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Factors Affecting Surface Wave Propagation
Janice Hendry
Roke Manor Research Limited, Old Salisbury Lane, Romsey, SO51 0ZN
Abstract
This project has been funded by the SEAS DTC as follow on work to IF012, ADD003 and
CC012 PRELIM. The objective of the study is to carry out research to underpin the
development of a covert communications system utilising a surface wave launch and receive
mechanism in place of conventional antennas.
This paper focuses on the factors affecting surface wave propagation; specifically it gives
details of a hypothesis for the relation between the skin depth of a medium and the amount of
surface wave launched. This demonstrates that the effect of the properties of the medium over
which a surface wave propagates is large.
This paper also shows the broad nature of applications and potential exploitation routes of a
surface wave based technology, in particular it meets a current UK MoD need, namely
tactical beyond line of sight operation priority technology for the UK MoD [1].
Keywords: surface waves,
electromagnetics, propagation.
ground
waves,
Summary of Work to Date
This phase of work focused on gaining a
theoretical
understanding
of
the
mechanisms affecting surface wave
propagation. This will assist with a system
design which is proposed to be undertaken
in the next phases of this research. The
main focus of this work was the factors
affecting the propagation of surface waves.
It has also been necessary to gain an
understanding of the various different types
of surface wave that can exist and which of
these are most likely to be useful.
Once the theory overview was complete,
potential system benefits and applications
were reviewed, showing the broad nature of
applications and potential exploitation
routes of a surface wave based technology.
Such a technology also assists with the
tactical beyond line-of-sight operation
priority technology for the UK MoD [1
(p71)] due to the surface wave’s terrain
following ability.
antenna,
communication,
monopole,
Underhill Research has also been
developing a calibration technique. This
will enable us to compare the performance
of different designs directly by calibrating
out the effect of the ground properties.
The final part of this work was simulation
based, using a simple monopole or dipole
as the base design. These simulations were
performed to back up the theory discussed
in the earlier stages of this work and the
techniques developed will be useful for all
future simulations.
This paper focuses on how the properties of
the media over which a wave propagates
affects the surface waves and the potential
benefits and applications of a surface wave
based system.
Types of Surface Wave
There are many different types of surface
wave and each can be defined by the
guiding structure required. This year’s
work has isolated two potential types of
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surface wave that may be useful for both
civil and military applications, namely the
Zenneck surface wave and the trapped
surface wave.
1.
no variation in
Therefore, ∂/∂y=0;
2.
variations in the x-direction can be
represented by exp(-γox) in the
dielectric (air) and by exp(-γ1x) in the
lower medium;
3.
the permeability, µ is the same in all
media considered and equal to the
permeability of free space, µo;
4.
variations in the z-direction are as yet
unknown and must be solved for.
Zenneck Surface Wave
The Zenneck surface wave is an
inhomogeneous plane wave supported by a
flat surface and can be represented in both
rectangular and cylindrical coordinates. It is
a transverse magnetic (TM) mode and
requires that the permittivities of the media
either side of the interface are different but
their permeabilities are the same [2]. It also
requires an inductive reactance term in the
surface impedance, Zs for the medium it
propagates along.
In order to excite a TM Zenneck surface
wave, two conditions [2] are required:
1.
incidence close to the Brewster angle;
2.
finite loss in one of the media.
A transverse electric (TE) mode is also
possible but not discussed in this paper as it
is not easily realisable over natural guiding
structures.
the
y-direction.
By solving Maxwell’s equations using
these boundary conditions, one obtains the
‘resonance condition’. This is defined at z =
0 m and is when the Zenneck surface wave
will propagate,
u1
σ 1 + jωε1
+
uo
=0
jωε o
(1)
where, ω = angular frequency, u = propagation
coefficient in the z-direction, ε = permittivity,
σ = conductivity. The subscript 1 refers to the
property of medium 1 and the 0 to medium 0,
in this case free space.
Trapped Surface Waves
Trapped and quasi-trapped surface waves
occur over a dielectric slab or dielectric
coated conductors and can support both TE
and TM surface waves. They can only exist
when the ground is not homogeneous or is
ideally stratified [4 (p99)].
A trapped mode occurs when the angle of
incidence from the dielectric medium to the
air-dielectric interface is greater than the
critical angle, θc which is defined by,
Figure 1: Boundary conditions for Zenneck wave
[3 (p7)]
The Zenneck surface wave decays
exponentially away from the surface. In
order to obtain a solution from Maxwell’s
equations, one must first set up the
boundary conditions (see Figure 1) and
make the following assumptions about the
surface wave:
sin θ c =
1
ε
(2)
When the angle of incidence is at or greater
than the critical angle total internal
reflection will occur, with the field outside
the dielectric being evanescent in nature,
i.e. it decays exponentially away from the
interface [5 (pp712-714)].
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conductivity and permittivity (assuming
relative permeability is 1). Taking these
into account, the equation for skin depth
can be derived in full,
dS =
In effect, when a layer of dielectric is on
top of a perfect conductor it acts like an
optical fibre or more generically as a
dielectric waveguide, as shown in Figure 2
[5 (p 717)].
Effect of Skin Depth
A material can be classified as a good
conductor or a good dielectric by using the
relations:
(3)
(4)
The reason for defining if a material is
either a good conductor or good dielectric
is to help determine the dominant loss
mechanism. In general, real ground has
dielectric properties with the only
exception being sea water which acts more
like a conductor due to its salt content.
The skin depth is defined to be the point
below the surface of a material when the
electric field drops to 1/e of its surface
value [6]. Generally this is quoted to be,
ds =
2
ωµσ
(6)
π f tan δ
where vp is the phase velocity and tan δ is
the dielectric loss tangent, which are
defined by,
Figure 2: Trapped surface wave
σ
〉〉 1 ⇒ good conductor
ωε
σ
〈〈 1 ⇒ good dielectric
ωε
υp
(5)
However, this relation is only true for good
conductors as defined by Equation (3). In
most cases, this work considers materials
that are neither good conductors nor good
dielectrics and so the skin depth calculated
using Equation (5) is inaccurate.
The skin depth of a material is dependent
on the material properties, namely
υp =
1
µε
and
tan δ =
σ
ωε
PEC is generally the optimum material for
a space wave to propagate over; therefore it
may not be immediately obvious that as
conductivity increases the magnitude of the
surface wave electric field decreases.
Bound surface waves cannot exist in or
over a perfect conductor (PEC) as it has
zero skin depth.
A surface wave requires an interface
between two media as it exists partially in
both. Therefore if the electric field is
unable to penetrate into one of the media, a
surface wave cannot propagate. This
implies that the skin depth is proportional
to the magnitude of surface wave produced
and indirectly proportional to the
magnitude of space wave produced with an
exponential dependence.
This can be explained mathematically by
applying boundary conditions to Maxwell’s
equations, but a novel way of thinking is to
use the concept of probabilities and the
photon transmission path to explain this
relationship.
Consider the electric field propagation as
photons travelling away from the source
with time. Assume the source is constantly
transmitting and there is zero loss.
Now take a transmitter in a vacuum over a
perfect conductor; the skin depth will be
0m. A bound surface wave requires the
electric field to be able to penetrate through
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the boundary, forming an interface between
the two media.
When a skin depth, ds exists, for a real
ground a potentially bound surface wave
can exist. The higher the surface reactance,
Xs the more tightly bound the surface wave
is to the interface and the more of the field
that is distributed within the surface wave
region. The surface wave region can be
defined as the region in which the surface
wave is able to exist (see Figure 3).
Why is this the case? Consider the
distribution from a statistical or probability
point of view. The larger the surface wave
region the higher the probability that a
photon will enter this region.
In reality, the material properties will vary.
These changes of properties can cause the
photon to change its direction such that it
leaves the surface wave region. This is
considered a loss mechanism as the space
wave is an unwanted field component in
this study. Once again, a simple probability
can be considered, the larger the surface
wave region the higher the probability that
the photon will remain within it.
If the skin depth were infinite, a wave in
the surface wave region should be greater
as the ratio of space to surface wave region
would approximate unity. However, there
will be a depth beyond which the
propagating wave is no longer a surface
wave as it is not bound to the interface.
Therefore one can define a useful surface
wave region or optimal skin depth for
surface wave propagation,
d s , optimum = d s ,useful + ∆d s
(7)
The ∆ds term in Equation 7 is due to the
fact that if the photon did leave the useful
surface wave region, there is still the
probability that it will re-enter this region
before being received. ds,useful includes some
of the area just above the interface as some
of the surface wave will be present there
also.
Figure 3: Figure detailing the surface wave
region
In summary, to maximise the initial
magnitude of surface wave electric field, a
larger skin depth is desirable, but for
reception, there will be an optimum skin
depth as described by Equation (7).
It is the author’s recommendation that this
explanation is further investigated, but not
necessarily as part of this contract; however
it should be kept in mind when designing a
system.
Surface Impedance
The properties, and thus surface
impedance, of the ground over which a
surface wave propagates has a large impact
on the ratio of surface wave to space wave
launched and how much loss the wave is
affected by, and the possible range of, the
signal.
The surface impedance also defines how
tightly bound the surface wave is to the
interface and how quickly the space wave
will be attenuated in the z-direction away
from the interface.
The surface impedance is defined in terms
of the surface reactance, Xs and resistance,
Rs,
Z s = Rs + jX s
(8)
which are found from
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Rs =
Xs =
ωµ1
(
ω 2ε12 + σ 12 + ωε1
(
2 ω 2ε12 + σ 12
ωµ1
(
)
ω 2ε12 + σ 12 − ωε1
(
2 ω 2 ε12 + σ 12
)
)
)
(9)
(10)
where the same notation is used as before.
Theory predicts that the higher the surface
reactance, the faster the decay of the space
wave away from the interface, whilst the
more tightly bound the surface wave
becomes. Therefore, a medium with a high
reactance should exhibit better terrain
following abilities.
A high reactance also results in a decreased
surface wave spread outside of the surface
increasing the energy within the surface
wave region. This can be further enhanced
by the fact that a high surface resistance
increases the tilt of the wave. However,
increasing the resistance also increases the
attenuation of the surface wave. This
implies that there is a trade-off with regards
to the optimum surface impedance for
production and propagation of a surface
wave whilst minimising the space wave. It
can be seen that a high reactance is
desirable. However, depending on the
application, the desired resistance may
vary.
One can artificially increase the reactance
of a structure by increasing the surface
roughness. By increasing the reactance, one
can increase how well bound the surface
wave is to the interface and reduce the loss
of the signal
Assuming the application of an antenna
propagating over a long distance, one
would require that the medium which it
propagates over has a high reactance to
reduce the space wave component and low
resistance to reduce the attenuation of the
surface wave. One can then determine the
optimum
medium
properties
by
differentiating Xs and Rs with respect to ω
then equating them to zero [3 (p 18)]. This
shows that when Xs is a maximum and Rs is
a minimum, the required medium
properties are,
σ = 3ωε
(11)
For short range applications, a high
resistance may be preferable as more
energy is directed into the surface wave
region and attenuation occurs with distance.
Over larger distances a low resistance
would be preferred to reduce this
attenuation.
Figure 4: Electric field penetration: fresh water and key used for all simulations
Electric Field Penetration Simulations
Simulations were performed using the
frequency-domain software HFSS. The
total length simulated was 2.4 km, which is
equivalent to 8λ and just under 3λ in height,
where λ is the free-space wavelength at 1
MHz. All simulations used a 1 MHz
quarter-wave monopole and the colour
representation is interpreted using the key
in Figure 4 used for all simulations.
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Six sets of medium properties were
simulated, however only the most relevant
are detailed in this paper.
Figure 4 clearly shows the electric field
penetrating into the lower medium, in this
case fresh water. The penetration can be
seen to be consistent for the full 2.4 km and
the electric field has a high magnitude at
the interface. This is indicative of the
presence of a surface wave but not proof
that this is the cause of this increased
magnitude. Figure 5 shows the electric field
penetration into salt water, which has a
high conductivity.
Figure 7: Electric field penetration: dry ground
Dry ground is perhaps the most interesting
of the media simulated. The electric field
decays more slowly close to the interface
than further above it. Additionally, there is
more penetration of the electric field into
the dry ground, as predicted by the skin
depth equation.
Wave Tilt
Figure 5: Electric field penetration: salt water
The electric field does not penetrate very
deeply into salt water due to its high
conductivity. It is therefore thought
unlikely that much surface wave will be
present. One can clearly see that the
strength of the electric field in the upper
medium is higher than that for fresh water,
and shows some similarities to the expected
field over PEC.
The electric field, magnetic field and
direction of propagation should all be
perpendicular to each other under ideal
circumstances; however a surface wave
produces a forward tilt in the electric field.
The magnitude of this tilt depends on both
the conductivity and permittivity of the
medium over which it propagates. This tilt
can be calculated from the ratio of
horizontal electric field to vertical electric
field [7 (p654)],
EH
1
=
EV ηo
1
 σ 
∠ tan −1 

2
 ωε 
σ +ω ε
ωµ
2
2
(12)
2
Note: ∠ denotes that the relation
following it represents the phase and ηo is
the characteristic impedance of free space.
Figure 6: Electric field penetration: wet ground
Wet ground has a lower conductivity and
permittivity than salt water and therefore
has a larger skin depth, as can be seen by
comparing the penetration depth of Figure
5 and Figure 6.
Figure 8: Diagram to show angle descried in
Equation 12
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The arctangent of the magnitude part of
Equation (12) (θ) represents the angle by
which the electric field component is tilted
from the vertical in the direction of
propagation as shown in Figure 8. This
implies that there will be a small but finite
value of EH for a medium with finite
conductivity which is given by the first part
of Equation (12).
This result could be used to help identify
the surface wave in both simulations and
measurements. If it is known how much the
electric field vector will tilt, and that the
electric field is not perpendicular to the
direction of travel, the vertical component
of the Poynting vector should also be nonzero. It also indicates that the surface wave
is highly dependent on frequency and the
properties of the ground over which it
propagates.
Figure 9 shows the tilt angle θ over grounds
with different properties.
Effect of Frequency and Medium Properties on Wave Tilt
25.00
Wave Tilt (degrees)
20.00
15.00
`
10.00
5.00
0.00
0.1
1
10
100
Frequency (MHz)
Wet Ground
Avg Ground
Fresh Water
Salt Water
Dry Ground
Copper
Figure 9: Effect of frequency on wave tilt for different ground properties
Another implication of the phase part of
Equation (12) is that the resulting radiation
will have elliptical polarisation as opposed
to linear polarisation.
Local Electric Ground
Perhaps the main output regarding potential
future designs from the past year’s research
is the concept of a local electrical ground. It
has been found that the ground properties
have the largest effect on the propagation
of surface waves. If one were able to
control the ground properties over which
the surface wave propagates, one should
therefore be able to efficiently launch a
surface wave. The Goubau horn does
exactly this by using a wire between the
transmitter and receiver; however for this
application, it is unlikely that this design
type would be feasible. It is also impossible
to control all the ground over which a
surface wave propagates over. However,
one is able to control the ground
surrounding the launch and receive
mechanisms. This is common practice for
many antenna designs, utilising a local
ground plane; however this is usually
metallic in nature. In order to launch an
efficient surface wave, one requires an
optimised dielectric local ground plane. In
this work, it will be termed a ‘local electric
ground’ such that it is not confused with a
metallic ground plane.
Developing this idea, and assuming short
range covert communication is preferable, a
local electric ground with high impedance
and high resistance would be preferable.
This would maximise the transmission of
the energy into the surface wave region and
attenuate away quickly the space wave. The
exact size of the local electric ground
would need to be optimised and there is
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also the consideration of the preferred
shape, i.e. could this local electric ground
plane be used to direct the surface wave in
a particular direction as opposed to omnidirectional obtained using a standard single
line element launch mechanism.
In addition to considering a dielectric based
local electric ground, one could also
consider designs using a corrugated or
dielectric coated metallic local electric
ground. The latter would be advantageous
for the launch of trapped surface waves and
the former for the Zenneck surface wave.
Dielectric Filled Horn
The frequency is expected to be a key issue
for this design as at HF the horn will be
large.
Potential Benefits
This section briefly outlines some of the
potential system benefits if a surface wave
was used as opposed to a space or sky wave
based system. As these are system level
issues, they have not been fully
investigated in this document; however
some background research has been
performed to back up the following
statements.
Increased Range
This section combines the use of a
dielectric slab wave guide for trapped
surface waves and the Goubau horn.
•
Consider a half-horn on a medium with
finite conductivity. According to Barlow
and Brown [3 (p151)], theoretically, in
order to launch a pure surface wave, an
infinite aperture is required. However it is
known that a dielectric slab waveguide can
launch a trapped surface wave and a horn
can launch a Sommerfeld-Goubau surface
wave. Consider the medium 0 – medium 1
interface as the ‘wire’ (i.e. guiding
structure) required for the SommerfeldGoubau. Next combine a horn waveguide
and a dielectric waveguide by filling part of
the horn with a tapered dielectric slab (see
Figure 10). This should ensure that the
surface wave produced is tightly bound as
it exits the horn and enters free space, or in
this case a medium with finite conductivity.
This dielectric slab should then act as a
dielectric waveguide and ideally direct the
wave such that it becomes bound at the
interface for its continued propagation.
Surface waves are already utilised in some
applications indirectly. For example,
marine communication and terrestrial radio
broadcast can both be received over the
horizon. This is partly due to the sky wave
but also due to the surface wave. If one
could instead transmit all the power into the
surface wave, it is expected that much
greater ranges could be achieved. In
Zenneck’s 1915 book [8 (p249)], he states
Potential Capability: Increased range
for same power consumption, reduced
power consumption for same range.
the range could be extended from
1
r2
to
1
r
for a signal of the same power utilising
surface waves. This relationship can be
derived from Maxwell’s equations, but
does not necessarily take into account
conductive losses in the medium.
Covert Signal
•
Potential
Capability:
Covert
communications, covert sensors
In addition to the increased range, surface
waves are, by definition, non-radiating and
therefore could be considered for covert
systems. This assumes that a pure surface
wave can be launched or that the space
wave can be attenuated away rapidly close
to the transmitter. Various design
Figure 10: Dielectric filled horn
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considerations may be able to achieve the
latter methodology as some texts state that
it is impossible to launch a pure surface
wave. However, for real applications,
simply ensuring that the majority of the
power is transmitted into the surface wave
should be sufficient.
The main problem that may be encountered
is that when the signal travels over certain
topologies it may be re-radiated
(considered a loss mechanism) and some
energy transferred back to the space wave.
It is however, expected that the energy reradiated will be small in each incidence that
occurs.
MoD as stated in the Defence Technology
Strategy, published in 2008 [1 (p71)]. A
surface wave based technology could
provide the UK MoD with this capability in
a covert manner and with increased range.
The main limitation of terrain following
will be the ‘sharpness’ of angle around
which a surface wave can still remain
bound to the interface. It is expected that
some loss through radiation will occur
when passing over different topologies and
this loss will increase with its ‘sharpness’.
However, it is expected that this should not
cause excessive loss as most natural
topologies are relatively gradual or small
compared to the wavelength.
Terrain Following
•
Potential Capability: Non-line-of-sight
communication,
over-the-horizon
communication
Terrain following is the ability for the
signal, or in this case an electromagnetic
wave, to follow the topology of the Earth.
Figure 11: Antennas without line-of-sight
communication
Due to the surface wave being bound to the
interface, it should follow the terrain. Space
waves on the other hand are diffracted
around objects. By utilising a surface wave
based system, one could ensure more signal
power is transmitted to the desired location,
following the terrain rather than being
omni-directionally radiated when the space
wave is diffracted. This results in the
capability
of
non-line-of-sight
communication. This could be useful over
short distances due to local topology or
over longer ranges, such as over-thehorizon communication.
Tactical beyond line-of-sight operation is
currently a priority technology for the UK
It is unknown what the limits are for the
surface wave to remain bound. This
knowledge could be used to assist with
proving that the field seen over a specific
topology is purely the surface wave as
opposed to the diffracted or refracted space
wave. Two situations were modelled in
HFSS, both of which had a smooth,
shallow gradient of 108.5 degrees measured
clockwise from the z-axis. In the first
model (a) an imperfect ground plane with
Zs=10+j50 ohms was used,. The second
simulation (b) used a PEC ground plane
and no surface wave should be present.
Figure 12: Terrain following showing total
magnitude of electric field over (a) imperfect
ground plane; (b) PEC ground plane
Figure 12 shows the magnitude of the total
electric field and in both cases the wave
front appears to follow the terrain; however
there is more field present along the surface
in Figure 12(a), which has an imperfect
ground plane. This could be due to the
bound nature of the surface wave. To
conclusively
prove
this,
additional
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investigation needs to be completed.
Nonetheless, these simulations are highly
indicative that a surface wave is present
and that terrain following is occurring.
Potential Applications
This section details the broad variety of
applications of a surface wave based
technology, as shown in Table 1.
From the table, one can see that a surface
wave technology has diverse applications,
from land-based to marine, military to civil.
Each of these potential applications will
have different requirements and will
therefore require the design to focus on a
different area, e.g. for ground water
detection in agriculture, loss through
radiation will not be a major problem as
covertness is not a concern, whereas with a
covert military link, this could pose serious
problems. It will therefore be important to
focus future research on a few similar
applications to maximise the benefit of this
work.
Table 1: Potential applications of a surface wave based technology
Potential Capability
Surface Wave Characteristics Assisting with
Capability
Short range communications (e.g.
between sensor nodes)
Signal covertness
Long range communications / marine
communications (e.g. over-the-horizon
communications)
Increased range
Buried object detection
Ground would be main region of propagation
Terrain following over local topology (e.g.
small craters / holes)
Terrain following
Potential increased range compared to space
wave
Seabed (buried) object detection
Seabed would be main region of propagation
Covert communications
Signal covertness
Surface wave radar (e.g. over-thehorizon radar)
Terrain following
Communication and sensing through
pipes, tunnels, etc.
Terrain following
Ground water detection (e.g.
agriculture)
Wave tilt depends on the ground properties
Increased range
Increased range
.Conclusions
It has been found that the ground properties
have a large effect on surface wave
propagation and it may be possible to
manipulate the properties surrounding the
launch mechanism by the use of a ‘local
electric ground’. This should increase the
power directed into the surface and may be
a very useful technique to rapidly attenuate
the space wave component, making the
technology more covert.
This paper postulates that the skin depth
can be related to the efficiency of surface
wave propagation by the notion of a
‘surface wave region’. This gives a
qualitative view of why dry ground is
perhaps better for launching a surface wave
as opposed to wet ground. This was then
demonstrated in simulations.
Initial work was undertaken to examine the
surface wave’s terrain following ability.
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This has been investigated briefly in this
phase as tactical beyond line-of-sight
operation is currently a priority technology
for the UK MoD as stated in the 2008
Defence Technology Strategy [1 (p71)]. A
surface wave based technology could
provide the UK MoD with this capability in
a covert manner and potentially with
increased range.
This work will form part of an Engineering
Doctorate (EngD) at UCL, with fees funded by
the EPSRC.
Overall, this phase of work has laid good
foundations to proceed with the next stage,
which will be more practically based.
References
[1]
UK MoD, Defence Technology Strategy: for
the demands of the 21st century, UK MoD
(2008)
[2]
Overfelt, P., Review of Electromagnetic
Surface Waves: 1960 Through 1987, Naval
Weapons Center CA, NWC TP 6880 (Jan
1988)
[3]
Barlow, H., Brown, J., Radio Surface Waves,
Oxford University Press, London (1962)
[4]
Maclean,
T.,
Wu,
Z.,
Radiowave
Propagation Over Ground, Chapman & Hall,
1st Ed., London UK (1993)
[5]
Collin, R., Field Theory of Guided Waves,
IEEE Press, 2nd Ed., USA (1991)
[6]
Sander, K., Reed, G., Transmission &
propagation of Electromagnetic Waves,
Cambridge University Press, 2nd Ed. (1986)
[7]
Jordan, E., Balmain, K., Electromagnetic
Waves and Radiating Systems, Prentice-Hall
India, 2nd Ed. (2006)
[8]
Zenneck, J., Wireless Telegraphy, McGrawHill Book Company, 5th printing (1918)
Acknowledgements
The work reported in this paper was funded by
the Systems Engineering for Autonomous
Systems (SEAS) Defence Technology Centre
(DTC) established by the UK Ministry of
Defence.
The author would also like to acknowledge the
technical assistance provided by Mike Jessup
and Steve Simpson of Roke Manor Research
Limited and Mike Underhill of Underhill
Research.
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