1. How Earth Current Antennas Really Work David Gibson

2. 2 Who am I? I have … I have … …been involved with BCRA’s Cave Radio & Electronics Group since its inception 23 years ago …a PhD in Sub-Surface Communications …worked in the research division of the UK’s Mines Rescue Service since 2001 …been secretary of BCRA since January this year …recently started a second job for a company specialising in submarine communications …not had time to go caving for a long while …thought it must be time to retire soon

3. 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. 4 How Earth Current Antennas Really Work Recent trend away from use of induction loop antennas towards grounded wires Recent trend away from use of induction loop antennas towards grounded wires The popular explanation for how these work is fallacious 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 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

5. 5 Recap: Cave Communications H.f. radio is attenuated by conducting medium H.f. radio is attenuated by conducting medium Lower frequencies are better: 10 – 100 kHz Lower frequencies are better: 10 – 100 kHz Wire antennas too large (1500 m @ 100 kHz) Wire antennas too large (1500 m @ 100 kHz) Small antennas are inefficient 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 Small loops easier to use than small dipoles Hence use of induction loops Hence use of induction loops –Because they are small and portable –not because they generate a magnetic field

6. 6 Why Do We Need a Magnetic Field? E field is attenuated at air/rock boundary 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 E field is difficult to generate and detect –Stray capacitance dominates small antennas However… 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. 7 H field from a wire A steady current flowing in a wire generates a magnetic field A steady current flowing in a wire generates a magnetic field –NB: not an electric field We need a ‘circuit’ for current to flow 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 There is no way to avoid this –… or is there?

8. 8 H field from a wire

9. 9 Avoiding a Return Path Current must not flow in a “circuit” 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? 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 Low capacitance at l.f. is a problem –Most current will leak away, due to stray C, before it reaches end of antenna

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

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

12. 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. 13 If we could thread the loop through worm holes in the fabric of space-time, it might work.

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

15. 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. 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) 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 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 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. 17 Ampère-Maxwell law  H = D + J  H = D + J Relates loop C of magnetic field to current flow through surface S 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 Complicated to use with ‘real world’ problems –We know H field must be circular loops, which makes it easier

18. 18 Gauss’s Law From Ampère-Maxwell 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 This leads to a ‘duality’ relationship between charge and current

19. 19Duality 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) 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… 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. 20 Biot-Savart Law The resulting magnetic field can be derived from the Ampère-Maxwell law The resulting magnetic field can be derived from the Ampère-Maxwell law This is the Biot-Savart 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. 21 Electrostatic Field E field and J field coincide (duality) E field and J field coincide (duality) Inverse cube law 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. 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 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. 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. 24 Yes: its obvious! All the ‘great’ analyses of HEDs (Wait, Burrows etc) assume the antenna is grounded, without explaining why 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 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 But it is still difficult to explain it in simple terms Now we ‘know’ it is true (and obviously so), what can we deduce? Now we ‘know’ it is true (and obviously so), what can we deduce?

25. 25 Observations (1) We need a good connection to ground to get maximum current flow in the wire 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 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 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… 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. 26 Observations (2) We should be detecting this H field using an induction loop 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… 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. 27 Observations (3) The ground will never be a very good conductor compared with a wire 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 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. 28 Observations (4) A proper comparison of line v. loop requires 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 Assessing the loop for losses Compensating for variable ground resistance Compensating for variable ground resistance “Specific power consumption” “Specific power consumption” –A method of experimentally rating earth-current antennas for effectiveness … of which more later