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Air-gap Effects in Inductive Energy TransferK.D. Papastergiou and D.E. Macpherson†

Department of Electrical and Electronic Engineering, University of Nottingham, United Kingdom† School of Engineering and Electronics, University of Edinburgh, United Kingdom

Abstract— A transformer with a separation between theprimary and secondary windings can be used to transferpower to artificial organs, pacemakers or robot jointswithout electrical contacts or wires. This paper examines theimpact of the gap fringing field in the operation of the dc-dcconverter. As has been implied in previous work the powerlosses and EMI generated by the fringing field can have asignificant impact on the converter operation. This paperpresents the mechanism behind the winding power lossesusing FEA tools and actual measurements. Furthermore theeffect of the field vector in electromagnetic emissions of theconverter is investigated. A reduction of EMI by means ofadjusting the air-gap length is demonstrated and the benefitis quantified using field measurements.

I. INTRODUCTION

The possibility to transfer power to a rotating frame us-ing a high-frequency magnetic link has been demonstrated[1], [2] using a soft-switching dc/dc full bridge converterwith phase-shift modulation [3]. The magnetic component(rotating transformer) replaces the conventional slip ringsand transfers the energy magnetically from the stationaryto the rotating winding. A high frequency switching wave-form results in a smaller magnetic component. The squarewaveforms result in better utilisation of the magneticcomponents and semiconductors but have the drawbackof causing higher switching losses and AC power lossesin the transformer magnetic core and windings. A quasi-resonant topology is used to reduce the switching lossesand the harmonic content of the transformer waveforms.As has been shown in previous work the main challenge ina system with inductive coupling is to limit the switchingand conduction power losses and to achieve a satisfactoryvoltage gain of the power converter.

The paper focuses on the magnetic component andinvestigates the effects that are related with the trans-former air gap. In applications where a contact-less linkis needed, such as the transcutaneous medical devices [4],[5] and the inductive charging of batteries [6], the air gaplength is crucial to the magnetic components’ operation asgenerally a longer air gap results in more energy storage(leakage and magnetising energy) than a short or no air-gap.

Regardless of the converter topology and the rectifiersused with the rotating transformer, energy is stored in theform of a magnetic field, in the high reluctance areas suchas the space between the magnetic core parts. The ferriteitself being a high permeability material stores negligibleamounts of energy. The energy storage in the air-gap isresponsible for some of the proximity losses in the trans-former windings. The flux lines tend to interact with thecurrent in the conductors hence changing the current flow

H+J

top view

Main windingcurrent

Induced eddycurrent

Fringing field

-J

I

Fig. 1. Effect of the fringing field on the conductor current density.The affected turns are magnified to illustrate the restriction of the currentpath.

and affecting the windings AC conduction losses. Thispaper looks into the mechanism of the proximity effectand eddy currents and investigates methods to eliminatethe associated power losses. Furthermore the EM radiationdue to the air-gap is measured and its dependence onthe clearance is established mathematically. Some basicdesign principles are given to ease the design of such aninductive interface.

II. AIR-GAP FLUX EFFECT

The stray flux lines that cross the winding conductorsgenerate eddy currents that oppose the useful conductorcurrent. As the induced current opposes and cancels theuseful current in certain parts of the conductor cross-section (Fig.1), the effective area of the conductor is re-duced and hence the effective resistance of the conductoris increased.

A. Eddy Currents

Figure 2 illustrates the finite element analysis results ofa pot core transformer with 1mm air-gap and a simplifiedwinding structure comprising of 8 secondary and 17primary turns in a coaxial arrangement. The primarywinding carries a 6A current (including a magnetisingcurrent of 2A) and the secondary 8.5A with a 180 degreesphase-shift between the primary and secondary currents.The current waveforms are 100kHz sinusoidal.

As can be seen in Fig. 2 the high flux density near theprimary windings’ middle-turns alters the current path inthe conductor. The left-hand shape of Fig. 2 is a cross-section of the rotating with the flux density as given bythe FEA model. The right hand side is a magnificationof the area near the air-gap. The current density on thesurface of the winding turns that are near the air gap isaround 8×108A/m2 or 8-10 times more than the currentdensity around the surface of the other turns (note that the

978-1-4244-1668-4/08/$25.00 ©2008 IEEE

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Fig. 2. Illustration of the effect of the fringing field around the air-gap (a) the flux density and (b) the current density in the windings

Fig. 3. The current density vector in the turns of interest. Red colourcorresponds to a higher current density and the triangular shapes showthe direction of the current

specified average current density is only 1.6×108 A/m2).The restriction of the current paths in the transformerconductors is also a result of the proximity effect (amongneighboring turns) but as this has been accounted for inthe methodology presented in [1] and [2] it is not studiedhere.

Figure 3 shows a magnified cross-section of the con-ductors that are near the air gap. The direction of theuseful current is in to the page; however, J is oppositeat the conductor areas near the air gap (see currentdensity vectors illustration). This shows that not only theuseful winding current is cancelled in some areas of the

conductor cross-section but there is also a reverse currentflow that contributes to the I2R losses.

B. Power Losses

A 1kW phase-shifted full bridge (PSFB) dc/dc con-verter (fully specified [1]) was used to conduct the fol-lowing experiments. A rotating transformer build arounda P56/66 ferroxcube ferrite core was used to deliver powerfrom the power switches to the rectifier using squarepulse of 100kHz. This converter performs quasi-resonanttransitions of the power semiconductors. The transitionsthat result in a transformer current built up are calledpassive-to-active (PA) transitions. The transitions that leadto a period of freewheeling current in the transformerwindings are called active-to-passive (AP) transitions.The phase-shifted full bridge relies on the existence ofa circulating primary current to succeed in resonant PAand AP transitions. Following a period of inactivity,lossless PA transitions are more hard to achieve than APtransitions.

The generated eddy currents observed in the FEA resultin excessive heating of the winding turns that are aroundthe magnetic core clearance. The fringing field affectsmainly the coaxial winding arrangement dropping theoverall circuit efficiency by 1-2% and making it impos-sible for the transformer to deliver the required outputpower because of the high temperature exhibited locally.The middle turns exhibited temperatures of up to 40oCabove the average winding temperature. This observationresulted in the split coaxial winding arrangement thatappears in Fig. 4. The inner winding is split in twosections that are placed away from the air gap to avoidthe interaction with the fringing magnetic field.

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Fig. 4. The secondary winding has been split in two parts and takenaway from the fringing field area. The split winding arrangement resultsin reduction of the winding power losses.

The above problem of the increased effective windingresistance not only increases the conduction power lossesbut also lowers the voltage gain due to the voltage dropsacross the winding.

Figure 5 demonstrates the temperature variations onthe key components of the PSFB converter at differentoutput power levels. The primary winding temperature ismeasured next to the air-gap where the fringing field hasthe maximum effect. The term ”optimised” refers to thesplit winding arrangement of Fig. 4 whereas the ”non-optimised” refers to the coaxial winding arrangementhaving some turns in the fringing magnetic field area.

As can be seen in Fig. 5(a) and (b) the difference inwinding temperatures between the optimised and non-optimised windings is negligible at low output powerlevels. However the graphs of Fig. 5(c) and (d) thatcorrespond to 500W and 700W of output power respec-tively show increased temperatures of the primary andsecondary windings of the non-optimised transformer. Itis interesting to note that despite the inner (secondary)winding being primarily affected by the fringing field,the outer winding also exhibits high temperature. Thishappens for two reasons: a) there is still a fringing field(although of lower magnitude) of the outer transformer airgap (see Fig. 4) that generates eddy currents and b) thevoltage drop due to the eddy currents in the secondarywinding forces the control loop to increase the dutycycle in order to deliver the required output voltage andhence more current (including more magnetising current)is flowing in the primary winding.

The voltage drop across the non-optimised (non-split)windings also explains the higher MOSFET, rectifier andmagnetic core losses.

III. ELECTROMAGNETIC EMISSION

As seen in the previous section, the air-gap between theprimary and secondary ferrite cores results in a fringingmagnetic field. The varying magnetic field creates avariable electric field and the result is an electromagneticemission around the air-gap. This can generate conductednoise that propagates through to other components of thesame system or under conditions it can also be radiated.Restriction of the electromagnetic emissions is normallyrequired for both practical and regulation compliance

reasons. The aim of the the tests performed here is toestablish whether the presence of the air-gap generatesadditional EM noise and how this is connected with itslength. This study leads to a set of rules that can beused by designers to improve the EM profile of a systemincorporating a rotating transformer.

Two tests were performed using the near field probe, anamplifier and a spectrum analyser. Initially, the radiationaround the transformer air-gap was measured. The gaplength was varied to obtain a relationship between airgap length and EM radiation. The second test involveda measurement of the magnetic field around the powersemiconductors to identify the effect of the air-gap lengthin soft-switching of the converter and the related EMemissions.

Figures 6(a),(b) and (c) illustrate the rotating trans-former primary current (top waveform - channel 1), themeasured magnetic field (middle waveform - channel 2)and the respective fast fourier transformation (channel 3).As the air-gap length decreases from 1mm (fig. 6(a)) to0mm (fig. 6(c)) the primary current decreases and thedetected magnetic field also decreases in magnitude. Fora 1mm air-gap the induced waveform has a peak value of215mV and for a 0.5mm clearance this reduces to 106mVindicating a linear relationship between the air-gap lengthand the induced voltage.

As can be seen in Fig. 6 the near field probe output ispractically the derivative of the magnetising current. Thereason is that the magnetic field energy stored in the air-gap represents the magnetising energy of the transformer.In an ideal transformer the primary ampere-turns equalthe secondary ampere-turns and therefore the primaryand secondary magnetomotive forces (MMF) cancel eachother out. In a non-ideal transformer energy is beingstored in the magnetic path (and mainly in the highreluctance paths such as the air-gap).

The voltage Vf induced on the close-field probe is givenby,

Vf = Ntpdφm

dt(1)

where Ntp is the number of turns in the probe sensorand φm is the magnetic flux that induces the voltage.The stray magnetic flux is generated by the primarymagnetising current1 hence,

φm = NpriImμ0Ag

lg(2)

where Ag , lg are the air-gap area and length respec-tively and μ0 is the magnetic permeability of the air.

By combining Eq. 1 and 2 the induced voltage isassociated with the magnetising current derivative,

Vf =NtpNpriμ0Ag

lg

dimdt

(3)

1In an ideal transformer the primary generated flux is completelycancelled by the secondary counter flux, hence no energy is storedanywhere.

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Fig. 5. Measured MOSTFET (TMOS), magnetic core (Tcore), rectifier (Trect), primary (Tpri) and secondary (Tsec) winding temperatures at a)10Wb)300W c)500W and d) 700W of output power

1. 10A 2. 200mV 100us/div3.10db offset:-69db 5MHz/div

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Fig. 6. The primary current Ipri, output of the near-field probe Vfield and the respective frequency spectrum of the electromagnetic radiationaround a (a) 1mm, (b) 0.5mm, (c) 0mm air-gap. The higher EMI in the 100Khz to 5MHz area in (c) indicates the lack of soft-switching. The PSFBprototype delivers 500W of output power.

The first section in equation 3 represents a high induc-tance which acts as a low pass filter thus rejecting the highfrequency currents injected by the switching action. It canbe seen that dividing the air-gap length by two results in(approximately) half the magnetising inductance and thisin turn results in half the di/dt through it. Consequently,the voltage induced on the near-field probe is half of theone that would be induced around an 1mm air-gap.

The second test involves the measurement of theswitching-action related emissions. Hard switching is aprincipal reason for high frequency electromagnetic ra-diation. The sharp edges of the currents and voltagesturn printed circuit board tracks, components and everyconductor of appropriate dimensions into antennas. So,the aim of this series of experiments is to examine theeffect of the air-gap in soft-switching and consequentlyto the EM emissions of the phase-shifted full bridge

converter.

Figures 7 and 8 illustrate the measured magnetic fieldand the associated spectral analysis when the converterproduces a 100W output power with an 1mm gappedtransformer and a non-gapped transformer respectively.Due to the nature of the dc/dc converter the increasedprimary current of the rotating transformer assists the soft-switching of the power semiconductors. Figure 7 impliessuccessful soft-switching operation (the transformer pri-mary current does not cross the zero axis, in this casethe -39dbμV imaginary axis, during switch transitions)unlike the hard switching observed at point A (the passiveto active transition) of fig. 8 of the same converter witha conventional transformer. The above observations arereflected in the measured magnetic field as fig. 8 exhibitshigher spikes during switch transitions and particularlyduring the passive to active transition when less inductive

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Fig. 7. Primary current, close-field probe voltage and fft analysis (1mmair-gap and 10% loading). PA transitions marked A and AP transitionsmarked B.

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Fig. 8. Primary current, close-field probe voltage and fft analysis (noair-gap and 10% loading). PA transitions marked A and AP transitionsmarked B.

energy is available.The effect of the air-gap on soft-switching at higher

output power (500W) can be seen in figures 9 and10. Figure 9 illustrates an increased primary currentincluding a magnetising component due to the 1mm air-gap. Thanks to the magnetising current that accountsfor almost one fifth of the total current, the resonantswitch transitions are smoother and the associated close-field voltage is 30% lower (approximately 200mV versus300mV) than the respective emissions of the conventionalcircuit. Another resonant frequency (9MHz) that is seenas a low amplitude oscillation (ringing) immediately afterthe spike appears in the rotating transformer case andthis is related to some additional resonance between theMOSFET parasitic inductance and the magnetising induc-tance of the rotating transformer. The conventional phase-shifted bridge results show a slightly higher magnetic fieldspectral content up to the frequency of 30MHz.

An empirical observation is that in a quasi-resonanttopology like the one used in the tests the transformer air-gap that is present in an inductive interface such as therotating transformer can affect the emitted EM spectrum.There is previous proof that presence of the magnetisingcurrent due to the air-gap can secure the soft-switchingoperation and thus assist in reducing EMI. The above testssupport this claim and also demonstrate that the presenceof the air-gap despite its negative impact in conductionlosses does not automatically mean a negative effect inelectromagnetic emissions. It can in fact improve the EM

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Fig. 9. Primary current, close-field probe voltage and fft analysis (1mmair-gap and 50% loading). PA transitions marked A and AP transitionsmarked B.

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Fig. 10. Primary current, close-field probe voltage and fft analysis (noair-gap and 50% loading). PA transitions marked A and AP transitionsmarked B.

profile of the converter under circumstances (such as atlow power levels when the existing primary current is notsufficient to secure soft-switching).

The noise measurement results from the two circuitsare summarised in Table I

As a conclusion from this comparison:• The low frequency gap radiation is proportional to

the air-gap length (as long as the air-gap area remainsunchanged).

• In a soft-switching converter the air-gap related EMradiation is lower than in a non-soft-switching con-verter.

TABLE I

MAGNETIC FIELD MEASURED ON PCB TRACK OF THE TRANSFORMER

PRIMARY WINDING OF THE PSFB WITH SOFT AND HARD SWITCHING

(OUTPUT POWER 100W)

Frequency Soft-switched PSFB Hard-switched PSFB

(MHz) H-field (dBuA/m) H-field (dBuA/m)

0.1 150.0 138.0

5.0 110.0 115.0

7.5 96.8 107.8

10.0 105.0 103.0

15.0 80.5 84.5

20.0 75.0 94.0

25.0 75.0 90.0

30.0 67.8 73.8

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• The spectral improvement due to the air-gap of therotating transformer is more considerable at lowpower levels when the converter otherwise fails tosoft-switch.

• Attention is required in placing the windings in thecore window area as the air-gap fringing field isresponsible for the generation of eddy currents. Thesplit winding arrangement could reduce these powerlosses.

• Attention needs to be given to the design of the trans-former mechanical housing to avoid power losses dueto eddy currents. EM shields may be needed aroundthe gap.

IV. CONCLUSION

By looking into the magnetic flux distribution of thegapped transformer, a better understanding of transformerwinding power losses is gained. A modified split windingarrangement has been found to reduce the conductionpower losses and the temperature measurements supportthis claim. The presence of an air-gap in systems withcontact-less energy transfer results in low frequency EMemissions that are directly proportional to the air-gaplength. Nevertheless, the energy storage is shown to havea positive effect on reducing the high frequency emittednoise by means of improving the soft-switching capabilityof the converter at low operating power levels. The impactof the air-gap in systems with inductive energy transfershould be a critical element of the design process.

REFERENCES

[1] K. Papastergiou and D. Macpherson, “An airborne radar power sup-ply with contactless transfer of energy;part i: Rotating transformer,”Industrial Electronics, IEEE Transactions on, vol. 54, no. 5, pp.2874–2884, 2007.

[2] ——, “An airborne radar power supply with contactless transferof energy;part ii: Converter design,” Industrial Electronics, IEEETransactions on, vol. 54, no. 5, pp. 2885–2893, 2007.

[3] R. A. Fisher, K. D. T. Ngo, and M. H. Kuo, “A 500khz, 250w dc-dc converter with multiple outputs controlled by phase-shifted pwmand magnetic amplifiers,” in High Frequency Power ConversionConference, 1988, pp. p.100–110.

[4] M. Theodoridis and S. Mollov, “Distant energy transfer for artificialhuman implants,” Biomedical Engineering, IEEE Transactions on,vol. 52, no. 11, pp. 1931–1938, 2005.

[5] H. Matsuki, Y. Yamakata, N. Chubachi, S.-I. Nitta, andH. Hashimoto, “Transcutaneous dc-dc converter for totally im-plantable artificial heart using synchronous rectifier,” Magnetics,IEEE Transactions on, vol. 32, no. 5, pp. 5118–5120, 1996.

[6] Y. Jang and M. Jovanovic, “A contactless electrical energy trans-mission system for portable-telephone battery chargers,” IndustrialElectronics, IEEE Transactions on, vol. 50, no. 3, pp. 520–527,2003.