10 MHz ground constants at eleven locations in Great Britain. At each location the soil was sampled at several depths and then analyzed in a lab. Linear interpolation appears curved on a log scale. ESU ∕ 108 = 11.1 mS/m.
I modeled the British soil as stratified layers, each with uniform ground constants. Layer boundaries are halfway between sample depths, with the last layer infinitely deep. I calculated the complex reflection coefficient for vertically incident RF. Then I found constants for single-layer ground that yield the same coefficient. I calculated the response of a 12″ ground probe by averaging ground constants at the surface and 1′ below. For a 24″ probe I averaged 0′, 1′, and 2′.
Location Geology P12 C12 P24 C24 ■ Rugby 1 Lower lias 2.29 1.04 2.25 1.24 ■ Rugby 2 Lower lias ■ Baldock Chalk 1.17 1.39 1.13 1.16 ■ Tatsfield Upper greensand 0.77 1.18 0.63 1.08 ■ Brookmans Park London clay 1.56 0.97 1.54 0.97 ■ Daventry Upper lias ■ Washford Cross Red marls 2.74 0.91 3.07 1.06 ■ Brendon Hills Devonian ■ Moorside Edge Millstone grit 0.84 1.13 0.80 1.01 ■ Westerglen Boulder clay 1.28 1.06 1.30 1.17 ■ Teddington London clay 0.52 1.24 0.50 1.11
P12 and C12 are ratios of 12″ probe permittivity and conductivity to the effective ground constant. P24 and C24 are for the 24″ probe. Blank means no single-layer equivalent with valid constants exists.
Averaging the curves by eye, some of the permittivity errors seem to be in the wrong direction. Resonance effects within a ground layer can affect the reflection coefficient. To reduce them, I doubled the number of measured layers by interpolation. Though the error reduction was not great, the numbers shown include it. Experiment with resonance effects in two-layer ground with this.
The notion of effective ground constants is not entirely coherent. Consider an example with two soil layers. Reduce the ground constants of the upper layer until they become those of air. This increases antenna height by the depth of the first layer. But no set of effective ground constants can do this. In general, stratified ground requires a model more complex than NEC provides.
The British data is for 10 MHz. Subsurface soil effects are more likely to arise at lower frequencies where skin depth increases. Ground probe accuracy may degrade since the probe samples a smaller percentage of soil with current. To assess the sampling limitation, use this program to calculate skin depth.
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 near the trench.
MHz Perm Cond 28.5 1.18 0.74 21.2 1.15 0.69 10.0 0.99 0.60 3.7 0.65 0.63 1.8 0.58 0.71
I used the vertical surface measurement to represent the 3″ surface layer (1.5″ with interpolation) even though the 12″ probe overlapped two horizontal measurements..
This article explains how to determine ground constants with a low dipole. Unlike a ground probe, the method excites ground at relevant depth. However, it 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, the method may be useful if you suspect your ground is inhomogeneous. Use bare copper wire. At each end use the smallest possible loop through a tiny polystyrene insulator attached to nonconductive line. Minimize wire sag and model average height. Measure and model the excess shunt capacitance at the center insulator. Attach the VNA directly using a male-male adapter. Record measurements without touching the VNA. Increase model segmentation until impedance converges. Recalculate the Sommerfeld-Norton parameters whenever you alter ground constants. Since so many things can go wrong, do a sanity check against ground probe measurements. To overcome the single-band limitation, use this program to extrapolate ground constants to other bands.
A one-wavelength square loop eliminates dielectric at sensitive wire ends and may better fit the space available. Support with tiny polystyrene insulators without wire loops. Attach the VNA at the middle of one side.
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