What is an Earth Current Antenna?

How Earth Current
Antennas Really Work
David Gibson
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Who am I?

I have …
… been involved with BCRA’s Cave Radio &
Electronics Group since its inception 27 years ago
… a PhD in Sub-Surface Communications
… worked for 12 years in the research division of the
UK’s Mines Rescue Service
…recently been appointed a Senior Research Fellow
at the University of Exeter’s Camborne School of
Mines
… been secretary of BCRA since January 2010
… not had time to go caving for a long while
What is an Earth Current
Antenna?
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An amplifier connected to earth by two electrodes
A grounded horizontal electric dipole antenna
A line current antenna
Used for ELF comms (submarine / ionosphere)
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How Earth Current
Antennas Really Work
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Recent trend away from use of induction
loop antennas towards grounded wires
The popular explanation for how these work
is fallacious
– They do not “allow the current to flow in a big
loop” and they do not depend on current flow in
the ground at all

If we do not understand how the antenna
works, it is difficult to know the best way to
use it, or how to design a better one
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Recap:
Cave Communications
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H.f. radio is attenuated by conducting medium
Lower frequencies are better: 10 – 100 kHz
Wire antennas too large (1500 m @ 100 kHz)
Small antennas are inefficient
– They do not radiate much/any power
– This does not matter for close work

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Small loops easier to use than small dipoles
Hence use of induction loops
– Because they are small and portable
– not because they generate a magnetic field
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Why Do We Need a
Magnetic Field?

E field is attenuated at air/rock boundary
– But that doesnt prevent its use within
conducting medium

E field is difficult to generate and detect
– Stray capacitance dominates small antennas
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However…
– a time varying field must contain both E and H
components
– A loop is not the best way to generate a
magnetic field
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H field from a wire

A steady current flowing in a wire generates
a magnetic field
– NB: not an electric field

We need a ‘circuit’ for current to flow
– But the return current generates a field in
opposition to the wanted field
– One side of a loop cancels signal from other side
– Hence large loops are better than small ones
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There is no way to avoid this
– … or is there?
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H field from a wire
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Avoiding a Return Path

Current must not flow in a “circuit”
– No separate return path
– Current flows up and down the wire
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What does current do at the end of the wire?
– Need to have a reservoir to store the charge
before returning it during the next half cycle
– i.e. capacitor
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Low capacitance at l.f. is a problem
– Most current will leak away, due to stray C,
before it reaches end of antenna
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Left to its own devices, charge will not flow to the ends of a wire.
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One method of encouraging the charge is to provide somewhere (a
‘capacitor’) for it to reside.
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Another method to to provide a return path for the current, but this is
undesirable because the return path partially cancels the wanted field.
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If we could thread the loop through worm holes in the fabric of
space-time, it might work.
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Such an antenna would generate a magnetic field like this – concentric
loops falling off in magnitude beyond the ends of the wire.
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Grounding the antenna is an established method of drawing the current
to the ends of the wire. The return current does not cancel the wanted
field – but why not?
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Surely the Earth Current
Affects the Field?
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The effect of the line current and all the
current elements in the ground combines to
generate observed H field (concentric hoops)
But in the absence of grounding, and for the
same line current, the charge that builds up at
the ends of the antenna has the same effect
So, to model the antenna, it is only necessary
to consider an isolated current element
– E.g. think of “worm holes”
– Use Biot Savart Law (for d.c. case anyway)
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Ampère-Maxwell law

H = D + J

Hdl 
C

  J  d S

D

S
Relates loop C of magnetic field to current
flow through surface S
– Current is sum of conduction current and the ‘socalled’ displacement current
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Complicated to use with ‘real world’ problems
– We know H field must be circular loops, which
makes it easier
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Gauss’s Law
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From Ampère-Maxwell law…
– Using the equation of continuity (left), we obtain
Gauss’s Law (right)
 J dS  I
S
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 DdS  Q
S
This leads to a ‘duality’ relationship between
charge and current
Q
I



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Duality
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Any result we obtain for a static charge
distribution Q in a medium with permittivity
 (i.e. an isolated dipole) is applicable to a
slowly-varying current I in a medium with
conductivity  (i.e. a grounded dipole)
For an electric dipole…
– J is zero if it is isolated
– D is zero if it is grounded
– So the Ampère-Maxwell equation gives
the same answer
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Biot-Savart Law

The resulting magnetic field can be derived
from the Ampère-Maxwell law
I d
dH 
sin 
2
4r
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This is the Biot-Savart law
– Many textbooks assume this is axiomatic
– To assume so is to miss the very point we’re
trying to prove
– Strangely, this magnetostatic law requires, in its
derivation, manipulation of a time-varying quantity
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Electrostatic Field
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E field and J field coincide (duality)
E
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Q d
4 r 3
2 cos  rˆ  sin  θˆ 
Inverse cube law
– E or J field probably less strong than H field
– Receiver can be ungrounded (E) or grounded
(J) and same arguments apply concerning
current distribution; i.e. we must ‘make’ the
current flow in the full length of the antenna.
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The Story so Far

If an isolated electric dipole has a uniform
current flow then its magnetic field is not
affected by grounding the ends of the dipole
– i.e., the return current through the ground does
not materially contribute to the field
– the dipole must have a uniform current, which can
only be achieved by grounding
– The line current and all the elements of current in
the ground combine to generate the H field
– But in the absence of grounding, and for the same
line current, the charge that builds up at the ends
of the antenna has the same effect
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Is it Obvious?
The story is told of the eminent mathematician
G H Hardy that he was once giving a lecture
when he made a casual remark, and said, “Of
course that’s obvious.”
Then he stopped talking and looked puzzled
and then very thoughtful. Time wore on and he
continued staring dreamily into space.
After a while the class was getting very restless,
but finally the great man emerged from his deep
thoughts and said to the students: “Yes I was
right all along – it IS obvious.”
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Yes: its obvious!
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All the ‘great’ analyses of HEDs (Wait,
Burrows etc) assume the antenna is
grounded, without explaining why
You can work through the maths rigorously
step by step and prove the result
But it is still difficult to explain it in simple
terms
Now we ‘know’ it is true (and obviously so),
what can we deduce?
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Observations (1)
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We need a good connection to ground to
get maximum current flow in the wire
– Electrode design and spacing needs attention
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Contact area is not the main criterion
Electrodes must have a high “capacity” which means a
large “extent”. Useful to simulate a large electrode by
connecting several well spaced electrodes in parallel
The magnetic field…
– comprises loops centred on wire (i.e. not generated ‘underground’ by “large loop of current”)
– falls off with inverse square law (not inverse
cube, as it does for an induction loop)
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Observations (2)
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We should be detecting this H field using an
induction loop
– But it must be properly designed, not “hit and
miss”
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It may be convenient to detect the electric
field but…
– This falls of as the inverse cube of distance
– It requires a grounded dipole for same reason as
transmitter
– It is ‘convenient’ to think of it as detecting the
current flow in the ground
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Observations (3)
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The ground will never be a very good
conductor compared with a wire
– A return path through a distant wire will always be
better than a path through the ground
– Which is better…?
i) 100 m line antenna – walk out & back for 200 m
ii) 60 m loop – walk a 200 m perimeter
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The better option depends on many factors
– Proper design of loop antenna
– Skin depth in ground (return path can be hidden)
– Communication distance required
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Observations (4)
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A proper comparison of line v. loop requires
– A good analytical design of a loop antenna
– A good analytical design of the power amplifier
– A proper method of assessing the intrinsic
performance of the antenna
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Assessing the loop for losses
Compensating for variable ground resistance
“Specific power consumption”
– A method of experimentally rating earth-current
antennas for effectiveness … of which more later