The graphs show 10 MHz ground constants at eleven locations in Great Britain. At each location the soil was sampled at several depths to 10′. Linear interpolation can appear curved on a log scale. 10−8 ESU = 11.1 mS/m.
This writeup compares ground constants from a stratified ground model with those from surface ground probes. I model eight locations in Great Britain at one frequency and one location in Oregon at eight frequencies.
To reduce sampling artifacts, I oversample the ground constant data by a factor of 10. I use linear interpolation between the original samples. Imagine the curves with tiny stairstep layers, each with uniform ground constants. Layer boundaries are halfway between oversamples, with the last layer infinitely deep. I calculate the Fresnel reflection coefficient for a plane wave vertically incident on the stratified ground. Then I find ground constants for uniform soil that yield the same coefficient. The two ground models should be equivalent whenever the reflection coefficient is valid. I model a 12″ ground probe by averaging ground permittivity and conductivity at the surface and 1′ below. For a 24″ probe I use a 1:2:1 weighted average of 0′, 1′, and 2′.
Location Geology Peq Ceq P12 P24 C12 C24 ■ Rugby 1 Lower lias 22 7.3 2.22 2.14 1.03 1.24 ■ Baldock Chalk 20 .86 1.17 1.15 1.37 1.14 ■ Tatsfield Upper greensand 44 3.7 0.78 0.61 1.18 1.06 ■ Brookmans Park London clay 16 1.6 1.56 1.54 0.97 0.95 ■ Washford Cross Red marls 12 2.6 2.68 2.95 0.91 1.03 ■ Moorside Edge Millstone grit 45 3.1 0.85 0.81 1.15 1.02 ■ Westerglen Boulder clay 16 1.2 1.28 1.30 1.05 1.17 ■ Teddington London clay 24 .75 0.57 0.55 1.86 1.63
Peq and Ceq are equivalent ground constants. P12, P24, C12, and C24 are ratios of the ground probe response to the equivalent. No equivalent exists for ■ Rugby 2, ■ Daventry, or ■ Brendon Hills.
Geometric error < 20% (0.83–1.2) for 2 locations for P12 and 1 for P24. GE > 50% (0.67–1.5) for 4 locations for P12 and 5 for P24. GE < 20% for 6 locations for C12 and C24. GE > 50% for 1 location each.
Rudy Severns, N6LF, used a 12″ ground probe and NanoVNA 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.
The graph shows values for the stratified ground analysis. I derived ground constants for the 3″ surface layer from the surface measurement and those at 0.5′ and 1′ it overlapped. For the deepest measurement I used the mean probe depth of 6.5′. I simulated a 24″ probe by combining measurements at the surface, 1′, and 2′. I oversampled the data by a factor of 10, but it had little effect.
MHz Peq Ceq P12 P24 C12 C24 28.5 11 39 2.12 2.68 0.73 0.96 21.2 13 37 1.91 2.42 0.68 0.90 14.2 17 33 1.61 2.05 0.65 0.87 10.1 20 32 1.54 1.95 0.62 0.83 7.1 28 31 1.21 1.53 0.57 0.77 3.7 69 26 0.61 0.76 0.60 0.82 1.8 119 17 0.45 0.54 0.79 1.11 1.0 152 13 0.42 0.50 0.95 1.36
Geometric error < 20% (0.83–1.2) for 0 frequencies for P12 and P24. GE > 50% (0.67–1.5) for 7 frequencies each. GE < 20% for 1 frequency for C12 and 5 for C24. GE > 50% for 4 frequencies for C12 and 0 for C24.
Fresnel reflection coefficients are valid for plane waves, but fields near ground may not be planar for low antennas. If Sommerfeld-Norton and reflection coefficient ground differ little for a NEC antenna model, equivalent ground constants should be valid when used with the reflection coefficient method. Use calculator values to model antenna currents, impedance, and overhead gain. Equivalence is unlikely to be valid at lower elevation angles since it is derived from RF incident at 90°.
Several of the Peq values seem far from an eyeball average of the permittivity curve. But stratified ground does not average. It acts like a cascade of lossy transmission lines, each of which can transform its source impedance to something other than its characteristic impedance.
A stratified layer may resonate. It is an artifact of sparse sampling unless the layer actually is thick. Oversampling inhibits artificial resonance. Oversampling by a factor of 10, 100, or 1000 yields virtually identical results. Use the calculator to explore transformation and resonance.
The notion of equivalent ground constants is not entirely coherent. Reduce the ground constants of the upper soil layer until they become those of air. This increases antenna height by the layer depth. But no set of equivalent ground constants can do this. In general, stratified ground requires a model more complex than NEC provides.
A ground probe samples a smaller percentage of soil with current as skin depth increases. This occurs for drier soils or lower frequencies. To assess the sampling limitation, see tabulated skin depth for the Hagn generic curves or use this program to calculate skin depth.
8″ of concrete over pastoral ground Water table 200′ below desert
This Windows program calculates equivalent ground constants for stratified ground with two layers. The documentation includes typical permittivity and conductivity values for snow, ice, asphalt, concrete, and rock. Generic values for soil and water are here. Results have not been verified.
Ground probe permittivity is far from stratified ground values. Conductivity is closer, especially for a 24″ probe. But for efficiency analysis, both probe permittivity and conductivity should be valid for antennas with buried radials, which concentrate ground current near the surface.
Ground current drops quickly near a buried radial as the fields spread cylindrically. As they expand, the fields gradually become more planar and current decay approaches exponential. For symmetrical radials and soil, the horizontal field components cancel directly below. Away from center, they partially cancel at depth. All this should allow a ground probe to provide suitable ground constants for antennas with buried radials. This may be true for radials on the ground as well. However, subsurface soil can affect ground reflection coefficients. This can limit accuracy for far-field results since ground probes ignore subsurface soil. But accuracy should be good for studying the effect of radial number, length, and depth on antenna efficiency.
This article explains how to determine ground constants with a low dipole. Unlike a ground probe, the method excites subsurface soil. However, it is restricted to a single band, needs a large, flat, open area free of structures, vegetation, and ground conductors, requires meticulous construction, measurement, and modeling, and must be left in place or rebuilt to measure at different seasons. Ground excitation for a low dipole is shallower than for a high antenna. Ground current decreases more rapidly with depth because the fields are less planar. A low dipole may be insensitive at depths relevant for a high antenna.
Use bare copper wire. At each end use the smallest loop possible through a tiny polystyrene insulator attached to nonconductive line. Minimize wire sag and model average height. A height too low may incur error due to surface irregularity. Measure and model the excess shunt capacitance at the center insulator. Use a male-male adapter instead of a VNA cable. Record measurements without touching the VNA. Increase model segmentation until impedance converges. Recalculate the Sommerfeld-Norton interpolation grid as needed to maintain accuracy.
A one-wavelength square loop eliminates dielectric at sensitive dipole 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.
To mitigate 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 three locations with indefinite depths or no surface measurement.
88–108 MHz