Minimum Coupling Antenna Arrays

Minimum Coupling Antenna Arrays Hans G. Schantz James D. Fluhler Q-Track Corporation 2223 Drake Avenue SW Huntsville, AL 35805

Kazimierz Siwiak

George T. Shoemaker

TimeDerivative, Inc. 10988 North West 14th Street Coral Springs, FL 33071

AIST Executing Agent Code 709 Naval Undersea Warfare Center 1176 Howell Street Newport, RI 02841

Abstract: Mutually orthogonal three-axis electrically-small magnetic antenna arrays are of great interest for field probes, direction finding, and location systems. Orthogonality does not guarantee minimum coupling between two or more antennas, however. A poorly designed antenna array will exhibit mutual coupling even between orthogonal elements, confounding the independence of the measurements. We describe the origins of minimum coupling arrays in the work of Louis Alan Hazeltine. Then, we present analytic conditions for minimum coupling in electrically-small loops and experimental measurements of minimum coupling between two orthogonal antennas. NEC analysis demonstrates that symmetric arrangements of three mutually orthogonal electrically-small magnetic elements yield outstanding isolation, even when placed at separation distances on the order of the diameter of the magnetic elements. Minor asymmetries in the geometry make the coupling much worse. Finally, we describe the challenges in experimentally evaluating coupling in actual implementations and we present a technique using the null depth of the antenna as an indication of the minimum coupling. Measurements demonstrate that the compact minimum-coupling antenna arrangement exhibits pattern nulls on the order of -50dB or more, corresponding to a potential angular precision of about 0.2 degree to 0.4 degree.

1

Introduction

From a far-field point of view, orthogonal antennas couple to orthogonal field components. One might naturally assume that orthogonal antennas inherently exhibit minimum cross coupling characteristics. This assumption fails due to the near-field behavior of electrically small antennas placed in close proximity – well within the /2 or radiansphere boundary between the near-field and far-field zones. Orthogonality and minimum coupling are actually two independent characteristics of small antenna arrays, and neither condition implies or requires the other. We survey the pioneering work of Louis Alan Hazeltine (1886-1964) who first exploited minimum coupling arrangements of magnetic coils to avoid cross coupling from inductive coils. Then, we define the minimum coupling condition for electrically-small loop antennas in each other’s near field and present experimental results. Finally, we present a minimum coupling configuration for three mutually orthogonal loop antennas. We validate the high degree of isolation using both NEC analysis and measurement of antenna patterns.

Figure 1a (left): The fields of a magnetic dipole or small loop are orthogonal to the axis of the loop at p = 54.7° (courtesy, Wikimedia). Fig. 1b (right): Hazeltine discovered that any number of coils may be arranged linearly with co-parallel axes provided each is tilted p = 54.7° with respect to the line along which they are placed (Ref. [1]).

2

Hazeltine’s Minimum Coupling Configuration

Hazeltine implemented an arrangement of inductive coils in a radio receiver so as to eliminate mutual coupling [1]. One may arrange two or three coils at right angles to each other. Hazeltine sought a way to arrange any number of coils such that there would be no mutual coupling between any two. His solution relies on a basic feature of the dipole fields. The magnetic dipole field lines are orthogonal to the axis of the dipole at an angle p = 54.7° with respect to the axis. Thus, no field lines pass through another coparallel loop placed at this angle. Figure 1a shows the dipole field lines, and Figure 1b shows Hazeltine’s invention. His arrangement allows multiple resonant coils in an RF circuit to be placed in close proximity without mutual coupling. Hazeltine found that the minimum coupling angle was usually within a few degrees of the ideal value in most practical implementations. In fact, he was able to place his coils at separation distances as close as one-sixth of the coil diameter. Hazeltine’s invention enabled compact arrangements of resonant coils. His invention was of particular value in the implementation of regenerative receivers in which mutual coupling could easily turn the receiver into an oscillator.

' z

Mb



Ma

y

x



Fig. 2: The geometry of electrically small loop antennas is described by the orientation angle  and the tilt angle ’. We assume  and ’ are in the same plane and the loops are symmetrical with respect to each other.

3

Minimum Coupling Defined

Now consider the geometric orientation for which two small loops will have minimum coupling. We assume that the electrically-small loops lie in each other’s near field, so only inductive coupling is relevant, and far field contributions are negligible. To solve the problem, we invoke the principle of reciprocity between two electromagnetic systems, system “a” and system “b” [2]:

 E V

b

 J a  H a  M b dV   Ea  J b  H b  M a dV V

(1)

In other words, the interaction between the electric and magnetic fields of antenna b (Eb, Hb) and the electric current and magnetic moment of antenna a (Ja, Ma) must be identical to the interaction between the electric current and magnetic fields of antenna a (Ea, Ha) and the electric current and magnetic moment of antenna b (Jb, Mb). For the problem at hand, we may neglect the electric coupling of our two loops. We assume that the magnetic moment of loop A (Ma) is aligned with the z-axis. We assume that the magnetic moment of loop B (Mb) is aligned at an angle   with respect to the z-axis and lies within the z-y plane ( = 90). Figure 2 presents the geometry of the loops. The goal is to achieve a symmetric mutually orthogonal arrangement of three elements at which the magnetic moment Mi of the ith coil is orthogonal to the magnetic field vector Hj of the jth coil, or expressed mathematically:

z Ma

Mb

'

z

p

Ma

y

Mb

o y

x

x

Figure 3a (left): In 1926, Hazeltine demonstrated that co-parallel electrically small loops will exhibit no mutual coupling when aligned at an angle p = 54.74. Figure 3b (right) Geometry of orthogonal electrically small loops.

Hj  Mi = 0

(2)

For minimum coupling, we require that HaMb = 0. Thus:

0  H a  Mb



 

 H a 2 cos  rˆ  sin  θˆ  M b cos   rˆ  sin    θˆ  2 cos  cos     sin  sin    

 (3)

Noting that: cos     cos  cos    sin  sin  

(4)

sin     sin  cos    cos  sin   ,

(5)

and:

the minimum coupling condition becomes: 0  Ha  Mb

 2 cos  cos     sin  sin    





(6)

 2 cos   sin  cos    3 cos  sin  sin   2

2

Hazeltine discovered that two small loops in parallel planes will not couple in their near fields when aligned at an angle p = 54.74. Figure 3a shows the Hazeltine configuration. Hazeltine’s condition follows immediately from the result of (6) where   = 0:

0  2 cos 2  p  sin 2  p

(7)

tan  p  2

 p  tan 1 2  54.74  More recently, other investigators devised a broadband isotropic probe system including three mutually orthogonal antennas. [3] Mutual coupling between co-located orthogonal magnetic loops has also been a subject of recent interest. Although there has been a recent investigation of coupling between co-located orthogonal loops [4], the authors have not found any prior work on preferred orientation for minimal coupling of non-co-located orthogonal loops. Again, with  and ’ in the same plane, the orientation angle () for minimal coupling between orthogonal loops follows from (6) with   = 90:

0  3 cos  sin  .

(8)

The result of (8) is zero for = 0 or = 90. Figure 3b depicts the orthogonal loop coupling geometry. In general, a minimum coupling orientation for two orthogonal loops follows when the axis of one loop lies in the  direction of a coordinate system aligned with the axis of the other loop with respect to the axis. Figure 4 shows this configuration.

' z Ma

Mb

 y

x



Figure 4: Minimum coupling orientation for orthogonal electrically-small magnetic antennas.

4

Experimental Validation for Two Orthogonal Loops

This section will present experimental validation of the minimum coupling conditions derived in the previous section for two orthogonal loops. First, this section verifies Hazeltine’s condition for minimal coupling in co-parallel small loops. Then this section evaluates coupling between orthogonal loops in the y-z (o = 90) plane. Finally, this section presents results for coupling between orthogonal loops in the x-z (o = 0) plane. An HP 8753D vector network analyzer evaluated the coupling at 1.295 MHz between two standard AM band loopstick antennas. The loopstick antennas were at a range of 12.7cm (5.0in) and arranged at various angles. These 1 mH loopsticks are available from Science Toys (www.scitoys.com; P/N: FERRITECOIL). A 10-60 pF variable capacitor tunes the antennas. This trimmer capacitor was available from Ocean State Electronics (www.oselectronics.com; P/N: TC-1060). Using three secondary turns, the antenna input impedance is about 300. Figure 5 shows the antenna configuration.

L = 1000H Q~150 10-60pF

3 Secondary Turns ~300 ohm Figure 5: Diagram (left) and photo (right) of AM band loopstick antenna.



12.7cm (5.00in)

Figure 6: Diagram (left) and photo (right) of co-planar loop coupling measurement. The goal of the first measurement is to assess coupling between co-planar or coparallel loops. Figure 6 shows the experimental configuration and Figure 7 plots the measured data. There was about a 25dB null at 45, about 10 offset from the expected null at 55. In the second quadrant there was about a 30dB null around 125. This second null is 55 degrees away from the 180 axis, consistent with Hazeltine’s prediction.

Figure 7: Measured coupling between co-planar AM band loopstick antennas.



12.7cm (5.00in)

Figure 8: Diagram (left) and photo (right) of orthogonal loop coupling measurement (yz plane). The second measurement assesses coupling between orthogonal loops in the  = 90 or y-z plane. In this plane, the mobile loop lies in the plane of the stationary loop at o = 0, 90, and 180. Figure 8 shows the experimental configuration and Figure 9 plots the measured data. Nulls were about 25-30dB deep at o = 0, 90, and 180. These measurements are consistent with the theoretical expectations of Section 3.

Figure 9: Mutual coupling between orthogonal loops in the y-z plane.

Figure 10: Geometry of three loops for minimum coupling evaluation. The theoretical predictions assume ideal, point magnetic dipoles. The experimental measurements of this section are a good test of whether the theoretical minimum coupling orientations are still valid when the loop (or in this case, loopstick) has dimensions that are an appreciable fraction of the distance between the loops. Results were generally consistent with expectations. Despite the non-infinitesimal dimensions of the loopsticks, the theoretical orientations provided useful guidance for arranging loopstick antennas in a minimum coupling orientation. In the co-parallel case, Hazeltine’s condition was satisfied to within about 10 degrees. In the case of orthogonal loops, minimum coupling occurs when one loop lies in the plane of the other.

5

Three Axis Orthogonal Mutual Coupling Arrays

Imagine three co-located orthogonal loops, each aligned with one of the Cartesian axes. Translate each loop along its corresponding axis by a distance equal to the loop diameter, then translate each loop symmetrically along an orthogonal axis in the plane of the loop. Figure 10 shows a three loop array with this enforced symmetry and placement. This arrangement exhibits a remarkably low mutual coupling. Figure 11 shows what happens when one loop translates long the loop axis. All three loops remain mutually orthogonal, however the coupling increases dramatically as the symmetry is broken.

Figure 11: NEC Results for minimum coupling antenna array; distance in units of loop diameter.

Figure 12: NEC Results for minimum coupling antenna array; distance in units of loop diameter. Figure 12 illustrates what happens when we disrupt the arrangement by translating all three loops along their axes. Here again, a spacing of one diameter from the axes yields very low coupling and deviations from the minimum coupling orientation increase coupling dramatically. Figure 13 maintains the symmetry of the minimum coupling orientation by increasing the relative spacing. The greater the spacing, the lower the mutual coupling. However the ideal spacing of one diameter captures the bulk of the benefit. Larger separations may reduce the coupling further but with diminishing returns for increasing size. Minimum coupling is advantageous because it means that the functioning of each element does not interfere with the functioning of any other element. A minimum coupling condition represents a local minimum given other constraints such as the overall dimension of an antenna array. Three coil elements are particularly advantageous because use of three coil elements enables a minimum coupling antenna array to sample all components of an incident magnetic field.

Figure 13: NEC Results for minimum coupling antenna array; distance in units of loop diameter.

Figure 14: Minimum coupling antenna holder, array, and prototype. We created an element holder to support an individual magnetic loop element. The magnetic loop itself is wound around a ferrite toroid to enhance sensitivity and further minimize undesired magnetic coupling. The holder also provides a mounting point for a varactor tuner PCB. An individual holder may be combined with two others to create a three element array maintaining each element in the ideal orthogonal and minimum coupling arrangement with respect to each other. The holder is also configured to allow a single pole Figure 14 shows a mechanical drawing of the element and the array, and a photo of the finished prototype array. A patent is pending on the invention [5].

5 Experimental Evaluation Direct cabled measurements of mutual coupling like those of the previous section are challenging. Ultimately the aim of a minimum coupling antenna design is to yield independent, orthogonal antenna patterns. In this section, we evaluate the patterns directly within a field of known orientation. We constructed a Reference Field Loop to create a magnetic field of known orientation and magnitude so as to calibrate our receiver and associated antenna array. Our Reference Field Loop design comprises ten turns of #28 AWG wire at 5.1 cm (2 in) spacing on a 76 cm x 76 cm (30 in  30 in) PVC pipe frame. Figure 17 shows a model. Our goal is a 250 kHz bandwidth centered at 1100 kHz so we can set up a precisely oriented magnetic field across that bandwidth. We found the center frequency at 1120kHz and bandwidth of 265 kHz – not far off the design goals of 1100 kHz center frequency and 250 kHz bandwidth. We then calibrated the field at the center of the loop with reference to an EMCO 6509 passive magnetic loop antenna. The photo of Figure 17 shows the reference loop and the EMCO 6509. The #28 AWG wire in the Reference Field Loop is not visible in the photo. We implemented a NEC model of the Reference Field Loop to assess, predict, and validate performance [6, 7]. Our NEC model predicted an inductance of 113 H. QMeter measurements indicated 111 H.

Figure 15: NEC model (left) and PVC implementation (right) of a Reference Loop antenna. The fields in the Reference Loop Antenna are oriented along the z-axis as defined in Figure 15. Of course, the field intensity is not exactly uniform across the aperture or length of the loop. We performed a near-field analysis in NEC to establish that there exists a sweet spot of about a cubic foot at the center of the loop within which the magnetic field is constant to within 10%. Figure 16 shows the distribution of the magnetic field in the x-y plane and the x-z plane as defined in Figure 15.

Figure 16: Magnetic field distribution within the reference loop.

Figure 17: Battery operated receiver within the reference loop.. We used a battery operated receiver, implementing the compact, minimumcoupling array, as shown in Figure 17. The receiver relays data via an embedded WiFi datalink. We oriented the receiver so that one antenna (C) was approximately vertical and so that the other two were in the horizontal plane. We mounted the receiver with the array approximately centered in the Reference Field Loop. The receiver rests on a mechanical turntable constructed from a 61 cm (2 ft) circular plywood disk mounted on a similarly sized square piece of plywood using a ball-bearing-based swivel plate. A template on the disk displays angle to the nearest degree and a nail provides a fixed reference point at which to read the angle. Approximately quarter degree precision is possible by extrapolating between the individual degree markings. We setup a magnetic field at a convenient frequency (1012 kHz) within the receiver’s operational range and evaluated the patterns at five degree intervals, as well as adjusting the angle to try to find the exact nulls. Figure 18 shows the result.

Figure 18: Antenna patterns.

The nominal received signal power was -63dBm. Limiting factors include the noise floor in our lab, and the geometric precision with which we were able to orient the receiver. For instance, comparing the Channel C signal power null depths to the nulls of Channels A and B suggests that the receiver was oriented 3-5 degrees off vertical. The expected patterns follow: PA  P0 sin 2   0 

PB  P0 cos 2   0 

(8)

where 0 = 71.7 deg. Figure 18 superimposes the theory curves of (8) on the data. The data of Figure 18 demonstrates that the minimum coupling orthogonal array works as designed. This array exhibits sharp nulls 50 to 55dB deep, suggesting that the isolation between elements is comparable to the analytical predictions of the NEC model results of Figures 11-13. The total pattern maintains

6 Relation Between Null Depth and Angular Accuracy How much null depth is “good enough?” One way to tackle this question is to ask what is the angular uncertainty in the measured bearing for a nulled signal? Figure 19 shows the geometry of the null at  = /2. We can relate a null depth (N) to the angular measure of a null width (NW) to discover the relationship between null depth and angular precision: N  sin 2 2 

NW 2

  sin 2 cos NW2  cos 2 sin NW2 2  sin 2 NW2

(9)

Figure 20 plots null width versus null depth. With null depths of 50dB to 55dB, the angular resolution is about 0.2 deg – 0.4 deg.

Figure 19: Null geometry.

Angular Resolution: Null Width Versus Null Depth

Null Width (deg)

100 10 1 0.1 0.01 -80

-70

-60

-50

-40

-30

-20

-10

0

Null Depth (dB) Figure 20: Angular resolution versus null depth.

7 Conclusion Hazeltine’s pioneering work established that a minimum coupling and orthogonality are not equivalent conditions for arrays of small loops. Hazeltine identified and made practical use of minimum coupling arrangements for co-parallel loops. The present work identifies minimum coupling conditions for closely spaced orthogonal loops antennas. There exists an optimal configuration for small loops in which each of three identical but orthogonal small loops are translated along their axes an amount approximately equal to their diameter and then translated at a right angle by an amount approximately equal to their diameter so as to maintain the overall symmetry of the array. Although each antenna lies about a diameter away from the other, the arrangement yields 50 dB to 60 dB isolation according to both NEC simulation and experimental measurement. This minimum coupling geometry enables the construction of compact, three-axis magnetic antenna arrays capable of sampling all components of the magnetic field. Figure 21 shows a prototype.

Figure 21: Prototype minimum coupling antenna array.

8

Acknowledgements

This work was supported by NSF under Grant OII-0646339 and by the Test Resource Management Center (TRMC) Test and Evaluation/Science & Technology (T&E/S&T) Program through the U.S. Army Program Executive Office for Simulation, Training and Instrumentation (PEO STRI) under Contract No. W900KK-13-C-0032.‖ Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of NSF, the Test Resource Management Center (TRMC) Test and Evaluation/Science & Technology (T&E/S&T) Program and/or the U.S. Army Program Executive Office for Simulation, Training and Instrumentation (PEO STRI).

9

References

1) L.A. Hazeltine, “Means for eliminating magnetic coupling between coils,” U.S. Patent 1,577,421, March 16, 1926. 2) K. Siwiak, Radiowave Propagation and Antennas for Personal Communications, 2nd ed., Norwood, MA: Artech House, 1998, pp. 16-17. 3 ) Tadeusz M. Babij, and Howard Bassen, “Broadband isotropic probe system for simultaneous measurement of complex E- and H- fields,” U.S. Patent 4,588,993, May 13, 1986. 4) Yikun Hunag, Arye Nehori, and Gary Friedman, “Mutual Coupling of Two Collocated Orthogonally Printed Circular Thin-Wire Loops,” IEEE Transactions on Antennas and Propagation, Vol. 51, No. 6, June 2003. 5) U.S. Patent Application No. 14/313,932. 6) Roy Lewallen, EZNEC Pro/4 v. 5.0.20, 2008. See: http://www.eznec.com/ 7) Arie Voors, 4nec2, Version: 5.7.6, November 2009. See: http://home.ict.nl/~arivoors/