Extended post processing for simulation results of FEM ...Figure 4. Ansoft HFSS simulation model of the spiral antenna and distribution of the observation points inside the simulation

Adv. Radio Sci., 5, 127–133, 2007www.adv-radio-sci.net/5/127/2007/© Author(s) 2007. This work is licensedunder a Creative Commons License.

Advances inRadio Science

Extended post processing for simulation results of FEM synthesizedUHF-RFID transponder antennas

R. Herschmann1,2, M. Camp1,2, and H. Eul1

1Leibniz Universitat Hannover, Institute of Radiofrequency and Microwave Engineering, Appelstraße 9a, 30167 Hannover,Germany2Smart Devices GmbH & Co. KG, Schonebecker Allee 2, 30823 Garbsen, Germany

Abstract. The computer aided design process of sophisti-cated UHF-RFID transponder antennas requires the applica-tion of reliable simulation software. This paper describes aMatlab implemented extension of the post processor capa-bilities of the commercially available three dimensional fieldsimulation programme Ansoft HFSS to compute an accuratesolution of the antenna’s surface current distribution. Theaccuracy of the simulated surface currents, which are phys-ically related to the impedance at the feeding point of theantenna, depends on the convergence of the electromagneticfields inside the simulation volume. The introduced methodestimates the overall quality of the simulation results by com-bining the surface currents with the electromagnetic fieldsextracted from the field solution of Ansoft HFSS.

1 Introduction

The development and optimization of passive transpondersfor application in UHF-RFID systems with wide read rangeis directly correlated to the supply of appropriate antenna de-signs. On the one hand these antennas must be frequencyselective in order to suppress interferences of radio systemsin adjacent wave bands. Otherwise the antennas should ex-hibit enough bandwidth to compensate for tolerances of chipimpedance and to account for the influence on impedancefrom the adjacencies of the antenna. A largely stable use ofa passive transponder makes sense in a moderately variableenvironment only in such a way. The dependence betweengeometry and impedance qualities of the antenna makes thesynthesis of suitable antenna structures possible for the ful-filment of the qualification profile under consideration of theat most permitted geometric measurements.

Correspondence to:R. Herschmann([email protected])

The design process of a transponder antenna for the ap-plication in an UHF-RFID system using the Finite ElementMethod (FEM) allows for the consideration of extended, ge-ometrical complex objects with arbitrary material character-istics in the near field region. The material specific quali-ties of these objects generally lead to an impact on the an-tenna impedance associated with changes of the resonantfrequency, bandwidth and matching between antenna andtransponder chip. Recent simulation programmes allow foran optimization of the antenna design by the variation of de-fined geometry parameters of simulation models parameter-ized correspondingly under consideration of predefined en-vironmental conditions.

This work evaluates the quality of the simulation results ofAnsoft’s FEM based simulation programme High FrequencyStructure Simulator (HFSS). This product is used as a de-sign tool for the synthesis of plane transponder antennas (seeHerschmann et al., 2006). Despite the various areas of ap-plication, which arise by the use of this sophisticated sim-ulation tool, limits also exist in the calculation possibilities.For instance it is not possible to calculate the electromagneticfields outside the simulation model in arbitrarily defined fieldpoints or field point areas. Moreover, the quality of the cal-culation of the surface current distribution of plane antennastructures is insufficient. Therefore a module implementedin Matlab is introduced that offers extended possibilities forthe post processing of HFSS simulation results. A check ofthe convergence of the electromagnetic field can be carriedout in the complete simulation volume by the calculation ofthe surface currents of the antenna structures examined here.The knowledge of the frequency dependent current distribu-tion forms the base for calculating the electromagnetic fieldsin arbitrary space points.

Published by Copernicus Publications on behalf of the URSI Landesausschuss in der Bundesrepublik Deutschland e.V.

128 R. Herschmann et al.: Extended post processing of FEM based simulation results

Figure 1. Convergence of the electromagnetic field at defined observation points versus the number of adaptive passes; while the electric field shows well convergence properties in (a), the magnetic field shows substantial changes in (b)

Figure 2. Surface current distribution of a 2λ -dipole at resonant frequency extracted from Ansoft HFSS

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Fig. 1. Convergence of the electromagnetic field at defined observation points versus the number of adaptive passes; while the electric fieldshows well convergence properties in(a), the magnetic field shows substantial changes in(b).

Figure 1. Convergence of the electromagnetic field at defined observation points versus the number of adaptive passes; while the electric field shows well convergence properties in (a), the magnetic field shows substantial changes in (b)

Figure 2. Surface current distribution of a 2λ -dipole at resonant frequency extracted from Ansoft HFSS

10

Fig. 2. Surface current distribution of aλ/2-dipole at resonant fre-quency extracted from Ansoft HFSS.

2 HFSS simulation results: convergence of electromag-netic fields and impedance

It is appropriate to clarify the necessity for dealing with thesubject of field and impedance convergence by observing thesimulation results for a simple resonant dipole antenna usingHFSS. The surface current distribution of that antenna is wellknown to be sinusoidal along the dipole’s centre line (seeStutzman and Thiele, 1998). In Fig. 1 the Cartesian compo-nents of the electromagnetic fields are represented. Whilethe observation points of the electric field are distributedinside the simulation volume, the magnetic fields are com-puted along the antenna surface. The electromagnetic fieldsare plotted against the number of adaptive passes. In con-trast to the electric fields the magnetic fields show substantialchanges in field magnitudes even at a high number of adap-tive passes. HFSS computes the surface current distributionby processing the magnetic fields on the antenna structure.But the results for two dimensional antennas with neglected

metal thickness are not correct as depicted in Fig. 2. On theother hand convergence of the impedance at the antenna’sfeeding point shown in Fig. 3 is already reached within a fewadaptive passes. Due to the physical relation between an-tenna impedance and antenna surface current distribution itis appropriate to check the field solution.

3 HFSS eXtension Module: a Matlab implemented pro-cedure for post processing FEM based simulation re-sults

In order to validate the simulation results of HFSS the con-vergence of impedance as well as the convergence of elec-tromagnetic fields surrounding the antenna have to be con-sidered because of the physical relation between these char-acteristic quantities. The electromagnetic fields inside thesimulation volume are caused by the antenna’s surface cur-rents. A method implemented by use of Matlab permits thecomputation of a corrected distribution of the surface cur-rents. Therefore this method permits statements about thequality of the field convergence in the complete simulationvolume and puts aid at the assessment of HFSS results in thedesign of antenna prototypes. On the basis of a simple spiralantenna the approach is described detailed in the followingsections.

Adv. Radio Sci., 5, 127–133, 2007 www.adv-radio-sci.net/5/127/2007/

R. Herschmann et al.: Extended post processing of FEM based simulation results 129

Figure 3. Impedance convergence at the antenna’s feeding point versus the number of adaptive passes

Figure 4. Ansoft HFSS simulation model of the spiral antenna and distribution of the observation points inside the simulation volume (blue markers represent observation points for the electric field, red markers are used for the magnetic field)

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Fig. 3. Impedance convergence at the antenna’s feeding point versus the number of adaptive passes.

Figure 3. Impedance convergence at the antenna’s feeding point versus the number of adaptive passes

Figure 4. Ansoft HFSS simulation model of the spiral antenna and distribution of the observation points inside the simulation volume (blue markers represent observation points for the electric field, red markers are used for the magnetic field)

11

Fig. 4. Ansoft HFSS simulation model of the spiral antenna and distribution of the observation points inside the simulation volume (bluemarkers represent observation points for the electric field, red markers are used for the magnetic field).

3.1 The principle of the calculation method

The Matlab procedure performs a comparison between theelectric fields taken directly from the solution of the finite el-ement method implemented in HFSS and the electric fieldswhich are derived from the distribution of the antenna’s sur-face currents. To this end a suitable observation point areahas to be defined within the boundaries which are providedby the used simulation model. It is possible to use differentgeometries for this observation point area, e.g. lines, planesor cuboids. The higher the dimension of this geometricalstructure chosen as the observation point area the better theresults regarding the corrected surface current distribution.The electric fields are used for comparison because HFSS de-termines the magnetic fields by a numeric calculation basedon the solution of the electric fields. The electric fields are

therefore computed with a higher precision. Aim of the pro-cedure is the optimization of a scaling factor applied to cal-culated initial surface current distribution in order to min-imize the difference between the compared electric fields.This initial current distribution of the antenna is calculatedfrom the magnetic fields in close proximity to the antennasurface. As a working example the method is applied tothe analysis of the field convergence of a two arm spiral an-tenna. The equally spaced observation points of the elec-tric fieldsE=h (f, ra2) are positioned between an inner andouter cuboid. The observation points of the magnetic fieldsH=g (f, ra1) are distributed along the antenna surface witha defined gap between antenna plane and observation pointplanes. The field distribution of the observation point areasis summarised in Fig. 4. Consequently the quality of theoptimized scaling factor of the surface current distribution

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Figure 5. Schematic representation of the surface currents calculation procedure

Figure 6. Generation of observation points for the calculation of the magnetic field strength vectors

12

Fig. 5. Schematic representation of the surface currents calculation procedure.

Figure 5. Schematic representation of the surface currents calculation procedure

Figure 6. Generation of observation points for the calculation of the magnetic field strength vectors

12

Fig. 6. Generation of observation points for the calculation of the magnetic field strength vectors.

is associated directly with the convergence qualities of theelectromagnetic fields calculated by HFSS within the simu-lation model. Only by a sufficient number of adaptive passesa convergence of the fields can be expected besides the con-vergence of the scattering parameters at the antenna’s port.The necessary number of iterations and therefore the qualityof the results depends on the complexity of the simulationmodel. The flowchart in Fig. 5 represents the described pro-cedure graphically.

3.2 Determination of the equivalent Huygens sources

The computation of the surface current distribution on a twodimensional antenna structure by assuming the antenna asa bounding plane between separated spaces. A variation ofEq. (1) leads to an initial current distribution which has to becorrected by use of the above mentioned iterative optimiza-tion process.

RotH=n12 × (H 2−H 1) =JQ (1)

Equation (1) is only valid at the boundary of adjoining spaceareas. In the approach discussed in this paper the observa-tion points for extracting the magnetic fields are computedfrom the centre points of the triangles used for antenna seg-mentation and are placed at a distanceda above and belowthe antenna plane as shown in Fig. 6. Therefore the initialcurrent distribution is approximated using Eq. (2):

RotH=n12 ×(H 2,da−H 1,da

)=JQ=JQ,initial value (2)

To discretise the two dimensional antenna geometry a freeavailable mesh programme introduced in Persson (2005) isapplied.



Figure 7. Comparison of simulated (HFSS) and computed (HFSS XM) electric fields at defined observation points with regard to initial and optimized scaling factor

Figure 8. Power balance of the spiral antenna; the calculations are performed using different boundary layers in the HFSS simulation

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Fig. 7. Comparison of simulated (HFSS) and computed (HFSS XM) electric fields at defined observation points with regard to initial andoptimized scaling factor.

3.3 Calculation of the radiation fields on basis of the equiv-alent Huygens sources

The optimization process for calculating the corrected valuesof the surface current distribution combines these currents tothe electromagnetic fields at the defined observation pointsinside the simulation volume by applying the formalism sum-marised in Eq. (3).

H (rA) =jk4π

· (m×rA) · C · e−jkrA

E (rA) =η

4π·

((M−m) ·

(jk

|rA|+C

)+2MC

)· e−jkrA

C =1r2A

·

(1 +

1jk|rA|

)M =

(rA·m)·rA

|rA|2

η =

√µ0ε0

= 120π�

(3)

The electromagnetic fields are computed directly from anelectric dipole momentm=JQ · AQ, whereAQ representsthe area of a single triangle used for segmentation of the an-tenna surface, without determining the magnetic vector po-tential and necessary application of the subsequent functionsof vector calculus in order to calculate the radiation fields(see Makarov, 2002). The segmented antenna structure con-tains a high number of dipole moments depending on thenumber of elements necessary for a high quality mesh tri-angulation. Therefore the electromagnetic field in a specificobservation pointrA inside the simulation volume is a super-position of the contributions of allN dipole moments cover-ing the antenna surface.

H (rA) =

N∑n=1

H n

(rA − rQ,n

)E (rA) =

N∑n=1

En

(rA − rQ,n

) (4)

The quality of the calculated radiation fields depends on thequality of the generated mesh and the field solution inside the

simulation volume of HFSS. The interrelation between thesurface currents and the electromagnetic fields surroundingthe antenna is the basis for the computation of an optimizedscaling factor for the current distribution. The iterative pro-cess starts with an initial value ofsfinitial=1. The expressionsdefined in Eq. (5) are used as a criterion to evaluate the differ-ence between the electric fields based on the field solution ofHFSS and the electric fields computed by applying Eqs. (3)and (4) to the surface current distribution. The optimal valueof the scaling factor is found for the minimum of the residualerror using a Matlab implemented optimizer.

Fx,real,m (sf ) =∣∣Re

{Ex,HFSS (rm)

}−Re

{Ex,HFSS XM (rm)

}∣∣2Fy,real,m (sf ) =

∣∣Re{Ey,HFSS (rm)

}−Re

{Ey,HFSS XM (rm)

}∣∣2Fz,real,m (sf ) =

∣∣Re{Ez,HFSS (rm)

}−Re

{Ez,HFSS XM (rm)

}∣∣2Freal(sf ) =

1

M·

M∑m=1

[Fx,real,m (sf ) + Fy,real,m (sf ) + Fz,real,m (sf )

]⇒ sfoptimal,real = min {Freal(sf ) : sf ∈ (0, 5)}

Fx,imag,m (sf ) =∣∣Im

{Ex,HFSS (rm)

}−Im

{Ex,HFSS XM (rm)

}∣∣2Fy,imag,m (sf ) =

∣∣Im{Ey,HFSS (rm)

}−Im

{Ey,HFSS XM (rm)

}∣∣2Fz,imag,m (sf ) =

∣∣Im{Ez,HFSS (rm)

}−Im

{Ez,HFSS XM (rm)

}∣∣2Fimag(sf ) =

1

M·

M∑m=1

[Fx,imag,m (sf ) + Fy,imag,m (sf ) + Fz,imag,m (sf )

]⇒ sfoptimal,imag = min

{Fimag(sf ) : sf ∈ (0, 5)

}JQ,optimal = sfoptimal,real · Re

{JQ,initial

}+ j · sfoptimal,imag · Im

{JQ,initial

}

(5)

The electric fields calculated by HFSS in the defined obser-vation point area are indicated by the indexHFSS. The ex-pressions indexed byHFSS XMrepresent the electric fieldsobtained from the surface currents correspondingly. Deter-mining the squares of the differences in the Cartesian compo-nents atM observation points leads to a stronger weightingof high deviations compared to small errors. The separate



Figure 7. Comparison of simulated (HFSS) and computed (HFSS XM) electric fields at defined observation points with regard to initial and optimized scaling factor

Figure 8. Power balance of the spiral antenna; the calculations are performed using different boundary layers in the HFSS simulation

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Fig. 8. Power balance of the spiral antenna; the calculations areperformed using different boundary layers in the HFSS simulation.

treatment of the real and imaginary parts generally deliversdifferent optimal scaling factors. An important reference re-garding the quality of the simulator’s field solution is a goodagreement betweensfoptimal,real and sfoptimal,imag. There isa risk that an adaption of the electric fields is possible in-side the simulation volume also at an insufficient field con-vergence by the surface currents of the antenna structure, ifthe number of degrees of freedom of the optimization pro-cess is increased. For instance it is possible to establish sepa-rate scaling factors for the Cartesian components of the elec-tric fields. However the physical significance of the currentsurface distribution optimized this way is challenged. Thechosen implementation of the HFSS XM method avoids thissituation. An insufficient convergence of the electromag-netic fields inside the simulation volume results in remainingsignificant deviations between the HFSS based field compo-nents and the fields extracted from the surface current distri-bution.

3.4 Results and ranges of application

A comparison of the electric fields simulated by HFSS andthe electric fields computed on basis of the surface currentdistribution by HFSS XM in the observation point area in-troduced in Fig. 6 is presented in Fig. 7 at a frequency nearthe first serial resonance. The two graphics show only anextract of all defined observation points and are restricted tothe magnitude of the x-component of the complex electricfield vector. Deviations and agreements of the other vector

Figure 9. Statistical evaluation of differences regarding the antenna’s radiated electric fields extracted from HFSS field solution and computed from the surface current distribution; the calculations are performed using different boundary layers in the HFSS simulation

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Fig. 9. Statistical evaluation of differences regarding the antenna’sradiated electric fields extracted from HFSS field solution and com-puted from the surface current distribution; the calculations are per-formed using different boundary layers in the HFSS simulation.

components as well as phase values range at the same or-der of magnitude. While distinct deviations are visible byuse of the initial scaling factor, a very well agreement be-tween the simulated and computed electric field distributionby applying the optimized scaling factor is achieved. But itis insufficient to estimate the quality of the computed sur-face current distribution this way only. Further criteria arenecessary for an evaluation of the reliability of the computedresults and the necessary validation of the field convergenceof the HFSS simulation process. Therefore a power balanceand a statistical evaluation with regard to the comparison ofthe simulated and computed electric fields are applied. Toreduce the physical size of the simulation model it is pos-sible to use perfectly matched layer instead of a radiationboundary applied conventionally. The effects on the conver-gence of electromagnetic fields inside the simulation volumecaused by different boundary conditions is analysed as well.In Fig. 8 the calculated radiated powerPrad based on the sur-face currents is compared to the accepted powerPacc. Thespiral antenna is simulated without any losses. Thus all ac-cepted power should be radiated. The percentage deviation isless than1P=4% independent of the applied boundary con-dition over the frequency range of interest. The maximumdifferences occur in the range of the resonant frequency. Fi-nally Fig. 9 represents an assessment of the residual errors bycalculation of the mean average valuem and varianceσ 2 ofthe error vector defined in Eq. (6) regarding the differences



of the simulated and computed solutions of the electric fields.The error vectors contain the absolute values of the differ-ences of the magnitudes of the electric fields for every Carte-sian component at the definedM observation points. Thelow mean average values as well as moderate variances forall three Cartesian components validate the sufficient numberof adaptive passes and the very well converged field solutioninside the simulation volume.

1Ei (f ) =

∣∣∣∣Ei,1,HFSS (f )∣∣ −

∣∣Ei,1,HFSS XM (f )∣∣∣∣

...∣∣∣∣Ei,m,HFSS (f )∣∣ −

∣∣Ei,m,HFSS XM (f )∣∣∣∣

...∣∣∣∣Ei,M,HFSS (f )∣∣ −

∣∣Ei,M,HFSS XM (f )∣∣∣∣

,

i = x, y, z, m = 1..M (6)

Based on the optimized surface current distribution it is pos-sible to separate ohmic losses of the antenna from radiationlosses and select a proper equivalent antenna circuit. Fur-thermore it is possible to compute the electromagnetic fieldsin arbitrary observation point areas and extract informationon polarisation states for example. The implemented methodis capable to compute the surface current distribution of ge-ometrical complex shaped antennas for use in UHF-RFIDtransponder systems.

4 Conclusion

The Matlab implementation of HFSS XM makes the calcu-lation of the surface current distribution of plane antennasas well as the computation of the electromagnetic fields andmeasures derived from them possible in arbitrary observationpoints and areas. Furthermore the convergence of the fieldsolution computed by HFSS is checked during the determi-nation of optimized scaling factors for the real and imaginaryparts of the antenna’s surface currents. Therefore it improvesthe capabilities implemented in HFSS already and antennaprototyping for UHF-RFID transponder becomes more so-phisticated. The introduced method is capable to computethe surface current distribution of three dimensional antennaswith finite metallization thickness as well as conformal an-tennas. Based on the surface current distribution it is possibleto lay out a library containing the geometrical data of param-eterized transponder antennas, the impedance at the feedingpoint and the related surface current distribution as a functionof frequency. Therefore it is not necessary to save the mem-ory intensive HFSS models. The quality of the computedsurface current distribution depends on the convergence ofthe electromagnetic fields inside the simulation volume ofHFSS. According to the examinations made in this paper thefield convergence necessary for accurate calculation of thesurface current distribution requires significant higher num-ber of adaptive passes than a merely impedance convergenceat the antenna’s feeding point.

References

Herschmann, R., Camp, M., and Eul, H.: Design und Analyse elek-trisch kleiner Antennen fur den Einsatz in UHF RFID Transpon-der, Adv. Radio Sci., 4, 93–98, 2006,http://www.adv-radio-sci.net/4/93/2006/.

Makarov, S. N.: Antenna and EM Modeling with MATLAB, JohnWiley & Sons Inc., 2002.

Persson, P.-O.: Mesh Generation for Implicit Geometries, in: De-partment of Mathematics, PhD thesis, Massachusetts Institute ofTechnology, 2005.

Stutzman, W. L. and Thiele, G. A.: Antenna theory and design, 2nded., New York, Wiley, 1998.


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Extended post processing for simulation results of FEM ...Figure 4. Ansoft HFSS simulation model of the spiral antenna and distribution of the observation points inside the simulation