basic theoretical principles

The fundamental principle of ECC utilises the inherent "resistance" of the earth.    Signals are detected by a distant receiver by currents induced to flow through the earth at the receiver by the transmitter causing a potential difference to exist between points in the earth at the receiver.    This is possible because current forced to flow between two earth rods at the transmitter does not all flow in a straight line between the two rods.    Some proportion of the current flows in arcs away from a straight line between the two rods.   The more pronounced arcs trace out a path well away from the direct line between the two rods.     It is the current in these pronounced arcs that can be used to communicate information to locations well outside the direct line between the two rods.

NOTE: To (hopefully) avoid confusion the term "probe spacing" refers to the spacing between the two individual rods of a probe pair, while "distance" or "range" refers to the distance between probe pairs (i.e., the communication path).

One principle that is useful to appreciate is that the "resistance" between two earth rods or probes is an apparent resistance.    That is, it can be calculated from the voltage and current applied to the probes as would normally be done for an actual resistance component (resistor).      However, further analogy is not wise.    For example, if one were to apply a voltage of 100V between two probes spaced 100 metres apart and measured a current of 1A the apparent resistance is 100 ohms (R = V/I = 100/1 = 100 ohms).    It might seem reasonable to expect that if the probes were now placed 200 metres apart the doubled distance would mean a halving of the current to 0.5A for an applied 100V giving a resistance between the probes of 200 ohms.    In fact the current would still be close to 1A (assuming the ground conditions are the same under the 200m layout as the 100m layout).     That is, the apparent resistance is still close to 100 ohms.    So the behaviour is not the same as tacking resistors in series.    This may be explained by considering that the more the current paths arc away from the direct line between the two probes, the more parallel paths there are for the current to flow.   Using a gross simplification - when the distance is increased between the transmitting earth probes, the increase in direct line resistance is cancelled out by reduction in resistance due to an increasing number of effectively parallel paths made available.

Be aware that the above description and that which follows are general.   Individual installations will differ greatly due to local soil type and moisture conditions.    In other words, it may be found that the resistance remains reasonably constant with increased earth probe spacing, but don't be surprised if does not.

The relationship between resistance R (V/I) and resistivity of a material (Rho) is:-

 R = Rho * L / A 

where L is the length of the material and A is the cross-sectional area.    In the case of increasing spacing of earth probes, as L is increased, the effective cross-sectional area A available to carry current increases as well.    Therefore the ratio L/A tends to remain constant leaving the actual value of resistance largely dependent on Rho, the resistivity of the soil.    Note that if the soil under the probes is not homogeneous then the apparent resistivity measured in a survey will change with changing probe spacing.     This is because as the probe spacing is increased the current flows deeper and therefore is affected by the characteristics of the soil at depth.     For example, if the soil beneath the probes is layered with a high resistivity layer near the surface and a lower resistivity layer deeper down, then the apparent resistivity will fall as probe spacing is increased.    Conversely, for a low resistivity layer near the surface and a high resistivity layer deeper down, the apparent resistivity will rise with increased probe spacing.    Finally, for three layers starting with a high Rho layer near the surface, then a low Rho layer in the middle, then a high Rho layer as the deepest, the apparent resistivity will firstly fall with increasing probe space as the middle layer increases in influence and then rise again as the bottom layer increases in influence...     So R can basically wander about as probe spacing is increased depending on the non-homogeneity of the soil beneath the probes.

Another way of looking at this effect is imagine the area that the current has to pass through right adjacent to the earth probe.    This area is essentially the cylindrical surface area of the rod which for a rod of 10mm diameter and 1.2m length is 1.2 * (PI * 0.01) square metres = 0.038 sq m.    At a distance of 0.5m from the rod the area is a cylinder (1.2 + 0.5) * (PI * (0.01 + 0.5)) = 2.72 sq m.    At a distance of two metres from the rod the area available for current flow is (1.2 + 2) * (PI * (0.01 + 2)) =  20.2 sq m.    So the resistance presented to the current right next to the rod compared to the resistance present at a distance of 2m is in the ratio of (20.2 / 0.038) = 532:1 assuming the resistivity remains the same.    Basically the resistance to general earth is almost totally governed by the soil resistivity within about 3m to 5m of the earth probe and the rod-to-earth contact area.    when trying to effectively double the rod-to-earth contact area by adding an extra rod and electrically shorting the two rods together (making 4 rods altogether), the distance between two paralleled rods should therefore be at least 6m to 10m.   If the rod spacing was originally a few 10s of metres then this obviously becomes difficult.    A better method of of doubling the rod-to-earth contact area is to double the length of the earth rod.   Note that in terms of volume of steel (closely related to cost) it is better to double the length than to double the diameter of the rod.   Both give a doubling of surface area but doubling the diameter multiples the volume of the rod by 4, while doubling the length only multiplies the volume of the rod by 2.    Also it is probably easier to hammer in a rod twice as long than it is to hammer in a rod of twice the diameter.   Plus the longer rod will reach down to more moist soil not affected by ambient weather conditions.

By the way, if a 100m capped length of PVC pipe were to be filled with local soil and the apparent resistance measured between the ends and then the measurement repeated with a 200m length filled with the same type of soil, then it would be found that the 200m exhibits roughly twice the apparent resistance of the 100m length.    Here the length of the path L increases while the cross-sectional area A is held constant by the constraint of the insulating pipe.

The actual apparent resistance measured at any transmitting site is largely governed by the efficacy of the earth probes (how well they couple into the earth) and the resistivity Rho of the earth between the probes down to a depth roughly equal to one-third the distance between the probes.

The dependence of the apparent measured resistance (as calculated by the voltage applied to a pair of earth probes divided by the current flowing between these earth probes) mainly on the "contact" resistance of the probes to earth is the reason that geological surveys use a separate current injection probe pair and a separate voltage capture probe pair.     By using the current reading only from the transmitter probe pair and measuring voltage from a separate probe pair the effect of the voltage drops across the "contact" resistance of the probes is eliminated.    This is because the measurement of current injected is not affected by the voltage drop across the injecting probe pair and by use of high impedance (very low input current) measuring devices across the voltage receiver probes the voltage drop across the receiver probe contact resistance is virtually eliminated.

For a one-way ECC link it would seem important to have good transmitting earth probes with low contact resistance to minimise the power required to achieve a given current magnitude, while the receiving earth probes can be of lesser quality provided the receiver presents a high impedance load to the receiving earth probe pair.

The received voltage as measured between the distant receiver electrodes is directly proportional to the product of the induced earth current at that point and the resistivity of the earth between the receiver probes at that point down to a depth roughly equal to one-third the distance between the receiver probes.    The induced current flowing in the ground at the receiver probes is directly proportional to transmitter current and inversely proportional to the cube of the distance between transmitter and receiver (ouch !!!).

A great deal of information can be inferred about ECC from the information associated with geological and archaeological surveys that employ DC resistivity surveys to locate subterranean objects or features.    These employ a number of probes in various configurations.    Each of these configurations have strengths and weaknesses for resistivity surveys, but the only configurations of interest to ECCers are the dipole-dipole (in-line) and the equatorial dipole-dipole (broadside or goal posts) configurations.    These two resistivity survey configurations are the only ones where the receiving probe pair lies outside the transmitting probe pair.    The "geometric factor" of each of these two configurations gives a measure (as applied to ECC) of the received signal strength at a distance.    The following diagram is from the documentation of the freeware program RES2DMOD ver 2.2 provided by M.H.Loke.

The dependence of the apparent measured resistance (as calculated by the voltage applied to a pair of earth probes divided by the current flowing between these earth probes) mainly on the "contact" resistance of the probes to earth is the reason that geological surveys use a separate current injection probe pair and a separate voltage capture probe pair.     By using the current reading only from the transmitter probe pair and measuring voltage from a separate probe pair the effect of the voltage drops across the "contact" resistance of the probes is eliminated.    This is because the measurement of current injected is not affected by the voltage drop across the injecting probe pair and by use of high impedance (very low input current) measuring devices across the voltage receiver probes the voltage drop across the receiver probe contact resistance is virtually eliminated.

For a one-way ECC link it would seem important to have good transmitting earth probes with low contact resistance to minimise the power required to achieve a given current magnitude, while the receiving earth probes can be of lesser quality provided the receiver presents a high impedance load to the receiving earth probe pair.

The received voltage as measured between the distant receiver electrodes is directly proportional to the product of the induced earth current at that point and the resistivity of the earth between the receiver probes at that point down to a depth roughly equal to one-third the distance between the receiver probes.    The induced current flowing in the ground at the receiver probes is directly proportional to transmitter current and inversely proportional to the cube of the distance between transmitter and receiver (ouch !!!).

A great deal of information can be inferred about ECC from the information associated with geological and archaeological surveys that employ DC resistivity surveys to locate subterranean objects or features.    These employ a number of probes in various configurations.    Each of these configurations have strengths and weaknesses for resistivity surveys, but the only configurations of interest to ECCers are the dipole-dipole (in-line) and the equatorial dipole-dipole (broadside or goal posts) configurations.    These two resistivity survey configurations are the only ones where the receiving probe pair lies outside the transmitting probe pair.    The "geometric factor" of each of these two configurations gives a measure (as applied to ECC) of the received signal strength at a distance.    The following diagram is from the documentation of the freeware program RES2DMOD ver 2.2 provided by M.H.Loke.

Here C1,2 are the transmitter probes and P1,2 are the receiver probes.    Interestingly, the Equatorial Dipole-Dipole configuration seems to be the assumed configuration of choice (except for several experimenters).   However, if the "Geometric Factor" relationship is correct, the Dipole-Dipole (inline) configuration has an advantage of about 12dB over the Equatorial Dipole-Dipole configuration.    Mark (G0KZZ) reports that he has observed this advantage experimentally over short distances.    Of course, the inverse distance-cubed factor means that an extra 18dB is required to double the distance, so the 12db advantage mentioned only gets an increase in distance by a factor of 1.6 times.

The relationship for the voltage V received between P1 and P2 using the above configurations is:

 V = Rho * I / k 

where I is the current driven between C1 and C2, k is the geometric factor and Rho is the resistivity of the earth between and below each of the probe pairs (location identified by 'a' in the diagram above).    The resistivity of the earth between the probe pairs (location identified by 'na' in the diagram above) has a lesser effect.

ECCers are not really interested in quantifying the resistivity of the earth, but rather the interest lies in maximising the received voltage V relative to background noise for any given input power and distance 'na'.

One thing that may be significant from the field of resistivity surveys - fundamentally the excitation current used there is DC, but because of self-polarisation potentials at the probes and the effect of Telluric currents, it is common for these surveys to use AC excitation.    Of particular note is the mention that such AC is usually low frequency (< 20Hz) to replicate the results of DC surveys.    This may indicate that there may exist some significant benefit in using frequencies below 20Hz for ECC.