effects of reinforced concrete structures on rf

486 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 42, NO. 4, NOVEMBER 2000

illumination is still not correctly predicted, but it may result from ameasurement problem due to the very low values of the magnetic fieldin that case.

VI. CONCLUSION

The refined model of the apertures and the adaptive mesh techniqueare efficient at frequencies lower than 500 MHz. At higher frequencies,the internal details are important, and generally any internal structuresof sizes greater than�=5 have to be taken into account. An optimalmesh of a realistic enclosure has been built. Let us assume that if thenumerical code and the defined mesh provide accurate results whenthe shielding is illuminated from the outside, they should also providea good basis in the reciprocal configuration, when the shielding is il-luminated from the inside by an equivalent numerical source. This lastconfiguration is the closest to the actual one in which the power con-verter illuminates its enclosure and radiates toward the outside. Finally,by means of the receiving configuration, we have developed a methodto model the EUT in order to precisely predict the shielding effective-ness and a way for defining an optimal mesh of the enclosure, suitablefor starting to model the emissions problem.

ACKNOWLEDGMENT

The authors would like to thank V. Levillain, Aerospatiale Company,Les Mureaux, France, and R. Leveillé and C. Cottard from PSA Peu-geot Citroën Company, La Garenne Colombes, France, for the helpprovided.

REFERENCES

[1] J. M. Lograsson, M. A. Wisnewski, and J. P. Souther, “Electromag-netic compatibility and electric vehicles—General Motors advancedtechnology vehicles,” in14th Int. Elect. Veh. Symp., Orlando, FL, Oct.1997.

[2] R. Chotard, R. Léveillé, V. Levillain, W. Tabbara, and G. Alquié, “Cou-pling of an electromagnetic wave to a metallic box through two types ofaperture,” inEuroEM 94, Bordeaux, France, May 30–June 4, 1994.

[3] V. Robin, P. Bonamour, and B. Lepetit, “Étude de la réponse électro-magnétique d’un avion: Apport d’une modélization théorique,” inActesdu Colloque CEM 94, Toulouse, France, Mar. 1994, pp. 213–218.

[4] S. Dop and G. Alquié, “Modèle multiconducteur d’un simulateur largebande. Évaluation de l’onde guidée,” inActes du Colloque CEM 98,Brest, France, June 1998.

[5] J. E. Bridges, “An update on the circuit approach to calculate shieldingeffectiveness,” IEEE Trans. Electromagn. Compat., vol. 30, pp.211–221, Aug. 1988.

[6] H. A. Bethe, “Theory of diffraction by small holes,”Phys. Rev., vol. 66,pp. 163–182, Oct. 1944.

[7] D. Lecointe, W. Tabbara, and J.-L. Lasserre, “Coupling of an EM waveto a wire in a cavity variations with wire position,” inEuroEM 94, Bor-deaux, France, May 30–June 4, 1994.

[8] C. M. Butler, “Electromagnetic Penetration through apertures in con-ducting surfaces,”IEEE Trans. Antennas Propagat., vol. AP-26, pp.82–93, Jan. 1978.

[9] K. S. H. Lee,E.M.P. Interaction: Principles, Techniques, and ReferenceData. New York: Hemisphere, 1986.

[10] V. Levillain, “Couplage éléments finis-équations intégrales pour la ré-solution des équations de Maxwell en milieu hétérogène,” Ph.D. disser-tation, de l’École Polytechnique, Palaiseau, France, June 1991.

[11] A. Bendali, “Numerical analysis of the exterior boundary value problemfor the time-harmonic Maxwell equations by a boundary finite elementmethod—Part 1: The continuous problem,”Math. Computat., vol. 43,no. 167, pp. 29–46, July 1984.

[12] P. A. Raviart and J. M. Thomas, “A mixed finite element method forsecond order elliptic problems,” inMathematical Aspects of Finite El-ement Methods, ser. Lecture Notes 606 in Mathematics. Berlin, Ger-many: Springer-Verlag, 1975.

Effects of Reinforced Concrete Structures on RFCommunications

Roger A. Dalke, Christopher L. Holloway, Paul McKenna,Martin Johansson, and Azar S. Ali

Abstract—The proliferation of communication systems used in andaround man-made structures has resulted in a growing need to determinethe reflection and transmission properties of various commonly usedbuilding materials at radio frequencies typically used in businesses andresidential environments. This paper describes the calculation of reflectionand transmission coefficients for reinforced concrete walls as a function ofwall thicknesses and rebar lattice configuration over a frequency range of100–6000 MHz. The transmission and reflection coefficients were calcu-lated using a finite-difference time-domain (FDTD) solution of Maxwell’sequations. The rebar structures analyzed include both a two-dimensional(2-D) trellis-like structure and a one-dimensional (1-D) structure, wherethe reenforcing bars are all oriented in the same direction. In general, theresults show that the reinforced concrete structures severely attenuatesignals with wavelengths that are much larger than the rebar lattice andthat the transmitted signal has a complex structure withresonancesandnulls that strongly depend upon the geometry of the reinforcing structureand the concrete wall thickness.

Index Terms—Finite-difference time-domain (FDTD), propagationmodel, reflection and transmission coefficient, reinforced concrete.

I. INTRODUCTION

The growing use of high data rate communications systems forresidential and business communications (e.g., local area networks,vehicular communications, personal communications services) inand around buildings and other man-made structures has increasedthe need to understand and predict how commonly used buildingmaterials can affect the propagation channel. In particular, signalfading and intersymbol interference resulting from reflections andwall penetration can severely degrade system performance.

Characterization of a wireless communications channel that includesman-made structures requires a knowledge of the reflection and trans-mission properties of commonly used building materials. Until recently[1]–[10], little emphasis has been given to characterizing reflection andtransmission properties of building materials for use by communica-tion systems designers in predicting system performance. This paperdescribes the calculation of electromagnetic (EM) reflection and trans-mission characteristics for a reinforced concrete wall as a function ofrebar geometry and wall thickness over a frequency range of 100–6000MHz using finite-difference time-domain (FDTD) techniques.

There are a wide variety of methods used to reinforce concrete wallssuch as wire meshes and reinforcing rods (rebar) of various dimensionsand spacings depending on the structural requirements of the building.Such rebar structures have various geometrical designs ranging fromsimple lattice or trellis type structures to more complex and dense ar-

Manuscript received May 24, 1999; revised April 18, 2000.R. A. Dalke and P. McKenna are with the Institute for Telecommunication

Sciences, U.S. Department of Commerce, Boulder Laboratories, Boulder, CO80303 USA.

C. L. Holloway was with the Institute for Telecommunication Sciences, U.S.Department of Commerce, Boulder Laboratories, Boulder, CO 80303 USA. Heis now with the National Institute of Standards and Technology, U.S. Depart-ment of Commerce, Boulder Laboratories, Boulder, CO 80303 USA.

M. Johansson is with Ericsson Microwave Systems, Core Unit Antenna Tech-nology, SE-43184 Mölndal, Sweden.

A. S. Ali is with the Air Force Research Laboratories, Eglin AFB, FL 32542USA.

Publisher Item Identifier S 0018-9375(00)10716-1.

U.S. Government work not protected by U.S. copyright.

IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 42, NO. 4, NOVEMBER 2000 487

(a)

(b)

(c)

Fig. 1. Lattice configuration. (a) Rebar parallel to incidentE field. (b) Rebarperpendicular to incidentE field. (c) 2-D grid with rebar both parallel andperpendicular to the incidentE field.

rangements when a high degree of strength is required. It would be pro-hibitive to study all possible structural designs. The intent of this paperis to report on results from a study involving reinforced concrete struc-tures that were encountered in a radio-link analysis involving wirelesscommunications through buildings.

The three general rebar configurations that were analyzed are shownin Fig. 1. In the case of parallel reinforcing bars (no crossbars), thetransmission and reflection coefficients for a normally incident planewave were calculated with the incident electric field both perpendic-ular and parallel to the rebar, as shown in Fig. 1(a) and (b). The thirdconfiguration corresponds to a two-dimensional (2-D) trellis-like rebarstructure. In this case, the reflection and transmission coefficients werecalculated for an incident electric field oriented parallel to one direc-tion of the rebar lattice [see Fig. 1(c)].

For this analysis, we are primarily interested in evaluating the reso-nant phenomena of a reinforced concrete structure. Therefore, we have

Fig. 2. Reinforced concrete wall.

assumed that the material properties are independent of frequency andequal to typical values at 1 GHz. In a separate publication, we willpresent the results for the effects of dispersion due to frequency-de-pendent material properties of concrete.

II. FDTD SOLUTION

There are various numerical and quasi-analytical methods that canbe used to determine the transmission and reflection characteristicsfor a periodic reinforced concrete wall of infinite extent (e.g., mode-matching, Floquet analysis, etc.). For this study, we used a numericalFDTD method that exploited the symmetry of the structure. Plane wavereflection and transmission characteristics were calculated for variouswall thicknessesW , rebar diametersD, and periodsP (see Fig. 2). Theresults of this analysis are given in terms of transmission and reflectioncoefficients for a normally incident plane wave. The transmission co-efficientT is defined by

Et = TEo (1)

whereEo is the incident electric field andEt is the transmitted electricfield. The reflection coefficientR is defined by

Er = REo (2)

whereEr is the reflected electric field.In general, the FDTD technique requires the volume of the compu-

tational space (i.e., the reinforced concrete wall and the air region oneither side of the wall) to be subdivided into unit rectangular paral-lelepiped cells. The magnetic (~H) and electric (~E) field vector compo-nents on these cells are represented by a Yee space lattice [11]. Usingthis scheme [11], [12], the coupled Maxwell’s curl equations are solvedfor both the~H and ~E fields in time and space.

The algorithm is implemented using a staggered grid in both spaceand time with the electric and magnetic fields offset by one-half ofthe spatial increment and one-half of the time increment. For example,using Cartesian coordinates and central differences with time incre-ment�t and space increments�x, �y, �z; thex component of the~E and ~H fields is given as follows:

Hn+1x (i; j + 1; k + 1)

= Hnx (i; j + 1; k + 1)�

�t

�

�

En+1=2z (i; j + 1; k + 1)� E

n+1=2z (i; j; k + 1)

y(j + 1)� y(j)


Fig. 3. Three-dimensional (3-D) reinforced concrete computational volume.

+�t

�

En+1=2y (i; j + 1; k + 1)�E

n+1=2y (i; j + 1; k)

z(k + 1)� z(k)

�

�t+

�

2En+3=2x (i; j; k)

=�

�t�

�

2En+1=2x (i; j; k)

+Hn+1z (i; j + 1; k)�Hn+1

z (i; j; k)

y0(j + 1)� y0(j)

�

Hn+1y (i; j; k + 1)�Hn+1

y (i; j; k)

z0(k + 1)� z0(k)

y(j) = j �1

2�y; y0(j) = (j � 1)�y

z(k) = k �1

2�z; z0(k) = (k � 1)�z (3)

where the integersi, j, k, andn represent the discrete Cartesian spaceand time coordinates respectively and�, �, and� denote permittivity,permeability, and conductivity. The other components have a similarstructure. Note that the electric and magnetic field components are stag-gered in both space and time in order to achieve an explicit centraldifference scheme. Typically, the finite-difference technique is imple-mented by first advancing all the~H fields in the computational volumeby using the~E fields at the previous time step. Then the~E fields areadvanced by using the~H fields that were just calculated, and so on.The scattering object (i.e., reinforced concrete wall) was included bysetting� = 1:95 mS/m and the relative permittivity�r = 6 at cell lo-cations occupied by the concrete wall and setting the tangential electricfields on the boundaries of the rebar equal to zero. The values used for� and� are typical for concrete at 1 GHz.

An incident plane wave was introduced into the computationalvolume by using a numerical implementation of the EM equivalenceprinciple. This was accomplished by creating aHuygenssurfacebounded by z-planes near the ends of the computational volume (seeFig. 3). The equivalent electric and magnetic currents on this surfaceare set to produce the desired plane wave fields inside the surface (inthe absence of the concrete wall) and zero field outside the surface.Thus, when the scatterer is introduced, the numerical code producesthe total field (incident+ scattered) inside the surface and the scatteredfield outside of the surface. For this problem, the time dependence ofthe incident electric field was

E(t) =sin2(2�f0t); t <

1

2f0

0; t >1

2f0

(4)

wheref0 = 1:5 GHz which provides adequate resolution for frequen-cies up to 6 GHz.

For stability of this scheme, one needs to ensure that

�t <1

v1

�x2+

1

�y2+

1

�z2

(5)

wherev is the maximum velocity of the propagation in the computa-tional volume. This criterion is referred to as the Courant or the CFL(Courant–Friedricks–Lewy) stability condition [13] and [14] and es-sentially states that the numerical speed of propagation must exceedthe physical speed of propagation for numerical stability.

The size of the spatial increment is governed by two requirements.First, the finite-difference grid should resolve the highest frequency of


(a)

(b)

Fig. 4. Comparisons of the FDTD results to results obtained from modematching and from finite-element simulations (P = 1:5 cm,D = 0:75 cm).(a)E field perpendicular to rods. (b)E field parallel to rods.

interest, which is usually accomplished by using at least ten cells perwavelength at this frequency. Second, the cells should be small enoughto resolve all scattering objects in the computational volume (rebar inthe present case). For this calculation, sizing the finite-difference cellsto resolve the rebar was the more restrictive condition. In this analysis,the cell size used was approximately equal to a tenth of the radius ofthe rebar (e.g., 1 mm for rebar 1.91 cm (3/400) in diameter).

A. Boundary Conditions for the Computational Volume

For the cell sizes required to resolve the rebar (on the order of mil-limeters), the computational volume must be kept as small as possibleso as not to exceed computer resources. This was accomplished by ex-ploiting the periodic structure of the concrete wall and using a normallyincident plane wave polarized parallel (or perpendicular) to the orien-

TABLE IREINFORCEDCONCRETEWALL PARAMETERS

tation of the rebar. Under these conditions, symmetric boundary condi-tions were applied in two spatial directions and, hence, two dimensionsof the computational volume were reduced to half a period of the struc-ture. Absorbing boundary conditions were applied on boundaries thatwere not planes of symmetry.

Fig. 3 shows a typical rebar lattice structure and the planes wherethe symmetric boundary conditions were applied. In this example, theelectric field is in thex direction and there are twox planes of sym-metry (i.e.,x is normal to the plane) and twoy planes of symmetry.Denoting the discrete finite-difference coordinates of thex planes ofsymmetry asi = 1 andi = imax, the discrete boundary conditions are

Hz(1; j; k) = Hz(2; j; k)

Hz(imax; j; k) = Hz(imax � 1; j; k)

Hy(1; j; k) = Hy(2; j; k)

Hy(imax; j; k) = Hy(imax � 1; j; k): (6)

Similarly, denoting the discrete coordinates of they planes of sym-metry asj = 1 andj = jmax, the discrete boundary conditions are

Hz(i; 1; k) = �Hz(i; 2; k)

Hz(i; jmax; k) = �Hz(i; jmax � 1; k)

Hx(i; 1; k) = �Hx(i; 2; k)

Hx(i; jmax; k) = �Hx(i; jmax � 1; k): (7)

Note that for this example, thex-plane boundary conditions are sym-metric and they-plane boundary conditions are antiasymmetric.

The incident field propagates in thez direction and, hence, the fieldsare not symmetric aboutz planes. The computational volume was trun-cated alongz planes by using first-order Mur absorbing boundary con-ditions [15] (see Fig. 3). This type of boundary condition is adequatefor this problem since it is designed to absorb normally incident fields.

III. N UMERICAL RESULTS AND DISCUSSION

To validate this approach, we compared FDTD results for a thin wiregrating (see Fig. 1) to those obtained from a calculation using modematching [16] and also to those obtained from a calculation using fi-nite-elements. Fig. 4 gives the comparison of the results using thesethree methods for a structure consisting of a wire grating. Note that theFDTD solution is in good agreement with the other two methods. Theconclusion here is that the FDTD method and the boundary conditions


(a)

(b)

Fig. 5. Normal incidence reflection and transmission coefficients for (a) rebar lattice in free-space (P = 7:62 cm andD = 1:91 cm) and (b) plane conductingsheet (� = 6, � = 1:95 mS/m,W = 20:32 cm).

described above can be used to accurately calculate transmission andreflection coefficients for the reinforced concrete wall.

The reflection and transmission properties of a reinforced concretewall is a complicated function of the wall thickness and rebar config-uration (e.g., lattice spacing and diameter). First consider the behaviorof a 2-D rebar lattice in free-space (�r = 1 and� = 0). The lattice willseverely attenuate the transmitted field at wavelengths that are muchlarger than the lattice periodP . In general, the attenuation due to arebar lattice in free-space should be monotonic and decreasing (withfrequency) up to the first resonance (i.e., peak in the transmitted field).For example, Fig. 5(a) shows results for a rebar lattice in free-spacewhereP = 7:62 cm andD = 1:91 cm.

At low frequencies, the lattice acts inductively and the transmittedfield strength increases with frequency to a maximum at the first reso-nance where the wavelength (� � P ). It should be noted that the shapeof the curves as well as the wavelength at the first resonance are, in

general, a function of the rebar diameter as well as the lattice dimen-sions. The first resonance occurs when� � P (and not�=2 � P )because the plane wave excitation causes currents to flow in the samedirection on adjacent parallel conducting elements of the lattice that arealigned with the incident electric field. Since the currents on two adja-cent conductors are equal in magnitude and direction, there is a null inthe induced magnetic and electric fields halfway between the conduc-tors which is consistent with this mode.

Now consider the behavior of a plane sheet of moderate conduc-tivity, (i.e., the nonreinforced concrete wall with�r = 6 and� = 1:95mS/m). It is expected that maximum transmission (resonances) willoccur at wavelengths (in the concrete�c) when�c=2 = W , W=2,W=4, W=8; � � � and minimums will occur when�c=4 = W , W=3,W=5; � � �, as shown in Fig. 5(b), which gives the reflection and trans-mission coefficients for a 20.32 cm sheet. The results presented inFig. 5(b) are from an analytic calculation.


Fig. 6. Reflection and transmission coefficients for a concrete wall with a 2-D rebar lattice.P = 7:62 cm,D = 1:91 cm,W = 15:24 cm.


The reflection and transmission coefficients for a concrete wall con-taining a 2-D lattice reinforcing structure using the parameters given inTable I (with� = 1:95 mS/m and�r = 6) are shown in Figs. 6–14.These coefficients exhibit a combination of the trends (e.g., resonances)described above. For example, Figs. 6–8 give the transmission and re-flection coefficients for a rebar structure having a period of 7.62 cm,rebar diameter of 1.9 cm, and wall thicknesses of 15.24, 20.32, and30.48 cm. In all three cases, thelowestfrequencies are attenuated bythe rebar structure as expected. The first peak in the transmission coeffi-cient roughly corresponds to the frequency of the first resonance due tothe conducting wall alone or�c = 2W . The following peaks are not ateven integer multiples of the first resonance frequency as expected andare due to the interaction between the wall and the reinforcing struc-ture. It should be noted that after the first peak, the reinforced concretewall has generally larger transmission coefficients than the rebar latticealone. As the frequency increases, the structure of the transmission andreflection coefficients becomes quite complex.

Fig. 9 shows the results when the rebar lattice period is increased to15.24 cm for a wall thickness of 20.32 cm and a diameter of 1.91 cm.Here, the first peak is at alower frequency and has ahigheramplitudethan the corresponding case described in the previous paragraph. Thisis due to the fact that the slope of thelow-frequency transmission coeffi-cient increases as the period increases. This effect alters the form of thetransmission and reflection coefficients atlower frequencies (vis-à-visthe previous example).

As shown in Fig. 5(a) and (b), the resonant behavior of the rebar infree-space and the unreinforced slab are quite distinct. When the rebarstructure is embedded in the slab, the resonant behavior changes con-siderably from that of the slab or rebar structure alone. The influenceof the combination of the embedded rebar structure and slab thicknesson the resonant behavior can be observed by contrasting the results pre-sented in Figs. 5(a) and (b) and 7.

Fig. 10 shows the reflection and transmission coefficients when therebar diameter is increased to 5.08 cm for a wall thickness of 20.32 cm




and a period of 15.24 cm. The increased diameter significantly altersthe low frequency behavior of the interaction of the fields and the rebarstructure resulting in a decrease in the transmission coefficient (whencompared to the 1.91-cm-diameter rebar).

The remainder of the figures show the same general trends as the wallthickness, period, and rebar diameter are varied. In all cases, the highfrequency behavior is very complex. The amplitude of the reflectionand transmission coefficients slowly declines with frequency due to theconductivity of the concrete wall.

The results for the case where the rebar is one-dimensional (1-D) (nocrossbars) and in free-space were presented in Fig. 4. When the incidentelectric field was parallel to the rebar, the results were similar (at thelower frequencies) to what would be obtained for a trellis structure (i.e.,a relatively large reflection coefficient). When the incident electric fieldis perpendicular to the rebar, the low frequency reflection coefficientis small. If this structure were embedded in concrete, the resonances

due to the wall thickness would be superimposed on the general trendsshown in the figure.

For the purposes of this study the rebar lattice was electricallyconnected at the junctions. As may be expected, if the rebar is notelectrically connected, the resonance characteristics of response willvary. For a comparison, we calculated the response when the rebarwas not directly electrically connected (except for the conductingproperties of the concrete) forP = 7:62 cm, D = 1:91 cm, andW = 15:24 cm. The results are depicted in Fig. 15, where theresponse for connected and disconnected structures are presented.Low-frequency behavior remains essentially unchanged and, at higherfrequencies, the resonant structure of the response differs somewhatin the two cases. The low-frequency response is affected primarily bythe rebars that are parallel to the incident electric field. In general,the spacing between the disconnected rebar structures will affect thecharacteristics of the response. In this example, the spacing of the




disconnected case is about one rebar diameter. Of note, the responseas a function of frequency remains quite complicated as in the otherexamples shown in this paper.

The results shown in Figs. 6–14 illustrate that any reinforced con-crete wall will have a complicated series of nulls and resonances.In general, the depth of nulls and frequency dependence cannot bepredicted from measuring or analyzing one particular frequency orstructure. The point being that systems designers need to observe thata single frequency measurement or analysis of a particular geometrywill not be applicable to other structures with just minor changesin parameters such as wall thickness and reinforcing geometry. Thisnotwithstanding, these results can be used to obtain estimates of worstcase link analysis for communications systems that are required topenetrate such structures. The average loss in most cases appears tobe about 10 dB, with rapid fluctuations (on the order of 10 dB) with

frequency. The results presented here do show that for these struc-tures, a 20–30 dB loss can be experienced over the frequency rangeof 1–6 GHz, which must be accounted for in the link budget used bysystems designers.

IV. CONCLUDING REMARKS

In summary, at the lowest frequencies, the transmitted signal is at-tenuated by the rebar structure. As the frequency increases, the effectsof the wall become more pronounced and result in larger than expected(vis-à-vis the rebar only case) transmission coefficients. The maximaand minima of the transmission (and reflection) coefficients depend oncomplicated interactions between the rebar geometry, wall thickness,and electrical properties. These results show that the transmission co-efficient for the reinforced wall can be much larger than what would be




predicted for a rebar structure alone. Also, as the frequencies increase,the transmission and reflection coefficients vary significantly. Whilethe frequency response of the structures analyzed here varies signifi-cantly, on average, the loss in most cases appears to be about 10 dB,with rapid fluctuations on the order of 10 dB. From a communicationsystem designer’s view point a 20–30 dB link margin may be neededto obtain the required signal-to-noise ratio when the signal penetratessuch reinforced concrete structures.

Clearly, the effects of reinforced concrete walls on a narrowbandsignal depend on the particular wall structure, electrical properties, andfrequency and changes in these variables can significantly alter the re-flection and transmission properties of the structure. Hence, reflectionand transmission properties based on single frequency measurementsor calculations for a particular wall structure cannot be reliably extrap-olated to predict the characteristics for similar structures with differentphysical dimensions or frequencies.

The results presented show that the complicated resonance nature ofa reinforced concrete wall can have a detrimental effect on communi-cation systems used in and around such structures in terms of multipathinterference, losses due to wall penetration, and strong frequency-se-lective fading. In particular, broad-band signals will be severely de-graded by transmission through reinforced concrete structures.

In this work, we have assumed that the material properties of the con-crete are constant and equal to typical values at 1 GHz. In general, con-crete (likemost materials)has frequency-dependentmaterial properties.However, by assuming frequency-independent material properties, wewere able to investigate the different resonant phenomena of the rein-forced concrete structure. The results presented are reasonable for ul-trahigh frequencies (UHFs) typically used for communications systems(e.g., personal communications and cellular systems) and at lower fre-quencies, where the rebar structure dominates the behavior of the reflec-tion and transmission coefficients. The effects of frequency-dependent



Fig. 15. Comparision of the transmission coefficient when lattice structure is electrically connected and disconnected with a 2-D rebar lattice.P = 7:62 cm,D = 1:91 cm,W = 15:24 cm.

material properties for this type of structure will be the subjectofa futurepaper.

Reinforced concrete wallshave acomplicatedseries ofnulls and reso-nances, thedepthofnullsand frequencydependencecannotbepredictedfrom measuring or analyzing one particular frequency for a particularstructure. It is our intent in the future to perform a series of broadbandmeasurementsofRFbuildingpenetration tobetterunderstand theeffectsof radio propagation involving various types of concrete structures.

Finally, this effort demonstrates the efficacy of using FDTD methodsto calculate EM penetration characteristics of periodic structures. Fu-ture efforts will involve expanding the use of this methodology to othertypes of structures that are encountered by typical RF communicationssystems.

REFERENCES

[1] K. Sato, H. Kozima, H. Masuzawa, T. Manabe, T. Ihara, Y. Kassahima,and K. Yamaki, “Measurements of reflection characteristics and refrac-tive indices of interior construction material in millimeter-wave bands,”in Proc. IEEE 45th Veh. Technol. Conf., Chicago, IL, 1995, pp. 449–453.

[2] C. L. Holloway, P. L. Perini, R. R. DeLyser, and K. C. Allen, “Analysis ofcomposite walls and their effects on short-path propagation modeling,”IEEE Trans. Veh. Technol., vol. 46, pp. 730–738, 1997.

[3] M. O. Al-Nuaimi and M. S. Ding, “Prediction models and measurementsof microwave signals scattered from buildings,”IEEE Trans. AntennasPropagat., vol. 42, pp. 1126–1137, Aug. 1994.

[4] W. Honcharenko and H. L. Bertoni, “Transmission and reflection char-acterization of concrete block walls in the UHF bands proposed for fu-ture PCS,”IEEE Trans. Antennas Propagat., vol. 43, pp. 232–239, Feb.1994.


[5] O. Landron, M. L. Feuerstein, and T. S. Rappaport, “A comparison oftheoretical and empirical reflection coefficients for typical exterior wallsurfaces in a mobile radio environment,”IEEE Trans. Antennas Prop-agat., vol. 44, pp. 341–351, Mar. 1996.

[6] H. Chiba and Y. Migazakim, “Reflection and transmission characteris-tics of radio waves at a building site due to reinforced concrete slabs,”Electron. Commun. Japan, pt. 1, vol. 81, no. 8, pp. 68–80, 1998.

[7] C. D. Taylor, S. J. Gutierret, S. L. Langdon, and K. L. Murphy, “Onthe propagation of RF into a building constructged of cinder block overthe frequency range 200 MHz to 3 GHz,”IEEE Trans. Electromagn.Compat., vol. 41, pp. 46–49, Feb. 1999.

[8] J. Rohrbaugh, “Shielding effectiveness of concrete: Literature search re-sults,”, Phillips Lab. Rep., Oct. 1995.

[9] C. J. Myers and D. E. Voss, “Material modeling approaches for thestudy of microwave propagation in concrete,”, Voss Scientific DocumentVS-701, Aug. 1997.

[10] S. Chrisatina and A. Orlandi, “An equivalent transmission line model forelectromagnetic penetration through reinforced concrete walls,”IEICETrans. Commun., vol. E78-B, no. 2, pp. 218–229, 1995.

[11] K. S. Yee, “Numerical solution of initial boundary value problems in-volving Maxwell’s equations in isotropic media,”IEEE Trans. AntennasPropagat., vol. AP-14, pp. 302–307, 1966.

[12] A. Taflove, Computational Electrodynamics: The Finite-DifferenceTime-Domain Method. Boston, MA: Artech House, 1995.

[13] A. Taflove and M. E. Brodwin, “Numerical solution of steady-state elec-tromagnetic scattering problems using the time-dependent Maxwell’sequation,” IEEE Trans. Microwave Theory Tech., vol. MTT-23, pp.623–630, 1975.

[14] G. M. Smith,Numerical Solution of Partial Differential Equation: FiniteDifference Method, 3rd ed. Oxford, U.K.: Clarendon, 1985.

[15] G. Mur, “Absorbing boundary conditions for the finite-difference ap-proximation of the time-domain electromagnetic-field equations,”IEEETrans. Electromagn. Compat., vol. EMC-23, pp. 377–382, Nov. 1981.

[16] V. P. Shestopalov, L. N. Litvinenko, S. A. Masalov, and V. G. Sologub,Difratsiya Voln na Reshetkakh (Diffraction of Waves from Gratings)(in Russian). Khar´kov: Izdat. Khar´kov. Universiter., 1973, ch. 3, pp.119–135.

effects of reinforced concrete structures on rf

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