Near Field Phase Behavior
Hans Gregory Schantz ([email protected])
Q-Track Corporation; 515 Sparkman Drive; Huntsville, AL 35816
ABSTRACT
This paper presents a theoretical analysis of near field phase behavior in free space. Then this paper validates
the theoretical model by numerical modeling and comparison to experimental data. Near field phase behavior
is the basis of a novel RF tracking technology with a demonstrated accuracy of 30 cm at ranges up to 70 m.
1. INTRODUCTION
RF engineers and scientists often think of radio signals as a wave propagating inexorably away
from a transmit antenna. An electromagnetic wave is not a single wave, however. Rather, an
electromagnetic wave is a superposition of an electric wave and a magnetic wave. In the far field,
many wavelengths away from a transmit antenna, this distinction is not terribly important, because
the electric and magnetic waves move in lock step with perfectly synchronized phase. In the near
field, within about a half wavelength or so from an electrically small antenna, the electric and
magnetic field phases radically diverge. Close to an electrically small antenna, these fields are in
phase quadrature, i.e. 90 degrees out of phase.
A simple thought experiment involving electromagnetic energy flow establishes why the
fields are in quadrature close to an electrically small antenna and in phase far away. The Poynting
vector (S = ExH) is the measure of the energy flux around the hypothetical small antenna. If the
electric and magnetic fields are phase synchronous, then when one is positive, the other is positive
and when one is negative the other is negative. In either case, the Poynting flux is always positive
and there is always an outflow of energy. This is the radiation (or "real power") case. If the
electric and magnetic fields are in phase quadrature, then half the time the fields have the same
sign and half the time the fields have opposite signs. Thus, half the time the Poynting vector is
positive and represents outward energy flow and half the time the Poynting vector is negative and
represents inward energy flow. This is the reactive (or "imaginary power") case. Thus, fields in
phase are associated with far field radiation and fields in quadrature are associated with near field
quadrature. As this paper will describe in detail, there is a gradual transition from near field phase
quadrature to far field phase synchronicity.
This paper will present a theoretical analysis of near field phase and compare the results to
open field data. Then, this paper will discuss how near field phase phenomena enable a novel RF
tracking technology. The aim of this paper is to demonstrate how the anomalies of near field phase
behavior can be put to practical use.
2. HERTZIAN DIPOLE PHASE BEHAVIOR
Figure 1(a) shows how a Hertzian electric dipole may be thought of as equal and opposite charges
±Q separated by a distance d, or as an infinitesimal current I with length t. The strength of this
dipole is given by the dipole moment:
p=pOT(t)i
(1)
where the magnitude of the dipole moment is po = Q d and the time dependence is given by the
function T(t). Note also that It = p = d (Qd). Thus, a Hertzian dipole is a good model for an
electrically small dipole antenna, one much smaller than the wavelengths involved.
The electric fields of a Hertzian dipole are given by:
E=
1
47L5o
r2
(
IT(2( 0 i+ +sin60)+ 47ts0l1
rc)
and the magnetic fields are:
0-7803-8883-6/05/$20.00 02005 IEEE
134
i
c 2r
(2)
H1
=
(iT i sin OO
P
+
4nr , r
c )
AJA
(3)
rThie
elsewhere [I].
To evaluate the phase response of E,and H, set
the fields to zero and evaluate the behavior of the
zero-crossing. E6, -0 yields:
r(t)= -C..(-
T2
-4TT1)
Il
d
These results use the geometry of Figure 1(b).
present derivation closely follows one availa
(a)
z
(4)
and H -+yields:
r(t) = -c T
(5)
-
For a time harmonic dipole, one may take T(t
sin ot, so T(t)= cocoscot and T(t)= _Co2 sin2
Accounting for retarded time, the zero-cross
conditions become:
1-t = -{
+
[cotC{) +
(b)X
Figure I(s) A Hertzian dipole may be
thought of as equal and opposite charges
or as an infinitesimal current segment.
Figure l(b) Coordinate system around a
Hertzian dipole.
(6)
and Ho -* 0 yields:
op
r, =-{c +
r,1I tt1r,
PU) )
_Ph_.R
FI.M
I. .- t--
-lOt
O~H
-
-
-.
-
-
-
OE
I
-~
-90
_15
.1
0.1 02 03 0A4 0. b. 0.7 OA OJ
Figure 2(a) Hertz's plot of near field phase (Ref.
[2]). (b) Near field phase relations [Q-Track,
e2004].
(b)
ro)
]}
(7)
180(or ( cotQr
W
z LC
c
c
(8)
and
PbwRu
so-
c
Finally, converting the time of the zero crossing
into phase yields relationships for the electric and
magnetic field phases:
I
(a)
[cot
180 cor [cot- cor _c2n
=--__ )JJ
+ nsgJ
Lc [ -ct
+
c
rco
(9)
respectively. Figure 2(b) presents a graphic
representation of this phase behavior and the phase
delta. Figure 2(a) presents a similar diagram of
phase versus range originally presented by
Heinrich Hertz [2]. Figure 2(b) presents phase on a
"retarded" basis. In other words, increasing range
means an ever earlier time and a decreasing phase.
Hertz's figure (Figure 2(a)) presents phase on an
"advanced" basis. In other words, Hertz plots what
the phase will be as the wave advances to a
particular range [3].
135
Figure 3 (a) The results of the Ansoft IFSS model are consistent with the theoretical results of Figure 2(b).
(b) Experimental results acquired using prototype near field ranging hardware [Q-Track, 020041
3. NUMERICAL ANALYSIS
An Ansoft HFSS simulation further validates the results shown in Figure 2(b). The Ansoft HFSS
model of a small dipole comprises two 10 mm long by I mm diameter cylindrical elements
defined to be perfect electric conductors. These elements are spaced with a 0.2 mm gap and
excited using a 50 ohm lumped port across the gap. The model is embedded in a 1.000 m radius
vacuum sphere and analyzed at 299.79 MHIz so that the sphere is one wavelength in radius. Thus
the dipole has elements of length 0.01X and may be consider a good approximation to a point
dipole source. A radiation boundary condition is imposed at the surface of the sphere. Figure 3(a)
shows the result of the Ansoft HFSS simulation. The results of Figure 3(a) agree with the
theoretical result of Figure 2(b) except for numerical anomalies that crop up at the boundaries.
4. EXPERIMENTAL RESULTS
Repeated trials of a prototype transmitter and receiver in open field testing yielded results in close
agreement with theoretical predictions. The prototype hardware operated at a frequency of
1295 kHz where X = 231.5 m. Figure 3(b) overlays six experimental trials with the theoretical
prediction. The theoretical prediction breaks down within about 3 m where the antenna dimensions
become a significant fraction of the range. In this limit, the small antenna approximation
underlying the theoretical phase behavior is no longer valid. Details of the prototype hardware
employed are presented in the following section.
5. NEAR FIELD ELECTROMAGNETIC RANGING
The Q-Track Corporation has developed near field electromagnetic ranging (or NFERTM)
technology to use this near field phase behavior as the basis for a system of RF tracking [4]. A
transmitter beacon radiates an unmodulated sine wave at a known frequency. A locator receiver
includes an electric field receiver and a magnetic field receiver. The locator receiver compares the
phase delta between the electric and magnetic fields and determines the range to the transmitter
beacon. Figure 4(a) depicts this system and Figure 4(b) shows typical accuracy results.
More recently, Q-Track has developed a full, 2-D tracking system. This system provides real
time (<I sec update) 2-D tracking out to about 60 m (200 ft) with a mean accuracy of about 30 cm
(I ft). Figure 5(a) shows Q-Track's test transmitter, Figure 5(b) shows one of the two Q-Track
receivers used in this system, and Figure 5(c) shows the graphical user interface for Q-Track's real
time 2-D tracking system.
6. CONCLUSION
This paper presents a theoretical and computational analysis of near field phase and presents
experimental measurements that closely match predictions. The near field phase behavior
described in this paper forms the basis of a novel means for RF tracking.
Near field electromagnetic ranging technology is:
136
Accuracy vs Range 1295 kHz
10
Ei
0
~0.1
0.05k
0.01
0.50
0.001
s
0 10 20 30 40 50 60 70 80 90
Range (m)
(b)
Figure 4(a) System for near field ranging (After Ref 4). (b) Typical accuracy results [Q-Track, 02004].
(a)
(aY)
')-_
Figure 5(a) Transmitter with 60 cm whip antenna. (b) Q-Track's receiver with box loop and dipole antennas
(c) GUI for Q-Track's 2-D real time tracking system showing a 40 ft by 50 ft rectangular path on a
200 ft x 200 ft grid (10 ft/div) [Q-Track, 02004].
o Extremely simple: exploits basic electromagnetic physics without requiring precise timing or
oK
synchronization.
Accurate: can measure within 30 cm at ranges up to 70 m using an extremely narrowband
signal that requires very low bandwidth and very high channelization.
`- Relatively inexpensive: operates at low frequencies using relatively inexpensive and readily
available commercial off-the-shelf components.
K Fully Authorized: operates on a low power basis under the provisions of FCC Part 15 rules
(§15.219). No regulatory approval needed for outdoor use.
7. ACKNOWLEDGEMENTS
The author is grateful to the Q-Track Corporation for support, assistance, and permission to
disclose Q-Track proprietary performance information and results.
8. REFERENCES
[1] Hans Gregory Schantz, "Electromagnetic Energy Around Hertzian Dipoles," IEEE Antennas and
Propagation Magazine, Vol. 43, No. 2, April 2001, pp. 50-62.
[2] Heinrich Hertz, Elctric Waves, London: Macmillan & Co., 1893, p. 152
[3] The distinction between retarded and advanced phase is analogous to the distinction between Eulerian and
Lagrangian coordinates in fluid dynamics.
[4] Hans Schantz and Robert DePierre, "System and Method for Near Field Electromagnetic Ranging," U.S.
Patent Publication 2004/0032363 Al, February 19, 2004.
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