May 1951 QST
Table of Contents
articles are scanned and OCRed from old editions of the ARRL's QST magazine. Here is a list
of the QST articles I have already posted. All copyrights are hereby acknowledged.
An old electrician's saying goes "Ground is ground the world around*,"
implying that every point on Earth's surface is at the same potential
- specifically 0 volts. We know, of course, that it is not so. Maybe
on average such a claim could be made, but just as 'sea level' is
not the same at all points on the ocean's surface (hence we speak
of 'mean sea level'), neither is the voltage potential the same
everywhere. Further, just as the salinity of all points on the ocean
surface do not have the same salinity (and thereby conductivity),
the conductivity of various places on dry land vary - often significantly.
Electric power systems are very concerned with soil electrical conductivity
in the vicinity of power generation (source), distribution stations
(transmission lines) and end users (load). Soil conductivity measurements
are made in critical installations and if necessary, multiple ground
rods and/or even chemical enhancements to the soil are used to achieve
the required values. Antennas likewise rely on a specific ground
potential value to operate according to theoretical calculations
(if a 'perfect' ground is assumed). When a Yagi antenna is mounted
on a mast at some physical distance above ground level, its feed
point impedance and radiation pattern will come close to agreeing
with its advertised performance specifications only if the ground
underneath it sufficiently approximates a perfect ground. Achieving
that type of ground often means running multiple copper conductors
radially out from the support mast (usually buried, but not necessarily)
and sinking ground rods. Modern electromagnetic field solvers easily
and accurately predict antenna radiation patterns when the system
model parameters are accurately determined and input. One of the
most popular and affordable programs for amateur radio enthusiasts
is called EZNEC
(pronounced "easy neck"). EZNEC uses the
(Numerical Electromagnetics Code )
calculating engine and allows the user to input antenna dimensions,
soil conductivity, ground radials, antenna height, guy wires, nearby
structures, and other relevant parameters.
* A variation is "Green is ground the
world around," referring to the nearly universal use of the color
green for the insulation of a 'ground' wire. The National Electric
Code (another, but different,
NEC) does not specify a color for a grounding conductor; however,
an equipment grounding conductor must be color coded green.
Ground Resistance and Its Measurement
By J. M. Bruning, K2BZ
Proper operation and protection of electronic equipment usually
requires that some part of the circuit be "grounded." Ground in
this sense signifies an earth connection. The objective is to connect
the apparatus through a low-resistance path to that portion of the
surrounding earth - or water - which is highly conductive.
Fig. 1 - A ground rod has a large number
of separate paths from it to one or more layers of the earth's
crust. In this sketch each path is represented as having the
same resistance, r, but this is not necessarily the case.
A water-pipe ground is not always satisfactory, and a ground-rod
system mayor may not operate properly. When trouble is experienced,
the cause will usually be too high a resistance in the path between
the pipe or rod and the surrounding earth. We must remember that
the aim is to establish contact with that portion of the earth which
is highly conductive. The better this objective is attained, the
lower will be the ground resistance of the system.
The conductivity of the earth depends upon the composition of
the earth's crust, and is determined largely by the moisture content
of the soil and by the nature and amount of raw or dissolved minerals
in the soil. Considering these factors and the nonuniform distribution
of rock, shale, sand, etc., it should be evident that the problem
of establishing a low-resistance path to the earth is somewhat more
complex than it ordinarily appears.
Good practice decrees that the ground lead should consist of
a fairly heavy copper wire securely fastened to the equipment and
to the water pipe or ground rod. The inherent resistance of this
part of the ground system is usually negligible, but there is no
sure method for estimating the effectiveness of the over-all installation.
While existing literature describes at length various ways to install
a ground system, little information is available to explain how
to compare the effectiveness of existing grounds or how one can
quantitatively determine the amount by which a ground system is
improved by soil treatment or by the installation of multiple rods.
Each and every portion of the surface of a ground rod is connected
through a separate path to one or more highly-conductive layers
in the earth's crust, as shown in Fig. 1. Each path will have its
own value of resistance, r. All of these paths are in parallel with
each other, and the number of such paths is nearly infinite. Our
problem consists of determining the joint resistance of a nearly
infinite number of parallel resistors, each having an arbitrary
and varying value of resistance. Skipping the mathematics, it can
be shown that the summation for an infinite number of such parallel
paths would be numerically equal to zero. This value of zero resistance
is what we try to obtain in our ground system. While this figure
cannot be reached, it can be approached. If the ground rod in Fig.
1 is increased in length, or in diameter, or if more rods are driven
and connected in parallel, the number of parallel paths to the true
earth will be increased and the resistance of the system will more
closely approach zero.
Fig. 2 - The resultant or effective resistance
of the ground path can be lumped in a single value, rg
in (A) Three separate ground rods might have different resistances
to ground, as represented in (B).
Fig. 3 - With three ground paths as in Fig.
2B, the calculation of anyone becomes a simple problem in algebra,
since direct measurements can be made between A and B, B and
C, and A and C.
Fig. 4 - To measure the ground resistance
at the rod M requires two or three auxiliary rods, A1
A2 and A3, and a series of ohmmeter readings
of all possible combinations.
Fig. 5 - A simple Wheatstone bridge for measuring
resistance in the presence of large earth currents. Resistors
A and B should be equal and about 1000 ohms, and C should be
a 100-ohm rheostat. R is the unknown resistance.
Fig. 6 - A graph showing the variation in
resistance with rod length for five different cases. The variation
decreases as the rods are made longer.
Let us assume that the combined resistance of all the possible
earth paths from a single ground rod can be represented by a single
resistor, rg, connected from the bottom tip of the rod
to a zero-resistance conductive layer in the earth, located some
distance below the rod. The value in ohms of the resistor, rg,
is the resistance to ground of the rod in question. This is represented
in Fig. 2A.
Any other ground rod may be similarly assumed to have its individual
value of ground resistance, essentially unaffected by the presence
of any additional rods, provided these other rods are placed a reasonable
distance away. This is shown in Fig. 2B.
For all practical purposes, the internal resistance of a rod
having a diameter of one-half inch or more is negligible. Also,
since one thousand feet of No. 10 copper wire has a resistance of
about one ohm, it is apparent that a short and heavy ground lead
between the equipment and the grounding system can have but negligible
resistance. Thus our ground resistance is concentrated in the earth
itself, and the additional circuit resistance of the rod and its
connecting lead can be disregarded. We can now redraw Fig. 2B, leaving
out unnecessary elements, as in Fig. 3.
Solving for the Resistance
Fig. 3 consists of three unknown resistors strapped together
at one end. If these resistors were placed on a text bench and a
technician were provided with an ohmmeter, he could determine the
value of each resistance simply by connecting his meter to the terminals
marked A, B and C. By reading the values for different combinations
and doing a little arithmetic, he could easily determine the resistance
of anyone unit.
If, for example, a = resistance reading between A and B, b =
reading between B and C, and c = reading between A and C, simple
algebra proves that
In exactly the same manner it is possible to measure the ground
resistance of any water-pipe or ground-rod system. Let us proceed
to determine the ground resistance of a single rod. It will first
be necessary to drive at least two and preferably three auxiliary
test rods. These rods should be placed in a roughly symmetrical
disposition around the master rod. Two test leads made of No. 14
insulated wire, terminated with heavy clips, will be needed to connect
in sequence each two rods to an ohmmeter, as in Fig. 4. The series
resistance of each pair of rods will be measured and recorded as
in Table I. This table lists actual values measured on one ground
The ground resistance of the master rod can now be found in the
same manner used for solving the resistor network of Fig. 3. By
using the readings for M, A1 and A2, one value
for M can be determined. By similarly using M, A2 and A3 and M,
A1 and A3, two other values of M can be found.
Substituting the above figures, values for M will be found to be
6.5, 5.5 and 7 ohms. The average is 6.3 ohms.
By similarly combining the indicated readings for rods A1,
A2 and A3, we could determine their three
values and their over-all average to be:
Rod A1 = 7, 10.5, 6.5 = 8 ohms average
Rod A2 = 11, 12.5, 12 = 11.8 ohms average
Rod A3 = 22, 22.5, 21 = 21.8 ohms average
The accuracy of the above readings can be estimated by noting
how closely the three separate values agree. Any set of readings
indicating a major discrepancy should be discarded and a new set
of readings taken. Measurements should be made in opposite directions
and the results averaged before tabulating.
Rods should be driven a reasonable distance apart. Results have
been found to be good if the separation is anywhere between ten
and fifty feet. If the rods are too close, the accuracy of the readings
may be affected. If too far apart, excessive ground potential may
be encountered, causing the readings to fluctuate over a wide range.
After rods have been driven there will usually be a gradual rise
in resistance measurements taken over a period of a. few days as
moisture and chemicals in the earth attack the surface of the rod.
After several days this rise will taper off and subsequent measurements
will remain relatively stable for fairly long periods of time. However,
no ground system should be neglected for a period of greater than
a year without rechecking the system's resistance. This should preferably
be done in the spring of the year just before the lightning season,
to insure adequate protection.
In some locations the use of the d.c. ohmmeter becomes unsuitable
because of large d.c. or a.c. components in the earth currents.
For such cases the measurements can be readily made by using a Wheatstone
bridge excited by a tone source of several hundred cycles or more
and balancing the bridge for the lowest or null indication in a
telephone headset indicator. This arrangement is shown in Fig. 5.
If a Wheatstone bridge is not available, an acceptable substitute
can be improvised by using two exactly equal resistors of about
1000 ohms for legs A and B in Fig. 5. A rheostat or pot having a
range from 0 to 100 ohms can be substituted for bridge arm C, and
the amount of resistance cut in by the rheostat at the point of
balance determined by subsequent ohmmeter test. When the null indication
is achieved, the bridge is balanced, and C is equal to the unknown
Variation of Ground-Rod Resistance with Depth
Using the method described above, measurements were recently
taken on a number of ground rods driven to a depth of twelve feet.
These rods were used to form the grounding system for a steel tower
erected in an exposed location. Due to the rocky and dry type of
earth encountered, it was necessary to connect five rods in parallel
to the central tower before the over-all ground system resistance
was reduced to a reasonable figure.
Since the variation of ground resistance with rod depth is of
interest, the actual values measured are plotted in Fig. 6.
It will be noted from Fig. 6 that there was a wide range in the
values measured for different rods at identical depths. This variation
was most evident at shallow levels and decreased as the rods were
driven deeper into the earth. At a six-foot depth the rate of decrease
in resistance began to taper off. At ten feet all rods had a nearly
uniform resistance. Readings at the twelve-foot level indicated
that a practical limit had been reached. Driving the rods to greater
depths would not decrease the obtainable resistances sufficiently
to warrant the increased labor and expense.
The procedure given above enables a fairly accurate measurement
to be made of the ground resistance of a rod, water-pipe or other
grounding system. The measurement may be rapidly taken using conventional
equipment in most cases.
It would appear that in order to be effective and uniform from
day to day, ground rods should be driven at least eight feet deep.
However, the improvement achieved beyond the eight-foot level will
taper off so rapidly that there is little point in sinking a rod
below a twelve-foot depth.
Still further improvement in reducing the ground resistance of
a system can most simply be achieved by driving a number of rods
to the desired depth and then connecting the rods in parallel, using
heavy copper conductors.
The grounding capability of any ground-rod system may be improved
by conventional methods of treating the adjacent soil with dissolved
rock salt or similar agent. However, the immediate improvement achieved
may be at the expense of more rapid deterioration of the rod itself,
necessitating frequent replacement.
When available for use, brass pipe or copper-plated iron rod
will give superior results from the viewpoints of initially low
resistance and long trouble-free life. For really low-resistance
ground systems totaling less than one ohm, an entirely different
technique is called for.
Cold water-pipe grounds should measure less than 20 ohms. Single
ground rods may range from 20 to 500 ohms. When short rods are used
or where dry soil is encountered, it may be necessary to parallel
several rods. Of two grounds being compared, the one showing the
lowest resistance usually will be superior in performance. Although
satisfactory results may be expected if the measured ground resistance
is below 10 ohms, every effort should be made to reduce this value
as much as practicable.
The reader is cautioned to note that this article has dealt exclusively
with the "d.c." resistance aspect of a grounding system. The dissipation
of r.f. energy in the ground is an entirely different matter. Where
an effective r.f. ground plane is required at or near the earth's
surface, the use of an elevated counterpoise or a buried radial
system may be required.
From the foregoing, it is evident that if a water-pipe or driven-rod
system is to be used, the resistance of the system should be determined.
The procedure described in this article will enable the required
measurements to be accurately and quickly made.
Posted May 3, 2016