Data from Dave Bowker

Extracted from antennaware mailing list archives ( at as of 1 May 2006).

Note that the post of 30 Sep 1998 referred to isn't available. It doesn't show up in the archives for antennaware, and the two email addresses for K1FX (at and both bounce. The figures below summarize the measurements side by side. Bowker gives all 16 measurements, even though, by reciprocity and symmetry, only 10 needed. This is useful, because it allows one to estimate some of the measurement uncertainties, which, with a casual inspection looks like about 2 ohms or around 5%.

Bowker Data, Dry Earth Bowker Data, Wet Earth



Since my original posting of 30 Sep 1998 (which will be referred to as
“Phased Vertical Array Experiment, Part I” in future postings), I have had
an opportunity to continue some experiments and gather additional data,
particularly in response to emails I received from LB (W4RNL) and Eric
(N7CL).  Please understand that this array was designed electrically and
mechanically  to facilitate experimentation and data collection on
4-element square arrays (either cardioid or the more common 4-square) and I
welcome any and all suggestions for additional data points and experiments.
It is very easy to reconfigure any mechanical/electrical aspect of the
array (except for element spacing) for such purposes, as you will see in
the entry below ragarding decoupling and isolation of elements and in Part
I where I reconfigured it for gathering data at 4.6 MHz.  Such
reconfigurations usually take less than 1/2-hour to accomplish.

I have had a break in the weather (and bird hunting) to continue gathering
data.  Two new points of interest and associated data follow.  First, to
follow up on my intentions to retake all the data with a saturated ground
and grass overgrown the radial system, I will summarize both the previous
data (from Part I) and current data in the table below.  I’ve included both
self-impedances and coupled impedance's in this note.  

Also, I failed to mention in the original posting that my radials consist
of PVC insulated 24 gauge copper wire (essentially insulated from contact
with the sod/earth and that the ‘cross-bus’ through the geometric center of
 the array is #16 bare copper wire, NOT insulated from the sod/earth).  The
radials which connect to the ‘cross-bus’ at the inner areas of the array
are essentially in contact with sod/earth at the ends of the radial by
connection to the bare copper bus.

(numbers indicate element and position) [this will be important to some
data and discussion to follow].

	4	2

	3	1

24 August 1998
4 - 1/4-wave elements @ 7.010 MHz 
120 radials under each element (see posting for configuration)
Very dry soil conditions.

Z1,1 = 45 + j4.64		Z2,2 = 43 + j5.0
Z1,2 = 52 + j24.3		Z2,1 = 46 + j24.3
Z1,3 = 54 + j23.6		Z2,3 = 52.5 + j 7.1
Z1,4 = 59 + j7.1		Z2,4 = 46.6 +j22.1

Z3,3 = 45 + j6.1	  	Z4,4 = 43 + j3.3
Z3,1 = 50.5 +j 24.3		Z4,1 = 52.5 + j5.3
Z3,2 = 54 + j8.1		Z4,2 = 48.2 +j20.0
Z3,4 = 48 +j24.3		Z4,3 = 46 +j20.7

02 October 1998
4 - 1/4-wave elements @ 7.010 MHz 
120 radials under each element (see Part I for configuration)
Very moist earth, approx. 10 hours after heavy rains

Z1,1 = 48 + j6			Z2,2 = 45.8 + j8.3
Z1,2 = 52 + j23.3		Z2,1 = 51.0 + j26.3
Z1,3 = 53.1 + j25.0		Z2,3 = 58.5 + j10.7
Z1,4 = 62 + j6.7		Z2,4 = 46.6 +j22.1

Z3,3 = 45 + j9.1		Z4,4 = 45 + j8.3
Z3,1 = 53.5 +j 27.4		Z4,1 = 58 + j8.9
Z3,2 = 59 + j9.6		Z4,2 = 50.5 +j24.3
Z3,4 = 51.5 +j26.7		Z4,3 = 50.1 +j24.7

Second, an additional experiment was carried out this date (02 October
1998), in response to Eric’s email, to investigate how well the
“traditional” method of decoupling by open-circuiting 1/4-wave elements
achieves TRUE decoupling in a 1/4-wave spaced array.  This experiment
consisted of selectively and physically removing an element or elements
from the array and determining the self-impedance of a single element and
the influence of adding elements back into the array and measuring the
self-impedance of a single element and comparing the results to the
self-impedance of that element when measured in the “traditional” manner. 
In the diagrams and data below, the numerals 1,2,3,4 indicate the physical
presence of a specific element in the array configuration and an “X”
indicates that that element has been physically removed from the array for
measurement purposes.  All data were taken at and are relative to element 3
of the array.  The measured impedance's are indicated below the physical
description in each case.  For comparison, these data should be compared to
the self-impedance Z3,3 (45.0 + j9.1)  measured on 02 October 1998
(immediately above).  This experiment will be repeated next spring in the
1/8-wave spaced elements when the 80M capability is added.


3	X
Z3,3 = 48 + j9.1

4	2			X	2
3	X			3	X
-------------------------		------------------------
Z3,3 = 46.5 + j9.1		Z3,3 = 47.6 +j9.1

4	X			4	X

3	X			3	1
-----------------------			-------------------------
Z3,3 = 47 + j9.1			Z3,3 = 45.5 + j9.1


Decoupling/isolation of 1/4-wave elements in a 1/4-wave spaced square array
by means of open-circuiting the respective element is effective.  Although
a minimal amount of coupling between open-circuited elements and the
element under test appears to be in effect, it is probably insignificant
insofar as calculation of mutual impedance's, phasing network component
values, and array performance is concerned.

The apparent disparity between the commonly accepted self-impedance of a
1/4-wave vertical element over 120 radials of 1/2-wavelength (Brown, Lewis,
Epstein) and this experiment remains to be resolved.  An additional
experiment will be designed, implemented, and data taken to determine the
effects of INSULATED wire used in the radial system versus BARE COPPER wire
to determine whether or not coupling to the sod/earth constants is a
contributing factor in the somewhat higher than expected self-impedances

73, Dave, K1FK
Fort Kent, ME


radio/antenna/phased/bowker.htm - 2 May 2006 - Jim Lux
(phased array) (antenna) (radio) (Jim's home)