Recently I have been doing some research into cave radio. Much of the material published in the caving press is technically 'hazy' and indicates some confusion as to the principles involved. The theory is covered in textbooks on submarine communications? but this does not have a direct bearing on cave radio. Fortunately it is not necessary to understand the theory in order to build a cave radio, and many of the interesting implications of the theory would be dismissed by a critic as either semantic, or unimportant in practice. To design a better radio it is important to understand the principles, but there are other more practical ways a cave radio can be improved. I have written several papers describing improvements that can be made. Two have appeared in the BCRA Cave Radio Group Newsletter. They are reproduced later in this journal. They are copyright © BCRA and David Gibson.
Briefly, a cave radio consists of two induction loops. Within limits you can apply the ordinary 'laws of induction' and show that the induced signal depends on the number of turns and the cube of the distance between the two (co-axial) loops. The true situation is complicated and has led to some incorrect ideas being perpetuated. Some of these statements are examined later in this article.
The first paper (Gibson 1989) reproduced here derives an expression to show that the number of turns on the transmitting loop has no effect on its performance. One would think that the more turns one put on the loop, the more powerful the transmitter. This is only correct up to a point. If we measure performance as magnetic field strength obtained for 'cost' factors such as mass and power dissipation then the number of turns is not a factor in the equation. The paper goes on to show that the number of turns on the receiving loop can also be irrelevant, though here the reason is to do with signal to noise ratio. Interestingly, the performance is proportional to the density and conductivity of the wire. The relationship is such that aluminium performs 50% better than copper for the same mass. I am designing an aerial based on a few turns of aluminium tape, spaced to reduce self capacitance, with the length chosen to match the aerial to the power stage of the amplifier which has an output impedance of around 0.1 .
The second paper (Gibson 1989) derives similar performance figures to the above, but which include the mass of the power source and the type of amplifier used to drive the loop. For a given size of battery we can either transmit a powerful signal for a short time, or a weaker signal for a longer time. The paper shows how the product of transmission time and the sixth power of the distance is proportional to the product of battery mass and antenna mass. If the total mass is fixed, then the best performance is obtained when the battery mass is equal to the antenna mass. This is an interesting example of the 'matching' principle. There are a lot of assumptions made, but in general, if one has a battery of 900g and a flimsy ribbon aerial of 100g, one can improve things by reducing the battery mass to 500g and building a 500g aerial. The system then weighs the same, but produces a 3x improvement in transmission time, or a 20% increase in range. If the antenna mass is increased further, and the battery mass is reduced correspondingly, then the masses again become mismatched and the performance reduces.
These results contradict earlier suggestions (Lord, 1969) that the coil should be by far the biggest mass in the system, and that the receiver should have perhaps a thousand turns - many more than the transmitter. Admittedly Lord was working with the electronics of 20 years ago; and although my statements are true in theory, there are practical limits as to how far you can apply them.
Another area I have looked at concerns the size of the aerials. I showed that, although a larger diameter of loop gives a better performance, once a certain size of receiver loop is reached, there is no point increase in performance to be gained by making it bigger still. This critical size turns out to be quite small - less than 0.5m diameter. The range then depends on the transmitter size, but may require a very sensitive, low noise amplifier. Notes on this, and other aspects of design, will appear from time to time, when I get around to it.
As mentioned above, there are certain misconceptions about how cave radio works. I am collecting some notes together into a magnum opus. This will not be ready for some time, but here are some quick jottings on the subject. Although I've mentioned various authors by name, I don't wish to denigrate their work. The misconceptions go back much further in time, and the authors are only repeating what was believed to be fact.
A cave radio in its usual form consists of two induction loops. Within limits you can apply the ordinary 'laws of induction' and show that the induced signal depends on the number of turns and the cube of the distance between the two (co-axial) loops. If we consider a slowly time-varying current then we can visualise the field lines collapsing to zero and building up again in step with the current. A time-varying magnetic field always co-exists with a time-varying electric field. The electric field lines generated by a small current loop are concentric rings at a very low field strength.
Now suppose we collapse the field very quickly. Since the field lines can only travel at the speed of light, the lines that are far away do not have time to return to the transmitter. Instead they detach themselves and float away. Beyond this 'detachment' region, the magnetic field lines form concentric rings at right angles to the electric field lines. Both sets of field lines are at right angles to the radial direction and they flow outwards. Both fields now drop off in magnitude as 1/r. Close to the transmitter the magnetic field lines look like a traditional 'bar magnet', The axial component of magnetic field drops off as 1/r3, and the electric field as 1/r2.
To a first approximation the critical distance is /4 ( is wavelength), since at this distance it would take a time equal to half a cycle of oscillation for the field line to collapse and reform in anti-phase. Any distance further than this and it would not have time. An exact analysis gives a distance of /2 or 480m at 100kHz. For the fields to be fully as described we must either be much closer than this, or much further away. In other words the transition region extends a long way either side of this critical distance. A second condition is that the loop diameter must be much smaller than a wavelength and the field point must be much further away than a loop diameter. If any of these conditions are not met then the field expressions become more complicated and, to us, irrelevant. The fields near to the source are called the electrostatic or electric field and the induction or magnetic field. Together they are called the near field. The field far away is called, not surprisingly, the far field. Because it carries a flow of energy it is also called the radiation field.
The fact that the shape of the field lines changes with the transition from near-field to far-field means that the orientation of the receiver has to be changed in order that the field lines pass through the receiver loop (Lord, 1988). This could have an effect on cave surveying, since the equations usually quoted do not take into account any far-field components. The error depends on frequency, and on conductivity of the rock, and it is probably swamped by errors due to ore-bearing strata, pipelines and the like.
We can work out the power flow by integrating the product of the two fields over a spherical surface. It turns out that the radiation field has a power density (in Watts/m2) given by ExH, so the power in this field drops off as 1/r2. The near-field does not convey any power because the electric and magnetic parts are in phase quadrature, or to look at it another way, the fields expand and contract but never get detached from the source in order to flow away. The energy they contain ebbs and flows in a similar way to the energy in a reactive circuit. Engineers will be familiar with the concept of reactive power - instantaneously it exists, but it never actually goes anywhere.
An analogy can be made with a skipping rope. One end is tied down and the other end is waggled up and down. Waves are seen to travel along the rope. But close to the waggled end all that is seen is the rope moving up and down - the waves do not establish themselves until later on. The waggled region is the near-field and the region with the waves in it is the far-field.
If a loop is placed to intercept the near-field, it will generate a voltage that can be made to cause power dissipation in a resistor. If the field conveyed no power how can this be?. The answer is that in collecting the energy, the field was modified by the current it induced in the receiving coil. The modified field then affected the source by feedback and the source compensated for this by altering the current flow. This is the principle of induction used in transformers. If the receiving loop was not close to the transmitter then the flux linkage would be so low as to make the receiver almost invisible to the transmitter, but this is not the same as saying that the receiver is in the far field, where power flow carries on regardless of whether it is intercepted. This point is confused by Mackin (1984).
The radiation field from a small dipole (either electric or magnetic) is minimal at low frequencies. This point was confused by Bedford (1986) who stated that "it is [electric waves] that require aerials of the order of a quarter or half wavelength in order to propagate. A magnetic wave on the other hand can be radiated from much smaller aerials, a current carrying multi-turn loop being a classic example". The distinction is partly semantic, but it is not true to suggest that a small loop radiates. The dimension of the loop must approach a wavelength in order to get a reasonable radiation. Bedford was not comparing like with like. He compared the induction field from a small loop with the radiation field from a long wire. A better description would be "electric and magnetic waves are always radiated together, but only significantly from an aerial (loop or linear) approaching a wavelength in dimension."
There is another error, in that a multi-turn loop does not perform in the same way as a single-turn loop. (Lord 1988). A single-turn loop with a perimeter of a wavelength will radiate. However, because it is of this dimension the current is not uniform, and it turns out that two or more turns in close proximity will produce phases of current such that the radiation fields cancel out. A small loop does not radiate appreciably either, due to the fact that it is 'small'. It is therefore meaningless to talk about radiated power from a small multi-turn loop.
Bedford also states "the disadvantage of communicating by magnetic waves is that the field strength decreases with the cube of the distance compared with the electric waves which diminish with the square of the distance. This means that long distances are out of the question for magnetic wave communications and is the reason why only the electric waves are considered as radio". The first part of this statement is true as far as it relates to the 1/r3 and 1/r2 relationships in the near-field, but it is wrong to state that it is a disadvantage since the electric field from a small loop is at a very low level. The second sentence is basically wrong. Bedford may have erroneously associated the '1/r2' of the electrostatic field with the 'inverse square law' usually bandied about. However the inverse square law relates to power, not field strength. Anyone who has used a frame aerial for direction-finding will know that magnetic signals make just as good radio. The sentence should be re-written as "This means that long distances are out of the question for induction and electrostatic field communications, but since the magnetic and electric fields both drop off as 1/r in the radiation field, they are both equally suitable for radio".
A magnetic field alone does not 'contain' power, but energy. This might be pedantic, but several writers have wrongly stated the significance of the 'power' in the magnetic field. The magnetic field strength in the induction field drops off as 1/r3. This induces a voltage, U, in the receiver which drops off as 1/r3. The power received, being proportional to U2, drops off as 1/r6. This is quoted by Glover (1976), by Mackin, and by Williams & Todd (1987), but is not of direct relevance since we are not interested in power, but signal voltage - the received signal strength is proportional to 1/r3. However, since the signal strength is proportional to the transmitter current, and therefore to the square root of transmitter power then a sixth power does eventually find its way into the equations, but not for the reasons usually given. The erroneous statement that the power drops off as 1/r6 is sometimes given (eg Williams & Todd) as the reason why cave radios do not cause long distance radio interference. This is another example of a correct result obtained through a false argument. The elements of the field that give rise to long distance interference drop off as 1/r, but they are at a very low level (for a single turn loop) or non-existent (for a multi-turn loop).
Textbooks often mention the penetration of e-m waves into the earth, but few deal with the penetration of the near-field. An electromagnetic wave is attenuated as it penetrates a conducting medium. The field strength is attenuated at a rate of 8.7dB per 'skin depth', where skin depth, , is a distance which depends on the parameters of the rock, and the frequency of the radiation. (8.7dB is 20log10e. There are indications that the skin effect does not govern induction field behaviour. These doubts are expressed by Lord (1988).
The conductivity of the rock is represented by assigning a complex value to the permittivity. This alters a constant called the wave number. The wave number appears in the expressions for radiation field and electrostatic field, but not in the expression for the induction field suggesting that the exponential decay due to the skin depth phenomenon is not relevant to the induction field. This could be put down to the fact that the e-m wave dissipates its power in a surface current, whilst the electrostatic field behaviour depends on permittivity.
We must be careful of making too many simplifications to the formulæ. For the above statement to be true we must have the two conditions of 2r « X and r « so that the near-field predominates. For a good conductor with a/ » 1, is given by (2/µ), whilst for a poor conductor with /) « 1, is given by 2/·(/µ), independent of . As an approximation, a good conductor can be taken to be one with / ». Using a free space value for , this is true for the dual condition of frequency less than about 300kHz and conductivity greater than 5x10-5/m.
Using these figures, the skin depth is seen to be a more crucial distance than the /2 distance given previously. There seems to be no choice but to use the full expressions for field strength, since it is not at all certain that all the above conditions can be satisfied. It would be interesting to carry out some tests on signal attenuation, but the effects may well be masked by geological features.
A further item for analysis is the way the fields couple into the earth. To a transmitter on the surface, the earth looks like an imperfect reflector. The result of this is that most of the field lines get reflected up into the atmosphere. In this respect a vertical loop (a horizontal dipole) behaves differently to a horizontal loop, to which the earth looks like an imperfect short circuit. This is analysed by Burrows (1978), but I have not looked into it yet. An interesting test would be to compare the signal strength in a receiver where the two loops were horizontally aligned, to that where both were vertically aligned, and in the same plane. If the ground effects were the same then the latter case should result in half the signal strength. One source of error in this measurement would be the contribution from the far-field vector which, as explained earlier, is in a different direction.
The computer-generated plot reproduced below shows the magnetic field lines from a 'mathematically small' current loop energised with a time-varying current. Close to the loop the lines have the familiar bar magnet shape whilst, further away, they become detached and change shape. eventually forming concentric rings which 'float away'.
The 'bar-magnet' field lines constitute what is known as the induction or near-field. The concentric rings form the radiation, or far-field, and are usually omitted from a discussion of magnetic loop behaviour, though they can have a significant effect.
Although the plot was based on the full expression of the field equations, some liberties were taken in order to try to represent a time-varying pattern in a static diagram at a suitable scale. Mathematical details will be published at a later date.
Since the above text was submitted I have had a chance to seek further references. Thanks are due to Ian Drummond of Canada for comments and lists of further reading.
The description of the field applies to free-space. In the presence of a conducting medium the field lines are modified considerably. Not only is the 'primary' field altered, but a 'secondary' field is generated due to induced currents. The phases of these fields, together with the 'far field' components make for a difficult description, but a full and accurate analysis cannot ignore them. Burrows provides useful reading, as do geophysics books, and other scientific texts. My reason for only attempting to explain the free-space field was that it provides a suitable basis for the understanding of the concepts.
My derivations of antenna size ('Loop Antenna Size Considerations') relied on using a noise temperature ratio of 100dB at 45kHz. In view of the approximations involved, and the uncertain nature of atmospheric noise, the result is possibly only useful in that it gives an order-of-magnitude result.
Speleonics is published quarterly by the NSS in the USA.
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