Electronics Guide

Quality Factor Fundamentals

The quality factor quantifies the ratio of energy stored to energy dissipated per cycle in a resonant system:

Q = 2*pi * (Energy stored) / (Energy dissipated per cycle)

For an inductor-capacitor resonant circuit, Q can be expressed in terms of component values:

Q = (1/R) * sqrt(L/C)

where R represents the total resistance (including coil resistance, capacitor ESR, and any other losses), L is the inductance, and C is the capacitance.

High-Q resonant circuits (Q values of 100 or more) enable efficient power transfer with weak coupling, making them attractive for extended-range wireless power systems. However, high Q comes with EMC implications that must be carefully managed.

Emissions Characteristics

Quality factor significantly affects electromagnetic emissions:

Fundamental frequency emissions: High-Q resonators store large amounts of energy at the resonant frequency, creating strong fields at that frequency. The field intensity at resonance can be Q times higher than would be achieved with the same input power in a non-resonant system.

Spectral purity: High-Q systems have narrow bandwidth, meaning their emissions are concentrated in a narrow frequency range around resonance. This can be advantageous for avoiding interference with other systems operating at different frequencies, but creates intense emissions at the operating frequency.

Harmonic content: The resonant tank filtering provided by high-Q circuits attenuates harmonics, potentially reducing harmonic emissions. However, this attenuation applies to harmonics well outside the resonant bandwidth; harmonics close to resonance may not be significantly attenuated.

Transient behavior: High-Q circuits ring for longer when excited by transients. This extended ringing can create emissions that persist after the driving signal stops, potentially interfering with time-division communication systems.

Immunity Considerations

High-Q resonant circuits have distinctive immunity characteristics:

Frequency selectivity: The narrow bandwidth of high-Q resonators makes them selectively sensitive to interference at or near the resonant frequency while rejecting interference at other frequencies. This can be beneficial or problematic depending on the interference environment.

Resonant amplification: External interference at the resonant frequency will be amplified by the Q factor of the circuit. A system with Q=100 can develop internal voltages 100 times the externally induced voltage at resonance.

Bandwidth vulnerability: While narrow bandwidth provides rejection of off-frequency interference, any interference that does fall within the bandwidth will couple efficiently into the system.

Q Factor Trade-offs

System design must balance Q-related trade-offs:

• Efficiency versus bandwidth: Higher Q improves efficiency but reduces bandwidth, making the system more sensitive to frequency accuracy and component tolerances
• Range versus emissions: Higher Q enables power transfer at greater distances but creates stronger fields at the resonant frequency
• Selectivity versus sensitivity: The same narrow bandwidth that rejects off-frequency interference makes the system highly sensitive to in-band interference
• Power handling versus Q: Very high Q can create excessive voltages or currents in resonant components, limiting power handling capability

Practical resonant WPT systems typically use Q values from 50 to 500, with the specific choice depending on application requirements and EMC constraints.

Frequency Accuracy Requirements

The required frequency accuracy depends on system Q and application:

For a resonant system with quality factor Q, the 3 dB bandwidth is:

BW = f0/Q

where f0 is the resonant frequency. To maintain high efficiency, the operating frequency must stay within this bandwidth. For a system with f0 = 100 kHz and Q = 200, the bandwidth is only 500 Hz, requiring frequency stability better than 0.25% to remain within the half-power points.

Additionally, regulatory requirements often specify frequency bands for intentional emissions. Operation must remain within designated ISM bands or licensed frequency allocations to avoid causing interference to other services.

Sources of Frequency Variation

Several factors cause frequency variation in resonant WPT systems:

Component tolerances: Inductor and capacitor values vary with manufacturing tolerances, typically 5% to 20% for standard components. The resonant frequency varies as the square root of component variation, so 10% component tolerance can cause 5% frequency variation.

Temperature effects: Component values change with temperature. Inductors typically have temperature coefficients of 50 to 200 ppm/C; capacitors range from near-zero (NPO/C0G) to several hundred ppm/C or worse (X7R, Y5V).

Coupling variation: In coupled resonator systems, the effective resonant frequency depends on coupling coefficient. As coupling varies with alignment, the resonant frequency shifts.

Load variation: Receiver load changes affect the reflected impedance seen by the transmitter, shifting the apparent resonant frequency.

Environmental effects: Nearby metallic or magnetic objects can alter inductance through eddy current or magnetic coupling effects, shifting resonant frequency.

Frequency Control Techniques

Several approaches maintain frequency stability:

Fixed-frequency operation: The transmitter operates at a fixed frequency determined by a stable reference oscillator (crystal or similar). The resonant circuits must be tuned to match this frequency. This approach provides precise frequency control but requires careful component selection and may need tuning adjustment.

Frequency tracking: The system monitors operating conditions and adjusts frequency to maintain resonance. Phase-locked loops, frequency synthesizers, or direct digital synthesis can provide adaptive frequency control. This approach accommodates component variation but requires careful design to maintain stability and avoid frequency excursions outside permitted bands.

Tunable resonators: Variable capacitors, saturable inductors, or switched component networks allow the resonant circuit to be tuned to match a fixed operating frequency. This separates the frequency reference from the resonant circuit, allowing independent optimization.

Hybrid approaches: Many practical systems use a combination, such as crystal-controlled operating frequency with fine tuning of resonant circuits to compensate for coupling variation.

EMC Implications of Frequency Variation

Frequency instability creates several EMC concerns:

• Band exceedance: If operating frequency drifts outside designated ISM bands or licensed allocations, the system may cause interference to protected services
• Harmonic migration: Frequency variation shifts harmonics, potentially moving them into sensitive frequency bands
• Phase noise: Frequency instability manifests as phase noise, spreading energy across a range of frequencies and potentially increasing interference to adjacent channels
• Measurement challenges: EMC compliance testing assumes stable operating conditions; frequency drift during measurement can affect results

Causes of Detuning

Detuning can result from various conditions:

Misalignment: When transmitter and receiver coils are not optimally aligned, the mutual inductance changes. This affects the coupled resonant frequency and can detune the system from its intended operating point.

Foreign objects: Metal objects near the coils alter inductance through eddy current effects. Ferromagnetic objects additionally change permeability of the magnetic circuit. Both effects shift resonant frequency.

Multiple receivers: Adding receivers to a single transmitter changes the loading and coupling conditions, detuning the combined system from its single-receiver optimization.

Component aging: Long-term drift in component values from aging, thermal cycling, or environmental exposure gradually detunes the system.

Intentional frequency offset: Some systems intentionally operate slightly off-resonance for control purposes, such as power regulation or soft-switching optimization.

Effects on Power Transfer

Detuning reduces power transfer efficiency through several mechanisms:

Reduced coupling efficiency: Operation away from resonance decreases the effective power transfer, requiring increased drive to maintain output power. This increases losses and may exceed component ratings.

Phase shift: The phase relationship between voltage and current shifts away from the optimal in-phase condition, reducing real power transfer and increasing reactive power circulation.

Control instability: Severe detuning can cause power transfer to become unstable or erratic, with potentially rapid changes in operating conditions.

EMC Effects of Detuning

Detuning influences EMC characteristics in several ways:

Increased drive levels: To maintain power delivery when detuned, the system may increase voltage and current levels, proportionally increasing emissions at the fundamental frequency.

Harmonic generation: Operation away from resonance can increase harmonic content due to waveform distortion and nonlinear effects in power electronics.

Changed field patterns: The spatial distribution of electromagnetic fields may change with detuning as the current distribution in the coils changes.

Frequency pulling: In frequency-tracking systems, detuning causes the operating frequency to shift, potentially moving toward band edges or out of permitted frequency ranges.

Detuning Compensation

Systems employ various techniques to compensate for or tolerate detuning:

• Adaptive tuning: Active circuits adjust resonant component values to maintain tuning as conditions change
• Frequency tracking: The operating frequency follows the varying resonant frequency of the system
• Wider bandwidth design: Accepting lower Q enables operation across a wider range of conditions without significant detuning effects
• Multiple resonant frequencies: Systems with multiple resonant modes may switch between modes depending on conditions
• Robust control algorithms: Control systems designed to maintain stable operation across a range of tuning conditions

Physics of Frequency Splitting

When two identical resonant circuits with resonant frequency f0 are coupled with coupling coefficient k, the combined system exhibits two resonant frequencies:

f1 = f0 / sqrt(1 + k)

f2 = f0 / sqrt(1 - k)

For weak coupling (small k), these frequencies are close together near f0. As coupling increases, the frequencies split farther apart. The lower frequency corresponds to currents in phase (even mode); the higher frequency corresponds to currents out of phase (odd mode).

This frequency splitting is analogous to the normal modes of coupled pendulums or the bonding and antibonding orbitals of coupled atomic systems. The splitting increases with coupling strength.

Implications for Power Transfer

Frequency splitting affects power transfer optimization:

Optimal operating point: Maximum power transfer occurs at different frequencies depending on coupling and load. At critical coupling, the optimal frequency is near f0; at stronger coupling, operating at one of the split frequencies may be more efficient.

Frequency tracking challenges: Adaptive frequency systems must handle the bifurcation of the optimal frequency as coupling varies. Simple peak-tracking algorithms may jump discontinuously between the split frequencies.

Power transfer valleys: At strong coupling, operating at f0 (between the split frequencies) can result in poor power transfer even though it was optimal at lower coupling. Systems must avoid this operating region.

EMC Consequences

Frequency splitting creates distinctive EMC situations:

Multiple emission frequencies: Systems operating near or at both split frequencies will have emissions at multiple frequencies. Even if the drive is at a single frequency, the response may include both resonant modes.

Mode excitation: External interference at either split frequency can excite the corresponding mode, potentially more effectively than interference at the uncoupled resonant frequency.

Beating phenomena: When both modes are excited simultaneously, beating at the difference frequency creates amplitude modulation. This can generate intermodulation products at frequencies not present in the original signals.

Frequency hopping: Adaptive systems that hop between split frequencies create time-varying emissions that may require different measurement approaches than steady-state systems.

Managing Frequency Splitting

Design approaches for managing frequency splitting include:

• Operating regime selection: Design the system to operate consistently in either the weakly-coupled (unsplit) or strongly-coupled (split) regime, avoiding the transition region
• Asymmetric tuning: Intentionally detuning transmitter and receiver resonant frequencies can modify splitting behavior
• Multiple-coil topologies: Adding relay coils or using coil arrays can create different splitting patterns with potentially beneficial characteristics
• Active control: Sophisticated control algorithms can manage operation across the full range of coupling conditions, including the splitting transition

Configuration Types

Multi-transmitter systems take several forms:

Array configurations: Multiple transmitter coils arranged in an array can provide power across an extended area. Adjacent coils may be driven in phase, out of phase, or with controlled phase relationships.

Overlapping coverage: Coils with overlapping coverage regions can provide continuous power as a receiver moves between coil service areas. This requires coordination between coils.

Selective activation: In large arrays, only the coils nearest the receiver may be activated, reducing power consumption and emissions from inactive regions.

Multiple independent systems: Separate WPT systems operating in the same environment create multi-transmitter situations even without intentional coordination.

Inter-Transmitter Coupling

Transmitter coils in proximity couple to each other as well as to receivers:

Direct coupling: Adjacent transmitter coils share magnetic flux, creating mutual inductance that affects each coil's impedance and resonant characteristics.

Cross-coupling effects: Energy intended for one receiver may couple through the transmitter array to appear at other locations, reducing efficiency and potentially affecting unintended receivers.

Resonant mode complexity: A system of N coupled resonators exhibits up to N resonant modes. The mode structure can become very complex in large arrays.

Stability considerations: Strong inter-transmitter coupling can create feedback paths that cause oscillation or instability if not properly managed.

EMC Challenges

Multi-transmitter configurations create specific EMC challenges:

Field superposition: The fields from multiple transmitters add vectorially in space. Depending on phase relationships, this can create regions of constructive interference (higher field intensity) or destructive interference (lower field intensity).

Interference hot spots: Constructive interference can create localized regions where field intensity exceeds single-transmitter levels. These hot spots may exceed exposure limits even when individual transmitters comply.

Complex field patterns: The spatial field distribution from multi-transmitter systems can be highly irregular, making measurement and compliance assessment more difficult.

Synchronization requirements: Coordinating multiple transmitters to achieve desired field patterns requires synchronization. Phase drift between transmitters causes time-varying field patterns that may be difficult to characterize.

Design Strategies

Managing multi-transmitter EMC involves:

• Phase coordination: Controlling the relative phase of transmitter drive signals to create beneficial interference patterns that enhance coupling while reducing far-field emissions
• Selective activation: Activating only the transmitters needed for current receivers, minimizing active field sources
• Power sharing: Distributing power among multiple transmitters to reduce the field intensity from any single source
• Geometric optimization: Arranging transmitter coils to minimize inter-transmitter coupling while maintaining receiver coverage
• Decoupling networks: Adding components to reduce magnetic coupling between adjacent transmitters

Near-Field Patterns

Close to the transmitter, field patterns are dominated by the coil geometry:

Magnetic field distribution: The magnetic field from a circular coil is strongest along the axis and decreases rapidly with radial distance. The field has both axial and radial components, with the radial component strongest at the coil edge.

Standing wave effects: In resonant systems, standing waves can develop in the resonant structure, creating fixed patterns of high and low field intensity. These patterns are frequency-dependent.

Position sensitivity: The strong spatial variation in near-field intensity means that small position changes can significantly affect coupling efficiency and exposure levels.

Far-Field Radiation

At distances beyond the near-field region, resonant WPT systems exhibit radiation patterns:

Antenna behavior: The transmitter coil acts as a magnetic loop antenna. The radiation pattern is toroidal, with maximum radiation perpendicular to the coil axis and nulls along the axis.

Directivity: Small loop antennas (circumference less than wavelength/10) have low directivity. Larger or more complex coil structures may have more directional patterns.

Polarization: The radiated field is primarily magnetic (or equivalently, horizontally polarized if the coil axis is vertical). Polarization-sensitive receivers may show orientation-dependent susceptibility.

Distance dependence: Far-field radiation intensity decreases as 1/r (field strength) or 1/r-squared (power density), in contrast to near-field intensity which decreases more rapidly (1/r-squared or 1/r-cubed).

Environmental Interactions

The environment modifies interference patterns:

Reflections: Metal surfaces, walls, and floors reflect electromagnetic fields, creating standing wave patterns in enclosed environments. Field intensity at a given location depends on the superposition of direct and reflected waves.

Absorption: Lossy materials (including human bodies) absorb electromagnetic energy, creating shadowing effects and altering field distribution.

Resonant cavities: In metal-enclosed environments, cavity resonances can amplify fields at specific frequencies. If the WPT operating frequency coincides with a cavity resonance, internal field intensities can be much higher than expected.

Ferromagnetic materials: Nearby ferromagnetic structures concentrate magnetic flux, potentially creating local high-field regions or altering the coupling characteristics.

Interference with Other Systems

Resonant WPT systems can interfere with other electronic equipment:

• Radio receivers: Strong fields at the WPT frequency can desensitize or overload receivers operating at or near that frequency
• Medical devices: Pacemakers, insulin pumps, and other implanted or worn medical devices may be susceptible to WPT fields
• Magnetic storage: Magnetic stripe cards and some magnetic storage media can be affected by strong magnetic fields
• Sensors: Magnetic field sensors, compasses, and magnetically-sensitive instruments may give erroneous readings
• Audio equipment: Magnetic fields can induce hum in audio circuits, particularly high-impedance inputs and moving-coil transducers

Human Protection

Protecting humans from excessive field exposure involves multiple approaches:

Exposure assessment: Field measurements or calculations verify that accessible areas comply with exposure limits. Assessment must consider all operating conditions including maximum power and worst-case alignment.

Exclusion zones: Areas where field levels exceed exposure limits are designated as exclusion zones. Physical barriers or warning systems prevent unauthorized access.

Presence detection: Sensors detect human presence in high-field regions and reduce power or cease operation. Detection systems must be reliable and respond quickly enough to prevent harmful exposure.

Power limiting: Automatic power reduction when exposure limits could be exceeded provides a backup to presence detection. The system monitors conditions that correlate with increased exposure risk.

Foreign Object Protection

Foreign object detection (FOD) in resonant systems must account for the high Q characteristics:

Q-factor monitoring: Metallic objects in the field absorb energy and reduce the system Q. Monitoring Q or efficiency can detect foreign objects. The sensitivity depends on object size, material, and position.

Frequency shift detection: Metallic objects shift the resonant frequency through eddy current effects. Monitoring frequency can detect objects, particularly ferromagnetic materials that cause larger shifts.

Temperature monitoring: Objects that heat in the field can be detected through temperature sensing. This provides direct detection of the hazard condition but may not respond quickly enough for all scenarios.

Multi-modal detection: Combining multiple detection methods improves reliability and covers different object types and positions.

Safety System EMC

Safety systems create their own EMC considerations:

Immunity to WPT fields: Safety sensors must operate reliably in the strong electromagnetic fields created by the WPT system. Sensors may need shielding or signal processing to reject interference from the WPT operating frequency.

False alarm prevention: EMI-induced false alarms reduce system usability. Safety systems must distinguish actual hazards from interference-induced artifacts.

Safety system emissions: Active sensing systems (such as radar-based presence detection) may generate their own emissions that must comply with applicable limits.

Communication immunity: Safety-related communications between transmitter and receiver must be reliable despite the electromagnetic environment. Robust modulation, error correction, and redundancy may be required.

In-Band Communication

Communication using the same frequency band as power transfer:

Load modulation: The receiver modulates its impedance, creating amplitude or phase variations in the transmitted signal that can be detected by the transmitter. This requires no additional frequency allocation but has limited bandwidth and range.

Frequency modulation: Small frequency variations around the power transfer frequency can carry information. The narrow bandwidth of high-Q systems limits data rate.

Time-domain multiplexing: Alternating between power transfer and communication intervals allows sharing the same frequency for both functions.

Out-of-Band Communication

Using separate frequencies for communication and power transfer:

Radio communication: Standard wireless protocols (Bluetooth, WiFi, proprietary RF links) can carry control information independently of the power link. This provides high bandwidth but requires additional radio hardware and frequency coordination.

Near-field communication: NFC or similar technologies operating at different frequencies than the power transfer can handle authentication and initialization. Limited range is acceptable for applications where transmitter and receiver are always in proximity.

Separate inductive link: A second set of loosely-coupled coils at a different frequency can provide a communication channel that naturally follows the power transfer path.

EMC Considerations for Communication

Integrating communication with resonant WPT requires attention to EMC:

• Receiver desensitization: Strong WPT fields can desensitize communication receivers, reducing range and reliability. Filtering and automatic gain control help maintain communication performance
• Harmonic interference: WPT harmonics may fall in communication bands. Filter design must consider both conducted and radiated harmonic levels
• Intermodulation: Mixing of WPT and communication signals in nonlinear elements can create interference products at unexpected frequencies
• Timing coordination: Time-multiplexed systems must maintain accurate timing to avoid power and communication signals overlapping

Industry Standards

Several organizations develop resonant WPT standards:

Wireless Power Consortium (WPC): The Qi standard, while primarily inductive, includes resonant-mode extensions for extended power range. WPC also develops the Ki standard for kitchen applications at higher power levels.

AirFuel Alliance: Formerly the Alliance for Wireless Power (A4WP), AirFuel develops resonant magnetic coupling standards allowing multiple device charging with spatial freedom. The standard specifies 6.78 MHz operation with Bluetooth communication.

SAE International: SAE J2954 for electric vehicle wireless charging includes resonant operation at 85 kHz, with alignment classes specifying position tolerance requirements.

IEC: IEC 61980 series addresses electric vehicle wireless power transfer including resonant systems. IEC 63028 specifies low-power resonant systems for consumer electronics.

EMC Requirements in Standards

WPT standards address EMC through various mechanisms:

Operating frequency specification: Standards typically specify ISM band operation (6.78 MHz, 85 kHz regions) to ensure regulatory compliance for intentional emissions.

Emission limits: Standards may reference existing EMC standards (CISPR 11, FCC Part 18) or specify product-specific emission limits appropriate to the application.

Human exposure: Compliance with ICNIRP or IEEE exposure guidelines is typically required, with specified test methods and assessment procedures.

Foreign object detection: Standards specify FOD requirements including detection thresholds, response times, and test methods.

Immunity: Requirements for operation in the presence of external interference ensure reliable and safe operation.

Regulatory Developments

Regulatory frameworks continue to adapt to resonant WPT technology:

ISM band usage: Operation in ISM bands provides a relatively straightforward path for intentional emissions, though harmonic and spurious emissions must still meet general limits.

Power level classifications: Regulations may distinguish between low-power consumer systems and high-power industrial or automotive systems, with different requirements for each.

International harmonization: Efforts to harmonize WPT regulations across regions reduce compliance complexity for global products.

Automotive-specific regulations: Electric vehicle charging is subject to additional automotive EMC requirements beyond general WPT regulations.