research article rf field build-up inside a manned space...

Hindawi Publishing CorporationInternational Journal of Aerospace EngineeringVolume 2013, Article ID 438239, 9 pageshttp://dx.doi.org/10.1155/2013/438239

Research ArticleRF Field Build-Up inside a Manned Space Vehicle Using NovelRay-Tracing Algorithm

Balamati Choudhury, Hema Singh, and R. M. Jha

Centre for Electromagnetics, CSIR-National Aerospace Laboratories, Bangalore 560017, India

Correspondence should be addressed to Balamati Choudhury; [email protected]

Received 25 February 2013; Accepted 3 October 2013

Academic Editor: Linda L. Vahala

Copyright © 2013 Balamati Choudhury et al. This is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properlycited.

The radio-frequency (RF) field mapping and its analysis inside a space vehicle cabin, although of immense importance, representa complex problem due to their inherent concavity. Further hybrid surface modeling required for such concave enclosures leadsto ray proliferation, thereby making the problem computationally intractable. In this paper, space vehicle is modeled as a double-curvatured general paraboloid of revolution (GPOR) frustum,whose aft section ismatched to an end-capped right circular cylinder.A 3D ray-tracing package is developed which involves a uniform ray-launching scheme, an intelligent scheme for ray bunching,and an adaptive reception algorithm for obtaining ray-path details inside the concave space vehicle. Due to nonavailability of imagemethod for concave curvatured surfaces, the proposed ray-tracing method is validated with respect to the RF field build-up insidea closed lossy cuboid using image method. The RF field build-up within the space vehicle is determined using the details of raypaths and the material parameters. The results for RF field build-up inside a metal-backed dielectric space vehicle are comparedwith those of highly metallic one for parallel and perpendicular polarizations. The convergence of RF field within the vehicle isanalyzed with respect to the propagation time and the number of bounces a ray undergoes before reaching the receiving point.

1. Introduction

In the fore section of any space vehicle, astronauts workin the presence of multiple radiating sources. This makesthe astronaut cabin of space vehicle an important indoorenvironment which necessitates RF field mapping. The spacevehicle cabin is essentially a concave structure. Over thelast decades, ray tracing has been employed for site-specificindoor propagation models [1–3], and it has been shown thatmultiple reflections are dominant for the RF field build-upwithin the cavity compared to the phenomenon of diffraction[4]. Although ray tracing has been used earlier for elec-tromagnetic (EM) analysis of aircraft cabin-like enclosures,a closer scrutiny reveals that these predominantly employmeasurements to merely fit their predictions or to validatetheir empirical models [5–7].

For EM environment analysis within the space shuttleinterior (payload bay area), attempts have been made earlierto overcome the computational complexity by approximatingthe curved surfaces with large planar faceted plates [8].

However, this leads to a completely different ray solutionset, which may not necessarily approximate to the case ofcurvatured surfaces under consideration. Further there aresections of space vehicle, which cannot be approximated bysingle-curvature surfaces (e.g., circular and elliptic cylinders)and necessitate modeling with double-curvatured surfaces(e.g., spherical, paraboloidal, and ellipsoidal sections). EManalysis for convex structures, including double-curvaturedstructures, has been done using high-frequency methodsalong with analytical ray-tracing technique such as theGeodesic Constant Method (GCM) [9]. But this is restrictedonly to the external geometries, that is, the convex part ofsuch aerospace structures.

The ray tracing becomes extremely cumbersome in theimportant applications of crevices and concavities within anenclosure (such as space vehicles, aircraft engine, cockpit, andpassenger cabins) due to ray proliferation, arising frommulti-ple reflections, transmission, and diffraction. In fact the onlyroute to ray tracing available in such cases is ray casting [7],which improves the prediction only when the spatial rays are

2 International Journal of Aerospace Engineering

GPOR frustumheight

Right circularcylinder

Figure 1: Schematic of the space vehicle.

increasingly dense, leading to computational intractability.Hence, a feasible ray-tracing method is required to generateray-path data for practical applications.

In the present work, a novel refined ray-tracing methodis developed for RF field computation inside a space vehicleincluding that for the microwave frequencies in the GHzregion.A comprehensive 3D ray-tracing package is developedin conjunction with analytical surface modeling to generatethe ray-path data inside a typical space vehicle.The proposedray-tracing method is validated with respect to the RF fieldbuild-up inside a closed lossy cuboid using the imagemethod.This is because the image method is known to be valid forplanar surfaces, whereas the concave curvatured surfaceslike space vehicle or aircraft in-cabin have mostly nonplanarsurfaces. The space vehicle is modeled as a hybrid of rightcircular cylinder and a general paraboloid of revolution(GPOR) frustum. The aft section is modelled by an end-capped right circular cylinder (Figure 1). The dimensions ofa currently used space vehicle are considered for the RFsimulations [10]. Test rays are launched from a radiatingsource located inside the space vehicle and are allowed topropagate inside the space vehicle. The reflection pointsat each surface and the corresponding reflected rays areobtained using the parametric equation of the surface andthe surface normal [9] at each incident point. As the surfaceparameters of the modeled space vehicle are defined throughanalytical equations, the ray-path computation time reducedsignificantly.

The cumulative ray-path data up to𝑁th bounce includingthe direct ray is used for the estimation of RF field inside aspace vehicle. It includes the details of each ray path traversedwithin the space vehicle before reaching the receiving point.Moreover the constitutive parameters of the space vehiclematerial are taken into account in calculating the totalreflected power at the receiving point. It is well known that,unlike the convex surfaces, the RF field mapping inside aconcave structure is an extremely complex problem domi-nated by the proliferation of reflected ray solutions. Hencein this paper, an empty space vehicle cabin is considered to

analyze the problem of concavity. The transmitting and thereceiving antennas are taken as a directional antenna (half-wavelength dipole). The RF field build-up at the receiverplaced within a manned space vehicle is reported for boththe perpendicular and parallel polarizations. The resultantfield build-up at the receiving point is obtained by a coherentsummation of the fields associated with each ray reaching thereceiver after undergoing multiple bounces from the walls ofthe space vehicle. The results for a metallic space vehicle arecomparedwith that of ametal-backeddielectric space vehicle.The convergence of the RF field build-up is studied withrespect to the propagation time and the number of reflectionsa ray undergoes before reaching the receiving point.

2. Surface Modeling of a Space Vehicle

Hybrid quadratics such as general paraboloid of revolu-tion (GPOR) frustum and finite right circular cylinder aresufficient enough to model a typical space vehicle for RFanalysis. In analytical surface modeling, the surfaces aredefined by parametric equations and the shaping parametersof the corresponding surfaces are calculated towards perfectmatching.

2.1. Geometry of Space Vehicle. The schematic of the spacevehicle is shown in Figure 1. The vehicle is modeled as adouble-curvatured general paraboloid of revolution (GPOR)frustum, whose aft section is matched to an end-capped rightcircular cylinder. To describe the analytical modeling, thedimensions of a typical space vehicle considered [10] aretaken as follows:

length of the cylindrical body: 7.50m;

right circular cylinder diameter: 4.50m;

matched GPOR diameter: 4.50m;

height of GPOR frustum: 5.00m.

2.2. Calculation of Shaping Parameters in Hybrid Structure.The parametric equation of right circular cylinder is given by[9]

𝑥 = 𝜌cyl cos𝜙, 𝑦 = 𝜌cyl sin𝜙, V1

≤ 𝑧 ≤ V2, (1)

where 𝜌cyl is the radius of the right circular cylinder, 𝜙 isits azimuth angle that varies from 0 to 360∘, and (V

2−

V1) represents the finite length of the cylinder. To model

the hybrid structure, one needs to determine the shapingparameters of the structure. The parametric equation of aGPOR is given by [11]

𝑥 = 𝑎𝑢 cos𝜙, 𝑦 = 𝑎𝑢 sin𝜙, 𝑧 = −𝑢2, (2)

where 𝜙 is now the azimuth angle of GPOR varying from0 to 360∘, 𝑢 is the GPOR basis parameter, and 𝑎 is theshaping parameter that represents the sharpness/flatness ofthe GPOR.

International Journal of Aerospace Engineering 3

15-bounce cumulative-perpendicular polarization

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Figure 2: RFfield build-up at the receiver inside a lossy cuboid usingimage method and refined ray tracing method.

3. Propagation inside a Space Vehicle

A novel refined ray-tracing algorithm is developed for raypropagation analysis inside the concavities. The developedalgorithm is validated with respect to a lossy cuboid usingimage method as image method is not available for concavesurfaces. The proposed refined ray-tracing algorithm alongwith the RF field validation is given below.

3.1. Validation of Refined Ray-Tracing Algorithm. As imagemethod is simply not available for curved concavities suchas the space vehicle, the RF field due to the rays obtainedby the existing image method inside a lossy cuboid (2.70m× 2.38m × 2.40m) and those obtained by the refined ray-tracing method developed in-house are compared. The RFfield build-up analysis is carried at 2.4GHz. The source iskept at origin (0, 0, 0). The receiver is at (0.9, 1.85, 1.1). Thecumulative ray paths up to 15 bounces are considered for thesimulation studies. The constitutive parameters of the lossywalls of the cuboid are taken into account while estimatingthe net field build-up. Figure 2 presents the RF field build-up at the receiving point within the lossy cuboid (𝜀

𝑟=

10.74 − 𝑗2.01, 𝑑 = 4mm) for perpendicular polarization.It may be observed that the refined ray-tracing algorithmhas excellent agreement with image method in providingray-path descriptions for RF field build-up within the closedcavity.

3.2. RefinedRayTracing inside the SpaceVehicle. Asdescribedabove, a closed analytically modeled hybrid space vehicle isconsidered for ray-propagation analysis and the transmitterand the receiver are located inside the space vehicle withoutloss of generality at 𝑆(0.5, 0.9, −15.5) and 𝑅(0.5, −0.4, −6.0).Figure 3 illustrates the schematic of the same.

Initially a uniform ray-launching scheme [12] is used fromthe isotropic source (transmitter), which is subsequently

S

R Frustum height

Right circular cylinder

Frustum radius

Figure 3: Schematic of the ray propagation inside a space vehicle.

adapted for convergence of ray solutions at the receiver. Eachray is uniquely defined by its (𝜃, 𝜙) values. The rays are thenallowed to propagate inside the cabin. The first intersectionpoint is determined by the intersection formula between aline and the surface of the corresponding hybrid structure[13].

As the hybrid structure has four different quadratic sur-faces at different heights, initial intersection point is checkedwith respect to 𝑧-coordinate and the surface equation isadopted for calculation of first incident point.Theunit surfacenormal vector (Figure 4) at the first intersection point iscalculated using the following equations with respect to thesurface [9].

The unit surface normal equation of a second degreequadric patch is given by

�̂� = 𝑥𝑁

�̂� + 𝑦𝑁

𝑗 + 𝑧𝑁

�̂� (3)

which for a right circular cylinder is expressed as

𝑥𝑁

= cos𝜙, 𝑦𝑁sin𝜙, 𝑧

𝑁= 0, (3a)

while for the GPOR, it is given by

𝑥𝑁

=2𝑢 cos𝜙

√𝑎2 + 4𝑢2𝑦𝑁

=2𝑢 sin𝜙

√𝑎2 + 4𝑢2𝑧𝑁

=𝑎

√𝑎2 + 4𝑢2.

(3b)

The unit surface normal corresponding to the above fourconstituent surfaces of the hybrid structure is shown inFigure 4.

Once the surface normal at the point (where the rayis incident) is determined, the reflected ray is obtained byemploying the Snell law of reflection.This process is repeatedfor the subsequent bounces.

An adaptive reception sphere is considered to capture therays. The rays that reach the reception sphere are consideredas the required set of rays for the RF field build-up inside thecabin. Further, an intelligent ray-bunching scheme is used toavoid duplication of ray solutions.


Table 1: Rays reaching receiver cumulatively up to 𝑁-bounce andthe execution time (4126183 rays are launched) in Intel Core DuoCPU, 3GHz, and 4GB RAM.

𝑁-Bounce Number of raysreceived

Program executiontime

1 bounce 4 25 sec5 bounces 120 1.55min10 bounces 538 6.67min15 bounces 893 11.00min20 bounces 1082 17.56min25 bounces 1205 24.35min30 bounces 1279 29.45min35 bounces 1318 34.12min40 bounces 1345 42.35min

02

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Figure 4: The unit surface normal vector representation of GPORfrustum and right circular cylinder.

3.3. Results and Visualization of Ray Path. The ray-pathpropagation characteristics inside the modeled space vehicleare checked for conditions of reflection, and the ray-pathdata up to 40 bounces (cumulative) are generated. Anangular separation of 0.1∘ is considered. It is observed thatbesides the direct ray only 66 rays reach the reception spherecumulatively, up to 4 bounces. The ray-path visualization ofthese 66 rays is shown in Figure 5.

The corresponding number of rays converging on to thereceiver with respect toN-bounce and the program executiontime are given in Table 1.

It is pointed out that for the RF field mapping applicationunder consideration, as discussed in the next section, it issufficient to consider the ray-path data up to 40 bounces.

4. RF Field Build-Up inside the Space Vehicle

RF field mapping problem is formulated in three steps,namely, (i) analytical surface modeling of the space vehicle

−2−1

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One bounceTwo bounces

Three bouncesFour bounces

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Figure 5: Ray-path visualization of cumulative rays up to fourbounces inside the space vehicle.

enclosure and (ii) ray-path data generation within the enclo-sure using a refined ray-tracing algorithm, followed by (iii)frequency and polarization dependent EM field computationfor the RF field mapping inside the space vehicle.

The RF field estimation within an enclosure needs thedetails of ray paths, reflection points, and radiation patternof the transmitting and receiving antennas. In this paper, theray-path details and the coordinates of reflection point(s)are obtained using a novel adaptive three-dimensional ray-tracing procedure, explained in the previous section. Whenmultiple bounces and numerous ray paths are considered,the ray tracing becomes computationally intense and com-plicated. However, for an arbitrary concave environment,volumetric ray tracing still offers an efficient approach for RFsimulation.

The resultant electric field at a receiving point 𝑃 withinthe enclosure [14] is given by

𝐸 (𝑃) = ∑

𝑖

𝐸𝑖(𝑃) = ∑

𝑖

𝐸𝑜𝐹𝑡𝑖𝐹𝑟𝑖

{∏

𝑙

𝑅𝑙} 𝑒−𝑗𝑘𝑑

𝐿𝑖(𝑑) , (4)

where 𝐸𝑖(𝑃) is the electric field due to the 𝑖th ray at the

receiver 𝑃. This ray experiences a finite number of reflectionsduring its path from the source to the receiver. The numberof the reflections a ray will undergo depends on the angle atwhich the ray is launched from the source.

The source is taken as a point source. The rays launchedwithin the cavity are weighted according to the radiationpattern of the transmitting antenna. Similarly at the receiver,the rays are weighted in accordance with the radiation


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Figure 6: (a) RF field build-up inside a metallic space vehicle. Frequency = 6GHz; 𝜎 = 1.8 × 105 S/m, polarization: perpendicular. Since

the walls of space vehicle are metallic, convergence has not been achieved. (b) RF field build-up inside a metallic space vehicle. Frequency =6GHz; 𝜎 = 1.8 × 10

5 S/m, polarization: parallel. Since the walls are metallic, convergence has not been achieved.

pattern of the receiving antenna. The time-independent fieldexpressed in (4) is the coherent sum of field contributionsof individual rays reaching the receiver. The phase of eachray (reaching the receiving point at different instants of time)is adjusted accordingly. 𝐸

𝑜is the initial field value at the

source and 𝐹𝑡𝑖and 𝐹

𝑟𝑖are the corresponding field values

intercepted in the direction of ray. These field values arebased on the radiation patterns of transmitting and receivingantennas, respectively. 𝑅

𝑙is the reflection coefficient of the

𝑙th interface/wall [15–17], 𝑑 is the total ray-path length, 𝑘

is the wavenumber, and 𝐿𝑖(𝑑) is the path loss [14]. The

dependence of the reflection coefficient on the materialproperties, namely, permittivity, conductivity, thickness, andthe angle of incidence, is appropriately incorporated.

5. Results and Discussion

The RF simulations are carried out for both a metallic (𝜎 =

1.8 × 105 S/m) space vehicle and a metal-backed dielectric

(𝜀𝑟

= 10 − 𝑗5; 𝑑 = 5mm) space vehicle. The transmittingand receiving antennas are assumed to be directional (as half-wave dipole).

The launching of rays within an enclosure can be doneefficiently for any angular separation. However, if the angularseparation between the adjacent launched rays is too large,fewer test rays are launched and the RF field does notconverge. This implies the requirement of launching the testrays at increasingly smaller angles, which at the other extremeis beset with the problem of computational intractability.It has been observed that a trade-off exists for the class

of problems being analyzed here, optimally in the rangeof 0.1∘ to 0.25∘. In this study, the RF field build-up at thereceiving point inside a space vehicle is obtained for the rayangular separation of 0.1∘ launched within the space vehicle.The effect of the frequency of operation on the RF fieldbuild-up is also studied. Simulations are carried out for twodistinct frequencies of 6 and 8GHz for both the paralleland perpendicular polarizations. It is pointed out that thesedistinct frequencies are commonly used in space and satellitecommunication applications.

First, the RF field build-up is estimated for the interiorof a highly metallic space vehicle. The normalized RF fieldbuild-up at the receiving point inside the metallic spacevehicle at 6GHz is shown in Figures 6(a) and 6(b) forthe perpendicular and parallel polarization, respectively. Thecorresponding results at 8GHz are given in Figures 7(a) and7(b), respectively. For a given ray bounce, the complete set ofrays is characterized by distinct 𝑡min and 𝑡max. Here, 𝑡min refersto the minimum time of the (shortest) ray path for a givenbounce. Likewise, 𝑡max corresponds to the maximum time ofthe (longest) ray within the set of rays for the same numberof bounces. It is pointed out that, for the preset number ofbounces, 𝑡min may be more than the propagation time ofseveral rays of a lower bounce type and even than some of therays of the higher bounce type. Hence one of the focuses ofthis study is to analyze the RF field convergence with respectto the cumulative bounce of the feasible ray paths (i.e., all theray paths cumulatively up to a preset number of bounces).

In the case of perpendicular polarization (Figures 6(a)and 7(a)), the field convergence requires a very large numberof bounces, and hence the time axis ought to be very


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Figure 7: (a) RF field build-up inside a metallic space vehicle. Frequency = 8GHz; 𝜎 = 1.8 × 105 S/m, polarization: perpendicular. Since

the walls are metallic, convergence has not been achieved. (b) RF field build-up inside a metallic space vehicle. Frequency = 8GHz; 𝜎 =

1.8 × 105 S/m, polarization: parallel. Since the walls are metallic, convergence has not been achieved.

large. However, the time window considered till 1.2𝜇sec issufficient for practical applications as shown later.The resultsare reported till 40 bounces (cumulative), which convergeswithin the ambit of computational tractability.

Since the walls of the space vehicle are considered to behighly metallic (𝜎 = 1.8 × 10

5 S/m), the rays do not suffersignificant attenuation at each reflection before reaching thereceiver. It can be observed fromFigures 6(a) and 7(a) that thelevel of RF field build-up for perpendicular polarization tendsto broadly increase with the number of bounces considered.This is ascribed to the fact that, as the number of bouncesincreases, the number of rays reaching the receiver alsoincreases. These numerous rays reaching the receiver arrivefrom different directions and hence tend to substantiallycancel leaving only a small net (positive or negative) RF field.This small net field contributes to the earlier threshold of theRF field build-up in the incremental sense, thereby leading tothe extremely slow rate of convergence for the metallic case.This is on the expected lines since convergence has not beenachieved within a highly metallic reverberation chamber-likeenvironment [18].

In contrast, for the parallel polarization (Figures 6(b) and7(b)), despite metallic walls, the RF field build-up convergesrapidly. This is due to the fact that, for the parallel polar-ization, the direction of E-field vector changes continually[17] after successive (oblique-incidence) reflections. Whenthe electric field associated with the multiple rays reachingthe receiver is coherently superimposed, the fields withopposite phase tend to cancel each other, resulting in therapid convergence of the total field build-up with respect tothe number of bounces.

The amplitude of total RF field build-up at receiver,particularly initially, fluctuates with the number of bounces.This may be due to the fact that this study is emphasizedwith respect to the preset cumulative number of bounces,which is used as the cut-off that ignores all the higher-bounceray paths. Although the higher bounces tend to result inincreasingly diminished (and hence negligible) electric fieldcontributions, their contribution during the initial RF build-up is not necessarily so, thereby leading to the observed RFfluctuations. However, with the increase in time, this errortends to cancel itself out.

A discerning reader may also notice that the total RF fieldbuild-up inside a metallic space vehicle is higher at 6GHzas compared to 8GHz for both the polarizations. This isexplained by the fact that the geometric path-length solutions(between the source and receiver points) are independent offrequency.Thus compared to 8GHz, each ray traverses fewerelectrical wavelengths over the fixed geometric path at 6GHz,leading to lesser attenuation and hence in general higher RFfield build up values.

A metal-backed dielectric space vehicle is considerednext. This dielectric in reality is highly absorbent in nature.Thus, a typical absorber permittivity is taken here, as 𝜀

𝑟=

10 − 𝑗5; 𝑑 = 5mm. These constitutive parameters of thewall material are employed in the estimation of reflectioncoefficients [17] of each of the ray paths, as a functionof polarization and all the successive angles of incidence.Thus, the contribution of each ray path reaching the receiverwithin the space vehicle can be coherently summed up afteradjusting them in phase.


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Figure 8: (a) RF field build-up inside a metal-backed dielectric (𝜀𝑟

= 10 − 𝑗5; 𝑑 = 5mm) space vehicle. Frequency = 6GHz; polarization:perpendicular. (Though the field is normalized, the 𝑦-axis considered is only up to 0.20 to facilitate closer scrutiny of the plots.) (b) RF fieldbuild-up inside a metal-backed dielectric (𝜀

𝑟= 10 − 𝑗5; 𝑑 = 5mm) space vehicle. Frequency = 6GHz; polarization: parallel. (Though the field

is normalized, the 𝑦-axis considered is only up to 0.20 to facilitate closer scrutiny of the plots.)

The resultant normalized RF field build-up within thespace vehicle for 6 and 8GHz is shown in Figures 8 and 9,respectively.The 𝑦-axis within these field normalized plots, islimited to 0.20 to facilitate a closer scrutiny. It can be readilyobserved that, for a metal-backed dielectric space vehicle, theray contribution converges rapidly for both the perpendicularand parallel polarizations, both over time and the numberof bounces. This is ascribed to the lossy nature of the metal-backed dielectric wall that the rays are incident upon, leadingto attenuation and thus lower RF field amplitude and a rapidconvergence [19].

6. Conclusion

The RF environment inside a space vehicle is analyzed basedon the novel application of a refined ray-tracing algorithmproposed here along with hybrid surface modeling for thespace vehicle. The refined ray tracing yields the required ray-path data, which also facilitates visualization of all the raysthat reach a particular subcube placed inside the space vehiclecabin. A ray-bunching algorithm is developed to differentiatethe ray solutions as ray bunches that travel nearly parallelto reach the reception subcube. A refinement algorithm isthen employed to identify the ray path within this ray bunch,which eventually converges on to the receiving point.

This algorithm generates the complete data for all theray paths cumulatively up to a given number of bounces. Inthe applications where higher bounces are required, denserrays need to be launched to achieve convergence, which oftenleads to computational intractability. In this study, the RF

field build-up at the receiving point inside a space vehicle isobtained for the rays launched at the angular separation of 0.1∘within the space vehicle. Again, for the class of space vehiclecabin problem analyzed in this work, for the convergence ofRF field build-up, it is sufficient to consider the ray pathscumulatively up to 40 bounces, which is within the realm ofcomputational tractability.

The RF field build-up at the receiving point within thespace vehicle is determined by summing the fields associatedwith each ray reaching the receiver after being adjusted inphase. The effect of operational frequency on the RF fieldbuild-up is also studied. Simulations are carried out for twodistinct (uplink/downlink) frequencies of 6 and 8GHz. Theresults for RF field build-up are compared for ametallic spacevehicle and a metal-backed dielectric space vehicle. Since thewavelength traversed by a ray over the fixed geometric pathis a function of frequency, the lower the frequency is, thelesser the number of wavelengths travelled by a ray will be,leading to lesser attenuation and hence higher RF field build-up values. It is due to this fact that the total RF field build-upinside a metallic space vehicle is found to be higher at 6GHzas compared to 8GHz for both the polarizations.

The number of rays reaching the receiver increaseswith the ray bounce. These numerous rays incidents fromdifferent directions tend to cancel out, leaving but a net (pos-itive/negative) RF field. Despite the large number of rays, it isonly this small net RF field that contributes to the incrementalrise/fall in the threshold of the RF field build-up. This leadsto the slow rate of convergence. In the case of perpendicularpolarization, the RF field build-up inside a metallic space


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E‖

(b)

Figure 9: (a) RF field build-up inside a metal-backed dielectric (𝜀𝑟

= 10 − 𝑗5; 𝑑 = 5mm) space vehicle. Frequency = 8GHz; polarization:perpendicular. (Though the field is normalized, the 𝑦-axis considered is only up to 0.20 to facilitate closer scrutiny of the plots.) (b) RF fieldbuild-up inside a metal-backed dielectric (𝜀

𝑟= 10 − 𝑗5; 𝑑 = 5mm) space vehicle. Frequency = 8GHz; polarization: parallel. (Though the field

is normalized, the 𝑦-axis considered is only up to 0.20 to facilitate closer scrutiny of the plots.)

vehicle tends to broadly increase with the number of bouncesconsidered. This trend is on the expected lines, since it iswell known that the RF field convergence is not achievedwithin a highly metallic reverberation chamber. In contrast,for the parallel polarization, the direction of the E-field vectorchanges continually after each (oblique-incidence) reflection.When the electric field associated with the multiple raysreaching the receiver is coherently superimposed, the fieldswith opposite phase tend to cancel each other, resulting in therapid convergence of the total field build-up with respect tothe number of bounces.

For a metal-backed dielectric space vehicle, which is thepractical case under consideration, the RF field build-upconverges rapidly with respect to both the elapsed time andthe number of bounces. This is true for both parallel andperpendicular polarizations.This is due to the lossy nature ofmetal-backed dielectric wall of the space vehicle enclosure.

References

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