Calculating Parasitic Capacitance of Three-PhaseCommon-Mode Chokes

S. Weber1, M. Schinkel1, S. Guttowski1, W. John1, H. Reichl2

1 Fraunhofer IZM, Gustav-Meyer-Allee 25, 13355 Berlin, Germany2 TU Berlin, Forschungsschwerpunkt Technologien der Mikroperipherik,

Gustav-Meyer-Allee 25, 13355 Berlin, Germany

stefan-peter.weber@izm.fraunhofer.de

AbstractIn this paper1 the parasitic behaviour of CM-chokes with three phases is discussed in afrequency range up to 30 MHz. ThereforeCM- and DM-impedances of three exemplars ofeleven choke types are measured and calculated.The DM-inductance is 0.5 to 1% of the CM-inductance. Leakage inductance of one phaseis 3

2LDM . Parasitic winding capacitances are in

the range of 4 to 23 pF. The DM-capacitance isabout 30% of the CM value. Furthermore theinuence of the winding technology is quanti-ed. Calculation of parasitic capacitance is ac-curate if the windings geometry is well dened.

1 IntroductionUnfortunately, fast switching of high current andhigh voltage, the basic principle of every powerelectronic system, has got a high potential in emit-ting electromagnetic interference. The challengeof electromagnetic compatibility is a crucial aspectregarding the reliability of power electronic appli-cations. State-of-the-Art in assuring electromag-netic compatibility in the radio frequency rangeare low-pass-lters with passive components.

~~~

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InputFilter

OutputFilter M~

~

~

Mains Power Converter Load

Fig. 1: Filter Design for a compatible ElectricDrive System

The rapid advances in the semiconductor technol-ogy have enabled an ongoing volume shrinking ofsystems for energy conversion. Consequently, otherdevices like energy storage and lter elements be-come more and more the important factor regard-

1This work is co-sponsored by the European Union

ing the system volume. In order to be able to ful-ll the request for reduced volume, new packagingconcepts are being investigated. Circuit compo-nents are arranged extremely closeby, sometimesin a real three-dimensional structure yet leavingthe conventional PCB technology. The proximityof components can cause signicant eld couplingproblems. In the past years, the systematic inves-tigation of electromagnetic coupling eects causedby high density assemblies in power electronic sys-tems has become another key aspect. [3]The common way of assuring EMC according toCISPR 16 is, to determine lter components andtopology for the necessary insertion loss at the low-est frequency, for example 150 kHz. After pro-totyping and measurement of the lters perfor-mance, a working solution for the whole frequencyrange up to 30 MHz is found by an iterative trialand error process. [1]A more ecient design process would take the par-asitic behaviour of the components into account, ifthose were known [4]. A lot of work was done tocalculate parasitics of EMI-lters capacitors [3, 4]and inductances [6, 7]. The rst calculations onparasitics can be found in papers from the earlyradio days in the 1930s [14]. Then electronic com-ponents were as big as power components are to-day.

2 Ferromagnetic Materials forCM-Chokes

Toroid cores are used to design chokes because theyare made of one piece. Therefore they are muchcheaper and provide a higher relative permeabilitythan other core shapes. As the number of turnsis small, the disadvantage of higher winding costsis not fatal and toroids are nearly always used forhigh power common-mode chokes.In the frequency range above 10 kHz ferromag-

Fig. 2: A 2.2mH choke with massive wire for 10A, a 2.4mH with Litzwire for 18A and a multi-layered choke with 0.85mH for 25A

Ferrites Iron Nanocristal-(Ni-Zn, Mn-Zn) Powder line Iron

Permeability + - ++Saturation ++ +Conductivity + + +Price ++ +

Tab. 1: Comparison of ferromagnetic materialsfor high frequency applications

netic materials with reduced conductivity pro-vide high permeability up to very high frequen-cies. The main types of materials, nickel-zinc andmanganese-zinc ferrites, iron-powder-cores andnanocristalline-iron-cores with resistivities higherseven orders of magnitude than that of iron, arecompared in Table 1. Although nanocristalline-iron-cores have the best performance they are veryseldom used because of their high price. Ap-plications with very high saturation currents areequipped with iron powder cores but the main ma-terial for common-mode chokes are the cheap fer-rites.

3 The Current CompensationPrinciple in Terms of CM-and DM-Impedance

The CM-choke is a transformer which provides ahigh inductance to CM signals and a very low in-ductance to DM signals. This function is calledcurrent compensation because the high power DMcurrent does not saturate the core.The CM impedance of a three phase CM choke isthe impedance of its three coils connected in par-allel. While the mutual magnetic coupling adds tothe impedance for CM signals, the magnetic ux ofDM signals cancel each other out. Only the leakage

Fig. 3: CM- and DM-impedance of three phaseCM-chokes.

inductance is magnetized by DM currents.

Llk = LMLCM = L 23 Llk LLDM = 1.5Llk

with LDM = 1% LCM

An empirically approved approximation for LDMis 1% of the CM-inductance. The 1% approxima-tion is a worst case value in terms of core satu-ration. As the power carrying nominal current isa DM signal the leakage inductance is an impor-tant parameter and may not be too big to preventcore saturation. On the other hand it is a use-ful parasitic element to attenuate DM signals athigher frequencies. For a good lter design theleakage inductance is optimized so it is as big aspossible, but small enough to prevent core satura-tion [6]. For example, if leakage inductance can behigher, one can use a core with lower permeability,with more windings needed there is more leakageinductance. Nave developed a calculation methodfor leakage inductance of two phase chokes whichtakes the geometry into account.For this study CM- and DM-impedances of elevenchoke types are measured. Figure 4 shows mea-

Fig. 4: Measurement of CM- and DM-impedance.

Fig. 5: DM-inductance as a percentage of theCM-inductance verifying the 1%-rule.

surement results. Parameters of equivalent cir-cuits are determined at certain frequencies. CM-and DM-inductance are determined at 10kHz.The CM-capacitance is determined where theimpedance is clearly capacitive with a phase of mi-nus 90. The DM-capacitance is determined at theresonance frequency in the range of MHz.Figure 5 shows the measured DM-inductances as apercentage of the rated CM-inductance of all choketypes. The DM-inductance follows no trend ac-cording to nominal current or absolute value of thenominal inductance but the measured values con-

Fig. 6: Parasitics of single phase ferrite chokes.

Fig. 7: Parasitics of three phase ferrite chokes.

rm the 1%-rule very well.

4 Parasitic Capacitances

The high frequency behaviour of inductors is de-scribed by the equivalent circuit shown in Figure 6.Besides the leakage inductance Llk, parasitics ofchokes are resistors accounting for copper and mag-netizing loss and the winding capacitance Cw.Presupposed the three phase choke with three coilson the same core is just a combination of threesingle phase chokes, the equivalent circuit of a CM-choke including parasitics looks like Figure 7.How do parasitics aect CM- and DM-impedance?With the impedance denition in Figure 3 theequivalent circuits in Figure 8 provide a CM-capacitance of three times the winding capaci-tance. The DM-capacitance is supposed to betwo thirds of the winding capacitance. Thereforethe ratio of DM- to CM-capacitance is 29 or 22%.

Figure 9 shows the measured values of elevenchoke types. DM values range from 4 to 19pF.Regarding the corresponding CM values from 13up to 68pF the measured ratio is higher than theexpected 22% due to additional parasitic capaci-tances between the three phases of the CM-choke.Measured ratios of parasitic capacitances of choketypes with nominal currents from 10 to 35 Ampre

Fig. 8: CM- and DM-impedance of three phaseCM-chokes including parasitics.

Fig. 9: Measured parasitic capacitances ofeleven choke types with nominal currentsfrom 10 to 35 Ampre

Fig. 10: Measured ratios of parasitics ofeleven choke types with nominal currentsfrom 10 to 35 Ampre

range from 23 up to 45% with a mean value of30%. Hence the equivalent circuit in Figure 7 witha single lumped parameter for each coil is only anapproximate physical model of a three phase choke.

5 Variation of Samples Pa-rameters

Variation of samples parameters measured in thiswork is up to 25% with both, inductive and ca-pacitive parameters due to tolerances of the corematerial on one hand and due to the variationof the assembly of samples windings on the otherhand. Reproducable machine wound samples donthave any measureable variation in parasitic capac-itance. The parasitic capacitances variation ofhand wound power components with few but largewindings can be very high.

6 Calculation of Winding Ca-pacitance

Single-layered cylindrical coils without any corehave a winding capacitance depending only on theradius R of the cylinder [14].

C = 48R pF (1)

Equation 1 shows, the winding capacitance of sin-gle layered coils in air is very small. The diameterof the coil had to be more than 40mm for C tobecome more than 1pF. The ferrite core acts asa perfect conducting electrode though the conduc-tivity of ferrite is much smaller than that of cop-per [8]. Thus, capacitive coupling to the core raisesthe winding capacitance of single layer coils signif-icantly. The distributed capacitance of a single-layered winding is calculated via the electrical en-ergy We = 12 C U

2. As the part of the energy inthe space between the windings is negligible theresulting winding capacitance C is one third of thecapacitance between the winding and the core [5].With cylindrical windings the surface of a cylinderis used to calculate the equivalent parallel platecapacitor [11]. This method is adapted to toroidwindings with toroid surfaces.

Cw =Ck3

with Ck = r 0area

distance(2)

Where area is the part of the toroid surface coveredby the winding. r depends on insulation materialand air enclosures. The main parameter to deter-mine the capacitance of single layer CM-chokes is

Fig. 11: Calculating the eective distance to the core and between two layers.

Fig. 12: Winding schematics for two-layer windings on toroids. The ongoing wound second layeron the left and the equally directed in the middle. The banked winding on the right has the lowestcapacitance

the equivalent distance between windings and thecore.The eective distance for the calculation of the ca-pacitance between layer and core is calculated eas-ily if the assembly is well dened. Referring to [14]with the identiers of Figure 11 the equivalent dis-tance becomes:

distance = i +12

(d0 1.15d + 0.26c) (3)

The distance i between windings and core maybe dicult to determine especially of cores withrectangular cross-section. The insulation diameterd0 equals approximately d with varnished wires.The distance c between windings is not constantalong the windings. Inside the core c usually equalsd0. Its variation depends on the shape of the coreand thus, there is to be determined the mean value.Multilayer windings capacitance is calculated fromthe layer-to-layer capacitances Cl. The global max-imum of parasitic capacitance is with the two-layerwinding because more layer-to-layer capacitancesare connected in series. Regarding a two-layerwinding with the second layer wound in the samedirection than the rst one, its capacitance be-comes:

Cequally directed =Ck12

+Cl4

(4)

Only the twelvth part of the capacitance betweenthe rst layer and the core adds to the two-layer

windings capacitance. The layer-to-layer capaci-tance is dominant when Ck is not huge. There isa big inuence of winding technology on Cl. Withthe second layer wound inversely directed Cl adds43 times more to the overall capacitance:

Cinverse =Ck12

+Cl3

(5)

Cl is calculated with the toroid surface betweenthe layers and the equivalent distance according toFigure 11.

7 Minimization of MultilayerWindings Capacitance

Generally the capacitance increases linearly withthe dimensions of the regarded assembly. Never-theless the parasitic capacitances does not increaselinearly with the nominal current respectively thewire diameter because the choke types are also dif-ferent in terms of core shape, number of turns andtype of wire. As it was shown all these parametersdo have an inuence on the parasitic capacitance.Hence it is very dicult to calculate in advance ifthe geometry is not well dened.The capacitance of single layered windings is smallcompared to multi-layer windings capacitances. Ifthese are not to avoid careful design of the windingcan reduce parasitic capacitance signicantly. The

Fig. 13: Parasitic capacitance of windings on aferrite core of approximately 32 turns.

maximum capacitance has the two layered windingwith the beginning and the end of the winding inclose proximity [7]. But even if two layers are nec-essary the parasitic capacitance can be reduced byclever winding techniques shown in Figure 12.Zuhrt calculates from energy considerations [14]that the capacitance of the inverse two-layer wind-ing is 133% of the winding wound in the same direc-tion like the rst layer. Figure 13 shows measure-ments with dierent wires on the same core andconrms both, the winding schematic reduces theparasitic capacitance by 33% and it increases lin-early with the wire dimensions. Compared to thesingle-layer capacitance of a winding with the samenumber of turns, the two-layer capacitance maybecome very high. Therefore it is worthwhile touse low-capacitive winding techniques like bankedwinding for multi-layer windings. The measuredvalues in Figure 13 show capacitances of bankedwindings in the range of single-layer capacitances.For high-end power chokes banked winding is thewinding technology to choose.

8 Conclusion

In this paper the parasitic behaviour of CM-chokes with three phases is discussed in a fre-quency range up to 30 MHz. Therefore CM- andDM-impedances of three exemplars of eleven choketypes are measured. The DM-inductance is 0.5to 1% of the CM-inductance. Leakage inductanceof one phase is 32 LDM . Parasitic winding capac-itances are in the range of 4 to 23 pF. The DM-capacitance is about 30% of the CM value.It is possible to calculate the parasitic capaci-tance of cylindrical chokes if the assembly is welldened. Winding capacitances of CM-chokes ontoroid cores are calculated analog to calculations ofcylindrical chokes. Because of the great inuenceof parameters like distance to the core and relative

position between windings, which is not constantalong each winding, the calculations in advance arenot exact. Nevertheless a good benet is gainedwhen taking into account realistic values. Further-more empirical found values for winding capaci-tances on toroids support EMI-lters design dueto the linear relationship between capacitance anddimensions. Knowing parasitics enables new op-timization approaches in designing EMI of powerelectronic systems.

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