling Capacitance

The coupling capacitance between transmitter and receiver electrodes is a primary efficiency determinant:

Capacitance calculation: For parallel plate electrodes with area A and separation d in a medium with permittivity epsilon:

C = epsilon * A / d

Larger electrodes and smaller gaps increase capacitance, but physical constraints typically limit these parameters. Practical coupling capacitances range from tens of picofarads to tens of nanofarads.

EMC implications: Larger electrodes produce larger fringing fields and may create more emissions. Smaller gaps reduce the accessible volume but may increase field intensity in the coupling region.

Resonant Compensation

To achieve practical power transfer with small coupling capacitances, CPT systems typically use resonant compensation:

LC resonance: Adding inductors to form resonant circuits with the coupling capacitance allows efficient power transfer at the resonant frequency. Several compensation topologies (series, parallel, LCL, LCLC) offer different characteristics.

Quality factor: Higher Q-factor resonant circuits enable more efficient power transfer but are more sensitive to frequency accuracy and component tolerances. High Q also means narrower bandwidth, which may affect harmonic content.

EMC considerations: The inductors added for compensation can themselves become emission sources through magnetic coupling. Shielding these inductors may be necessary to meet emissions limits.

Operating Frequency

Frequency selection significantly affects both efficiency and EMC:

Higher frequencies reduce the required voltage for a given power level (since power transfer scales with frequency times voltage squared). This can ease insulation requirements and reduce electric field intensity for equivalent power.

Component limitations: Higher frequencies increase losses in inductors, capacitors, and power semiconductor devices. Practical component limitations often constrain maximum operating frequency.

EMC regulations: Higher operating frequencies may fall under different regulatory categories. ISM frequency bands at 6.78 MHz and 13.56 MHz offer regulatory advantages but may not optimize efficiency for all applications.

Human exposure: Electric field exposure limits become more restrictive at higher frequencies in the MHz range. Higher frequency operation may require more aggressive field containment.

Power Electronics Design

The inverter and rectifier circuits significantly influence EMC performance:

Soft switching: Zero-voltage switching (ZVS) or zero-current switching (ZCS) inverter topologies reduce switching losses and generate fewer high-frequency harmonics than hard-switched converters.

Switching frequency: If the operating frequency differs from the switching frequency, intermodulation products can create emissions at unexpected frequencies.

Harmonic content: The inverter output waveform shape determines harmonic content. Class D and E amplifiers commonly used in CPT have characteristic harmonic spectra that must be filtered or managed.

Electrode Topologies

Several electrode configurations are used in CPT systems:

Two-plate systems: The simplest configuration uses one transmitter and one receiver electrode, with return current flowing through a ground connection. This creates large common-mode currents that can cause significant EMC issues.

Four-plate systems: Using two electrode pairs (each pair forming a transmitter-receiver coupling) enables differential operation with balanced currents. The four-plate configuration significantly reduces common-mode emissions and ground currents compared to two-plate systems.

Multi-plate systems: Arrays of electrodes can provide power transfer over larger areas or enable position tolerance. The complexity increases but EMC may benefit from field cancellation between adjacent plates.

Interdigitated electrodes: Interlocking finger patterns increase effective edge length and capacitance but may create complex field patterns with multiple emission sources.

Electrode Materials

Material selection affects electrical performance and practical implementation:

Copper: Excellent conductivity minimizes resistive losses. Requires protection from oxidation and corrosion.

Aluminum: Good conductivity with lighter weight. Surface oxide layer is stable but slightly increases surface resistance.

Transparent conductors: Indium tin oxide (ITO) or metal mesh can create transparent electrodes for display applications. Higher resistance affects efficiency.

Flexible conductors: Conductive fabrics or thin foils enable flexible electrode designs for wearable or conformable applications.

Surface finish and edge treatment affect field distribution. Smooth, rounded edges reduce field concentration; textured or rough surfaces may increase local field intensity.

Size and Spacing Optimization

Electrode dimensions must balance multiple requirements:

Electrode area: Larger electrodes increase coupling capacitance but also increase fringing field extent. For a given power level, larger electrodes operate at lower field intensity, potentially easing human exposure compliance.

Gap spacing: Smaller gaps increase capacitance and efficiency but reduce misalignment tolerance and may increase field intensity. Minimum gap is constrained by mechanical tolerances and breakdown voltage requirements.

Aspect ratio: The ratio of electrode size to gap spacing affects the fraction of field contained in the coupling region versus fringing. Higher aspect ratios (large electrodes with small gaps) improve field containment.

Shield electrode positioning: In four-plate systems, shield electrode size and position relative to coupling electrodes affects both shielding effectiveness and coupling efficiency. Shield electrodes too close to coupling electrodes reduce capacitance; too far reduces shielding.

Dielectric Properties

Key dielectric material parameters include:

Relative permittivity (dielectric constant): Higher permittivity materials increase coupling capacitance for given electrode geometry. Air has permittivity near 1; common polymers range from 2 to 4; specialized high-k ceramics can exceed 1000.

Loss tangent: Dielectric losses dissipate power as heat and reduce efficiency. Low-loss materials like PTFE (tan-delta approximately 0.0002) are preferred over higher-loss materials like FR-4 (tan-delta approximately 0.02).

Breakdown strength: The maximum field the material can sustain without breakdown limits maximum operating voltage. Thin, high-strength materials enable compact designs.

Temperature stability: Permittivity and loss tangent variations with temperature affect system performance across operating temperature range.

Material Selection

Common dielectric materials for CPT applications:

Air gap: Lowest loss and permittivity of 1. Suitable where mechanical design allows precise gap control. Breakdown strength approximately 3 kV/mm at sea level.

Polymer films: Polyester, polypropylene, PTFE offer good dielectric properties with practical handling. Permittivity 2-3, low loss, breakdown strength 100-300 kV/mm.

Ceramics: Alumina, glass, and specialized ceramics provide stable, low-loss dielectrics with good breakdown strength. High-k ceramics increase capacitance but often have higher losses.

Composite materials: Polymer-ceramic composites can provide tailored permittivity while maintaining practical fabrication characteristics.

EMC Implications of Dielectric Choice

Dielectric material selection affects EMC through several mechanisms:

• Field containment: Higher permittivity dielectrics concentrate fields within the material, potentially reducing external emissions
• Voltage reduction: Higher capacitance from high-k materials allows lower operating voltage for equivalent power, reducing field intensity
• Thermal effects: Dielectric losses cause heating that can affect temperature-dependent EMC characteristics
• Surface effects: Dielectric surfaces can accumulate charge, affecting field distribution and potentially causing discharge

Frequency Range Considerations

CPT systems operate across a wide frequency range, with different implications at different frequencies:

100 kHz to 1 MHz: Lower end of CPT operating range. Requires higher voltages for practical power levels. EMC regulations for ISM equipment apply. Human exposure limits are relatively permissive. Component selection is straightforward.

1 MHz to 10 MHz: Common operating range for many CPT systems. Moderate voltages achievable. ISM bands at 6.78 MHz offer regulatory advantages. Human exposure limits become more restrictive. Requires attention to component frequency response.

10 MHz to 30 MHz: Higher efficiency potential from increased frequency. Challenging component selection. Falls within HF radio bands requiring careful frequency planning. Human exposure limits most restrictive in this range.

Above 30 MHz: Uncommon for power transfer but used in some specialized applications. VHF/UHF regulations apply. Component and interconnect design becomes critical.

ISM Band Selection

Industrial, Scientific, and Medical (ISM) frequency bands offer regulatory advantages for CPT systems:

6.78 MHz: Popular ISM band for wireless power. Good balance of component availability, efficiency potential, and regulatory compliance. Falls between broadcast bands, reducing interference potential.

13.56 MHz: RFID frequency widely used for near-field communication and wireless power. Excellent component availability. Higher efficiency potential than lower frequencies but more restrictive exposure limits.

27.12 MHz: ISM band but less commonly used for CPT due to component challenges and stricter exposure limits.

Operating within ISM bands may simplify regulatory compliance but does not eliminate EMC requirements. Emission limits still apply, and out-of-band emissions (harmonics) must meet applicable limits.

Harmonic Management

Regardless of fundamental frequency selection, harmonics must be controlled:

Harmonic frequencies: Harmonics at 2f, 3f, 4f, etc. must meet emissions limits. Third harmonic is often significant in systems with non-sinusoidal waveforms.

Frequency planning: Fundamental frequency can be chosen to place harmonics away from sensitive frequency bands. For example, operation at 130 kHz places harmonics away from longwave broadcast bands.

Waveform shaping: Sinusoidal drive waveforms minimize harmonic content compared to square wave or trapezoidal waveforms, but may reduce power conversion efficiency.

Input Filter Design

Filters on the input (AC mains or DC bus) side control conducted emissions:

Common-mode filtering: Common-mode chokes and Y-capacitors attenuate common-mode noise generated by the high-voltage, high-frequency operation. Common-mode currents flowing through parasitic capacitances to ground often dominate conducted emissions.

Differential-mode filtering: Series inductors and X-capacitors attenuate differential-mode conducted emissions. The high operating frequency of CPT systems creates switching noise that must be prevented from propagating to the input.

Filter placement: Filters should be placed as close as possible to the noise source. Multiple filter stages may be needed to achieve required attenuation while managing resonance issues.

Parasitic effects: At CPT operating frequencies, filter component parasitics significantly affect performance. Self-resonant frequencies of capacitors and inductors must be considered.

Output Filter Design

Filters on the output (load) side ensure clean power delivery and prevent load-generated noise from coupling back:

Rectifier noise: The receiver-side rectifier generates harmonics that can couple through the CPT link and radiate. Filtering at the rectifier output reduces this reverse-path emission source.

Load isolation: Filtering prevents high-frequency energy from the CPT system from affecting sensitive loads, and prevents load-generated noise from modulating the CPT link.

Resonant Tank Filtering

The resonant compensation network inherently provides some filtering:

Bandpass characteristics: Properly designed resonant tanks pass the fundamental frequency while attenuating harmonics. Higher-order compensation networks (LCL, LCLC) provide steeper roll-off than simple LC resonators.

Q-factor trade-offs: Higher Q provides better harmonic rejection but increases sensitivity to frequency deviation and component tolerances.

Additional filtering: Even with resonant tank filtering, additional EMC filters may be needed to meet stringent emissions limits, particularly for higher-order harmonics outside the resonant tank's effective range.

Ground Current Sources

Several mechanisms create ground currents in CPT systems:

Parasitic capacitance: Capacitance between high-voltage electrodes and grounded structures allows displacement current to flow to ground. This current returns through the ground system, potentially creating EMC issues.

Unbalanced systems: Two-plate CPT configurations inherently have unbalanced currents that must return through ground. This creates large common-mode ground currents at the operating frequency.

Shield currents: Grounded shields around electrodes or cables intercept electric field and conduct current to ground. While this is the intended shielding function, the ground current path must be managed.

Control circuit coupling: Parasitic coupling between the high-voltage power circuit and low-voltage control circuits can inject noise currents into the control ground system.

Ground System Design

Proper ground system design minimizes EMC problems from ground currents:

Low-impedance ground: Ground connections should have low impedance at the operating frequency. At MHz frequencies, ground conductor inductance can create significant impedance, requiring wide, short ground straps or multiple parallel connections.

Single-point grounding: Where possible, grounding high-frequency circuits at a single point prevents ground loops that can couple interference between circuits.

Ground plane: Using a ground plane rather than discrete ground wires provides lower inductance and better shielding. The ground plane should extend to encompass all high-frequency circuits.

Separation of grounds: Keeping power ground, signal ground, and shield ground separate until they meet at a single star point can prevent noise coupling between functions.

Balanced Systems

Four-plate CPT configurations provide inherent balance that reduces ground currents:

Differential operation: With two coupling capacitor pairs driven differentially, the currents in the two paths are equal and opposite. Ideally, no net current flows to ground from the electrode assembly.

Balance requirements: Perfect balance requires matched electrode capacitances and symmetric drive. Component tolerances and parasitic capacitances introduce imbalance that creates residual ground current.

Balance adjustment: Tuning capacitors or adjustment of electrode positioning can improve balance and reduce ground currents to acceptable levels.

EMC Standards

Applicable EMC standards depend on product type and market:

CISPR 11: For industrial, scientific, and medical equipment. Defines Group 1 (incidental RF generation) and Group 2 (intentional RF use) categories, with different limits. CPT systems typically fall into Group 2, Class A (industrial) or Class B (domestic).

CISPR 32: For multimedia equipment. May apply to consumer electronics with CPT functionality.

FCC Part 18: US regulation for ISM equipment. Similar structure to CISPR 11 with some differences in limits and measurement procedures.

Regional standards: Various countries have national EMC regulations that reference or modify international standards.

Human Exposure Compliance

Demonstrating compliance with human exposure limits requires:

Field measurement: Electric and magnetic field measurements at accessible locations using calibrated probes. Measurement procedures should follow IEC 62311 or similar standards.

Spatial averaging: Some exposure standards allow spatial averaging over the body surface. Measurement protocols must specify averaging method and locations.

Numerical simulation: For complex field distributions or to assess internal exposure metrics (induced current, SAR), numerical simulation with validated human body models may be required.

Documentation: Compliance documentation should include measurement equipment, procedures, conditions, and results with uncertainty analysis.

Product Safety Standards

Safety standards addressing electrical hazards include:

IEC 62368-1: Audio/video, information technology, and communication equipment safety. Applies to many consumer electronics including wireless chargers.

IEC 61010-1: Safety requirements for electrical equipment for measurement, control, and laboratory use. May apply to industrial CPT systems.

IEC 60335 series: Household appliance safety standards. Specific standards may apply to appliances with CPT functionality.

These standards address insulation, creepage and clearance distances, protective bonding, and other electrical safety requirements relevant to high-voltage CPT systems.

Emerging CPT Standards

Standards specific to capacitive power transfer are still developing:

Unlike inductive wireless power, which has established standards like Qi and SAE J2954, CPT-specific interoperability and EMC standards are less mature. Developers should monitor standards development from organizations including:

• Wireless Power Consortium (WPC)
• AirFuel Alliance
• SAE International
• IEC TC 69 for electric vehicle charging