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 patrick@infieldscientific.com

2 martin@infieldscientific.com

4 a.pinchuk@ieee.org

* Concordia University, Department of Electrical Engineering

Montreal, QC, H3G 1M8, Canada 3 robert.paknys@concordia.ca

Abstract— This article describes a method to solve near-field

coupling based on Hu’s formulation [1] which is applied to a

complex navy ship electromagnetic environment where the

transmit antenna, receive antenna and obstacles may all be

located in the near-field. The method was developed for use with

boundary value based computational electromagnetic software

packages to overcome their inability of calculating received

power when using an aperture illumination antenna model.

I. INTRODUCTION

In a navy ship environment, the topside systems, structures

and obstacles are often located in the near-field zone of the

antennas. Without knowing the antenna internal geometries

and being only provided with limited information, coupling

calculations between antennas may be a complex task,

especially when far-field approximations are invalid.

Furthermore, exact models of the directional antennas are not

widely available either because of their complexity or due to

proprietary information.

An accepted practice for simulating the main beam of a

transmitting antenna when the internal geometries (radiator

components, feed, etc) are not known is to model the antenna

by its aperture illumination [2], [3]. It is straightforward using

Computational Electromagnetic Software (CEM) such as

FEKO [4] to model a transmit antenna using aperture

illumination. Unfortunately, the aperture illumination cannot

be used by most boundary value based software packages to

derive the received signal which is generally required for

source-victim coupling calculations.

A possible solution is to use an Ideal Receiver which is

conceptually similar to a point source. The Ideal Receiver

characteristics are derived from the simulated radiation pattern

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.

In addition, an Ideal Receiver is inherently based on all of

the obstructions and transmitters being in the far-field of the

receive antenna, which is not generally the case in the

shipboard application. Therefore, a coupling analysis method

is required which takes into account the near-field responses

of the antennas.

InField Scientific Inc. along with Professor Robert Paknys

of Concordia University developed a Near-Field Coupling

Method (NFCM) to solve this problem. Based on [1], the

near-field coupling of antennas can be calculated using the

transmitted fields of both the transmit and receive antennas in

a shared environment which may include obstacles.

The next section provides information on the ship

electromagnetic environment for which the near-field

coupling method was developed. It is directly followed by the

explanation of the technique along with verification examples

and an actual ship application.

II. GENERAL OVERVIEW OF NAVY SHIP PLATFORM

The analyses described in this article and in our companion

paper [5] are required to support the mid life refit of the

Canadian Forces Halifax Class Frigate, Fig. 1. The length of

the ship is 134.1 meters and the beam is 16.4 meters. The

Weatherdeck antenna farm comprises approximately 70

antennas, covering frequency ranges from High Frequency

(HF) to 40 GHz. There is unavoidable spectrum overlap

between systems and the source victim coupling analysis is

required to mitigate Electromagnetic Interference (EMI)

problems.

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

The Near-Field Coupling Method uses Hu’s formula [1] to

calculate the coupling:

21

2

2112

16

ˆ0

tt

S

t

r

PP

dSnHEHE

P

P

(1)

Pr is the power received by either Antenna 1 or 2.

Pt is the power transmitted by either Antenna 2 or 1.

E1, H1 is the field produced by Antenna 1 if it is

assumed to be transmitting.

E2, H2 is the field produced by Antenna 2 if it is

assumed to be transmitting.

S0 can be any surface that separates the two antennas.

n is the normal (the sign of n does not matter).

Pt1 and Pt2 are the power transmitted by Antennas 1

and 2 respectively so that

1

1

*

111ˆRe

2

1

St dSnHEP (2)

and

2

2

*

222ˆRe

2

1

St dSnHEP (3)

S1 is the aperture of Antenna 1 and 1n is the

aperture’s outward normal.

Antenna 2 has aperture S2 and outward normal 2n .

The Hu formula is useful because it derives the power

received by either antenna, Pr, from the transmit properties of

both antennas without explicitly requiring their receive

properties. This is key for the coupling analysis since CEM

software packages are able to use aperture illumination to

model antennas as transmitters; however, they are not able to

model them as receivers. The Hu method is based on the

reciprocity theorem and it is formally exact.

The shared Electromagnetic (EM) field plane S0, henceforth

referred to as the Hu plane, could be set anywhere between the

two antennas provided that the coupling energy goes through

the Hu plane.

In general, the NFCM would require two simulations to

calculate the field distributions on the Hu plane: one

simulation for each antenna assuming that each is transmitting.

(This is in contrast to most coupling calculations which

require one antenna transmitting and the other receiving.) A

simplification is possible if the Hu coupling plane is

positioned at one of the aperture fields, then one of these

simulations would not be required since the field distribution

can be approximated by the known aperture illumination. For

example, if the Hu plane coincides with the Antenna 1

aperture, then the field distribution on the shared plane due to

Antenna 1 would not have to be simulated because it would be

equal to the Antenna 1 known aperture illumination. The only

simulation required would be to calculate the Antenna 2

transmit field distribution on the Hu plane. This

simplification technique of placing the Hu plane directly on

one of the antenna apertures can be used for most of the

coupling calculations in order to reduce the required number

of simulations.

It should be noted that the above simplification introduces

the inherent aperture field assumptions (η ≈ 377 Ω and plane

wave) into a portion of the Hu formulation which otherwise

would have been exact. This would only introduce errors if

the aperture field is significantly distorted, in which case to

begin with, the aperture illumination model would most

probably not be applicable. Notwithstanding, this inaccuracy

can be avoided by positioning the Hu plane at a location other

than coincident with one of the antenna apertures and running

the two simulations to calculate the field distributions from

each of the transmitting antennas.

IV. VERIFICATION EXAMPLES

Often, we only have limited information about an antenna,

e.g. its beamwidth, directivity, and sidelobe level. Under

these conditions an aperture model is the best approach.

Accepting this limitation, the NFCM allows us to compute the

antenna coupling at any antenna separation with either or both

of the antennas modeled using aperture illumination. It

overcomes the near-field inaccuracy problem of the Friis

formula and those of the ideal point source receiver. The

following examples illustrate the use of the NFCM and for

verification purposes compare the results with other solution

methods.

A. Identical aperture antennas

The first example is a calculation of the coupling between

two identical aperture antennas operating at a frequency of

3 GHz (wavelength λ = 0.1 m). One aperture is located at z =

0, and oriented such that −a/2 ≤ x ≤ a/2, −b/2 ≤ y ≤ b/2. The

aperture size is a × b = 1 m × 0.5 m. Without loss of

generality, it is assumed that the aperture field is y-polarized

and has a uniform amplitude and phase. This gives a

directivity of about 28 dBi and a side lobe level of -13 dB.

This is a large antenna (10 λ × 5 λ) with a narrow beam in the

+z direction and high gain. A second identical aperture is

placed with its center at (x, y, z) = (0, 0, d). Its main beam

points in the −z direction towards the first antenna. The goal

is to calculate the coupling between the two antennas.

The simplest solution for coupling calculations is to use the

Friis formula,

rt

t

r GGdP

PCoupling

2

4

(4)

where the transmit gain and receive gain are

63110 10/28 rt GG . The far-field distance is 20 m; when

d < 20 m the Friis formula begins to fail.

To implement the Hu formula and the NFCM, it is

convenient to put both the Antenna 1 aperture S1 and the Hu

plane S0 at the same place, z = 0. Then, 1n = n = z .

257

Following the methods of [3] to model the apertures, we

assume a y-polarized aperture field having E1 = y E0 and

H1 = − x (E0/η) where E0 = 1 V/m and η ≈ 377 Ω. Because the

Hu coupling plane is at z = 0, we can use Antenna 1's aperture

field S1 to approximate the field distribution on the Hu plane

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).

The results are shown below in Fig. 2. As expected, the

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.

d

Coup

ling (

dB

)

Fig. 2. Coupling of the two apertures - Friis vs Hu formula.

B. Aperture and dipoles array

Another simulation, using the NFCM, was implemented to

verify its usage with typical shipboard antennas. This time,

the coupling was between an aperture illumination and a multi

port antenna in free space, as presented in Fig. 3. The NFCM

method naturally extends from this to the realistic shipboard

environment with its surrounding obstacles.

The simulated aperture, shown in Fig. 4, is an Identification,

Friend or Foe (IFF) Interrogator antenna (Antenna 1) using a

~0.1 λ spacing (2.4 m by 0.48 m, N = 83, M =17). The cosine

taper function powers used for the width and height are

respectively 2 and 2.27.

The multi port antenna, shown as well in Fig. 4, is a

Communication Link dipole array (Antenna 2) with sufficient

information available for a comprehensive model.

Both systems are assumed to be operating at 1.03 GHz. To

properly verify the NFCM in this case, three techniques were

used. The comparison of the coupling results is presented in

Table 1.

The far-field zone of the IFF Interrogator is approximately

9.89 meters and for the Communication Link antenna it is

5.21 meters. The shipboard distance between both antenna

centers is 10.44 meters. At this distance, both antennas are in

their far-field zones.

Fig. 3. Setup used for verifying the NFCM from an aperture (Antenna 1) to a

multi port antenna (Antenna 2).

Fig. 4. Aperture (Antenna 1) and the multi port antenna (Antenna 2).

The first technique uses the Induced Segment Current

Method (ISCM) which can be implemented using most CEM

software when a comprehensive model of the antenna

(including the receive ports) is available. The ISCM

calculates the currents induced on each wire segment of the

antenna model, this current is then used to calculate the power

received at the ports of the antenna. For this example, the

ISCM is used to calculate the coupling from the IFF

Interrogator aperture to the Communication Link antenna. To

do so, the IFF Interrogator aperture model is used to excite the

32 dipole segments of the Communication Link antenna, the

resulting current at the center of each dipole is then calculated,

which gives the coupling power. Specifically, the power

delivered (PD) can be calculated from the induced current at

the port of the receive antenna (IA) and the connected load

resistance (RL) [6]:

LAD RIP2

2

1 (5)

258

The maximum delivered coupling power will occur when

the load (ZL = RL+XL) corresponds to the antenna conjugate

impedance (ZA = RA+XA, where RA = RL and XA = -XL). To

obtain ZA, a separate simulation is required.

The second solution technique uses the Ideal Receiver

antenna (conceptually similar to a point source) to replace the

Communication Link antenna. To do so, the Communication

Link antenna is simulated alone in free space to generate the

far-field pattern file required to characterize the Ideal Receiver

antenna. Then, the simulation is run with the IFF Interrogator

aperture and the Ideal Receiver antenna which is located at the

center of where the Communication Link antenna would have

been placed. The same technique was repeated with the Ideal

Receiver replacing the IFF Interrogator antenna instead of the

Communication Link.

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

input into an in-house program which calculates the coupling

power by numerical calculation of the Hu integral (1).

To compare results between the different techniques, the

coupling power was calculated at five different distances d, in

the near-field and far-field, keeping the same relative angle

between both antennas. Table 1 lists the coupling values

calculated using each of the solution methods. From the table,

it can be seen that the coupling value calculated using the

Near-Field Coupling Method (based on the Hu formulation) is

in agreement with those of the other known methods when d >

9.89 meters (far-field boundary of the IFF Interrogator).

When d < 9.89 meters (in the near-field region of the IFF

Interrogator), the NFCM agrees with only ISCM because Friis

and the Ideal Receiver are not valid in the near-field. Fig. 5

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.

TABLE I

RESULTS OF DIFFERENT COUPLING TECHNIQUES USED BETWEEN THE IFF

INTERROGATOR AND THE COMMUNICATION LINK IN FREE SPACE

Coupling Value (dB)

Coupling

Technique

d/8 =

1.305 m

d/4 =

2.61 m

d/2 =

5.22 m

d =

10.44 m

2d =

20.88 m

Friis

Equation -30.88 -36.90 -42.92 -48.94 -54.96

Ideal

Receiver 1 -48.15 -43.76 -45.53 -49.91 -55.31

Ideal

Receiver 2 -36.63 -38.91 -43.43 -48.97 -54.84

ISCM -43.84 -41.76 -44.30 -49.25 -54.95

NFCM -43.4 -41.5 -44.2 -49.2 -54.9 1: Ideal Receiver set at the Communication Link antenna

2: Ideal Receiver set at the IFF Interrogator

Fig. 5. Graphical representation of the coupling values using different

technique.

V. SHIPBOARD EXAMPLE

As a final example, the NFCM was applied to the shipboard

source victim coupling analysis where a 3D Radar (air and

surface) and a Navigation Radar are both operating in the S-

Band. As illustrated in Fig. 6, the two antennas are in their

near-fields along with surrounding obstacles. In this example,

no detailed antenna geometries were available for either

antenna; therefore, aperture illumination models were required

and ISCM could not be used. Furthermore, due to the

antennas and obstacles being located in the near-field,

accurate coupling calculations could not be performed using

approximate methods such as Friis or the Ideal Receiver.

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

259

Fig. 7 illustrates the two antennas replaced by their aperture

illuminations, with both apertures aligned for maximum

coupling.

The following describes how the source victim coupling

was calculated using the NFCM. The Hu plane was chosen to

coincide with the Navigation Radar aperture. The Navigation

Radar aperture was assigned a length of 3.89 m and height of

0.3 m, with a point spacing of 0.15 λ. The source was the 3D

Radar modeled by an aperture with a length of 3.6 m and

height of 1 m. The aperture consisted of 39 points and 15

points respectively. Both apertures used tapered cosine

functions.

Fig. 7. Setup used to calculate the coupling between the 3D Radar (pointing

at 5° below horizon) and the Navigation Radar facing it.

The Multilevel Fast Multiple Method (MLFMM) solver

was then used to calculate the electric and magnetic field

values throughout the Hu plane, with a point spacing of 0.15 λ,

due to the transmitting 3D Radar. The results along with the

Navigation Radar aperture values were then processed by an

in-house program that calculates the coupling power by

numerical implementation of the Hu integrations using the

formulas described in Section IV.

To complete the E3 analysis, once the coupling value is

calculated for the pair of antennas it is compared to

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

iteratively at different pointing angles to determine the

smallest permissible blanked sector.

VI. CONCLUSION

The Near Field Coupling Method provides a useful

methodology for the calculation of source victim coupling

powers for antenna models by aperture illuminations in a

complex environment where the transmitters, receivers and

obstacles reside in their near field zones.

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.

REFERENCES

[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

Measured Antenna Radiation Pattern of a Parabolic Reflector Using

FSV", in 25th Annual Review of Progress in Applied Computational Electromagnetics, Monterey, CA, USA, p. 173-177, March 8-12 2009.

[3] Electrical and Electromagnetic Environmental Conditions, NATO

AECTP-250 (Edition 1) Leaflet 258, February 2009. [4] FEKO User's Manual Suite 5.5, Electromagnetic Software and

Systems (EMSS) Ltd, South Africa, July 2009.

[5] M. Coulombe, P. Deschênes, A. R. Pinchuk, R. Paknys, "E3 Computational Analysis of a Navy Frigate", in Proc. IEEE EMC 2012

Symposium, 2012.

[6] W. L. Stutzman, G. A. Thiele, Antenna Theory and Design, 2nd ed, John Wiley & Sons, Inc, 1998.

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