comparison of matching layers for automotive radome … of matching layers for automotive radome...

Adv. Radio Sci., 8, 49–54, 2010www.adv-radio-sci.net/8/49/2010/doi:10.5194/ars-8-49-2010© Author(s) 2010. CC Attribution 3.0 License.

Advances inRadio Science

Comparison of matching layers for automotive radome design

F. Fitzek1, R. H. Rasshofer1, and E. M. Biebl2

1BMW Group Research and Technology, Munich, Germany2Technische Universität München – Fachgebiet Höchstfrequenztechnik, Munich, Germany

Abstract. Hidden integration of 79 GHz sensors behind plas-tic and painted fascia represents a challenging task since bothelectromagnetic and car body design constraints have to bemet. This paper compares different possibilities for low-costintegration of radar sensors. Based on a model for strati-fied media, a study of the most important parameters such asbandwidth, angle and tolerances is shown. Our results sug-gest that for plastic fascia, the requirements of future radarsensors can be met with low-cost matching. Even with metal-lic paints, the requirements imposed by modern 79 GHz radarsensors can be met under certain conditions.

1 Introduction

Automotive radar systems, first introduced on the customermarket in the late 1990s, show a steady trend from com-fort (Advanced Driver Assistance, short ADAS) to safetyoriented vehicle functions (Active Safety, short AS). Radar-based systems tend to address scenarios of growing com-plexity, targeting urban or city traffic rather than highwayscenarios, which were the main application in recent years.Resolution in range, azimuth angle and target velocity is thekey feature to deal with demanding scenarios of high com-plexity and high dynamics (Rasshofer, 2007). In the Euro-pean Union, a new frequency band from 77 to 81 GHz – the79 GHz band – has been allocated to enable future ADAS andAS systems replacing the previously used 24 GHz ultrawideband radar sensors. To start the development of 79 GHz bandtechnology, the European funded project “Radar on Chip forCars" (short RoCC) started in fall 2008 (RoCC, 2009).

Integration of 79 GHz sensors into modern cars representsa challenging task since electromagnetic and car body de-sign constraints have to be met simultaneously. This prob-lem is even more evident when more than one sensor hasto be integrated, because hidden integration of the sensorsbehind a plastic bumper is often required. As is clear from

Correspondence to:F. Fitzek([email protected])

both theoretical investigations and from previous experiencewith 76 GHz radar systems, operation of these sensors be-hind painted, plastic fascia will lead to performance degrada-tion if no optimization of the stratified radome structures isperformed. In the millimetre wave regime, the electromag-netic field propagates quasi-optically, which results in highreflection and loss factors for obstacles or media in the line-of-sight. This is the case if the radar sensor is to be integratedin the bumper or behind other fascia of the car.

The performance degradation is due to the reflections be-tween the bumper and the sensor. The bumper consists gen-erally of a substrate and some layers of paint. This pa-per shows a detailed analysis of important electromagneticradome properties like bandwidth, angle and tolerances forsubstrate only and painted substrates. Additionally, the costof integration should be at a minimum, hence this paper con-siders low-cost matching possibilities for hidden integrationof radar sensors.

2 Mathematical model

The electromagnetic theory of the fields in stratified me-dia can be derived from the plane wave assumption andthe boundary conditions of electromagnetic waves (time-harmonic conventionejωt ). In Kurt Altenburg (1953) thistheory is derived. It can be found today in many books for op-tics, electromagnetics or microwave theory (Hecht, 2005). Inthe case of perpendicular incidence of a TE-wave (derivationfor TM-waves accordingly) forward- and backward wavesare defined, which summarize all waves in the same direc-tion (important difference to other approaches). The com-plete derivation can be found inHecht (2005) and a sum-mary of it in Fitzek and Rasshofer(2009). For each layeri with the material parametersni as the index of refraction(ki = ω/c0ni respectively),di as the thickness, andZi asthe wave impedance of the semi-infinite layer the followingcharateristic matrix can be derived.

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

http://creativecommons.org/licenses/by/3.0/

50 F. Fitzek et al.: Automotive radome design[M i

]=

[mi

11 mi12

mi21 mi

22

](1)

=

[cos(ki di) j Zi sin(ki di)

j 1Zi

sin(ki di) cos(ki di)

](2)

The amplitude transmission- and reflection factors of thelayeri embedded between semi-infinite layersi−1 andi+1are defined as

r =Zi+1mi

11+mi12−Zi+1Zi−1mi

21−Zi−1mi22

Zi+1mi11+mi

12+Zi+1Zi−1mi21+Zi−1mi

22

(3)

t =2Zi+1

Zi+1mi11+mi

12+Zi+1Zi−1mi21+Zi−1mi

22

(4)

With these equations, the transmission and reflection factorcan be derived using the loads and the characteristic matrixMi . For a multilayer media, the characteristic media matriceshave to be multiplied in the right order.

3 Theory and practice of matching

The theory of matching is well known from transmission linetheory. The aim is always to get a high transmission next toa low reflection (power matching). The losses in the materialcan’t be compensated, which results in a decreased transmis-sion. For semi-infinite layers, the methods shown here canbe used as well. Nevertheless, for mm-wave applicationsthe constraints of matching should be carefully considered(e.g.Fitzek and Rasshofer, 2009).

For a bumper consistent of one layer of substrate and sev-eral layers of paint, there exists different options for match-ing. One is to optimize the thickness of the substrate. Fora homogeneous material this results in a thickness of mul-tiple of half-wavelengths. For stratified media, the solutioncan be found with minimization of the reflection coefficientthrough the mathematical model. This matching has only onedegree of freedom – the decreased thickness of the substratematerial. Another possibility is an additional matching layerwhich is placed directly onto the bumper. This material canhave a desired thickness and relative permittivity, hence hastwo degrees of freedom. One could also consider artificialstructures or even metamaterials as an additional matchinglayer, but as mentioned above, low-cost matching is the fo-cus in this paper, hence these options are not considered.

The third matching option is a combination of these twomatching methods. Therefore, a structure (e.g. rib profile) isassembled into the subtrate material of the bumper. Becausethe overall thickness stays constant, this matching methodhas only two degrees of freedom (depth and relative permit-tivity of the integrated structure). Figure1 depicts the differ-ent possibilities. For all matching methods the mathematicalmodel can be used to calculate the optimal values for the de-sired matching. Therefore, an optimization algorithm basedon a direct search method is used. Two different simulations

2 F. Fitzek et al.: Automotive Radome Design

i with the material parameters ni as the index of refraction(ki = ω/c0 ni respectively), di as the thickness, and Zi asthe wave impedance of the semi-infinite layer the followingcharateristic matrix can be derived.[

Mi]

=[mi

11 mi12

mi21 m

i22

](1)

=[

cos(ki di) j Zi sin(ki di)j 1Zi

sin(ki di) cos(ki di)

](2)

The amplitude transmission- and reflection factors of thelayer i embedded between semi-infinite layers i−1 and i+1are defined as

r =Zi+1m

i11 +mi

12 − Zi+1 Zi−1mi21 − Zi−1m

i22

Zi+1mi11 +mi

12 + Zi+1 Zi−1mi21 + Zi−1mi

22

(3)

t =2Zi+1

Zi+1mi11 +mi

12 + Zi+1 Zi−1mi21 + Zi−1mi

22

(4)

With these equations, the transmission and reflection factorcan be derived using the loads and the characteristic matrixMi. For a multilayer media, the characteristic media matriceshave to be multiplied in the right order.

3 Theory and practice of matching

The theory of matching is well known from transmission linetheory. The aim is always to get a high transmission next toa low reflection (power matching). The losses in the materialcan’t be compensated, which results in a decreased transmis-sion. For semi-infinite layers, the methods shown here canbe used as well. Nevertheless, for mm-wave applicationsthe constraints of matching should be carefully considered(e.g. (Fitzek and Rasshofer, 2009)).For a bumper consistent of one layer of substrate and severallayers of paint, there exists different options for matching.One is to optimize the thickness of the substrate. For a ho-mogeneous material this results in a thickness of multiple ofhalf-wavelengths. For stratified media, the solution can befound with minimization of the reflection coefficient throughthe mathematical model. This matching has only one de-gree of freedom - the decreased thickness of the substratematerial. Another possibility is an additional matching layerwhich is placed directly onto the bumper. This material canhave a desired thickness and relative permittivity, hence hastwo degrees of freedom. One could also consider artificialstructures or even metamaterials as an additional matchinglayer, but as mentioned above, low-cost matching is the fo-cus in this paper, hence these options are not considered.The third matching option is a combination of these twomatching methods. Therefore, a structure (e.g. rib profile) isassembled into the subtrate material of the bumper. Becausethe overall thickness stays constant, this matching methodhas only two degrees of freedom (depth and relative permit-tivity of the integrated structure). Figure 1 depicts the differ-ent possibilities. For all matching methods the mathematical

c-1) c-2)b)a)

Fig. 1. a) substrate material of bumper (no matching), b) sub-strate with additional matching layer, c-1) substrate with integratedmatching layer (thickness optimization), c-2) substrate with inte-grated matching layer (rib profile)

model can be used to calculate the optimal values for the de-sired matching. Therefore, an optimization algorithm basedon a direct search method is used. Two different simulationscan be performed where the thickness and relative permit-tivity for the matching layer are optimized. This approachneglects the roughness of the material and assumes a non-magnetic, plane material.For the additional matching layer, the bumper materials (sub-strate or paint) are not changed. On the other hand, for anintegrated matching layer, the thickness of the substrate ma-terial is changed according to the thickness of this layer. Thisresults in a decreased thickness for the substrate material ofthe bumper. With this integrated matching the integratedstructure and the thickness optimization can be modeled. Forthe latter the relative permittivity is fixed to one, whereas itis a degree of freedom for the integrated structure.

3.1 Integrated matching structure

The integrated matching structure is a structured dielectric(e.g. rib profile) and can be any structure which fullfills thehomogeneity limit of p < λ/4 with p as the cell size in thedirection of propagation, in order to avoid parasitic scatteringeffects. For easy integration the rib profile is one possibility.There exists several methods to calculate the relative permit-tivity of such structures (Biber, 2003). Here a method basedon transmission line models is used in which the resultingrelative permittivity is described as the mean of the relativecharacteristic impedances (Z ′ =

√µr

εrwith µr = 1) of free

space and the substrate depending on the ratio of ribs andbars. Hence, a relative permittivity between 1 and εr,s of thesubstrate can be reached.

εr =(tbar Z

′substrate + trib Z

′0

tbar + trib

)−2

(5)

If the thickness of the ribs (trib) are predefined due to man-ufacturing constraints, one can easily calculate the thicknessof the bars (tbar) to reach the desired value for εr as calcu-lated by the optimization algorithm.Figure 2 shows the dependency of the relative permittivityversus the ratio of bars to ribs with constant rib thickness.It can be seen that the variation in relative permittivity foran increased bar thickness (resulting in higher εr values) is

Fig. 1. (a) substrate material of bumper (no matching),(b) sub-strate with additional matching layer,(c-1)substrate with integratedmatching layer (thickness optimization),(c-2) substrate with inte-grated matching layer (rib profile).

can be performed where the thickness and relative permit-tivity for the matching layer are optimized. This approachneglects the roughness of the material and assumes a non-magnetic, plane material.

For the additional matching layer, the bumper materials(substrate or paint) arenot changed. On the other hand, foran integrated matching layer, the thickness of the substratematerial is changed according to the thickness of this layer.This results in a decreased thickness for the substrate mate-rial of the bumper. With this integrated matching the inte-grated structure and the thickness optimization can be mod-eled. For the latter the relative permittivity is fixed to one,whereas it is a degree of freedom for the integrated structure.

3.1 Integrated matching structure

The integrated matching structure is a structured dielectric(e.g. rib profile) and can be any structure which fullfills thehomogeneity limit ofp < λ/4 with p as the cell size in thedirection of propagation, in order to avoid parasitic scatteringeffects. For easy integration the rib profile is one possibility.There exists several methods to calculate the relative permit-tivity of such structures (Biber, 2003). Here a method basedon transmission line models is used in which the resultingrelative permittivity is described as the mean of the relative

characteristic impedances (Z′=

√µr

εrwith µr = 1) of free

space and the substrate depending on the ratio of ribs andbars. Hence, a relative permittivity between 1 andεr,s of thesubstrate can be reached.

εr =

(tbarZ

′

substrate+ tribZ′

0

tbar+ trib

)−2

(5)

If the thickness of the ribs (trib) are predefined due to man-ufacturing constraints, one can easily calculate the thicknessof the bars (tbar) to reach the desired value forεr as calculatedby the optimization algorithm.

Figure2 shows the dependency of the relative permittivityversus the ratio of bars to ribs with constant rib thickness.It can be seen that the variation in relative permittivity foran increased bar thickness (resulting in higherεr values) islower, than for smaller values of the bar thickness. This willbe an important design possibility later on.

Adv. Radio Sci., 8, 49–54, 2010 www.adv-radio-sci.net/8/49/2010/

F. Fitzek et al.: Automotive radome design 51F. Fitzek et al.: Automotive Radome Design 3

0 0.5 1 1.5 2 2.5 31

1.2

1.4

1.6

1.8

2

2.2

bar thickness / rib thickness

relative permittivity

permittivity dependency of rib profile

Fig. 2. Permittivity dependency of rib profile

lower, than for smaller values of the bar thickness. This willbe an important design possibility later on.

4 Comparison of matching layers

For the comparison of these different approaches the opti-mization algorithm is visualized by graphs with all possibledegrees of freedom. This means that for all possible thick-ness of matching layer, all possible relative permittivities εrare shown. Obviously this can not be done for really all pos-sibilities, so discrete values are chosen in steps of 0.1 for therelative permittivity.This is done for one frequency f = 78.5 GHz and for theconsidered bandwidth B = 76−81 GHz. For the bandwidththe maximum reflection (meaning the worst case) within theband is considered for the evaluation. The best solution ofthe bandwidth analysis is taken for an angle variation in therange of ±40 deg. With the more exact solution (εr stepsize0.01) of the algorithm a tolerance analysis is shown with vari-ations of σ = ±0.1 mm. For the additional matching layerthe variation affects only the thickness of this layer. For thethickness optimization (integrated matching layer) the varia-tion only affects the thickness of the subtrate material of thebumper. The variation of the integrated structure (integratedmatching layer) affects on the one hand the thickness of thesubstrate material and on the other hand in our case the thick-ness of the bars.

4.1 Additional matching layer for substrate

The results for an additional matching layer for the sub-trate material of the bumper (no paint considered yet) aredepicted in Figure 3(a) and 3(b). In these figures the first(+), best (diamond) and last (x) graph are always highlightedto see the influence of increasing relative permittivity. Thesubstrate material has a relative permittivity in the range ofεr,s = 2.86 − 0.06i and a thickness of about ds = 3 mm.

0.3 0.35 0.4 0.45 0.5 0.55 0.6

-50

-40

-30

-20

-10

0

max. reflection / dB

thickness of matching layer / mm

εr = 1.0

εr = 2.6

εr = 3.0

(a) Optimization for a frequency

0.3 0.35 0.4 0.45 0.5 0.55 0.6-20

-15

-10

-5

0



εr = 1.0

εr = 2.4

εr = 3.0

(b) Optimization for a bandwidth

Fig. 3. Frequency and bandwidth analysis

Considering low-cost materials the relative permittivity forthe matching layer is varied between εr = 1 (initial con-dition) and εr = 3. It can be seen that for a relative per-mittivity of εr = 2.6 and a thickness of d = 0.43 mmthe reflection can be decreased by about 45 dB for one fre-quency (f = 78.5 GHz). Considering the maximum reflec-tion within the band (B = 76 − 81 GHz) the improvementis about 10 dB, resulting in a maximum reflection of -17 dB.This is achieved for a relative permittivity of εr = 2.4 and athickness of d = 0.47 mm.The angular dependency is depicted in Figure 4(a). Herethe optimal values for the relative permittivity and thicknesscombination from the bandwidth analysis are used to showthe behaviour. The combination mentioned before also givesthe best result for the angular dependency. Hence, the maxi-mum reflection coefficient within an angle of ±40 deg is stillbelow -10 dB. In Figure 4(b) the reflection is shown over fre-quency. The maximum reflection coefficient of about -17 dBcan be seen at the edges of the band (76/81 GHz) as calcu-lated before. Next to that the tolerance analysis for a varia-

Fig. 2. Permittivity dependency of rib profile.


For the comparison of these different approaches the opti-mization algorithm is visualized by graphs with all possibledegrees of freedom. This means that for all possible thick-ness of matching layer, all possible relative permittivitiesεr

are shown. Obviously this can not be done for really all pos-sibilities, so discrete values are chosen in steps of 0.1 for therelative permittivity.

This is done for one frequencyf = 78.5 GHz and for theconsidered bandwidthB = 76−81 GHz. For the bandwidththe maximum reflection (meaning the worst case) within theband is considered for the evaluation. The best solution ofthe bandwidth analysis is taken for an angle variation in therange of±40 deg. With the more exact solution (εr stepsize0.01) of the algorithm a tolerance analysis is shown with vari-ations ofσ = ±0.1 mm. For the additional matching layerthe variation affects only the thickness of this layer. For thethickness optimization (integrated matching layer) the varia-tion only affects the thickness of the subtrate material of thebumper. The variation of the integrated structure (integratedmatching layer) affects on the one hand the thickness of thesubstrate material and on the other hand in our case the thick-ness of the bars.


The results for an additional matching layer for the subtratematerial of the bumper (no paint considered yet) are depictedin Fig. 3a and b. In these figures the first (+), best (diamond)and last (x) graph are always highlighted to see the influenceof increasing relative permittivity. The substrate material hasa relative permittivity in the range ofεr,s = 2.86−0.06i anda thickness of aboutds = 3 mm. Considering low-cost mate-rials the relative permittivity for the matching layer is variedbetweenεr = 1 (initial condition) andεr = 3. It can be seenthat for a relative permittivity ofεr = 2.6 and a thickness ofd = 0.43 mm the reflection can be decreased by about 45 dB

F. Fitzek et al.: Automotive Radome Design 3

0 0.5 1 1.5 2 2.5 31

1.2

1.4

1.6

1.8

2

2.2










0.3 0.35 0.4 0.45 0.5 0.55 0.6

-50

-40

-30

-20

-10

0



εr = 1.0

εr = 2.6

εr = 3.0


0.3 0.35 0.4 0.45 0.5 0.55 0.6-20

-15

-10

-5

0



εr = 1.0

εr = 2.4

εr = 3.0






0 0.5 1 1.5 2 2.5 31

1.2

1.4

1.6

1.8

2

2.2










0.3 0.35 0.4 0.45 0.5 0.55 0.6

-50

-40

-30

-20

-10

0



εr = 1.0

εr = 2.6

εr = 3.0


0.3 0.35 0.4 0.45 0.5 0.55 0.6-20

-15

-10

-5

0



εr = 1.0

εr = 2.4

εr = 3.0





Fig. 3. Frequency and bandwidth analysis.

for one frequency (f = 78.5 GHz). Considering the maxi-mum reflection within the band (B = 76−81 GHz) the im-provement is about 10 dB, resulting in a maximum reflec-tion of −17 dB. This is achieved for a relative permittivity ofεr = 2.4 and a thickness ofd = 0.47 mm.

The angular dependency is depicted in Fig.4a. Herethe optimal values for the relative permittivity and thick-ness combination from the bandwidth analysis are used toshow the behaviour. The combination mentioned before alsogives the best result for the angular dependency. Hence, themaximum reflection coefficient within an angle of±40 degis still below −10 dB. In Fig. 4b the reflection is shownover frequency. The maximum reflection coefficient of about−17 dB can be seen at the edges of the band (76/81 GHz) ascalculated before. Next to that the tolerance analysis for avariation ofσ = ±0.1 mm is shown. The maximum reflec-tion is below−12 dB.

4.2 Integrated matching layer for substrate

The results for an integrated matching layer for the sub-trate material of the bumper (again no paint considered) are

www.adv-radio-sci.net/8/49/2010/ Adv. Radio Sci., 8, 49–54, 2010

52 F. Fitzek et al.: Automotive radome design4 F. Fitzek et al.: Automotive Radome Design

-40 -30 -20 -10 0 10 20 30 40-20

-15

-10

-5

0max. reflection / dB

angle / deg

εr = 1.0

εr = 2.4

εr = 3.0

(a) Angular dependency analysis

76 77 78 79 80 81-35

-30

-25

-20

-15

-10

-5

0

reflection / dB

frequency / GHz

σ = -0.1 mm

σ = 0 mm

σ = +0.1 mm

(b) Tolerance analysis

Fig. 4. Angular and tolerance analysis

tion of σ = ±0.1 mm is shown. The maximum reflection isbelow -12 dB.


The results for an integrated matching layer for the subtratematerial of the bumper (again no paint considered) are de-picted in Figure 5(a) and 5(b). This is done for the same ma-terial like before. The only difference is the above mentionedreduction of the substrate material. In the figures εr = 1shows the results for a thickness optimization, because onlythe thickness of the matching layer is varied. This results ina decreased thickness of the subtrate material of the bumper.The initial condition is represented by the relative permittiv-ity of εr = 2.8, which is nearly the same as the substrate ma-terial itself. The optimal solution for one frequency and forthe bandwidth is εr = 1.1 with a thickness of d = 0.74 mm.The maximum reflection within the band is about -21 dB,4 dB lower than that of the additional matching layer. Theangular dependency is depicted in Figure 6. The solution of

0.6 0.65 0.7 0.75 0.8 0.85 0.9-40

-35

-30

-25

-20

-15

-10

-5

0

reflection / dB


εr = 1.0

εr = 1.1

εr = 2.8


0.6 0.65 0.7 0.75 0.8 0.85 0.9-25

-20

-15

-10

-5

0



εr = 1.0

εr = 1.1

εr = 2.8



the bandwidth analysis shows no improvement concerningthe maximum reflection within the angular range. Neverthe-less for a smaller range (e.g. ±30 deg) the maximum reflec-tion would be below -10 dB. To cover the complete angularrange one ends up with another solution, εr = 1.4, whichreduces the maximum reflection below -10 dB, but increasesthe reflection for 0 deg by about 2 dB. Concerning only theangular dependency this would be the optimal solution. Thisshows that already in this stage the meaning of "optimal" isnot distinct. In the Section 4.3 this will be discussed. Never-theless we have now two possible "optimal" solutions. Theresults of the tolerance analysis are shown in Figures 7(a) forεr = 1.4 and 7(b) for εr = 1.1. Here the before mentionedcoherence between a higher permittivity and a smaller varia-tion in relative permittivity can be seen.

4.3 Discussion of substrate materials

The analysis of the reflections coming from the bumpershows that one optimal solution can not be defined with-



-40 -30 -20 -10 0 10 20 30 40-20

-15

-10

-5

0


angle / deg

εr = 1.0

εr = 2.4

εr = 3.0


76 77 78 79 80 81-35

-30

-25

-20

-15

-10

-5

0

reflection / dB

frequency / GHz

σ = -0.1 mm

σ = 0 mm

σ = +0.1 mm






0.6 0.65 0.7 0.75 0.8 0.85 0.9-40

-35

-30

-25

-20

-15

-10

-5

0

reflection / dB


εr = 1.0

εr = 1.1

εr = 2.8


0.6 0.65 0.7 0.75 0.8 0.85 0.9-25

-20

-15

-10

-5

0



εr = 1.0

εr = 1.1

εr = 2.8







Fig. 4. Angular and tolerance analysis.

depicted in Fig.5a and b. This is done for the same materiallike before. The only difference is the above mentioned re-duction of the substrate material. In the figuresεr = 1 showsthe results for a thickness optimization, because only thethickness of the matching layer is varied. This results in a de-creased thickness of the subtrate material of the bumper. Theinitial condition is represented by the relative permittivity ofεr = 2.8, which is nearly the same as the substrate materialitself. The optimal solution for one frequency and for thebandwidth isεr = 1.1 with a thickness ofd =0.74 mm. Themaximum reflection within the band is about−21 dB, 4 dBlower than that of the additional matching layer. The angulardependency is depicted in Fig.6. The solution of the band-width analysis shows no improvement concerning the maxi-mum reflection within the angular range. Nevertheless for asmaller range (e.g.±30 deg) the maximum reflection wouldbe below−10 dB. To cover the complete angular range oneends up with another solution,εr = 1.4, which reduces themaximum reflection below−10 dB, but increases the reflec-tion for 0 deg by about 2 dB. Concerning only the angulardependency this would be the optimal solution. This shows


-40 -30 -20 -10 0 10 20 30 40-20

-15

-10

-5

0


angle / deg

εr = 1.0

εr = 2.4

εr = 3.0


76 77 78 79 80 81-35

-30

-25

-20

-15

-10

-5

0

reflection / dB

frequency / GHz

σ = -0.1 mm

σ = 0 mm

σ = +0.1 mm






0.6 0.65 0.7 0.75 0.8 0.85 0.9-40

-35

-30

-25

-20

-15

-10

-5

0

reflection / dB


εr = 1.0

εr = 1.1

εr = 2.8


0.6 0.65 0.7 0.75 0.8 0.85 0.9-25

-20

-15

-10

-5

0



εr = 1.0

εr = 1.1

εr = 2.8








-40 -30 -20 -10 0 10 20 30 40-20

-15

-10

-5


angle / deg

εr = 1.0

εr = 2.4

εr = 3.0


76 77 78 79 80 81-35

-30

-25

-20

-15

-10

-5

0

reflection / dB

frequency / GHz

σ = -0.1 mm

σ = 0 mm

σ = +0.1 mm






0.6 0.65 0.7 0.75 0.8 0.85 0.9-40

-35

-30

-25

-20

-15

-10

-5

0

reflection / dB


εr = 1.0

εr = 1.1

εr = 2.8


0.6 0.65 0.7 0.75 0.8 0.85 0.9-25

-20

-15

-10

-5

0



εr = 1.0

εr = 1.1

εr = 2.8







Fig. 5. Frequency and bandwidth analysis.F. Fitzek et al.: Automotive Radome Design 5

-40 -30 -20 -10 0 10 20 30 40-25

-20

-15

-10

-5

0


angle / deg

εr = 1.0

εr = 1.4

εr = 2.8

Fig. 6. Angular analysis

76 77 78 79 80 81-20

-15

-10

-5

0

reflection / dB

frequency / GHz

σ = -0.1 mm

σ = 0 mm

σ = +0.1 mm

(a) Tolerance analysis for a rel. permittivity of 1.4

76 77 78 79 80 81-70

-60

-50

-40

-30

-20

-10

0

refl

ecti

on /

dB

frequency / GHz

σ = -0.1 mm

σ = 0 mm

σ = +0.1 mm

(b) Tolerance analysis for a rel. permittivity of 1.1

Fig. 7. Tolerance analysis

out knowing the sensor requirements. Nevertheless it ispossible to define a cost function from sensor requirementswhich clearly defines the optimal solution. Together with

0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1-12

-10

-8

-6

-4

-2

0

reflection / dB


εr = 1.0

εr = 2.8


0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1-12

-10

-8

-6

-4

-2

0



εr = 1.0

εr = 2.8



the detailed analysis shown above the optimal parameters canhence be calculated. Additionally, the evaluation shows thatthe integrated matching layer is superior over the additionalmatching layer concerning maximum reflection within thebandwidth. Because this is a strong requirement for futureradar sensors, the evaluation is focused on integrated match-ing layers in the following section.

4.4 Integrated matching layer for substrate and paint

The results for an integrated matching layer for the subtratematerial of the bumper with metallic paint (permittivity ofmetallic paint εr > 4 – condition depends on the substrate’spermittivity) are depicted in Figure 8(a) and 8(b). The sub-strate material is the same as before but with a slightly de-creased thickness of ds = 2.7 mm. Again, the integratedmatching layer results in a reduction of the substrate mate-rial. In the figures εr = 1 is coexistent for a thickness op-timization and εr = 2.8 represents the intial condition. Thefigures show that the reflections are increased for the sub-

Fig. 6. Angular analysis.

that already in this stage the meaning of “optimal" is not dis-tinct. In the Sect.4.3this will be discussed. Nevertheless wehave now two possible “optimal" solutions. The results ofthe tolerance analysis are shown in Fig.7a for εr = 1.4 and


F. Fitzek et al.: Automotive radome design 53


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76 77 78 79 80 81-20

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0reflection / dB

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76 77 78 79 80 81-70

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0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1-12

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0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1-12

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76 77 78 79 80 81-20

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76 77 78 79 80 81-70

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0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1-12

-10

-8

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reflection / dB


εr = 1.0

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0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1-12

-10

-8

-6

-4

-2

0



εr = 1.0

εr = 2.8







Fig. 7. Tolerance analysis.

7b for εr = 1.1. Here the before mentioned coherence be-tween a higher permittivity and a smaller variation in relativepermittivity can be seen.


The analysis of the reflections coming from the bumpershows that one optimal solution can not be defined with-out knowing the sensor requirements. Nevertheless it ispossible to define a cost function from sensor requirementswhich clearly defines the optimal solution. Together withthe detailed analysis shown above the optimal parameters canhence be calculated. Additionally, the evaluation shows thatthe integrated matching layer is superior over the additionalmatching layer concerning maximum reflection within thebandwidth. Because this is a strong requirement for futureradar sensors, the evaluation is focused on integrated match-ing layers in the following section.


-40 -30 -20 -10 0 10 20 30 40-25

-20

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-5

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angle / deg

εr = 1.0

εr = 1.4

εr = 2.8


76 77 78 79 80 81-20

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reflection / dB

frequency / GHz

σ = -0.1 mm

σ = 0 mm

σ = +0.1 mm


76 77 78 79 80 81-70

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0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1-12

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reflection / dB


εr = 1.0

εr = 2.8


0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1-12

-10

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εr = 1.0

εr = 2.8








-40 -30 -20 -10 0 10 20 30 40-25

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-5

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angle / deg

εr = 1.0

εr = 1.4

εr = 2.8


76 77 78 79 80 81-20

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reflection / dB

frequency / GHz

σ = -0.1 mm

σ = 0 mm

σ = +0.1 mm


76 77 78 79 80 81-70

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0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1-12

-10

-8

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reflection / dB


εr = 1.0

εr = 2.8


0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1-12

-10

-8

-6

-4

-2

0



εr = 1.0

εr = 2.8







Fig. 8. Frequency and bandwidth analysis.


The results for an integrated matching layer for the subtratematerial of the bumper with metallic paint (permittivity ofmetallic paintεr > 4 – condition depends on the substrate’spermittivity) are depicted in Fig.9a and9b. The substratematerial is the same as before but with a slightly decreasedthickness ofds = 2.7 mm. Again, the integrated matchinglayer results in a reduction of the substrate material. In thefiguresεr = 1 is coexistent for a thickness optimization andεr = 2.8 represents the intial condition. The figures show thatthe reflections are increased for the substrate material withmetallic paint. The optimal solution for one frequency andfor the bandwidth isεr = 1 with a thickness ofd = 0.81 mm1.The maximum reflection within the band is about−10 dB.The angular dependency is depicted in Fig.9a for the bestsolutions of the bandwidth analysis. The maximum reflec-tion within an angular range of±40 deg is about−4.5 dB.This can be optimized with a relative permittivity ofεr = 1.6below −6 dB, but with higher reflections within the band.

1For paints withεr < 4 the optimal solution differs.

www.adv-radio-sci.net/8/49/2010/ Adv. Radio Sci., 8, 49–54, 2010

54 F. Fitzek et al.: Automotive radome design6 F. Fitzek et al.: Automotive Radome Design

-40 -30 -20 -10 0 10 20 30 40-12

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angle / deg

εr = 1.0

εr = 1.6

εr = 2.8


76 77 78 79 80 81-12

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-8

-6

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0

reflection / dB

frequency / GHz

σ = -0.1 mm

σ = 0 mm

σ = +0.1 mm



strate material with metallic paint. The optimal solution forone frequency and for the bandwidth is εr = 1 with a thick-ness of d = 0.81 mm1. The maximum reflection within theband is about -10 dB. The angular dependency is depicted inFigure 9(a) for the best solutions of the bandwidth analysis.The maximum reflection within an angular range of ±40 degis about -4.5 dB. This can be optimized with a relative per-mittivity of εr = 1.6 below -6 dB, but with higher reflectionswithin the band. Nevertheless for a reduced angular rangeof ±10 deg the maximum reflection within the angular rangeand the bandwidth are below -10 dB. The tolerance analysisshows a maxmimum reflection below -7 dB. For σ = 0mmthe result of the bandwidth analysis can be checked with amaximum reflection within the band below -10 dB.

4.5 Discussion of painted materials

The evaluation of the different parameters show that it is pos-sible to reduce the maximum reflection within the bandwidth

1For paints with εr < 4 the optimal solution differs.

below -10 dB even with metallic paints. Metallic paints havethe highest permittivities of all paints, hence considering aworst case. It is clearly shown that the angular dependencyand the tolerances play an important role for the design ofan optimal matching layer. Again an "optimal" solution onlyexists for specific sensor requirements.

5 Conclusions

This paper compares different possibilities for low-cost in-tegration of radar sensors for the 79 GHz band. The as-sumptions of the model described are a plane wave incidenton a non-magnetic, plane material without roughness. It isshown for plastic fascia, that the bandwidth requirementsB = 76 − 81 GHz, the angular requirements ±40 deg andtolerance influences σ = ±0.1 mm can be met coexistentlywith low-cost matching. This can be realized using a rib pro-file (integrated matching layer).For painted fascia the bandwidth requirement can be metwith a maximum reflection of below -10 dB. The thicknessoptimization (integrated matching layer) delivers the bestsolution considering the mentioned realization possibilities.Because the angular dependency and the tolerance analysisare based on this evaluation, they suffer from the requirementof 5 GHz bandwidth. Nevertheless the maximum reflectioncan be reduced below -10 dB under certain conditions. Theoptimisation of the angular dependency and the tolerance in-fluence is considered for future work. An overall optimalsolution can be found knowing the detailed requirements offuture radar sensors.

Acknowledgements. The authors wish to thank the German FederalMinistry of Education and Research (BMBF) for the funding of theRoCC joint project.

References

Alitalo, P., Luukkonen, O., Vehmas, J., and Tretyakov, S. A.:Impedance-Matched Microwave Lens, 7, 187–191, 2008.

S. Biber, J. Richter, S. Martius, and L.-P. Schmidt, “Design of ar-tificial dielectrics for anti-reflection-coatings,” in European Mi-crowave Conference, 2003. 33rd, Oct. 2003, pp. 1115–1118.

Fitzek, F. and Rasshofer, R. H.: Automotive Radome Design - Re-flection Reduction in stratified media, Antennas and WirelessPropagation Letters, IEEE, 8, 2009.

Hecht, E.: Optik, Oldenbourg Wissenschaftsverlag, 2005.Jones, E. and Cohn, S.: Surface matching of dielectric lenses, in:

Proc. IRE International Convention Record, vol. 2, pp. 46–53,1954.

Kurt Altenburg, S. K.: Wellenausbreitung in geschichteten Medienbei senkrechtem Einfall [...], vol. 448, Annalen der Physik, 1953.

Rasshofer, R. H.: Functional Requirements of Future AutomotiveRadar Systems, in: Proc. of the European Radar Conference,Munich, Germany, 2007.

RoCC press release, http://www.eenova.de/news-presse/rocc/,2009.



-40 -30 -20 -10 0 10 20 30 40-12

-10

-8

-6

-4

-2

0


angle / deg

εr = 1.0

εr = 1.6

εr = 2.8


76 77 78 79 80 81-12

-10

-8

-6

-4

-2

0

reflection / dB

frequency / GHz

σ = -0.1 mm

σ = 0 mm

σ = +0.1 mm



strate material with metallic paint. The optimal solution forone frequency and for the bandwidth is εr = 1 with a thick-ness of d = 0.81 mm1. The maximum reflection within theband is about -10 dB. The angular dependency is depicted inFigure 9(a) for the best solutions of the bandwidth analysis.The maximum reflection within an angular range of ±40 degis about -4.5 dB. This can be optimized with a relative per-mittivity of εr = 1.6 below -6 dB, but with higher reflectionswithin the band. Nevertheless for a reduced angular rangeof ±10 deg the maximum reflection within the angular rangeand the bandwidth are below -10 dB. The tolerance analysisshows a maxmimum reflection below -7 dB. For σ = 0mmthe result of the bandwidth analysis can be checked with amaximum reflection within the band below -10 dB.


The evaluation of the different parameters show that it is pos-sible to reduce the maximum reflection within the bandwidth

1For paints with εr < 4 the optimal solution differs.

below -10 dB even with metallic paints. Metallic paints havethe highest permittivities of all paints, hence considering aworst case. It is clearly shown that the angular dependencyand the tolerances play an important role for the design ofan optimal matching layer. Again an "optimal" solution onlyexists for specific sensor requirements.

5 Conclusions

This paper compares different possibilities for low-cost in-tegration of radar sensors for the 79 GHz band. The as-sumptions of the model described are a plane wave incidenton a non-magnetic, plane material without roughness. It isshown for plastic fascia, that the bandwidth requirementsB = 76 − 81 GHz, the angular requirements ±40 deg andtolerance influences σ = ±0.1 mm can be met coexistentlywith low-cost matching. This can be realized using a rib pro-file (integrated matching layer).For painted fascia the bandwidth requirement can be metwith a maximum reflection of below -10 dB. The thicknessoptimization (integrated matching layer) delivers the bestsolution considering the mentioned realization possibilities.Because the angular dependency and the tolerance analysisare based on this evaluation, they suffer from the requirementof 5 GHz bandwidth. Nevertheless the maximum reflectioncan be reduced below -10 dB under certain conditions. Theoptimisation of the angular dependency and the tolerance in-fluence is considered for future work. An overall optimalsolution can be found knowing the detailed requirements offuture radar sensors.

Acknowledgements. The authors wish to thank the German FederalMinistry of Education and Research (BMBF) for the funding of theRoCC joint project.

References


S. Biber, J. Richter, S. Martius, and L.-P. Schmidt, “Design of ar-tificial dielectrics for anti-reflection-coatings,” in European Mi-crowave Conference, 2003. 33rd, Oct. 2003, pp. 1115–1118.

Fitzek, F. and Rasshofer, R. H.: Automotive Radome Design - Re-flection Reduction in stratified media, Antennas and WirelessPropagation Letters, IEEE, 8, 2009.



Kurt Altenburg, S. K.: Wellenausbreitung in geschichteten Medienbei senkrechtem Einfall [...], vol. 448, Annalen der Physik, 1953.


RoCC press release, http://www.eenova.de/news-presse/rocc/,2009.


Fig. 9. Angular and tolerance analysis.

Nevertheless for a reduced angular range of±10 deg themaximum reflection within the angular range and the band-width are below−10 dB. The tolerance analysis shows amaxmimum reflection below−7 dB. Forσ = 0 mm the resultof the bandwidth analysis can be checked with a maximumreflection within the band below−10 dB.


The evaluation of the different parameters show that it is pos-sible to reduce the maximum reflection within the bandwidthbelow −10 dB even with metallic paints. Metallic paintshave the highest permittivities of all paints, hence consid-ering a worst case. It is clearly shown that the angular de-pendency and the tolerances play an important role for thedesign of an optimal matching layer. Again an "optimal" so-lution only exists for specific sensor requirements.

5 Conclusions

This paper compares different possibilities for low-cost in-tegration of radar sensors for the 79 GHz band. The as-sumptions of the model described are a plane wave incidenton a non-magnetic, plane material without roughness. It isshown for plastic fascia, that the bandwidth requirementsB = 76−81 GHz, the angular requirements±40 deg and tol-erance influencesσ = ±0.1 mm can be met coexistently withlow-cost matching. This can be realized using a rib profile(integrated matching layer).

For painted fascia the bandwidth requirement can be metwith a maximum reflection of below−10 dB. The thicknessoptimization (integrated matching layer) delivers the bestsolution considering the mentioned realization possibilities.Because the angular dependency and the tolerance analysisare based on this evaluation, they suffer from the requirementof 5 GHz bandwidth. Nevertheless the maximum reflectioncan be reduced below−10 dB under certain conditions. Theoptimisation of the angular dependency and the tolerance in-fluence is considered for future work. An overall optimalsolution can be found knowing the detailed requirements offuture radar sensors.

Acknowledgements.The authors wish to thank the German FederalMinistry of Education and Research (BMBF) for the funding of theRoCC joint project.

References


Biber, S., Richter, J., Martius, S., and Schmidt, L.-P.: Design of ar-tificial dielectrics for anti-reflection-coatings, in: European Mi-crowave Conference, 33rd, October 2003, pp. 1115–1118, 2003.

Fitzek, F. and Rasshofer, R. H.: Automotive Radome Design – Re-flection Reduction in stratified media, Antennas and WirelessPropagation Letters, IEEE, 8, 2009.



Kurt Altenburg, S. K.: Wellenausbreitung in geschichteten Medienbei senkrechtem Einfall [...], Annalen der Physik, 448, 1–43,1953.


RoCC press release,http://www.eenova.de/news-presse/rocc/,2009.


http://www.eenova.de/news-presse/rocc/

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