In this article, we present the analysis of electromagnetic interference (EMI) shielding effects of wireless power transfer (WPT) using magnetic resonance coupling for board-to-board level interconnection. Board-to-board WPT consists of source coil, receiver coil, and load which are manufactured on printed circuit board (PCB).

The coil is expressed as a simple equivalent circuit model, of which the components are calculated using the physical dimensions of the coil. It is verified that the results of model estimation in both frequency- and time-domain show a good correlation with simulated and measured results under 1GHz. Voltage transfer ratio (VTR) of board-to-board WPT was achieved to be 0.49. In addition, EMI shielding effects in WPT with materials such as ferrite and metal film is analyzed using verified model. The shielding effects of each film in WPT are compared by observing their magnetic field distribution.

The wireless power transfer (WPT) technology is recently applied to multiple applications such as wireless charging systems for mobile phones, laptops and other handheld devices [1]. With miniaturization, this technology can be applied to more various applications such as board-to-board level interconnections, which mean that power is transferred from upper source board to lower receiver board, for mobile devices. Conventionally, board-to-board level power interconnections have been designed using connectors; however, as more and more components are mounted on the tiny board, the number of power lines increases dramatically, while the number of signal lines even exceeds that of power lines. Therefore, instead of using power lines, the required power needs to be transferred wirelessly.

The simplified diagram of WPT using magnetic resonance for board-to-board level interconnection is shown in Figure 1. The board of power source consists of inductive coils and DCAC inverter, while that of power receiver consists of inductive coils, rectifier, and DC-DC converter. In the view of performance of the board-to-board WPT, the magnetic resonant coupling between the inductive coils is a key factor because it dominantly determines the overall performance of the system: the magnetic resonance in an inductively coupled system efficiently increases the amount of magnetic flux linked between coils, which results in the significant improvement of voltage transfer ratio (VTR) [2][3].

**Figure 1: The simplified diagram of wireless power transfer using magnetic resonance for board-to-board level interconnection**

** **

The specification of the system is indicated by the following three parameters: resonant frequency, self-inductance of the coils, and electromagnetic interference (EMI) characteristic. First of all, resonant frequency is determined by the self-inductance of the coil and the tuning capacitance. Secondly, self-inductance of the coil is determined by the physical dimension of the coil. Lastly, EMI characteristic is affected by attaching shielding materials such as ferrite and metal film that could change self- and mutual inductance.

In this article, WPT using magnetic resonance coupling for board-to-board level interconnection is introduced, and especially we focus on the EMI shielding effects. For analyzing EMI shielding effects, we suggest simple equivalent circuit model which consists of self-inductance, parasitic resistance, and capacitance [4][5]. The coil for board-to-board WPT, designed as a spiral type, is manufactured on printed circuit board (PCB) for experimental verification and comparison with the model. The model is successfully verified by the 3D field simulated and measured results under 1GHz. We use verified model and 3D field simulator for investigating EMI shielding effects in WPT. The shielding material affects not only EMI shielding in WPT but also equivalent circuit model of the coil, hence the performance of WPT can be changed.

Wireless Power Transfer for Board-to-Board Level Interconnection

In this section, WPT for board-to-board level interconnection is presented on the manufactured PCB. The most important component in this system is the coil, which determines VTR of the entire WPT system. Therefore, analyzing the equivalent circuit model of the spiral coil is very important, of which the parameters can be obtained by a series of calculations using its physical dimensions. The equivalent circuit model will be thoroughly explained by the equations presented below. Mutual inductance is extracted from the 3D EM simulation. Through this sequence, board-to-board WPT is manufactured on PCB. This system can be adapted to board-to-board level interconnection, in which the boards can be separated by several millimeters.

**Figure 2: Conventional equivalent circuit model of spiral coil**

Equivalent Circuit Model of Spiral Coil

As shown in Figure 2, the spiral coil is modeled as a self-inductance, L, and a parasitic resistance, R_{Parasitic}. In addition, the capacitance between two ports of the spiral coil is represented as a parasitic capacitance, C_{Parasitic}. In order to calculate the self-inductance, the physical dimensions of the spiral coil should first be known, as listed in Table 1. From these dimensions, the self-inductance, L, is given by

(1)

(2)

where d_{m} is the average diameter and ρ is the fill ratio [4].

Physical Dimension |
Value |

Exterior Diameter, d_{e} |
10 mm |

Interior Diameter, d_{i} |
3.4 mm |

Number of Turns, N | 5 turns |

Metal Width, w | 0.5 mm |

Metal Space, s | 0.2 mm |

Metal Thickness, t | 0.018 mm |

The self-inductance, L, calculated by Equations 1 and 2 is 208 nH. Moreover, the parasitic resistance of the coil, R_{Parasitic}, is given by

(3)

(4)

where t_{eff} is the effective metal thickness and δ is the skin depth of copper at the resonant frequency of 110 MHz [5].

From Equations 3 and 4, it can be calculated that the parasitic resistance, R_{Parasitic}, is 677 mΩ. In order to come up with an exact equivalent circuit, the parasitic capacitance, C_{Parasitic} between the adjacent spiral lines of the coil should be calculated and taken into account. In general, however, this capacitance is negligible, since the adjacent metal lines in each turn have almost same potential. Therefore, the equivalent circuit model is represented only by the self-inductance, L, and the parasitic resistance, R_{Parasitic}.

Manufactured Printed Circuit Board

In the board-to-board WPT manufactured on the PCB shown in Figure 3, the source board is composed of a SMA connector, a tuning capacitor for matching the resonant frequency, and a source spiral coil. Similarly, the receiver board is composed of a tuning capacitor, a receiver spiral coil, and the same SMA connector. The measurement is conducted with the vector network analyzer to measure the S-parameters and also, with the oscilloscope to capture the time-domain waveforms at the SMA connectors.

**Figure 3: Wireless power transfer for board-to-board level interconnection on printed circuit board**

Comparison and Analysis of Simulation and Measurement

In this section, the comparison between the simulation and the measurement results in the frequency-and time-domain, as well as the analysis, is presented.

*Frequency-Domain*

Figure 4 shows the equivalent circuit model of the WPT system for board-to-board level interconnection used for frequency-domain simulation. L_{S}, R_{S} and L_{R}, R_{R} are the self-inductances and the parasitic resistances of the source and receiver coils, respectively. The tuning capacitors connected in series to the source and receiver coils are C_{S} and C_{R}. M is the mutual inductance between the coils and k is the coupling coefficient of the coils. In this case, the new parasitic capacitance from SMA connectors used for measurement should be connected in parallel. The capacitance of SMA connector is about 1 pF which is extracted from the frequency-domain measurement.

**Figure 4: Equivalent circuit model of the WPT system**

For comparison, the estimation using the equivalent circuit model and the simulation using 3D EM simulator, ANSYS HFSS are performed individually. In addition, the frequency-domain measurement of the WPT system is conducted as shown in Figure 5. The results are shown in Figure 6. The depicted input impedance (Z_{11}) and transfer impedance (Z_{21}) curves of Z matrix obtained from the simulations show a good agreement with the measurement results.

**Figure 5: Frequency-domain measurement setup for the WPT system**

**Figure 6: Input Impedance (Z _{11}) curves and transfer Impedance (Z_{21}) curves of each case at the board-to-board distance of 5mm**

From Z_{11} curve of the WPT system shown in Figure 6a, the series resonance peak, where the input impedance is minimized using the tuning capacitor, was found to be at 110 MHz, which coincides with fresonant calculated as

(5)

The maximum VTR are expected at the frequency where the input impedance has the minimum value [6][7].

The mutual inductance, M, between the source and receiver coils can be obtained simply from the slope of the Z_{21} curve of the WPT system, which is represented by the the black straight solid line shown in Figure 6b. Using the obtained mutual inductance, M, coupling coefficient, k, can be calculated by

(6)

The resonant peaks over 200 MHz in Figure 6 occur due to the parasitic capacitances of SMA connectors.

Time-Domain

The time-domain measurement is conducted for calculating VTR using the equivalent circuit model depicted previously in Figure 4. In this setup, the terminal voltage, V_{S} is modeled as a voltage source with the internal source resistance of 50 Ω and the load at receiver side is assumed to be a 50 Ω resistor.

For time-domain simulation, the sinusoidal voltage is supplied as the source at the frequency of 110 MHz, where the input impedance is minimized, and the voltage waveform at the load is detected. And for time-domain measurement, the oscilloscope is used for measuring the waveform at the load, while the sinusoidal voltage with the frequency of 110 MHz is supplied from the signal generator. The voltage waveforms at the load are shown in Figure 7 and it is found that the measurement shows a good correlation with the simulation.

**Figure 7: Voltage waveform from measurement and simulation using equivalent circuit model**

The maximum VTR at the resonant frequency is 0.34; with source voltage of 7 V_{PP}, load voltage becomes 2.4 V_{PP} and the maximum transferred power is expected at the same frequency. In other words, the frequency at which the maximum voltage is transferred coincides with the one where power transfer efficiency is the maximum, assuming that the source power is same.

As previously mentioned, the coupling coefficient, k, can be simply calculated by Equation 6, where M is obtained from the slope of Z_{21}. To find the relationship between the board-toboard distance and the coupling coefficient, the former is varied from 1 mm to 5 mm in both measurement and simulation. The results are shown in Table 2. The coupling coefficient increases as board-to-board distance decreases; however, load voltage with the fixed frequency of 110 MHz does not have the same trend and it can be observed that its maximum may be around 0.3 of k. This means that k becomes higher in case of decreased distance and hence, tighter magnetic coupling in WPT. In case of tight magnetic coupling, the minimum resonant peak of input impedance (Z_{11}) split into two sides of axis by the resonant frequency of non-tight magnetic coupling case [7]. In other words, higher k does not always guarantee higher VTR at the same frequency. Therefore, it is very important to find the appropriate coupling coefficient in order to maximize VTR at the specific frequency of the source.

Board-to-Board Distance (mm) |
Coupling Coefficient, k |
Voltage Transfer Ratio |

1 | 0.5 | 0.42 |

2 | 0.32 | 0.49 |

3 | 0.22 | 0.48 |

4 | 0.18 | 0.42 |

5 | 0.13 | 0.34 |

**Table 2: The performance of coil-to-coil**

Electromagnetic Interference Shielding Effect in Wireless Power Transfer Based on Simulation

In the previous section, VTR of WPT was found to be much smaller than that of wired power transfer. Moreover, low mutual and self-inductances and high resistance of the coil on PCB lead to small VTR, when compared to home-appliance wireless charging systems that adopt coils formed with wires of high self-inductance and low resistance. Therefore, once the receiver fails to capture all of the wirelessly transferred power, the non-transferred power might work as EMI to the other adjacent circuit or interconnection such as metal line and bonding wire. In order to suppress EMI in WPT, the shielding materials like ferrite and metal film are generally used as shown in Figure 8 [8]. Also, self- and mutual inductances can be increased by using ferrite. However, these shielding materials could affect the parasitic resistance of the coil, as well as VTR of WPT. In other words, the shielding materials for EMI suppression cause the side effects that can lower VTR.

**Figure 8: Wireless power transfer for board-to-board level interconnection on printed circuit board with shielding material**

In this section, the effects of shielding material in WPT, based on simulation and analysis, are presented.

Equivalent Circuit Model of Spiral Coil with Shielding Material

The new components due to the attached shielding material are added to the equivalent circuit model of spiral coil as shown in Figure 9. The additional self-inductance and the additional parasitic resistance are represented by Lm and Rm, respectively. Also the additional self-inductance makes additional mutual inductance. The additional capacitance, C_{m}, is also negligible as the spiral coil and the shielding material are separated by the thickness of the board, which is large enough for the capacitance to be ignored. In this equivalent circuit model, the values of the additional components are varied depending on the type of the shielding material attached, as well as the distance from the board. These results, with more detail, are arranged in Table 3. In case of ferrite film, its complex permeability (μ = μʹ − jμʹʹ) is 59.7 − j40.4, which has loss tangent of 0.677 at the resonant frequency of 110 MHz. This ferrite film is a commercial film generally adapted to many applications that utilize several megahertz range for RFID. The large loss tangent causes the large additional resistance and the real part of complex permeability increases the self- and mutual inductance [9]. On the other hand, when metal film is attached to the board, the additional self-and mutual inductance have negative values because of eddy current through metal and therefore, the summation of self- and mutual inductance decreases.

**Figure 9: Equivalent circuit model of spiral coil with shielding material**

Shielding Material |
Gap Between board and film (mm) |
Lm (nH) |
Rm (Ω) |
Resonant Frequency (MHz) |

Ferrite | 0.0 | 115.6 | 8.9 | 86.7 |

Ferrite | 0.3 | 83.6 | 6.7 | 92.3 |

Metal (Al) | 0.0 | -133.1 | 1.3 | 130.7 |

Table 3: The additional components due to shielding material

Analysis of Shielding Material Effect in Wireless Power Transfer

VTR of each case from top to bottom in Table 3 is 0.374, 0.383 and 0.005, respectively. Whereas the additional self-and mutual inductance from the ferrite film can improve VTR greatly, the additional resistance degrades it at the same time. Therefore, VTR is increased only a little with the attachment of the shielding material, compared to 0.34, which was the VTR without shielding. In the next case, by attaching the metal film, the negative value of self-and mutual inductance aggravates VTR very much.

As can be seen from the 3D EM simulation result in Figure 10, there appears to be a strong magnetic field distribution between the upper source and lower receiver board, which is shown in red. Magnetic field distribution of the source board without shielding material in Figure 10a tends to spread out much more than the other cases. However, ferrite film of source board in Figure 10c and d effectively shields magnetic field distribution regardless of gap between board and ferrite film. Moreover, the metal film in Figure 10b demonstrates much better shielding effect by reducing self-and mutual inductance due to the eddy current. Therefore, magnetic field distribution of each case is a little different depending on the shielding material.

**Figure 10: Magnetic field distribution of each case using 3D EM simulation**

** **

In addition, it was found that the bigger the gap between the board and ferrite film, the smaller the parasitic resistance, which accordingly results in improved VTR. The parasitic resistance is further reduced when ferrite film with low loss tangent at the resonant frequency is attached to the boards.

It should be noted that ferrite film is a better material considering its shielding effect and VTR. To improve VTR for board-to-board WPT, changing the gap between the board and ferrite film to control the parasitic resistance is more effective.

Conclusion

WPT using magnetic resonance coupling for board-to-board level interconnection is proposed to compare the equivalent circuit model and measurement using impedance curves and VTR. We have modeled the equivalent circuit of the spiral coil using R and L, and have presented the relationship between simulation and measurement in both frequency- and time-domain. Frequency of maximum VTR is predictable from the resonance peak of the input impedance curve (Z_{11}) of WPT. The maximum VTR of board-to-board WPT was achieved to be 0.49, when the distance between the boards was 2 mm, with 0.32 of k. Also, EMI shielding effects in WPT with materials such as ferrite and metal film are analyzed based on simulation. The performance of WPT can be either improved or degraded depending on the type of shielding material and the gap between the film and board. Finally, the shielding effects of each film in WPT were compared by observing magnetic field distribution. Therefore, with further researches to improve VTR and mitigate EMI from magnetic field of WPT, such a system can be widely adapted to applications with board-to-board level interconnection.

© 2013 IEEE. Reprinted, with permission, from the 2013 IEEE International Symposium on Electromagnetic Compatibility proceedings.

**Acknowledgement**

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (No. 2010-0029179) and supported by the Smart IT Convergence System Research Center funded by the Ministry of Education, Science and Technology as Global Frontier Project (STRC-2011-0031863).

References

- H. J. Brockmann and H. Turtiainen, “Charger with inductive power transmission for batteries in a mobile electrical device”, US Patent 6 118 249, 1999.
- A. Kurs, A. Karalis, R. Moffatt, J. D. Joannopoulos, P. Fisher, and M. Soljačić, “Wireless Power Transfer via Strongly Coupled Magnetic Resonances,”
*Science*, vol. 317, no. 5834, pp. 83–86, 2007. - A. Karalis, J. Joannopoulos, and M. Soljačić, “Efficient wireless nonradiative mid-range energy transfer,”
*Annals of Physics*, vol. 323, no. 1, pp. 34–48, 2008. - C. Pacurar, V. Topa, A. Racasan, and C. Munteanu, “Inductance calculation and layout optimization for planar spiral inductors,” 2012 13th International Conference on Optimization of Electrical and Electronic Equipment (OPTIM), pp. 225-232, 24-26 May 2012
- C.P. Yue and S.S. Wong, “Physical modeling of spiral inductors on silicon,”
*IEEE Transactions on Electron Devices*, vol. 47, no. 3, pp. 560-568, Mar 2000 - S. Kong, M. Kim, K. Koo, S. Ahn, B. Bae, and J. Kim, “Analytical expressions for maximum transferred power in wireless power transfer systems,” 2011 IEEE International Symposium on Electromagnetic Compatibility (EMC), pp. 379-383, 14-19 August 2011
- S. Kim, M. Kim, S. Kong, J.J. Kim, and J. Kim, “On-chip magnetic resonant coupling with multi-stacked inductive coils for chip-to-chip wireless power transfer (WPT),” 2012 IEEE International Symposium on Electromagnetic Compatibility (EMC), pp. 34-38, 6-10 August 2012.
- H. Kim, J. Cho, S. Ahn, J. Kim, and J. Kim, “Suppression of leakage magnetic field from a wireless power transfer system using ferrimagnetic material and metallic shielding,” 2012 IEEE International Symposium on Electromagnetic Compatibility (EMC), pp. 640-645, 6-10 August 2012.
- W. G. Hurley and M. C. Duffy, “Calculation of self- and mutual impedances in planar sandwich inductors,”
*IEEE Transactions on Magnetics*, vol. 33, no. 3, pp. 2282-2290, May 1997.

Sukjin Kim, Hongseok Kim, Jonghoon J. Kim, Bumhee Bae, Sunkyu Kong and Joungho Kim are associated with Terahertz Interconnection and Package Laboratory, EE, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Korea. Comments and questions can be directed to teralab@kaist.ac.kr.