Near-Field Coupling Method for a Complex Navy Ship Environment Patrick Deschênes #1, Martin Coulombe #2, Robert Paknys *3, Amy R. Pinchuk #4 # InField Scientific Inc. 171 avenue Labrosse, Pointe-Claire, Quebec, H9R 1A3, Canada 1 [email protected] 2 [email protected] 4 [email protected] * Concordia University, Department of Montreal, QC, H3G 1M8, Canada 3 [email protected]

Abstract— This article describes a method to solve near-field In addition, an Ideal Receiver is inherently based on all of coupling based on Hu’s formulation [1] which is applied to a the obstructions and being in the far-field of the complex navy ship electromagnetic environment where the receive , which is not generally the case in the transmit antenna, receive antenna and obstacles may all be shipboard application. Therefore, a coupling analysis method located in the near-field. The method was developed for use with is required which takes into account the near-field responses boundary value based computational electromagnetic software packages to overcome their inability of calculating received of the antennas. power when using an aperture illumination antenna model. InField Scientific Inc. along with Professor Robert Paknys of Concordia University developed a Near-Field Coupling I. INTRODUCTION Method (NFCM) to solve this problem. Based on [1], the In a navy ship environment, the topside systems, structures near-field coupling of antennas can be calculated using the and obstacles are often located in the near-field zone of the transmitted fields of both the transmit and receive antennas in antennas. Without knowing the antenna internal geometries a shared environment which may include obstacles. and being only provided with limited information, coupling The next section provides information on the ship calculations between antennas may be a complex task, electromagnetic environment for which the near-field especially when far-field approximations are invalid. coupling method was developed. It is directly followed by the Furthermore, exact models of the directional antennas are not explanation of the technique along with verification examples widely available either because of their complexity or due to and an actual ship application. proprietary information. An accepted practice for simulating the main beam of a II. GENERAL OVERVIEW OF NAVY SHIP PLATFORM transmitting antenna when the internal geometries (radiator components, feed, etc) are not known is to model the antenna The analyses described in this article and in our companion by its aperture illumination [2], [3]. It is straightforward using paper [5] are required to support the mid life refit of the Computational Electromagnetic Software (CEM) such as Canadian Forces Halifax Class Frigate, Fig. 1. The length of FEKO [4] to model a transmit antenna using aperture the ship is 134.1 meters and the beam is 16.4 meters. The illumination. Unfortunately, the aperture illumination cannot Weatherdeck antenna farm comprises approximately 70 be used by most boundary value based software packages to antennas, covering frequency ranges from High Frequency derive the received signal which is generally required for (HF) to 40 GHz. There is unavoidable spectrum overlap source-victim coupling calculations. between systems and the source victim coupling analysis is A possible solution is to use an Ideal Receiver which is required to mitigate Electromagnetic Interference (EMI) conceptually similar to a point source. The Ideal Receiver problems. characteristics are derived from the simulated of the antenna under study. However, verification tests performed by the authors using this approach demonstrated that the accuracy was strongly dependent upon the exact location of the Ideal Receiver within the antenna geometry. Certain Ideal Receiver locations received no power while other positions received the peak coupling power. Since this location is arbitrary, it is impossible to predict or bound the accuracy of any given result. Fig. 1 Computational model of the Canadian Forcers Halifax Class frigate.

978-1-4673-2060-3/12/$31.00 ©2012 IEEE 256 III. NEAR-FIELD COUPLING METHOD EXPLANATION simplification technique of placing the Hu plane directly on The Near-Field Coupling Method uses Hu’s formula [1] to one of the antenna apertures can be used for most of the calculate the coupling: coupling calculations in order to reduce the required number 2 of simulations.

E2  H1  E1  H2  nˆdS P S It should be noted that the above simplification introduces r  0 (1) P 16P P the inherent aperture field assumptions (η ≈ 377 Ω and plane t t1 t2 wave) into a portion of the Hu formulation which otherwise

would have been exact. This would only introduce errors if  Pr is the power received by either Antenna 1 or 2. the aperture field is significantly distorted, in which case to  Pt is the power transmitted by either Antenna 2 or 1. begin with, the aperture illumination model would most  E1, H1 is the field produced by Antenna 1 if it is probably not be applicable. Notwithstanding, this inaccuracy assumed to be transmitting. can be avoided by positioning the Hu plane at a location other  E2, H2 is the field produced by Antenna 2 if it is than coincident with one of the antenna apertures and running assumed to be transmitting. the two simulations to calculate the field distributions from  S0 can be any surface that separates the two antennas. each of the transmitting antennas.  nˆ is the normal (the sign of nˆ does not matter). IV. VERIFICATION EXAMPLES  Pt1 and Pt2 are the power transmitted by Antennas 1 and 2 respectively so that Often, we only have limited information about an antenna, e.g. its beamwidth, , and sidelobe level. Under these conditions an aperture model is the best approach. 1 * (2) Pt1  ReE1  H1  nˆ1dS 2 S1 Accepting this limitation, the NFCM allows us to compute the and antenna coupling at any antenna separation with either or both 1 of the antennas modeled using aperture illumination. It * ˆ (3) Pt 2  ReE2  H2 n2dS overcomes the near-field inaccuracy problem of the Friis 2 S2 formula and those of the ideal point source receiver. The following examples illustrate the use of the NFCM and for  S1 is the aperture of Antenna 1 and nˆ1 is the verification purposes compare the results with other solution aperture’s outward normal. methods.

 Antenna 2 has aperture S2 and outward normal nˆ2 . A. Identical aperture antennas The Hu formula is useful because it derives the power The first example is a calculation of the coupling between received by either antenna, P , from the transmit properties of r two identical aperture antennas operating at a frequency of both antennas without explicitly requiring their receive 3 GHz (wavelength λ = 0.1 m). One aperture is located at z = properties. This is key for the coupling analysis since CEM 0, and oriented such that −a/2 ≤ x ≤ a/2, −b/2 ≤ y ≤ b/2. The software packages are able to use aperture illumination to aperture size is a × b = 1 m × 0.5 m. Without loss of model antennas as transmitters; however, they are not able to generality, it is assumed that the aperture field is y-polarized model them as receivers. The Hu method is based on the and has a uniform amplitude and phase. This gives a reciprocity theorem and it is formally exact. directivity of about 28 dBi and a level of -13 dB. The shared Electromagnetic (EM) field plane S , henceforth 0 This is a large antenna (10 λ × 5 λ) with a narrow beam in the referred to as the Hu plane, could be set anywhere between the +z direction and high gain. A second identical aperture is two antennas provided that the coupling energy goes through placed with its center at (x, y, z) = (0, 0, d). Its main beam the Hu plane. points in the −z direction towards the first antenna. The goal In general, the NFCM would require two simulations to is to calculate the coupling between the two antennas. calculate the field distributions on the Hu plane: one The simplest solution for coupling calculations is to use the simulation for each antenna assuming that each is transmitting. Friis formula, (This is in contrast to most coupling calculations which require one antenna transmitting and the other receiving.) A 2 simplification is possible if the Hu coupling plane is P    Coupling  r  G G (4) positioned at one of the aperture fields, then one of these   t r Pt  4d  simulations would not be required since the field distribution can be approximated by the known aperture illumination. For where the transmit gain and receive gain are example, if the Hu plane coincides with the Antenna 1 G  G 1028/10  631. The far-field distance is 20 m; when aperture, then the field distribution on the shared plane due to t r Antenna 1 would not have to be simulated because it would be d < 20 m the Friis formula begins to fail. equal to the Antenna 1 known aperture illumination. The only To implement the Hu formula and the NFCM, it is simulation required would be to calculate the Antenna 2 convenient to put both the Antenna 1 aperture S1 and the Hu transmit field distribution on the Hu plane. This plane S0 at the same place, z = 0. Then, nˆ1 = nˆ = zˆ .

257 Following the methods of [3] to model the apertures, we The far-field zone of the IFF Interrogator is approximately assume a y-polarized aperture field having E1 = yˆ E0 and 9.89 meters and for the Communication Link antenna it is 5.21 meters. The shipboard distance between both antenna H = − xˆ (E /η) where E = 1 V/m and η ≈ 377 Ω. Because the 1 0 0 centers is 10.44 meters. At this distance, both antennas are in Hu coupling plane is at z = 0, we can use Antenna 1's aperture their far-field zones. field S to approximate the field distribution on the Hu plane 1 due to Antenna 1.

Antenna 2 can be simulated using an aperture, and since Antenna 2 is transmitting, the CEM simulator can easily calculate the transmit field E2, H2 at the points on the Hu plane S0 which is coincident with the aperture of Antenna 1 (S1). The Hu integral (1) can be calculated numerically. For our purposes, 41 samples in x and 21 samples in y (i.e. λ/4 sampling) provides sufficient accuracy. Coarser sampling can lead to errors at extremely small antenna separations (less than 0.05 m). Fig. 3. Setup used for verifying the NFCM from an aperture (Antenna 1) to a The results are shown below in Fig. 2. As expected, the multi port antenna (Antenna 2). coupling approaches 0 dB when the antennas are very close together. The Friis formula begins to fall apart at around d = 10 m. Agreement between the Friis and NFCM methods is excellent in the far-field, d > 20 m.

Coupling (dB) Coupling

d Fig. 2. Coupling of the two apertures - Friis vs Hu formula. Fig. 4. Aperture (Antenna 1) and the multi port antenna (Antenna 2).

B. Aperture and dipoles array The first technique uses the Induced Segment Current Another simulation, using the NFCM, was implemented to Method (ISCM) which can be implemented using most CEM verify its usage with typical shipboard antennas. This time, software when a comprehensive model of the antenna the coupling was between an aperture illumination and a multi (including the receive ports) is available. The ISCM port antenna in free space, as presented in Fig. 3. The NFCM calculates the currents induced on each wire segment of the method naturally extends from this to the realistic shipboard antenna model, this current is then used to calculate the power environment with its surrounding obstacles. received at the ports of the antenna. For this example, the The simulated aperture, shown in Fig. 4, is an Identification, ISCM is used to calculate the coupling from the IFF Friend or Foe (IFF) Interrogator antenna (Antenna 1) using a Interrogator aperture to the Communication Link antenna. To ~0.1 λ spacing (2.4 m by 0.48 m, N = 83, M =17). The cosine do so, the IFF Interrogator aperture model is used to excite the taper function powers used for the width and height are 32 dipole segments of the Communication Link antenna, the respectively 2 and 2.27. resulting current at the center of each dipole is then calculated, The multi port antenna, shown as well in Fig. 4, is a which gives the coupling power. Specifically, the power Communication Link dipole array (Antenna 2) with sufficient delivered (PD) can be calculated from the induced current at information available for a comprehensive model. the port of the receive antenna (IA) and the connected load Both systems are assumed to be operating at 1.03 GHz. To resistance (RL) [6]: properly verify the NFCM in this case, three techniques were used. The comparison of the coupling results is presented in 1 2 P  I R (5) Table 1. D 2 A L

258 TABLE I The maximum delivered coupling power will occur when RESULTS OF DIFFERENT COUPLING TECHNIQUES USED BETWEEN THE IFF INTERROGATOR AND THE COMMUNICATION LINK IN FREE SPACE the load (ZL = RL+XL) corresponds to the antenna conjugate impedance (ZA = RA+XA, where RA = RL and XA = -XL). To Coupling Value (dB) obtain ZA, a separate simulation is required. Coupling d/8 = d/4 = d/2 = d = 2d = The second solution technique uses the Ideal Receiver Technique 1.305 m 2.61 m 5.22 m 10.44 m 20.88 m antenna (conceptually similar to a point source) to replace the Friis -30.88 -36.90 -42.92 -48.94 -54.96 Communication Link antenna. To do so, the Communication Equation Link antenna is simulated alone in free space to generate the Ideal -48.15 -43.76 -45.53 -49.91 -55.31 far-field pattern file required to characterize the Ideal Receiver Receiver 1 Ideal antenna. Then, the simulation is run with the IFF Interrogator -36.63 -38.91 -43.43 -48.97 -54.84 aperture and the Ideal Receiver antenna which is located at the Receiver 2 center of where the Communication Link antenna would have ISCM -43.84 -41.76 -44.30 -49.25 -54.95 been placed. The same technique was repeated with the Ideal NFCM -43.4 -41.5 -44.2 -49.2 -54.9 1: Ideal Receiver set at the Communication Link antenna Receiver replacing the IFF Interrogator antenna instead of the 2 Communication Link. : Ideal Receiver set at the IFF Interrogator

The third technique uses the Friis equation (4), using only the gain values at the specified elevation angle of each antenna and the distance between them:

G1(towards Antenna 2 center) = 17.13 dBi G2(towards Antenna 1 center) = -12.99 dBi

Finally, the previous three techniques were compared with the NFCM. To implement the NFCM the Hu plane is placed coincidental with the IFF Interrogator aperture. Then, a simulation was run with the Communication Link model transmitting and the resulting E and H field values on the Hu plane are calculated. These values, along with the IFF Interrogator aperture illumination E and H field values, were Fig. 5. Graphical representation of the coupling values using different input into an in-house program which calculates the coupling technique. power by numerical calculation of the Hu integral (1). To compare results between the different techniques, the V. SHIPBOARD EXAMPLE coupling power was calculated at five different distances d, in As a final example, the NFCM was applied to the shipboard the near-field and far-field, keeping the same relative angle source victim coupling analysis where a 3D (air and between both antennas. Table 1 lists the coupling values surface) and a Navigation Radar are both operating in the S- calculated using each of the solution methods. From the table, Band. As illustrated in Fig. 6, the two antennas are in their it can be seen that the coupling value calculated using the near-fields along with surrounding obstacles. In this example, Near-Field Coupling Method (based on the Hu formulation) is no detailed antenna geometries were available for either in agreement with those of the other known methods when d > antenna; therefore, aperture illumination models were required 9.89 meters (far-field boundary of the IFF Interrogator). and ISCM could not be used. Furthermore, due to the When d < 9.89 meters (in the near-field region of the IFF antennas and obstacles being located in the near-field, Interrogator), the NFCM agrees with only ISCM because Friis accurate coupling calculations could not be performed using and the Ideal Receiver are not valid in the near-field. Fig. 5 approximate methods such as Friis or the Ideal Receiver. shows the divergence between the techniques in near-field: Friis and the Ideal Receiver start to fail when d < 9.89 m. The advantage of the NFCM is that it is readily applicable to the shipboard environment that includes near-field obstacles and is not dependent upon any of the obstacles or antennas being in the far-field. Furthermore, NFCM can be used with aperture models when there is insufficient information to create a comprehensive model that is necessary for the ISCM.

Fig. 6. Illustration of the 3D Radar and the Navigation Radar example.

259 Fig. 7 illustrates the two antennas replaced by their aperture iteratively at different pointing angles to determine the illuminations, with both apertures aligned for maximum smallest permissible blanked sector. coupling. The following describes how the source victim coupling was calculated using the NFCM. The Hu plane was chosen to VI. CONCLUSION coincide with the Navigation Radar aperture. The Navigation The Near Field Coupling Method provides a useful Radar aperture was assigned a length of 3.89 m and height of methodology for the calculation of source victim coupling 0.3 m, with a point spacing of 0.15 λ. The source was the 3D powers for antenna models by aperture illuminations in a Radar modeled by an aperture with a length of 3.6 m and complex environment where the transmitters, receivers and height of 1 m. The aperture consisted of 39 points and 15 obstacles reside in their near field zones. points respectively. Both apertures used tapered cosine functions. ACKNOWLEDGMENT This work was performed in support of the mid life refit of the Canadian Forces Halifax Class Frigate. The Canadian Department of National Defence (DND), with exceptional input from Dr. G. Hiltz of the Quality Engineering Test Establishment (QETE), provided much guidance in the development of the computational model. We would also like to acknowledge the guidance and reviews provided by F. Tiziano from Lockheed Martin Mission Systems & Sensors. Both DND and Lockheed Martin Canada motivated and supported this research.

EFERENCES Fig. 7. Setup used to calculate the coupling between the 3D Radar (pointing R at 5° below horizon) and the Navigation Radar facing it. [1] M.-K. Hu, “Near-zone power transmission formulas,” IRE National Convention Record, Vol. 6 Part 8, 1958, pp.128-135. [2] L. G. Hiltz, B.R. Archambeault, "Comparison of the Modelled and The Multilevel Fast Multiple Method (MLFMM) solver Measured Antenna Radiation Pattern of a Parabolic Reflector Using was then used to calculate the electric and magnetic field FSV", in 25th Annual Review of Progress in Applied Computational Electromagnetics, Monterey, CA, USA, p. 173-177, March 8-12 2009. values throughout the Hu plane, with a point spacing of 0.15 λ, [3] Electrical and Electromagnetic Environmental Conditions, NATO due to the transmitting 3D Radar. The results along with the AECTP-250 (Edition 1) Leaflet 258, February 2009. Navigation Radar aperture values were then processed by an [4] FEKO User's Manual Suite 5.5, Electromagnetic Software and in-house program that calculates the coupling power by Systems (EMSS) Ltd, South Africa, July 2009. [5] M. Coulombe, P. Deschênes, A. R. Pinchuk, R. Paknys, "E3 numerical implementation of the Hu integrations using the Computational Analysis of a Navy Frigate", in Proc. IEEE EMC 2012 formulas described in Section IV. Symposium, 2012. To complete the E3 analysis, once the coupling value is [6] W. L. Stutzman, G. A. Thiele, Antenna Theory and Design, 2nd ed, calculated for the pair of antennas it is compared to John Wiley & Sons, Inc, 1998. permissible levels to assess the EMI risk. If the EMI risk is high, then the antennas may have to be relocated or sector blanking may have to be applied. In the case of sector blanking, the coupling calculations must be repeated

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