# A Comprehensive Review on Wireless Power Transfer Systems for Charging Portable Electronics

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## Abstract

**:**

## 1. Introduction

## 2. Wireless Power Transfer System Modeling and Efficiency Optimization Techniques

#### 2.1. Model of a WPT System Using Series-Series Compensation

- ${V}_{in}$—peak value of the sinusoidal voltage source.
- ${\omega}_{s}$—switching frequency in rad/s.
- ${M}_{12}$—mutual inductance between the transmitter and receiver coils.
- ${k}_{12}$—coupling coefficient between the transmitter and receiver coils.
- ${R}_{1}$—series resistance of the transmitter coil (includes on-state resistance of switches and resistances (ESRs) of the transmitter coil and compensation capacitors).
- ${R}_{2}$—series resistance of the receiver coil (includes series resistance of diodes and resistances (ESsR) of the receiver coil and compensation capacitors).
- ${C}_{1}$—equivalent series compensation capacitance of the transmitter.
- ${C}_{2}$—equivalent series compensation capacitance of the receiver.
- ${L}_{1}$—coil inductance of the transmitter.
- ${L}_{2}$—coil inductance of the receiver.
- ${R}_{L}$—load resistance.
- ${i}_{1}$—peak value of the sinusoidal current flowing in the transmitter coil.
- ${i}_{2}$—peak value of the sinusoidal current flowing in the receiver coil.
- ${X}_{2}$—series reactance of the receiver side.
- ${i}_{1rms}$—rms value of the sinusoidal current flowing in the transmitter coil.
- ${i}_{2rms}$—rms value of the sinusoidal current flowing in the receiver coil.
- $\omega $—relative resonant frequency of the receiver.
- ${\omega}_{r}$—resonant frequency of the receiver.
- ${Q}_{L}$—loaded quality factor of the receiver.
- ${Q}_{p}$—unloaded quality factor of the transmitter.
- ${Q}_{s}$—unloaded quality factor of the receiver.

#### 2.2. Compensation Networks

#### 2.3. Maximizing Power Transfer between the Transmitter and Receiver

#### 2.4. Efficiency Optimization Techniques

#### 2.4.1. Using Impedance Matching with Reconfigurable Resonant Circuits

#### 2.4.2. Using Variable Operating Frequency

#### 2.4.3. Using Impedance Compression Networks

#### 2.4.4. Using DC-DC Converters for modulating Load Impedance

#### 2.5. WPT Systems with Multiple Coils

#### 2.5.1. Intermediate Multiple Coils Acting as Repeaters or Domino Resonators

- 1.
- Multiple intermediate coils introduce more degrees of freedom which can be utilized for improving efficiency or making the wireless link less sensitive to coupling variations.
- 2.
- The intermediate coils can also act as effective impedance matching elements [90] on both the source and load sides.

#### 2.5.2. Multiple Transmitter Coil Systems

#### 2.5.3. Multiple Receiver Coil Systems

#### Efficiency Optimization of Multiple Receiver WPT Systems without Cross-Coupling among the Receivers

- 1.
- Input Voltage Regulation—The efficiency of the system is highly dependent on the input voltage at various conditions of load and coupling. Using modulation techniques such as phase shift or pulse width modulation, the RMS input voltage to the WPT system can be varied. Another way is to use a DC-DC converter in front of the inverter or power amplifier on the transmitter side to provide the required input voltage. However, this increases the number of components as well as the losses in the system.
- 2.
- Optimizing the Load Resistance seen by the Receivers—The efficiency of a system with multiple receivers can be maximized by optimizing the load resistances seen by each of the receivers. The optimum value of the load resistances (${R}_{L,opt}$) can be given by the equation below [76]:$${R}_{L,opt}={R}_{i}\sqrt{1+\frac{{\sum}_{i=1}^{n}{\omega}_{s}^{2}{M}_{1i}^{2}}{{R}_{1}{R}_{i}}}$$

#### Efficiency Optimization of Multiple Receiver WPT Systems with Cross-Coupling among the Receivers

- ${M}_{1k}$—mutual inductance between the transmitter and the ${k}^{th}$ receiver coil.
- ${M}_{ik}$—mutual inductance between the ${i}^{th}$ and ${k}^{th}$ receiver coil.
- ${R}_{s}$—series resistance of the transmitter coil (includes on-state resistance of switches and resistances (ESRs) of the transmitter coil and compensation capacitors).
- ${R}_{i}$—series resistance of the ${i}^{th}$ receiver coil (includes series resistance of diodes and resistances (ESsR) of the receiver coil and compensation capacitors).
- ${C}_{1}$—equivalent series compensation capacitance of the transmitter.
- ${C}_{i}$—equivalent series compensation capacitance of the ${i}^{th}$ receiver.
- ${L}_{1}$—coil inductance of the transmitter.
- ${L}_{i}$—coil inductance of the ${i}^{th}$ receiver.
- ${R}_{Li}^{\prime}$—load resistance of the ${i}^{th}$ receiver.
- ${i}_{1}$—peak value of the sinusoidal current flowing in the transmitter coil.
- ${i}_{i}$—peak value of the sinusoidal current flowing in the ${i}^{th}$ receiver coil.
- ${X}_{2}$—series reactance of the first receiver.
- ${X}_{i}$—series reactance of the ${i}^{th}$ receiver.

## 3. Inverter, Rectifier, and Compensation Topologies for Wireless Power Transfer

#### 3.1. Inverter Topologies

#### 3.1.1. Class D Topology

#### 3.1.2. Class E Topology

#### 3.1.3. Class EF Topology

#### 3.2. Rectifier Topologies

#### 3.2.1. Class D Topology

#### 3.2.2. Class E Topology

#### 3.3. Transmitter Topologies with Constant Current Output

## 4. Coil Design

#### 4.1. Improving Coupling Coefficient between Coils

#### 4.2. Improving the Quality Factor of Coils

#### 4.3. Self-Resonant Coils

#### 4.4. Omnidirectional Wireless Power Transfer

- Multiple power sources used for multiple transmitter coils. Based on the location of the receiver, the amplitude and phase of the coil currents are controlled dynamically. This requires complicated external control circuits for measurements and feedback and can become expensive in practice.
- A single power source is connected to the transmitter. This technique is simpler to implement. However, the system can have blind spots where the coupling is much less.

#### 4.4.1. Two-Dimensional Omnidirectional Wireless Power Transfer

#### 4.4.2. Three-Dimensional Omnidirectional Wireless Power Transfer

#### 4.5. Use of Ferrite Cores

#### 4.6. Solenoidal Receiver Coils for Multiple Receiver Systems

## 5. Foreign Object Detection

- 1.
- Power difference method—The transmitted and received power are monitored. If the difference between them is higher than a set threshold, it indicates the presence of foreign objects. In this case, the transmitter stops delivering power to the receiver circuit.
- 2.
- Sensor method—Temperature and/or metal sensors are used to detect any anomaly in the transmission path. Anomalies detected by the sensors are communicated to the transmitter using load modulation. If the temperature sensed is higher than the threshold or there are metals present in the transmission path, the control circuit will shut down the power transmission.
- 3.
- Transient energy decay method—The transmitter is powered for a short time and then disabled to check the rate of transient energy decay. If this rate exceeds the set threshold, the presence of a foreign object is confirmed and the system is shut down.

## 6. EMC/EMI Issues and EMF Safety in Near-Field Wireless Power Transfer

#### 6.1. De-Sense Caused by In-Band Noise and Shielding in Smartphones

#### 6.2. EMF Safety Standards

- 1.
- Frequency, intensity, and polarization of the EMF.
- 2.
- Type of EMF source (near-field or far-field).
- 3.
- Size, the internal and external geometry of the exposed body part, and the dielectric properties of various tissues.
- 4.
- Reflection effects of the field from objects in the vicinity of the exposed body.

- 1.
- Between 100 kHz and 20 MHz: with decreasing frequency, absorption reduces rapidly in the trunk, and significant absorption may happen in the neck and legs.
- 2.
- Between 20 kHz and 300 MHz: absorption over the whole body is high, and if partial resonances are considered, then it is even higher.
- 3.
- Between 300 MHz and 10 GHz: significant non-uniform, local absorption occurs.
- 4.
- Above 10 GHz: absorption occurs primarily at the surface of the body.

#### 6.3. Studies on EMF Safety

## 7. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 4.**Lumped parameter model of inductive WPT systems with (

**a**) soils modeled as coupled inductors and (

**b**) effect of mutual coupling modeled as dependent voltage sources.

**Figure 5.**(

**a**) Efficiency of the link versus the k-Q product of the system. (

**b**) Quality factor of a coil versus frequency (three-turn coil of outer radius 10 cm).

**Figure 8.**Efficiency of the WPT system as a function of (

**a**) normalized load resistance, ${R}_{L}$, for different ${k}_{12}$ and (

**b**) relative frequency for different loaded quality factors and ${k}_{12}$ = $0.4$.

**Figure 9.**First harmonic model of a WPT circuit with two receivers (

**a**) with cross-coupling between them and (

**b**) without cross-coupling between them.

**Figure 10.**Circuit diagram of (

**a**) a conventional Class D resonant inverter and (

**b**) a Class D resonant inverter with a ZVS tank to achieve soft switching while operating at the resonant frequency.

**Figure 11.**Circuit diagram of (

**a**) a conventional Class E resonant inverter and (

**b**) a Class E resonant inverter with a semi-resonant tank to minimize the VA rating of the switch.

**Figure 12.**Normalized gate-to-source voltage and drain-to-source voltage (${V}_{ds}$/${V}_{in}$) for (

**a**) ${R}_{L}$ = ${R}_{opt}$, (

**b**) ${R}_{L}$ = $0.8$${R}_{opt}$, and (

**c**) ${R}_{L}$ = $1.2$${R}_{opt}$ in a Class E resonant inverter.

**Figure 14.**Normalized gate-to-source voltage and drain-to-source voltage (${V}_{ds}$/${V}_{in}$) for (

**a**) ${R}_{L}$ = ${R}_{opt}$, (

**b**) ${R}_{L}$ = 0, and (

**c**) ${R}_{L}$ = 2${R}_{opt}$ in a Class EF resonant inverter.

**Figure 18.**(

**a**) Interleaved coil structure. (

**b**) Magnetic field strength as a function of horizontal displacement of the receiver coil at a height of 1.8 cm from a transmitter coil of 50 cm diameter. (Reprinted with permission from Ref. [123], 2020, IEEE).

**Figure 19.**(

**a**) Three-dimensional orthogonal transmitter coil arrangement. (

**b**) Quadrature-shaped receiver coil arrangement for omnidirectional wireless power.

**Figure 20.**Magnetic field distribution in the x-z plane with (

**a**) coils only and (

**b**) coils with ferrites (Reprinted with permission from Ref. [137], 2013, IEEE).

**Figure 21.**(

**a**) WPT system with a spiral transmitter and a solenoidal receiver coil, (

**b**) radial magnetic flux density of a spiral transmitter coil, and (

**c**) axial magnetic flux density of a spiral transmitter coil simulated using ANSYS Maxwell (Reprinted with permission from Ref. [138], 2021, IEEE).

**Figure 22.**(

**a**) ICNIRP reference levels for limiting exposure to time-varying E-field, H-field and EMF. (Reprinted with permission from Ref. [142], 2014, IEEE). (

**b**) IEEE Standard for Safety Levels with Respect to Human Exposure to Radio Frequency EMF (3 kHz to 300 GHz) (Reprinted with permission from Ref. [141], 2006, IEEE).

**Figure 23.**(

**a**) H-field distribution near the anatomical model of Duke. (

**b**) Local SAR of two models, Duke and Thelonious, in two sagittal planes, centered and 75 mm off-center, for coronal exposure (Reprinted with permission from Ref. [144], 2013, IEEE).

**Figure 24.**(

**a**) The current at which the 10 g SAR limit is reached in the transmit coil. (

**b**) The current at which the whole body SAR limit is reached in the transmit coil (Reprinted with permission from Ref. [144], 2013, IEEE).

Era | Important Works |
---|---|

1900s and before | Tesla laid down the theoretical foundation and demonstrated wireless power transfer between resonating coils. Hutin and LeBlanc wrote a patent for a WPT system for electric railways in 1894 [13]. |

1960s | Shuder [14] worked on high-frequency resonant WPT systems for use in medical devices. William C. Brown [15] demonstrated radiative power transfer by using solar cells mounted on satellites which transmitted power to Earth by microwave beaming. |

1970s | In 1976, the Lawrence Berkley National Laboratory tested the feasibility of dynamic wireless charging for the first time [16]. |

1980s | In 1981, Brown [17] developed a thin-film rectenna that was suitable for airborne applications. |

1990s | Boys, Green, and Covic [8] developed dynamic IPT systems for material handling applications. |

Early 2000s | Boys and Covic [18] developed IPT systems for automated guided vehicles and buses. Hui worked on the development of planar inductive battery chargers for mobile devices [9]. |

Mid 2000s | Soljacic demonstrated Tesla’s magnetic resonant coupling theory by wirelessly transferring 60 W of power over a distance of 2 m [19]. Public interest in this experiment led to the development of a company named WiTricity. |

Late 2000s | Dynamic wireless charging of electric vehicles was researched at Korea Advanced Institute of Science and Technology (KAIST) in 2009 [20]. |

Early 2010s | Qi standard is released which is the most widely adopted charging standard for inductive chargers. |

Mid 2010s | Airfuel alliance was formed after Alliance For Wireless Power was merged with the Power Matters Alliance. |

Late 2010s to today | SAE charging standards for wireless charging of electric vehicles were developed. |

Inductive Coupling | Capacitive Coupling |
---|---|

Uses time-varying magnetic fields. | Uses time-varying electric fields. |

Magnetic fields flow through the coils and loop back to the source. | Electric fields start and terminate at the conductive plates. |

The magnetic field path needs to be monitored and guided and hence ferrites are needed. | Electric fields are constrained and hence do not require ferrites. |

More sensitive to misalignment. | More tolerant of misalignment. |

Induced voltages depend on the permeability of free space. | Displacement currents depend on the permittivity of free space. |

Less sensitive to parameter variations. | More sensitive to parameter variations. |

For the same power level and distance, the size of couplers is less for IPT. | For the same power level and distance, the size of couplers is more for CPT. |

**Table 3.**Qi versus AirFuel standards of wireless power transfer [61].

Standard | Qi (Single Transmitter) | Qi (Multiple Transmitter) | AirFuel |
---|---|---|---|

Frequency | 100–205 kHz | 100–205 kHz | 6.78 MHz |

Positioning of receiver | Exact | Flexible in horizontal directions | Free positioning (up to 3 cm vertical freedom) |

Number of receivers | One | One | Multiple (up to eight) |

Rx-Tx communication | In-band | In-band | Bluetooth or In-band |

**Table 4.**A comparative study of techniques for optimization of WPT systems in the presence of cross-coupling.

Technique | Simultaneous Power Delivery to Multiple Devices | Need for Estimation of Load and Coupling | Ability to Incorporate Additional Receivers | Design Complexity | Range of Operation (Load and Coupling) | Communication Network Requirement |
---|---|---|---|---|---|---|

Multi-resonant [95,96,97] | Yes | No | Yes (no. of receivers is based on the availability of frequencies) | Medium (requires extra circuits to avoid interfering with other frequencies) | Narrow | Yes |

Coil decoupling [98,99,100] | Yes | No | No (has to be designed specifically for a given number of receivers) | Medium (complicated for more than two receivers) | Narrow | No |

Time-division multiplexing [101,102] | No | No | Yes | Low | Wide | Yes |

Passive compensation [103] | Yes | No | No (coils and compensation networks need to be redesigned for more receivers) | Low | Narrow | No |

Active compensation technique [94,104] | Yes | Yes | Yes (more receivers increase the number of parameters to be estimated) | High (estimation algorithms could be computationally intensive) | Wide | Yes |

Current quadrature technique [106,107] | Yes | No | Yes (however, receivers require the phase angle of the transmitter current to be communicated to them) | Medium (needs switched capacitor networks or tuning-assisted circuits for orthogonalization of currents) | Narrow | Yes |

Topology | Class D | Class E | Class EF |
---|---|---|---|

No. of switches | Two | One | One |

High side gate drive | Required. | Not required. | Not required. |

Switching frequency range | Typically in the range of kHz to a few MHz. | Tens of MHz (typically 6.78 MHz or 13.56 MHz). | Tens of MHz (typically 6.78 MHz or 13.56 MHz). |

Peak voltage stress on switches | Input voltage. | 3.56 times the input voltage. | 2.31 times the input voltage when the added resonant tank is tuned to twice the switching frequency. |

Number of passive components | Two (one inductor and one capacitor). | Four (two inductors and two capacitors). | Six (three inductors and three capacitors). |

Soft switching dependence on load | ZVS can be obtained independent of load in lagging power factor operation. | ZVS or ZVDS is load-dependent. | Load-independent soft switching can be achieved when the added resonant tank is tuned to 1.5 times the switching frequency. |

Guideline | Average Mass | Body Region | General Public (W/kg) | Occupational (W/kg) |
---|---|---|---|---|

ICNIRP | 10 g contiguous volume | Head and trunk | 2 | 4 |

Limbs | 4 | 20 | ||

Whole body | 0.08 | 0.4 | ||

IEEE | 10 g cubical volume | All but extremities and pinna | 2 | 10 |

Extremities and pinna | 4 | 20 | ||

Whole body | 0.08 | 0.4 |

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**MDPI and ACS Style**

Laha, A.; Kalathy, A.; Pahlevani, M.; Jain, P.
A Comprehensive Review on Wireless Power Transfer Systems for Charging Portable Electronics. *Eng* **2023**, *4*, 1023-1057.
https://doi.org/10.3390/eng4020061

**AMA Style**

Laha A, Kalathy A, Pahlevani M, Jain P.
A Comprehensive Review on Wireless Power Transfer Systems for Charging Portable Electronics. *Eng*. 2023; 4(2):1023-1057.
https://doi.org/10.3390/eng4020061

**Chicago/Turabian Style**

Laha, Arpan, Abirami Kalathy, Majid Pahlevani, and Praveen Jain.
2023. "A Comprehensive Review on Wireless Power Transfer Systems for Charging Portable Electronics" *Eng* 4, no. 2: 1023-1057.
https://doi.org/10.3390/eng4020061