1. How Earth Current Antennas Really Work
David Gibson

2. 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

3. What is an Earth Current Antenna?
An amplifier connected to earth by two electrodes
A grounded horizontal electric dipole antenna
A line current antenna
Used for ELF comms (submarine / ionosphere)

4. How Earth Current Antennas Really Work
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
With cave radio equipment such as the HeyPhone and Nicola system there has been a trend away from the use of induction loop antennas towards earth-current antennas, i.e. long wires grounded at both ends. However, the popular explanation for how these antennas work is fallacious. They do not operate by allowing the current to flow in a ‘big loop’ in the ground and in fact, they do not depend, fundamentally, on current flow in the ground at all. The fact that the popular explanation is wrong is important because, 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. Back in 2003, I wrote an article for the CREG journal entitled ‘What We Don’t Know About Earth-Current Propagation’. It has taken me some time to get to grips with the problem but this talk will now go some way to filling in the gaps in this knowledge and will describe a method of experimentally rating earth-current antennas for effectiveness.

5. Recap: Cave Communications
H.f. radio is attenuated by conducting medium
Lower frequencies are better: 10 – 100 kHz
Wire antennas too large ( kHz)
Small antennas are inefficient
They do not radiate much/any power
This does not matter for close work
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

6. 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
However…
a time varying field must contain both E and H components
A loop is not the best way to generate a magnetic field

7. 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
There is no way to avoid this
… or is there?

8. H field from a wire

9. Avoiding a Return Path Current must not flow in a “circuit”
No separate return path
Current flows up and down the wire
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
Low capacitance at l.f. is a problem
Most current will leak away, due to stray C, before it reaches end of antenna

10. Left to its own devices, charge will not flow to the ends of a wire.

11. One method of encouraging the charge is to provide somewhere (a ‘capacitor’) for it to reside.

12. Another method to to provide a return path for the current, but this is undesirable because the return path partially cancels the wanted field.

13. If we could thread the loop through worm holes in the fabric of space-time, it might work.

14. Such an antenna would generate a magnetic field like this – concentric loops falling off in magnitude beyond the ends of the wire.

15. 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?

16. Surely the Earth Current Affects the Field?
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)

17. Ampère-Maxwell law H = D + J
Maths until slide 22
H = D + J
Relates loop C of magnetic field to current flow through surface S
Current is sum of conduction current and the ‘so-called’ displacement current
Complicated to use with ‘real world’ problems
We know H field must be circular loops, which makes it easier

18. Gauss’s Law From Ampère-Maxwell law…
Using the equation of continuity (left), we obtain Gauss’s Law (right)
This leads to a ‘duality’ relationship between charge and current

19. Duality
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

20. Biot-Savart Law
The resulting magnetic field can be derived from the Ampère-Maxwell law
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

21. Electrostatic Field E field and J field coincide (duality)
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.

22. 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

23. 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.”

24. Yes: its obvious!
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?

25. Observations (1)
We need a good connection to ground to get maximum current flow in the wire
Electrode design and spacing needs attention
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 gener-ated ‘underground’ by “large loop of current”)
falls off with inverse square law (not inverse cube, as it does for an induction loop)

26. Observations (2)
We should be detecting this H field using an induction loop
But it must be properly designed, not “hit and miss”
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

27. Observations (3)
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
The better option depends on many factors
Proper design of loop antenna
Skin depth in ground (return path can be hidden)
Communication distance required

28. Observations (4) 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
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