NEC-LIST: Ground Constants

All:

I have followed with interest the discussions on ground constants. Let
me add to the discussion:

1) The ITU-R Recommendation on Ground Constants is in error in the HF
band.

It is not possible to have no dispersion in both the conductivity
(sigma, in S/m) and the relative dielectric constant (epsilon r)
across the same span of frequency. The ITU-R data show constant values
across the HF band, and the ITU-R conductivity starts to increase with
increasing frequency at exactly 30 MHz. The Hilbert transform pair
relate the real and imaginary parts of a complex variable that
satisfies certain conditions. The complex relative permittivity
(epsilon r complex = epsilon r prime - j epsilon r double prime)
satisfies these constraints, and therefore the effective relative
dielectric constant (epsilon r prime, the real part) and the
conductivity (part of epsilon r double prime) are deterministically
related for any given soil at a given volumetric moisture content. The
relationship is given in the literature as the Kramers-Kronig
relationship, and an ACES paper a year ago or so gave an example of
this for a semiconductor. The K-K relationship implies that if one of
the terms has no dispersion, the other term must have maximum
dispersion. For example, if the relative dielectric constant of sandy
soil is very low (e.g., 3.5), then the conductivity has its maximum
dispersion (with conductivity increasing by over an order of magnitude
across the HF band). I have demonstrated this with measurements with
my open-wire line (OWL) kit many times (e.g., VOA site at Rhodes,
Greece; Eglin AFB, FL, etc.). Therefore, dont rely on the ITU-R data
for HF ground "constants." I am in the process of providing ITU-R
Study Group 3 with revised curves for the Recommnedation so that it
can be corrected. Anyone interested in more on this, please contact me
at my erols.com email address.

3) The comment by Ortiz that the conductivity decreases monotonically
with frequency is incorrect. The conductivity starts out with the DC
conductivity, which is due to the ions in the moisture that is "free
water" and not "bound water." As the frequency increses past about 1
MHz for most soils, the conductivity starts to rise. The term that
does decrease monotonically with increasing frequency is the term
epsilon r double prime, the loss term. It does so for frequencies up
to about 1.5 GHz. The loss term then starts to increase (as the
absorption of the water molecules start to dominate the loss process
over the ionic conductivity that was dominant at lower frequencies on
down to DC. The conductivity goes through a maximum value at about 17
GHz, the frequency at which epsilon r prime and epsilon r double prime
are equal, and then starts to decrease for frequencies above about 17
GHz. The exact frequency of the maximum varies with soil
characteristics, but it is a frequency below the absorption line at
22.235 GHz for pure deionized water.

4. So any table of "ground constants" that are truly constant are
inappropriate at RF since they dont exhibit the required dispersion
relationships between epsilon r prime and epsilon r double prime, as
required by the K-K relationship. The K-K relationship is based on
complex variable theory, and is derived using Cauchy's integral
equation.

I hope this clarifies some of the confusion in the emails on the
subject in recent weeks.

Regards,

George H. Hagn
Engineering Consultant
4208 Sleepy Hollow Road
Annandale, VA 22003-2046
(703) 941-7663

P.S. I thank my colleague, Roy Stehle of SRI International (my former
employer--through March 2000) for alerting me to the need to
contribute to this dialog on ground constants. We (Stehle and myself)
still retain the ability to do full-scale HF antenna pattern
measurements using the SRI RELEDOP system (see the June 1988 special
issue of IEEE Trans. Broadcasting, Stehle, et al., for a full
description of this system). Also, I still retain the capability to
measure ground constants at MF, HF and VHF using the open-wire line
(OWL) kit that I developed while at SRI (originally in the early
1960s). See my papers in the third and fourth ACES Symposium
proceedings for info on the OWL kit, and see an eratta in the ACES
Newsletter for correcting published data prior to the early 1980s). If
any of you have requirements for MF or HF full-scale pattern
measurements, please contact Roy at the email address above (or John
Cibosi, who is administratively responsible for the RELEDOP system).
If you have interest in the ground constants, contact me directly.
Received on Mon Jun 05 2000 - 18:23:30 EDT