JED - January 2018 - 25

plane wave. We do not! A close look at
Figure 2 reveals that the magnetic field
vectors are in different directions. If
we work through the math in detail, we
will find that the fields add together to
make an interference pattern. And that
the electric and magnetic field intensities are not simply related by the impedance of free space. If we want to get the
correct answer, we have no choice but to
solve properly for the electric and magnetic fields, with the power flow density
calculated as the vector cross product of
the overall electric and magnetic fields,
and subject to the constraint of conservation of energy.
But if we have an interference pattern, aren't the fields larger in certain
areas? Can't we get out more energy in
these areas and "trick" conservation of
energy? Again, the answer is no, heck
no, and not on your life! Yes, the power
flow density will be higher in certain
areas, but the size of these areas will
be small such that the total integrated
power flow can never exceed the conservation of energy limit. N equal power
fields can be stacked to produce an in-

terference pattern where the peak power flow density is close to N2, but this
density will only exist over an area proportional to 1/N such that the net power
flow is proportional to N.

So let's get to the heart of the EW
problem. At some level, every RF EW engagement succeeds or fails based on the
J/S ratio of jammer power to signal power at the targeted aperture. This is why
understanding what you can and cannot
achieve by stacking fields is critical to
getting it right as to what we should and
shouldn't expect from collaborative EW.
Figures 3 and 4 show two potential
collaborative EW configurations where
all of the electric field vectors have the
same polarization, and we can presume
that they are in-phase and add at the
targeted aperture. We also show the relevant magnetic field vectors and how
they add at the targeted aperture.
The first configuration, line abeam,
is nothing more than a superdirective
endfire array. The directive gain for

The Journal of Electronic Defense | January 2018

ties that vary from place to place. The
resulting power flow density will also
vary from place to place, and this can
involve both the magnitude and the direction of the power flow vector.
Let's look at a simple example to see
what all this means. Consider two jammers far away from a targeted aperture
as shown in Figure 2.
Both jammers have equal power, and
their electric fields E have the same polarization. We can assume that they are
in-phase at the targeted aperture and
add together to create an electric field
of 2E at the targeted aperture. This is referred to as "field-stacking." If we make
the mistake of thinking that we now
have a larger plane wave, then we will
also make the mistake of thinking that
the power is proportional to the square
of the E-field (our convenient rule of
thumb for plane waves) and expect the
power to be 2 x 2 = 4 times as great as
that of the individual jammers. And, we
will embarrass ourselves in thinking that
we can exceed the conservation of energy limit. Alas, we cannot, and the error
is in thinking that we just have a larger



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JED - January 2018

Table of Contents for the Digital Edition of JED - January 2018

The View From Here
Conferences Calendar
Courses Calendar
From the President
The Monitor
Washington Report
World Report
Thinking Through Collaborative Electronic Warfare
Report from the 6th Annual AOC Pacific Conference
EW 101
AOC News
Highlights from the AOC 54th Annual International Symposium & Convention
Index of Advertisers
JED Quick Look
JED - January 2018 - Intro
JED - January 2018 - cover1
JED - January 2018 - cover2
JED - January 2018 - 3
JED - January 2018 - 4
JED - January 2018 - 5
JED - January 2018 - The View From Here
JED - January 2018 - insert1
JED - January 2018 - insert2
JED - January 2018 - 7
JED - January 2018 - Conferences Calendar
JED - January 2018 - 9
JED - January 2018 - Courses Calendar
JED - January 2018 - 11
JED - January 2018 - From the President
JED - January 2018 - 13
JED - January 2018 - 14
JED - January 2018 - The Monitor
JED - January 2018 - 16
JED - January 2018 - 17
JED - January 2018 - 18
JED - January 2018 - 19
JED - January 2018 - Washington Report
JED - January 2018 - World Report
JED - January 2018 - Thinking Through Collaborative Electronic Warfare
JED - January 2018 - 23
JED - January 2018 - 24
JED - January 2018 - 25
JED - January 2018 - 26
JED - January 2018 - 27
JED - January 2018 - 28
JED - January 2018 - Report from the 6th Annual AOC Pacific Conference
JED - January 2018 - 30
JED - January 2018 - EW 101
JED - January 2018 - 32
JED - January 2018 - AOC News
JED - January 2018 - Highlights from the AOC 54th Annual International Symposium & Convention
JED - January 2018 - 35
JED - January 2018 - 36
JED - January 2018 - Index of Advertisers
JED - January 2018 - JED Quick Look
JED - January 2018 - cover3
JED - January 2018 - cover4