The plots show 10 MHz ground constants at eleven locations in Great Britain from a paper by R. L. Smith-Rose. At each location the soil was sampled at several depths to 10′ and then analyzed in a lab.
Antenna-induced ground current decays exponentially with depth. When ground constants vary with depth, a ground probe is too short when it samples too little soil with current. It is too long when it samples too much soil with little current. Except for one probe at the first location, the probes in the following model are too short.
I extended the deepest measurement to 100′ and divided the ground into 0.5″ layers. At each layer I linearly interpolated ground constants and calculated antenna-induced current. I weighted the ground constants by the current and averaged results over all layers. To model 12″ and 24″ ground probes, I averaged unweighted, interpolated constants over 12.5″ and 24.5″. The extra 0.5″ accounts for the open wire line end effect.
Location Geology Pavg P24 P12 Cavg C24 C12 SD CD
1 ■ Rugby 1 Lower lias 47 47 49 9.2 9.1 7.6 23 0
2 ■ Rugby 2 Lower lias 39 29 23 5.6 2.9 1.3 35 1
3 ■ Baldock Chalk 31 23 24 1.5 1.0 1.2 83 21
4 ■ Tatsfield Upper greensand 29 26 33 3.5 4.0 4.4 38 5
5 ■ Brookmans Park London clay 28 24 24 2.2 1.5 1.5 56 10
6 ■ Daventry Upper lias 23 19 23 .63 .81 1.1 159 49
7 ■ Washford Cross Red marls 47 36 33 4.2 2.7 2.4 40 3
8 ■ Brendon Hills Devonian 8.3 23 36 .064 .65 1.2 1069 83
9 ■ Moorside Edge Millstone grit 30 36 38 2.4 3.1 3.5 45 10
10 ■ Westerglen Boulder clay 21 20 20 2.1 1.5 1.3 60 8
11 ■ Teddington London clay 11 13 14 1.0 1.2 1.4 102 28
Pxx are permittivities, Cxx are conductivities in ESU ∕ 108 (11.1 mS/m), SD is skin depth in inches, and CD is current at the deepest measurement as a percentage of surface current.
Shown is the ratio of the probe response to the current-weighted average.
Rudy Severns, N6LF, used a 12″ ground probe and NanoVNA-H4 to measure ground constants in a newly dug trench in Oregon bottomland. He inserted the probe horizontally in the trench wall. The soil was loam down to the bottom at 6′ where it became gravel. He inserted the probe vertically at 6′ and at the surface 9″ from the trench. I modeled the ground as for the British measurements. The following table shows the ratio of the surface measurement to the current-weighted average. CD is current at the deepest measurement as a percentage of surface current.
Frequency MHz 1.8 3.7 10 28.5 Skin depth ft 14.1 9.2 4.7 2.6 CD % 58 47 30 11 Permittivity ratio 1.20 1.07 0.93 0.82 Conductivity ratio 1.23 1.14 0.99 0.96
The examples demonstrate that error for a short ground probe can be tens of percent when ground constants vary with depth. It can be much more for highly heterogeneous ground. The accuracy needed depends on your design objectives. Input impedance, forward gain, and radiation patterns may have different sensitivities to ground constants. To determine them, vary the ground constants in your antenna model and note the effect on the results of interest.
This article explains how to determine ground constants with a low dipole. Unlike a ground probe, this method samples ground at the proper depth. There is no need to average measurements at multiple locations. However, the method is restricted to a single band, needs a large, flat, open area free of interfering structures, vegetation, and ground conductors, requires meticulous construction, measurement, and modeling, and must be left in place or rebuilt to measure at different seasons. Despite these limitations, it may be worthwhile if you're optimizing a sensitive antenna design for a favorite band and you suspect your ground is inhomogeneous. To overcome the single-band limitation, use this program to extrapolate ground constants to other bands.
Smith-Rose, R. L., "Electrical Measurements on Soil with Alternating Currents," Proc. IEE, Vol. 75, pp. 221-237, 1934. I skipped the two locations with indefinite depths and the location with no surface measurement.
88–108 MHz