Comparison of losses in litz wires and round wires

In order to minimize converter losses not only semicon-ductor parts must improve. A key component of converters

– no matter if AC/AC, AC/DC, DC/DC or DC/AC – is the ma-gnetic energy storage in form of inductors or transformers.A research project analyzes the electrical characteristics of

wires and litz wires in order to reduce the winding losses.

nductor and transformer los-ses in power electronic appli-cations can be minimized by

ding. The latter indeed mostlyconsists of copper, but is realizedin a large variety of cross sec-tions, reaching from thin foils, rec-tangular cross sections, solid round

wires to the different kinds of litzwires. How winding losses can bereduced using either round wireor litz wire is investigated in theresearch project „Characteri-zation and Optimization of LitzWire Windings in Chokes andTransformers for Higher EnergyEfficiency“ (see box next page),which is funded by the GermanFederal Ministry of Economicsand Technology.

Losses in round wires

The winding losses in round wirescan be classified into:

frequency independent ohmic(rms) losses,frequency dependent skinlosses,proximity losses dependingon an external magnetic field

...keeping pulses flowing

1 www.pack-feindraehte.de

Optimized Winding =Optimum in Power Efficiency

From Prof. Dr.-Ing. M. Albach, J. Patz, Dr.-Ing. H. Roßmanith, D. Exner, Dr.-Ing. A. StadlerTranslated by Marc Döbrönti and Dr.-Ing. Hans Roßmanith

The original text was released in the German magazine Electronik Power, April 2010

Ioptimizing the cores - size, form,material - and optimizing the win-

1752ohneCD.pmd 09.06.2010, 14:341

Dielectric losses in the enamelcoating play only a minor role inpractice. They will be neglectedin the following considerations.

Winding losses depend on thewinding current, more specific onits rms value, on harmonics in-cluded in time dependent wave-forms and on the design of thewinding layout. Proximity lossesadditionally depend on the coregeometry and the number, geo-metry and position of optional airgaps. The most simple case willbe a straight round wire withradius a, according to fig. 1a, andcross section A = πa2, which car-ries the dc current I. With its den-sity of J0 = I/A the current isdistributed homogenously overthe wire cross section. The lossescan be calculated by P = I2R0,where R0 = l /κA is the dc resis-tance of the wire of length l andconductivity κ.

When a time dependent current,e.g. i(t) = i sin(ωt) with ampli-tude i and frequency f or rather

the angular frequency ω = 2 π f,flows through the wire, then themagnetic field inside the wirecaused by this current will be timedependent as well. According toFaraday’s law, additional eddycurrents are generated inside thewire changing the current dis-tribution. The so called skin effectdescribes the current displace-ment, concentrating in areaswhere for dc excitation the ma-gnetic field strength was high. In-side a round wire, the dc magne-tic field strength increases linearlywith the distance to the wire axis.On the wire surface it reaches itsmaximum and outside it decrea-ses with the inverse of the dis-tance to the wire axis (fig. 2).

In case of time dependent cur-rents, the current density near theaxis decreases with increasingfrequency, so that the currentdensity is concentrated more andmore to the surface of the wire.This effect can be describedmathematically in a very simpleway by the so called skin depth

Search forthe optimal winding

In the scope of the German Federal Government’s5th Energy Research Program „Innovation andNew Energy Technologies“, the Rudolf Pack GmbH& Co. KG (www.pack-feindraehte.de), the Spe-zial-Transformatoren Stockach GmbH & Co. KG(www.sts-trafo.de) and the Chair of Electromagne-tic Fields of the University Erlangen-Nuremberg(www.emf.eei.uni-erlangen.de) joined forces for aresearch project, with the aim to optimize the windingof inductive components of electronic converters.

The project „Characterization and Optimization ofLitz Wire Windings in Chokes and Transformers forHigher Energy Efficiency“ started on October 1st,2008, and is scheduled for 3 years. Its intention is tooptimize the layout of litz wires by an extendeddescription of the electrical properties of rf litz wirecables. A better insight into these properties shalllead to the development of new designs of litz wirecables, which reduce the winding losses of inductivecomponents in switched mode power supplies.

In addition, with optimized windings, the partnershope to achieve a better utilization of material andlower product costs. The joint project – with fundingmanaged by Projektträger Jülich (www.fz-juelich.de/ptj) – is attributed to the focus „Energy Efficiency inIndustry“ and is funded by the German FederalMinistry of Economics and Technology (BMWi,www.bmwi.de) on decision of the German Bundes-tag, funding identification: 0327494 A,B,C.

a) RUPOL® b) RUPALIT® Classic c) RUPALIT® Classicd) RUPALIT® Profil e) RUPALIT® Planar

Figure 1: Enameled copper wire (a) and different litzwire from PACK Feindraehte: classical round litz wire„Rupalit Classic“ without (b) and with wrapping (c), withsquare cross section to improve the copper fillingfactor „Rupalit Profil“ (d) and with rectangular crosssection as alternative to foils „Rupalit Planar“ (e)

Figure 2: The magneticfield strength H – for a in-finitely long round wire –increases linearly insidethe wire and decreasesby 1/r outside the wire

δ = 1/(πfκμ0)1/2. With

the permeabilityof copper, which isalso the permea-bility of free spaceμ0 = 4π 10-7Vs/Am,the skin depth willbe about 1cm at50Hz and onlyabout 0.21mm at100kHz. Fig. 3 dis-plays the absolutevalue of the currentdensity over the wi-re cross section fordistance values0 ≤ r ≤ a from theaxis, standardizedto the dc value ata/δ = 0. This effectbecomes more andmore important withincreasing frequen-cy or more specificwith increasing ratioof a/δ, thus increa-sing the losses athigher frequencies.

The losses can be calculated byeq. 1, where irms = i / 2½ :

with

and

Usually the frequency dependentresistance R is expressed by theproduct of the dc resistance R0

and the skin factor Fs. The lossesfrom eq. 1 may be separated intorms and skin losses in a straight-forward way

2 www.pack-feindraehte.de

1752ohneCD.pmd 09.06.2010, 14:342

If the ratio a/δ is well known, theskin factor is determined bythe modified Bessel functions I0

and I1. Its separation into thefrequency independent part Prms

and the additional skin lossesPskin can directly be seen in fig. 4.For a few selected round wires of1m length the resistance R isdisplayed in fig. 5 as a functionof frequency. At low frequenciesthe resistances are inversely pro-portional to the cross sectionareas, i.e. to 1/a2. When the skineffect becomes more significant,the current is distributed just overa small rim of the cross section.Thus the resistance will changewith the circumference of thewire, which means R is then pro-

considerably to the total windinglosses. This external magneticfield depends on:

the position and number ofneighboring strandsthe current flowing throughthese wires, which means,does the wire belong to theprimary or one of the secon-dary sidesthe core geometry and the airgaps

For the special case of a roundwire in a homogenous, time har-monic magnetic field perpen-dicular to the wire axis, thecurrent density of the inducededdy currents is shown in fig. 6,for a ratio a/δ = 5. These eddycurrents are diametrically orien-tated at the upper and lower rimof the conductor. Although the

Figure 3: For dc (a/δδδδδ = 0) the current is distributed evenlyover the cross section. The relative current density –normalized to the current density at dc – is constant fromthe wire axis to the rim. With increasing frequency(a/δδδδδ = 2.5 and 5) the current density decreases at the wireaxis and increases greatly at the rim.

Figure 4: The skin factor Fs is frequency dependent.Starting from the dc value 1 (Prms), the skin losses Pskin –after a transitional phase – increase linearly withthe ratio a/δδδδδ .

Figure 5: The skin effect is responsible for a frequencydependent increase of resistance of the wire, which variesfor different wire diameters d (d = 2a). Thinner wires cor-respond with higher frequencies, where the skin effectstarts increasing the resistance. With higher frequency theresistance changes its dependence from the wire diameter:a quadratic dependency on the radius will change to alinear dependency.

Figure 6: External magnetic fields affect the current den-sity and the field distribution in the wire via the proximityeffect. In this example, the magnetic field weakens at theleft and right of the wire, but gets stronger at the top andbottom, in comparison to the excitation field.

portional to 1/a. If the currentwaveform and the temperaturedependent conductivity κ(T) areknown, the rms and skin los-ses for any round wire with thediameter of 2a can be calculatedexactly.

The calculation of the previouslymentioned proximity losses is abit more complex. The proximityeffect appears if a conductor isexposed to an external timedependent magnetic field, whichmay be generated e.g. byneighboring wires. It does notmatter whether the wire carriesany current or not. Proximityeffect induces likewise eddycurrents, which may contribute

3 www.pack-feindraehte.de

1752ohneCD.pmd 09.06.2010, 14:343

integral of the eddy currents overthe complete cross section iszero, nevertheless extremely highlosses can be generated at bothrims of the wire. The eddy cur-rents themselves generate a ma-gnetic field – similar to the fieldof a line dipole – which adds tothe original field, so that the re-sulting field will be displaced fromthe inside of the wire. Referringto the direction of the externalfield, the resulting field is re-duced in front of as well as be-hind the wire – to the right and tothe left of the wire in fig. 6 – andincreased on the sides of the wire– above and below the wire infig. 6. The proximity effect be-comes increasingly importantinside a litz wire, because of in-teractions between the singlestrands. For the special case ofthe originally homogeneous ex-ternal field, the average proximitylosses can be calculated by:

with

and

The proximity losses are propor-tional to the wire length l and tothe square of the amplitude of themagnetic field Hext. The dimen-sionless proximity factor is dis-

played in fig. 7. Ifthe construction ofthe winding of aninductor or a trans-former is known,the magnetic fieldin the winding win-dow and thus themagnetic field atthe position of eachsingle turn can becalculated. Eq. 3allows an estima-tion of the proximi-ty losses. A moreexact calculation ispossible with com-puter programs

density enforced to the wire. Thecurrent displacement to the wiresurface is avoided by interchan-ging in various ways the singlestrands of a litz wire, being electri-cally insulated from each other.Litz wires are characterized bythe number of strands, the stranddiameter, the diameter or ratherthe profile of the wire bundle andby the pitch length together witha left or right handed twist.

The behavior of an ideally twistedlitz wire – where every singlestrand changes its position withevery other strand after a veryshort distance – is characterizedby an equal distribution of thetotal current over all strands. Ifthe copper cross section of around wire is equal to the coppercross section of a litz wire con-sisting of N strands, then theradius of a single strand is givenby as = a/N1/2. The skin losses ofthe litz wire can be calculatedlikewise by eq. 2, now as sum ofthe skin losses of the singlestrands. However the skin factorfrom fig. 4 is not to be evaluatedat a/δ, but at as/δ, further left in

Figure 7: Like the skin factor, the proximity factor Dsdepends on the frequency – here plotted as a functionof the ratio a/δδδδδ . It is responsible for the increase ofproximity losses with the frequency.

Figure 8: With increasing frequency, the skin effect for litz wires (blue curve)has less negative effect on the resistance than for solid round wires (red curve).But further increasing the frequency, the inner proximity effect in litz wiresbecomes more and more predominant, so that at very high frequencies solidround wires are to be preferred.

4 www.pack-feindraehte.de

which take the inhomogeneity ofthe magnetic field at the positionof the round wire into account.

Losses in ideal litz wires

Reduction of rms losses with afixed rms value of the current isonly possible if the dc resistanceR0 is reduced.The additional skinlosses can be reduced, however,if more of the copper cross sec-tion can be used as conductor –by a more homogeneous current

1752ohneCD.pmd 09.06.2010, 14:344

the diagram by a factor of N1/2. Butthis obvious advantage is dimi-nished because of the so calledinner proximity effect. The innerproximity effect characterizesthe losses of every single strandwhich is exposed to the magneticfield of the neighboring strands.Due to the equal distribution ofthe current between the strands,the magnetic field increases ap-proximately linearly from thebundle axis to its surface (fig. 2).Using the well known fieldstrength at the position of everysingle strand, the proximity los-ses can be calculated by eq. 3and added up.

Of course, the radius as must beused again for the calculation

mediate dotted line. The resultsin fig. 9 show that for ideal litzwires with only a few strands and

Figure 9: The alignment of parallel wires in an externalmagnetic field affects the proximity losses. Thisexample shows the proximity losses [W] in two roundwires of 1m length and 0.2mm diameter for a homo-geneous excitation field Hext = 1kA/m. The configu-ration on the left – wires in a row along the directionof the magnetic field – produces smaller losses thanthe configuration on the right, where the wires areexposed to the magnetic field side by side.

Figure 10: The resistance of real litz wires (Rreal) dueto skin and inner proximity effect stays between theresistance of ideal litz wires (Rid) and the resistanceof parallel strands (Rpar).

5 www.pack-feindraehte.de

instead of a. For the time depen-dent current, the sum of rms, skinand inner proximity losses can becalculated by

where

In eq. 4, aL stands for the radiusof the bundle of strands formingthe litz wire, and d for the averagedistance between two strands in-side the litz wire. R0= l /(κNπas

2)is the dc resistance of the litz wire.In fig. 8, measurement results forthe frequency dependent resis-tances of a litz wire 80x0.1mmand a solid wire with equal coppercross section are compared. Thedc resistances are identical. Withincreasing frequency, the litz wirehas significant benefits becau-se of a less pronounced increasein resistance due to skin effect.Above a certain frequency – inthe example of fig. 8 above 1.5MHz – the inner proximity effectleads to higher losses in the litzwire, and the solid wire is thebetter choice.

Evaluating the proximity losses inlitz wires due to an external ma-gnetic field leads to another pro-blem, concerning the interactionbetween the single strands asconsequence of the eddy cur-rents induced there. To help und-erstand this interaction, two par-allel solid wires are examined,which are aligned either in a row,or side by side in relation to theexcitation field. According to theexplanations to fig. 6, the lossesfor the first case are expected tobe lower. A quantitative exampleis presented in fig. 9. This dia-gram corresponds to the proxi-mity factor in fig. 7, but now in aloglog scale. The direction of theexternal field has been indicatedby the arrow. Without mutual in-teraction – i.e. the losses of asingle wire are multiplied by fac-tor 2 – there would result the inter-

also for litz wireswith a distinct rec-tangular profile, thedirection of theexternal field willhave significantinfluence on thewinding losses.

For round litz wires with manystrands these influences com-pensate mutually. The sameholds for litz wires with rectan-gular profiles, if they are placednext to each other in severallayers inside a winding. The ave-rage proximity losses in ideallitz wires may be calculated inanalogy to eq. 3 by

with

and

As before, as denotes the radius

of a single strand and N the num-ber of strands in the litz wire.

Losses in real litz wires

The loss calculations made be-fore, however, are not yet appli-cable in general to practical pro-blems. Because litz wires aresoldered at both ends, i.e. allstrands are electrically connec-ted to each other, loop currentsmay form, flowing in one direc-tion in some strands and in oppo-site direction in others. In thiscase, the integral of proximitycurrents over the cross section ofa single strand will not be zero,i.e. the condition that all strandsare equal and the litz wire can beconsidered as „ideal“, does nothold any more.

As a second limit case, besidesthe ideal litz wire, a situation willbe examined, where the strands

1752ohneCD.pmd 09.06.2010, 14:345

do not interchange and thereforerun in parallel. This happens, ife.g. the length of a litz wirebetween the soldered ends isshort compared to its pitch. Skinand proximity losses may becalculated in this case like for asolid wire, if the somewhat grea-ter litz wire radius aL according toeq. 4 and its mean specific con-ductivity κL, which is somewhatlower, are taken into account.Denoting the average distancebetween strands by d, then byequating the dc resistances, themean specific conductivity can beexpressed as κL=κ2πas

2 /(31/2 d2).The sum of rms and skin lossesaccording to eq. 1 is given by

with

and

Proximity losses are now

Fig. 10 shows the frequencydependent resistances for a15x0.1mm litz wire. Rid denotesthe ideal litz wire calculated by eq.4, Rpar has been calculated by eq.6 for the case of parallel wires,and the intermediate curve is themeasurement value for the reallitz wire. Of course it was to beexpected, that the frequencydependent resistance of the reallitz wire would stay between bothlimit cases. Starting from thecommon intercept point of allthree curves, it makes sense todescribe the litz wire with a singleparameter λs by a linear combi-nation of both limit cases:

The value λs may be interpretedas quality parameter:

λs = 1 signifies anideal litz wire,λs =0 an arrayof parallel strands.

An examination of proximitylosses in a real litz wire shows,that the real case may becombined in a similar way fromboth limit cases, too. It leads tothe approximation for a real litzwire:

Measurement techniquesto characterize litz wires

For a description of litz wire be-havior, two independent mea-surements are necessary to de-termine the parameters λ

s and λ

p.

On the one hand, the frequencydependent behavior of the wireplays an important role for rms,skin and additional internal pro-ximity losses in litz wires, whichmeans, that the impedance ofdifferent solid and litz wires mustbe described as a function offrequency according to fig. 8. Onthe other hand, a major part ofthe winding losses is causedby the proximity effect, whichmeans, that here the design ofthe winding and thus the positionof each turn in the winding areaplays an important role. Indeed,knowledge of the field distribu-tion inside the winding area isnecessary in order to calculatethe proximity losses. However,independent of that, the behaviorof litz wires in an external fieldhas to be characterized – similarto solid round wires as shown infig. 6. The second challenge tomeasurement and test enginee-ring therefore consists of determi-ning the losses of a litz wire lo-cated in an external magneticfield.

The frequency dependent resis-tance of a solid or litz wire maybe measured easily by connec-

ting a section of length e.g. 1mto the terminals of an impedanceanalyzer. Although the instru-ment can be calibrated for shortand open circuit initially, therearise some inherent measure-ment errors. The magnetic fieldproduced by the wire loop gene-rates losses in all neighboringmetal structures, like housings ofmeasurement devices, but alsothe wire loop itself. To avoid theseproximity losses, the measure-ment setup shown in fig. 11 maybe used, where the outside isshielded completely against themagnetic field. The test sampleis fixed by spacers in the axis ofa brass pipe acting as returnconductor and is electrically con-nected to it at the far end. Thefrequency dependent resistanceof the pipe may be subtractedmathematically. Calibrationof this setup is easily done with asolid round wire.

Figure 12: In order to measure the proximity effect, atransformer was constructed, which allows aligningseveral wire samples (solid or litz) of a determinedlength in its air gaps. The proximity effect can bederived from the difference of two resistancemeasurements in the excitation winding – with orwithout test samples in the air gap.

Figure 11: In order to measure the skin effect in solidwires as well as in litz wires, a setup similar to a coaxialcable has been developed, which eliminates externalinfluences and ensures reproducible measurementconditions.

6 www.pack-feindraehte.de

with

1752ohneCD.pmd 09.06.2010, 14:346

Fig. 12 shows the test setup todetermine the proximity lossesin solid and litz wires. In the airgap of a UI-core combination –consisting of four parallel U93

cores of material 3F4 – a magne-tic field is generated by meansof an excitation coil. From a re-ference measurement withouttest sample, the loss resistance

of the setup is determined, pro-duced by winding losses in theexcitation coil and core losses.For the final measurement, se-veral lengths of the test sampleare placed in the air gap, and theloss resistance of the setup isdetermined again. From the diffe-rence of both loss resistancesand a model of the magnetic cir-cuit, the proximity factor for onestrand of the test sample is cal-culated. The model of the magne-tic circuit may be further correc-ted by evaluating the reactiveparts of the impedances, whichare measured in both cases.Several sections of the litz wireunder test are placed into the airgap, where the soldered ends arenot exposed to the magnetic field.Allowing for some inherent mea-surement errors, this setup pro-vides quite useful results in thefrequency range between 3 kHzand about 8 MHz. Below thisrange, proximity losses becometoo small compared with the dclosses of the excitation coil.Above 8 MHz the core losses be-come too dominant.

Measurement results

Measurements of a great numberof different litz wires show thatthe parameter λ

s can vary within

Figure 13: Test results have been collected in a data base, which allows e.g.to calculate winding losses directly from the test results when looking for theoptimal wire type.

7 www.pack-feindraehte.de

Prof. Dr.-Ing. M. Albach

has been holding the chair for Elec-tromagnetic Fields of Friedrich-Alex-ander-Universität Erlangen-Nurem-berg since 1999. The areas of re-search cover a.o. the Maxwell FieldTheory as well as Power Electronicswith the focus on electromagneticcompatibility and inductive compo-nents.m.albach@emf.eei.uni-erlangen.de

Dipl.-Ing. Marc Döbrönti

studied Electrical Engineering at theFriedrich-Alexander-Universität (FAU)Erlangen-Nuremberg until 2009. Since2009 he has been working as Re-search Assistant with the main focuson the project „Characterization andOptimization of Litz Wire Windings inChokes and Transformers for HigherEnergy Efficiency“marc.doebroenti@emf.eei.uni-erlangen.de

Dr.-Ing. Hans Roßmanith

has been with the department of Elec-trical Engineering, Electronics and In-formation Technology at the UniversityErlangen-Nuremberg as scientific as-sistant since 1993. In 1999 he joinedthe chair for Electromagnetic Fields.His areas of research are electroma-gnetic field theory, electromagnetic com-patibility and numerical field calculation.h.rossmanith@emf.eei.uni-erlangen.de

1752ohneCD.pmd 09.06.2010, 14:347

8 www.pack-feindraehte.de

a wide range of values between0.15 and 0.9. The resulting valuedepends in particular on the follo-wing criteria:

In which way are the strandstwisted together to form the litzwire?How many strands are twistedin advance and then bunchedtogether with each other?Which pitch lengths were cho-sen?

In general can be stated, that bet-ter litz wires are characterized bya more uniform distribution pro-bability of the strands on the litzwire cross section, over to the litzwire section length. This can beachieved by an appropriatestranding of bundles formingsubsets of the litz wires.

A different picture appears whenlooking at the parameter λp. Allmeasured values exceed 0.95.Whether a litz wire shows „ideal“or rather „real“ behavior, is deter-mined essentially by the distan-ce between its soldering points,i.e. by the litz wire length in thecorresponding winding. For litzwire sections with lengths abovethe pitch length, λp approachesthe value 1. The smallest and thusleast desirable value λ

p appears

if the litz wire length exposed tothe field matches approximatelyhalf the pitch length. In this casethe currents in the single strands,which close over both solderedends, will assume a maximalvalue. The parameter λp reducesthen to about 0.9. Another factorinfluencing the quality parame-ter λp is the form stability of thelitz wires. Litz wires without wrap-ping change their form during thewinding process to a more ellip-tical cross section. If the larger si-de of the cross section is oriented

transformers is known, then, star-ting from the litz wire profiles, theposition of the turns in the windingarea can be determined and sothe anticipated field distributioncan be calculated. With this in-formation, from the wide rangeof different rf litz wires – e.g. oftype RUPALIT ® – may be chosen.The manufacturer Pack Fein-draehte can take advantage of adetailed characterization of stan-dard litz wires, stored in a data-base (fig. 13).

The most important parametersfor the choice of litz wire types arethe number of strands and thestrand diameter, as well as pitchlength and direction of twist. Thepitch length is influenced by theouter wrapping of the litz wire,consisting of natural silk or poly-amide yarn. With increasingnumber of strands in a litz wirebundle, the number of options forforming bundles of multiple sub-sets of strands increases.

vertically to the magnetic field, themagnetic flux through the areasbetween the strands increases,and thus increase the inducedcurrents which close over the sol-dered ends. Litz wires with doub-le wrapping have the highestquality parameter with regard tothe proximity effect. In real win-ding packs there adds as an ad-ditional advantage for these ty-pes of litz wires the greater dis-tance between neighboring turns.For rectangular profiles the di-rection of the external field hasgreat influence on the quality pa-rameter λp. If the external fieldenters the litz wire through thenarrow side of the profile, it isshielded better by the inducededdy currents of the strands thanif it enters through the long side.In winding packs this effect isreduced, however, by neighbo-ring litz wires.

The road to theoptimal winding

A number of different parametersmust be kept in mind when choo-sing an optimal litz wire for a givenapplication. When the harmoniccontent of the currents in coils or

Dipl.-Ing. Dietmar Exner

has been Assistant to the Manage-ment at the Rudolf Pack GmbH & Co.KG since 1999. The focus of his workis the customer support and the im-plementation of the customer requestswithin the company.dietmar-exner@pack-feindraehte.de

Dr.-Ing.Alexander Stadler

has been research assistant at thechair of Electromagnetic Fields ofFriedrich-Alexander-Universität in Er-langen-Nuremberg. Since 2009, hemanages the Research & Develop-ment of the Spezial-TransformatorenStockach GmbH & Co. KG (STS). Hisareas of work cover the simulation andmeasurement technique of inductivecomponents as well as the develop-ment of special components and newtechnologies.

stadler@sts-trafo.de

Rudolf Pack GmbH & Co. KG

Am Bäuweg 9-11

D-51645 Gummersbach

Tel.: +49 (0)2261/9567-0Fax: +49 (0)2261/9567-67www.pack-feindraehte.deE-mail: info@pack-feindraehte.de

1752ohneCD.pmd 09.06.2010, 14:348