How Earth Current How Earth Current Antennas Really Antennas Really WorkWork

David GibsonDavid Gibson

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Who am I?Who am I?

I have …I have ……… been involved with BCRA’s Cave Radio & been involved with BCRA’s Cave Radio &

Electronics Group since its inception 23 years agoElectronics Group since its inception 23 years ago

…… a PhD in Sub-Surface Communicationsa PhD in Sub-Surface Communications

…… worked in the research division of the UK’s worked in the research division of the UK’s Mines Rescue Service since 2001Mines Rescue Service since 2001

…… been secretary of BCRA since January this yearbeen secretary of BCRA since January this year

…… recently started a second job for a company recently started a second job for a company specialising in submarine communicationsspecialising in submarine communications

…… not had time to go caving for a long whilenot had time to go caving for a long while

…… thought it must be time to retire soon thought it must be time to retire soon

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What is an Earth What is an Earth Current Antenna?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)

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How Earth Current How Earth Current Antennas Really WorkAntennas Really Work Recent trend away from use of induction Recent trend away from use of induction

loop antennas towards grounded wiresloop antennas towards grounded wires The popular explanation for how these The popular explanation for how these

work is fallaciouswork is fallacious– They do not “allow the current to flow in a big They do not “allow the current to flow in a big

loop” and they do not depend on current flow loop” and they do not depend on current flow in the ground at allin the ground at all

If we do not understand how the antenna If we do not understand how the antenna works, it is difficult to know the best way works, it is difficult to know the best way to use it, or how to design a better oneto use it, or how to design a better one

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Recap: Recap: Cave CommunicationsCave Communications H.f. radio is attenuated by conducting mediumH.f. radio is attenuated by conducting medium Lower frequencies are better: 10 – 100 kHzLower 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 inefficientSmall antennas are inefficient

– They do not radiate much/any powerThey do not radiate much/any power– This does not matter for close workThis does not matter for close work

Small loops easier to use than small dipolesSmall loops easier to use than small dipoles Hence use of induction loopsHence use of induction loops

– Because they are small and portableBecause they are small and portable– notnot because they generate a magnetic field because they generate a magnetic field

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Why Do We Need a Why Do We Need a Magnetic Field?Magnetic Field? E field is attenuated at air/rock boundaryE field is attenuated at air/rock boundary

– But that doesnt prevent its use But that doesnt prevent its use withinwithin conducting mediumconducting medium

E field is difficult to generate and detectE field is difficult to generate and detect– Stray capacitance dominates small antennasStray capacitance dominates small antennas

However…However…– a time varying field a time varying field mustmust contain both E and H contain both E and H

componentscomponents– A loop is A loop is notnot the best way to generate a the best way to generate a

magnetic fieldmagnetic field

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H field from a wireH field from a wire

A steady current flowing in a wire A steady current flowing in a wire generates a magnetic fieldgenerates a magnetic field– NB: NB: not not an electric field an electric field

We need a ‘circuit’ for current to flowWe need a ‘circuit’ for current to flow– But the return current generates a field in But the return current generates a field in

opposition to the wanted fieldopposition to the wanted field– One side of a loop cancels signal from other sideOne side of a loop cancels signal from other side– Hence large loops are better than small onesHence large loops are better than small ones

There is no way to avoid thisThere is no way to avoid this– … … or is there?or is there?

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H field from a wireH field from a wire

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Avoiding a Return PathAvoiding a Return Path

Current must not flow in a “circuit”Current must not flow in a “circuit”– No separate return pathNo separate return path– Current flows up and down the wireCurrent 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 Need to have a reservoir to store the charge

before returning it during the next half cyclebefore returning it during the next half cycle– i.e. capacitori.e. capacitor

Low capacitance at l.f. is a problemLow capacitance at l.f. is a problem– Most current will leak away, due to stray C, Most current will leak away, due to stray C,

before it reaches end of antennabefore 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?

1616 Surely the Earth Surely the Earth Current Affects the Current Affects the Field?Field? The effect of the line current and The effect of the line current and allall the the

current elements in the ground current elements in the ground combinescombines to to generate observed H field (concentric hoops)generate observed H field (concentric hoops)

But in the But in the absenceabsence of grounding, of grounding, and for the and for the same line currentsame line current, the charge that builds up at , the charge that builds up at the ends of the antenna has the same effectthe ends of the antenna has the same effect

So, to model the antenna, it is only necessary So, to model the antenna, it is only necessary to consider an isolated current elementto consider an isolated current element– E.g. think of “worm holes”E.g. think of “worm holes”– Use Biot Savart Law (for d.c. case anyway)Use Biot Savart Law (for d.c. case anyway)

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Ampère-Maxwell lawAmpère-Maxwell law

HH = = DD + + JJ

Relates loop Relates loop CC of magnetic field to of magnetic field to current flow through surface current flow through surface SS– Current is sum of Current is sum of conductionconduction current and the current and the

‘so-called’ ‘so-called’ displacementdisplacement current current Complicated to use with ‘real world’ Complicated to use with ‘real world’

problemsproblems– We We knowknow H field must be circular loops, which H field must be circular loops, which

makes it easiermakes it easier

SC

SJDlH dd

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Gauss’s LawGauss’s Law

From Ampère-Maxwell law…From Ampère-Maxwell law…– Using the equation of continuity (left), we Using the equation of continuity (left), we

obtain Gauss’s Law (right)obtain Gauss’s Law (right)

This leads to a ‘duality’ relationship This leads to a ‘duality’ relationship between charge and currentbetween charge and current

IS

SJ d QS

SD d

IQ

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DualityDuality

Any result we obtain for a static charge Any result we obtain for a static charge distribution distribution QQ in a medium with permittivity in a medium with permittivity (i.e. an isolated dipole) is applicable to a (i.e. an isolated dipole) is applicable to a slowly-varying current slowly-varying current II in a medium with in a medium with conductivity conductivity (i.e. a grounded dipole) (i.e. a grounded dipole)

For an electric dipole…For an electric dipole…– JJ is zero if it is isolated is zero if it is isolated– DD is zero if it is grounded is zero if it is grounded– So the Ampère-Maxwell equation gives So the Ampère-Maxwell equation gives

the same answerthe same answer

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Biot-Savart LawBiot-Savart Law

The resulting magnetic field can be derived The resulting magnetic field can be derived from the Ampère-Maxwell lawfrom the Ampère-Maxwell law

This is the Biot-Savart lawThis is the Biot-Savart law– Many textbooks assume this is axiomaticMany textbooks assume this is axiomatic– To assume so is to miss the very point we’re To assume so is to miss the very point we’re

trying to provetrying to prove– Strangely, this magnetostatic law requires, in its Strangely, this magnetostatic law requires, in its

derivation, manipulation of a time-varying quantityderivation, manipulation of a time-varying quantity

sin4 2r

dIdH

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Electrostatic FieldElectrostatic Field

E field and J field coincide (duality)E field and J field coincide (duality)

Inverse cube lawInverse cube law– E or J field probably less strong than H fieldE or J field probably less strong than H field– Receiver can be ungrounded (E) or Receiver can be ungrounded (E) or

grounded (J) and same arguments apply grounded (J) and same arguments apply concerning current distribution; i.e. we must concerning current distribution; i.e. we must ‘make’ the current flow in the full length of ‘make’ the current flow in the full length of the antenna.the antenna.

θrE ˆsinˆcos24 3

r

dQ

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The Story so FarThe Story so Far If an isolated electric dipole has a uniform current If an isolated electric dipole has a uniform current

flow then its magnetic field is not affected by flow then its magnetic field is not affected by grounding the ends of the dipolegrounding the ends of the dipole– i.e., the return current through the ground does not i.e., the return current through the ground does not

materiallymaterially contribute to the field contribute to the field– the dipole must have a the dipole must have a uniformuniform current, which can only current, which can only

be achieved by groundingbe achieved by grounding– The line current and The line current and allall the elements of current in the the elements of current in the

ground combine to generate the H fieldground combine to generate the H field– But in the But in the absenceabsence of grounding, of grounding, and for the same line and for the same line

currentcurrent, the charge that builds up at the ends of the , the charge that builds up at the ends of the antenna has the same effectantenna has the same effect

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Is it Obvious?Is it Obvious?

The story is told of the eminent mathematician G H The story is told of the eminent mathematician G H Hardy that he was once giving a lecture when he Hardy that he was once giving a lecture when he made a casual remark, and said, “Of course that’s made a casual remark, and said, “Of course that’s obvious.” obvious.”

Then he stopped talking and looked puzzled and Then he stopped talking and looked puzzled and then very thoughtful. Time wore on and he then very thoughtful. Time wore on and he continued staring dreamily into space. continued staring dreamily into space.

After a while the class was getting very restless, but After a while the class was getting very restless, but finally the great man emerged from his deep finally the great man emerged from his deep thoughts and said to the students: “Yes I was right thoughts and said to the students: “Yes I was right all along – it IS obvious.”all along – it IS obvious.”

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Yes: its obvious!Yes: its obvious!

All the ‘great’ analyses of HEDs (Wait, All the ‘great’ analyses of HEDs (Wait, Burrows etc) Burrows etc) assume assume the antenna is the antenna is grounded, without explaining whygrounded, without explaining why

You can work through the maths You can work through the maths rigorously step by step and prove the rigorously step by step and prove the resultresult

But it is still difficult to But it is still difficult to explainexplain it in simple it in simple termsterms

Now we ‘know’ it is true (and obviously Now we ‘know’ it is true (and obviously so), what can we deduce?so), what can we deduce?

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Observations (1)Observations (1) We need a good connection to ground to get We need a good connection to ground to get

maximum current flow in the wiremaximum current flow in the wire– Electrode design and spacing needs attentionElectrode design and spacing needs attention

Contact area is not the main criterionContact area is not the main criterion Electrodes must have a high “capacity” which means a Electrodes must have a high “capacity” which means a

large “extent”. Useful to simulate a large electrode by large “extent”. Useful to simulate a large electrode by connecting several connecting several well spacedwell spaced electrodes in parallel electrodes in parallel

The magnetic field…The magnetic field…– comprises loops centred on wire (i.e. not gener-ated comprises loops centred on wire (i.e. not gener-ated

‘underground’ by “large loop of current”)‘underground’ by “large loop of current”)– falls off with inverse falls off with inverse square square law (not inverse cube, law (not inverse cube,

as it does for an induction loop)as it does for an induction loop)

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Observations (2)Observations (2)

We should be detecting this H field using an We should be detecting this H field using an induction loopinduction loop– But it must be properly designed, not “hit and But it must be properly designed, not “hit and

miss”miss” It It maymay be convenient to detect the electric be convenient to detect the electric

field but…field but…– This falls of as the inverse This falls of as the inverse cubecube of distance of distance– It requires a grounded dipole for same reason as It requires a grounded dipole for same reason as

transmittertransmitter– It is ‘convenient’ to think of it as detecting the It is ‘convenient’ to think of it as detecting the

current flow in the groundcurrent flow in the ground

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Observations (3)Observations (3)

The ground will The ground will nevernever be a very good conductor be a very good conductor compared with a wirecompared with a wire– A return path through a A return path through a distantdistant wire will always be wire will always be

better than a path through the groundbetter than a path through the ground– Which is better…?Which is better…?

i) 100 m line antenna – walk out & back for 200 mi) 100 m line antenna – walk out & back for 200 mii) 60 m loop – walk a 200 m perimeterii) 60 m loop – walk a 200 m perimeter

The better option depends on many factorsThe better option depends on many factors– Proper design of loop antennaProper design of loop antenna– Skin depth in ground (return path can be hidden)Skin depth in ground (return path can be hidden)– Communication distance requiredCommunication distance required

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Observations (4)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 antennaA good analytical design of a loop antenna– A good analytical design of the power amplifierA good analytical design of the power amplifier– A proper method of assessing the A proper method of assessing the intrinsicintrinsic

performance of the antennaperformance of the antenna Assessing the loop for lossesAssessing the loop for losses Compensating for variable ground resistanceCompensating for variable ground resistance

““Specific power consumption”Specific power consumption”– A method of experimentally rating earth-current A method of experimentally rating earth-current

antennas for effectiveness … antennas for effectiveness … of which more laterof which more later