THE THEORY AND ARCHITECTURE OF A PLANEWAVE GENERATOR
Clifton C. Courtney and Donald E. Voss.
Voss Scientific, 418 Washington St., SE
Albuquerque, NM 87108
Randy Haupt
Utah State University, 4120 Old Main Hill
Logan, UT 84322-4120
Larry LeDuc
412 TW / EWD, 30 Hoglan Ave.
Edwards Air Force Base, CA 93524-8210
ABSTRACT
The radiation properties of an antenna are defined in the
far field, since this is the environment that they will
operate. Creating far field conditions when testing a large
aperture antenna is quite challenging. This is particularly
true if testing occurs within the confines of an anechoic
chamber, or if other complicating field characteristics
(like angle-of-arrival simulation) are desired. Rather than
attempt to generate a true planewave in the usual manner,
we propose an instrument that creates a field distribution
in the near field of a transmit array that is planewave-like
in nature only over specified regions of interest (a region
occupied by an antenna under test, for example); we do
not require that the incident field be a true planewave at
other locations. In these other locations the field is free to
assume any value demanded by the governing equations
of electromagnetics. By relaxing the requirement on the
electromagnetic field in the test volume, we considerably
reduce the complexity of the problem and define a
tractable problem with a potential engineering solution.
Keywords: planewave generator, far field, near field,
antenna, SUT, genetic algorithm, T-factor, test fidelity
1. INTRODUCTION
Planewave stimulus and the measured response of
integrated aircraft electronic systems are critical
components of aircraft test and certification programs. To
conduct a test, a planewave environment in the volume
occupied by the system under test (SUT) is typically
required (see Figure 1a.). Unfortunately, for large SUTs
(e.g. aircraft), the ability to generate a planewave over the
entire extent of the test volume is limited, to a large
extent, by the operating frequency and size of the test
facility. Traditionally, to improve the quality of the
incident field, the SUT is located at a
Lines of constant
magnitude,
constant phase.
(a)
True plane wave
illumination over the
entire asset.
Locally, lines of constant
magnitude, constant phase.
(b)
Plane wave illumination over
local areas of the asset.
Figure 1 – True planewave and pseudo-planewave.
position far from the transmitting antenna (far field), but
the size of the test facility limits the available separation
distance, and for frequencies below 1 GHz this separation
is practically unachievable in indoor facilities for even
moderately sized SUTs.
This paper describes an
approach to the development of a radio frequency
Planewave Generator1 for the measurement of integrated
aircraft electronic systems coupled to the environment
through electromagnetic (EM) aperture(s). Instead of
demanding that a planewave environment exist over an
entire volume, we suggest that to measure an electronic
systems response, it is only necessary to create an incident
field that is planewave in nature only over local points and
volumes on the SUT as shown in Figure 1b. In practice,
the test engineer would identify the locations on an asset
where the apertures of interest are located. A Planewave
Generator (PWG) would then produce an electromagnetic
field distribution where the incident field has planewavelike qualities only over these locations. By relaxing the
requirement on the EM field over the entire test volume,
we have greatly reduced the complexity of the problem.
Such a PWG system could be comprised of a set (one, or
more) of transmitting stations, each an array of broadband
elements with individual amplitude and phase control.
These stations could then be distributed about the test
facility. The excitation of each element (phase and
amplitude) is determined using a Genetic Algorithm (GA)
1
Patent Pending
optimizing procedure. The exact aperture location(s) on
the asset, and the direction and polarization of the desired
planewave are input to the GA by the user. The GA then
searches the large number of possible excitation vectors
for a near-optimal solution, one that produces a “best-fit”
field distribution with “local” planewave behavior over
the SUT’s apertures. This presentation will begin with a
brief description of the concept. Next, an explanation of
the use of a GA will be presented for this specific
application, and will include a description of the GA
process and definition of the GA “fitness” criteria used to
evaluate the quality of the electromagnetic field associated
with a particular excitation vector. A PWG hardware
architecture and typical microwave channel design is then
described, and finally, a simulated result of PWG
operation is given.
2. PWG CONCEPT DESCRIPTION
Based on our studies we have concluded that the ability to
produce planewave regions over entire large assets in
confined areas typical of an anechoic chamber (even a
large one) is difficult, if not impossible. This is
particularly true if other more sophisticated
characteristics, like angle of arrival simulation, are
desired.
Rather than attempt the generation of a
planewave with operation in the far field of a radiator we
propose a system that uses a transmit phased array, with
operation in the nearfield region of the transmit array, but
in the farfield of the elemental radiators of the array.
Although the field at large distances from a radiator takes
on propagation characteristics that are impossible to
tailor, the nearfield can be fashioned to exhibit planewave
properties over limited extents.
The technique we describe here employs an optimizing
algorithm to iteratively seek an array excitation vector that
will generate planewave-like regions only over limited
extents of a large asset. In other words, the effort will be
to produce a field distribution with planewave amplitude,
phase, and polarization relationships only over the
locations occupied by, for example, distributed apertures
of the SUT. The field distribution is planar and coherent
only over the distributed apertures; we do not require that
the incident field be planewave-like at locations not
occupied by apertures of interest. The field may assume
any value in other areas of the test volume and on the
asset where no specific value is demanded (i.e. between
two distributed apertures). By relaxing the requirement
on the EM field in the entire test volume occupied by the
SUT, we considerably reduce the complexity of the field
the planewave generator must produce, and define a
tractable problem with a potential engineering solution.
But this sort of field tailoring can only occur in the
nearfield of the transmitting station of the PWG.
We assert that the suggested approach can produce the
desired local field behavior, i.e. the resulting EM field of
the PWG will be an approximation to the desired
planewave field behavior over limited extents of the
volume occupied by the SUT. Clearly, the departures
from planewave behavior will produce some second-order
effects, and these effects may limit the capability and
fidelity of the PWG in some respects. The more important
second order, non-ideal effects include:
1.
Nearfield scattering produced by true planewave
illumination of the SUT will not be reproduced
correctly by the local planewave illumination.
Typically, however, this scattered energy affects the
response of distributed apertures on the SUT only
minimally. These effects can even be accounted for
by including multiple locations in the system vector
optimization procedure.
2.
The local planewave field will not properly produce
farfield planewave scattering needed to measure radar
cross section of the entire asset, but many other
mission-relevant test configurations are now possible
with the proposed PWG system.
3.
Field components or polarizations may exist in the
local planewave case, especially extremely close (in
the reactive nearfield region of each element of the
array distances of order λ or less) that would not exist
in the true planewave environment. Here again, the
relative magnitude of the unwanted components
should be small with proper placement of the asset,
and the effects on the response of the distributed
apertures would be minimal.
Even with these limitations, the proposed system will be
extremely capable. The proposed “local planewave”
concept will permit the in-situ test and evaluation of
avionics systems with coupling apertures that occupy
limited extents ( 10λ × 10λ regions and greater) on large
test assets (100’s of feet in extent). The proposed system
will also permit the evaluation of their response to a wide
variety of EM field engagement scenarios (simulate angle
of arrival to ±5o or greater), in both static and dynamic test
(computer controlled simulation of fly-by) modes. In
addition, due to the modular and distributed nature of the
proposed PWG, we believe it will be possible to
simultaneously evaluate the response of multiple aperture
locations spread across the extent of the asset to coherent
stimulation of a pre-described incident field.
3. GENETIC ALGORITHM OPTIMIZATION
Genetic Algorithms find or uncover optimal, or near
optimal, solution(s) from members of a population. In
essence the GA is a search technique. In an abstract
sense, a GA optimizing procedure is based on the
mechanics of natural selection and genetics. They
combine survival of the fittest and reproduction concepts
with random but structured search methodologies to locate
and identify solutions which best satisfy a given problem.
While many optimization problems can be succinctly
stated (mathematically in many cases), there is a class of
problems for which the problem definition and
identification of all parameters is impossible (the
economy, for example). For these types of problems the
GA technique has found much success [2, 3].
The major actions of the GA procedure are to: (1) form
the initial population. This means to choose a set of
possible solutions (often at random) for the initial
population. Then (2) evaluate the “fitness” of each
population member, which is the way in which the GA
determines how well a specific member of the population
produces a field that satisfies the requirements. Next (3)
choose a reproduction scheme using a pair of “parents”
from the population to form “offspring” or new members
of the population, and implement a scheme to reduce the
number of members in the current population. And finally
(4) determine whether a termination condition has been
reached (either a satisfactory solution has been found, or a
maximum number of iterations has been reached).
For the GA to operate, the characteristics of the individual
members of the population (possible solutions) need to be
expressed in a distinguishable way. The population for
this application consists of the value of the magnitude and
phase of the drive signal of each element in the PWG
transmit array, and we have chosen to represent these
values as a concatenated binary number. For example, we
could let both the magnitude and phase of the excitation
of each array element be represented as 4-bit quantities as
shown in Figure 2. The complete genetic code for each
possible solution then would be a collection of 8-bit
strings appended to one another to form the
“chromosome” of a population member.
Reproduction is the term used to describe the mechanism
by which the GA “evolves” the current generation into the
next generation. Many types of reproduction schemes
have been studied, but the one employed in this work is
4-bit Magnitude code for the
1st array element
0
1
1
0
4-bit Phase code for the
nth array element
4-bit Phase code for the
1st array element
0
1
0
1
0
1
1
0
1
Figure 2. - The genetic code of an n-element array.
simple. First, all members of the present population are
ranked according to their fitness. A probability is then
assigned to each member with the most fit members
assigned a higher probability. This probability is then
used to select two members of the population who will be
used to create a population member of the nextgeneration. Once the two “mating” members are selected
another random number, p , is generated. This random
number specifies the crossover point, the location in the
chromosome where the parent is split. For example, if the
chromosome length is 480 bits long, and p = 0.27 , then
the chromosomes of both parents will be split into two
sections that are p × 480 bits and (1 − p ) × 480 bits in
length (rounding to the nearest integer, and preservation
of the chromosome length is maintained). The four partial
chromosomes are then paired to form two next generation
offspring. The next generation is filled in this way until
the maximum population number is reached. In our
approach, the worst half of the members of the previous
generation with respect to the fitness function are then
discarded, and replaced by the offspring to form the next
generation. Other procedures are also used to introduce
random processes in the formation of the next generation.
The process repeats for the generation next until a
terminating condition is reached.
A terminating condition is required since the size of the
solution space can be quite large. For example, if we
consider an array with 16 elements, each with 15 bits of
amplitude and phase, then the size of the solution space is:
216 elements ×2×15 bits = 2 480 = 3.1217 × 10144 . With a population
size of 400 and for a simulation that evolved through 300
generations, the total number of possible solutions
examined is < 400 ( pop size) × 300 ( gen ) = 120k which
represents a ratio of solutions evaluated / total solutions =
3.84 × 10 −140 . In spite of this relatively small sampling of
the solution space, the GA procedure typically will
converge to a near-optimum solution.
4. T-FACTOR FIGURE OF MERIT
The GA procedure must assess the fitness of each member
of the population. The fitness for this application is
defined as a measure of the ability of the PWG transmit
array to satisfy a desired electromagnetic field distribution
over predefined spatial locations. We use a modified Tfactor [1] to evaluate the fitness of a potential excitation
vector candidate. The T-factor is defined as
&
& &
E (r ) − E (r ; rref )
& &
&
E (r ; r ) + E (r )
& &
T (r ; rref ) = 1 −
ref
*
where E (r& ) is the radiated field of the array at the
*
position r& , E (r&ref ) is the radiated field at the reference
position, r&ref , E (r&ref ) = ª ( kˆ × E (r&ref ) ) × kˆ º pˆ pˆ is the value
¬
¼
{
}
of the reference field at the reference position,
& &
& &
&
− jk ( r − r ) is the value of
E (r ; rref ) = ª( kˆ × E (rref ) ) × kˆ º pˆ pˆ e
{¬
¼
}
ref
the reference field translated to the evaluation position,
and the quantity T ( r&; r&ref ) is the T-factor, a scalar function
of vector position variables. The geometrical quantities
associated with this confusing amalgam of definitions are
depicted in Figure 3. The figure shows the origin
(location) of the radiating elements of the PWG, the
reference position, and the evaluation location (field
point). The reference position is the location taken as the
“perfect” planewave value since we are free to choose one
position as perfect. Fitness optimization points (FOP) are
defined as locations where the fitness of the radiated field
is evaluated. These FOPs are typically distributed over
the extent of the desired planewave regions, as shown in
Figure 6, and the T-factor is computed at each FOP
location. The fitness for a candidate array excitation
vector is defined as the minimum T-factor value for all
FOPs.
k̂ =
Unit vector in desired
direction of propagation
p̂ =
Unit vector in direction
of desired polarization
&
rref =
&
r=
Reference position
Evaluation point
Planewave
Polarization
p̂
z
Evaluation Position
&
r
x
&
rref
k̂
& &
r − rref
Planewave
Reference
Direction
Planewave
Reference Position
Figure 3 – Geometry for T-factor definition.
The T-factor has a number of valuable and useful features.
First, it is bound by zero and one, 0 ≤ T ( r&; r&ref ) ≤ 1 , with
& &
T ( r ; rref ) = 1 indicating a perfect planewave-like field
condition. Second, its definition can be altered slightly to
consider just amplitude or just phase when computing the
fitness of a potential solution. Values of the T-factor for
various amplitude and phase differences are given in the
tables below. Note that the values of T-factor bound the
deviation for both amplitude and phase. For example,
T = 0.9 implies that the amplitude and phase variation is
both less than 1-dB and 15-degrees respectively.
The radiated electromagnetic field of the PWG transmit
array is computed in the usual way [4]. However, we
have found that certain simplifying assumptions can be
used to accelerate the field calculations. One of these
methods is to use an omni-directional, scalar radiator
model for the array elements. This technique is described
in more detail in [6].
Properties of the T-factor (amplitude only)
& &
& &
E / ERef
T (r , rRef )
E / ERef
T (r , rRef )
dB
dB
1
0.9
0.8
0.7
0.6
0.5
0.25
0.01
0
-0.91
-1.94
-3.09
-4.43
-6.02
-12
-20
0
0.947
0.889
0.823
0.75
0.667
0.4
0.182
1
1.1
1.2
1.42
1.5
2
5
10
0
+0.828
+1.58
+3.04
+3.52
+6.02
+13.97
+20
Properties of the T-factor (phase only)
0
0.952
0.910
0.826
0.8
0.667
0.333
0.182
Δϕ
& &
T (r , rRef )
0
1
5
10
15
20
25
30
1.
0.991
0.956
0.912
0.869
0.826
0.783
0.741
Δϕ
& &
T (r , rRef )
45
60
75
90
135
0.617
0.5
0.391
0.292
0.076
180
0.
5. HARDWARE DESIGN
A hardware design concept for a single transmit array of
the PWG is shown in Figure 4 (sized for L-band
operation). A standard PC controls the input RF source,
and the characteristics of each RF channel of the array.
No permanent reference sensors are required for feedback
in this system, but feedback would improve the robustness
of the PWG field. In general the PWG transmit array and
SUT can be arbitrarily positioned in the chamber. The
positioning information is used as input to the GA to
calculate an optimal excitation vector (element drive
magnitude and phase) solution for the test at hand. Once
the solution is calculated, the computer converts the
desired vector information into actual control settings
from a calibration table residing in local memory. The
calibration table is a characterization of each channel’s
properties including cable effects, vector modulator
properties, etc. These excitation settings then are applied
to each of the sub-array’s transmitter control components
to produce to the desired radiated RF signal.
This system is designed to provide frequency agility and
limited beam steering.
Complex scenarios may be
calculated in advance, then “played back” sequentially to
simulate, for example, a source that is changing its relative
location with respect to the SUT over time. The PWG may
also utilize multiple transmit arrays in unison to accomplish
a desired field distribution, or the system may operate each
PWG transmit array independently. Considerable system
testing and operating experience will be required to
determine the optimum system configuration for a given
SUT and test field requirement.
Figure 4 depicts a PWG transmit array with 16 radiators
arranged in a square matrix.
This number and
configuration of radiators was found through analysis to
produce acceptable results, and the size associated with
this number of radiators in the frequency band of interest
(0.5 – 2.0 GHz) was considered manageable. The 500
MHz circular waveguide radiators are also shown in this
figure.
The design’s modular nature is indicated;
reconfiguring for operation at the upper frequency bands
is simply a matter of exchanging the transmit modules. A
functional block diagram for each channel of the PWG is
depicted in Figure 5. Each PWG transmit array will have:
•
•
a ÷ N signal divider, where N = number of elements
of the PWG transmit array;
Fixed Wideband Cell Components
3dB
the proper number of fixed, independent microwave
channels;
•
removable radiating assemblies designed to operate at
the center frequency of the center band;
•
a compact computer controller for local instrument
control, calibration file storage, etc.;
•
a GPIB link between the user (master) computer and
the PWG transmit array; and
•
fixed fiducial markings to permit accurate surveying
of each transmit station.
Interchangeable Narrowband
Cell Components
O.5-2.0 GHz
Vector
Modulator
I
÷16
RF Source
To
Verification
Circuits
To Identical
Circuits
CPU
+20dB
Q
Isolator
Directional Coupler
Low Pass
Filter
Open Ended Circular
Waveguide
Interchangable
Bands:
0.5-0.8 GHz
0.8-1.3 GHz
1.3-2.0 GHz
16 bit
DAC
Figure 5 – PWG: channel hardware architecture.
6. PWG SIMULATION
Extensive simulations of the performance of the PWG
have been conducted. First, the desired planewave region
(test zone) is described mathematically, and then the
required planewave fidelity is specified. Specification of
the desired test zone is accomplished by defining the
central point of a rectangular surface (in this case) over
which constant phase and amplitude is desired (planewave
at normal incidence). The relationship between the
transmit linear array, the desired planewave region (test
zone), and the fitness optimization points is depicted in
Figure 6.
z
kth Scalar
Isotropic
Radiator
Figure 4 – L-band Planewave Generator concept.
The key control component of each channel of the PWG
is a vector modulator, it provides the needed phase and
amplitude control for each channel. These modulators are
standard commercial-off-the-shelf units, which can be
found in typical phased array systems [5]. The nominal
operating specification for the modulator is typically
insufficient for the current application. Consequently a
component calibration will be required. It has been
shown [7] that much greater accuracy can be achieved
with proper calibration. The calibration and operational
verification of the PWG system will involve the
comprehensive compiling of its output characteristics as a
function of many parameters (frequency, power level, I
and Q settings of the vector modulators, etc.). These
characteristics will be assembled in calibration files stored
on the system computer that the PWG will access during
operation. Calibration of the vector modulators is a timeconsuming operation, and the optimal approach is still
being developed.
&
rk′
Fitness
optimization
Points
&
r
y
d
x
Fitness
optimization
Points
Reference
Position
Figure 6 – Geometry of fitness points.
Next, the GA conducts an optimization to determine the
array excitation vector. Finally, using the value of the
optimum array excitation vector, the radiated field is
computed for various spatial regions of interest, and other
figures of merit are calculated.
A 1-D simulation was conducted with the following
parameters: 25 transmitters aligned in a linear array,
frequency = 3 GHz, transmitter element-to-element
separation = 4 inches, separation between transmit array
and planewave region = 2.5 meters, size of planewave
region = 1.5 meter in width ( or 15 wavelengths wide).
The GA algorithm of the PWG simulation computed a
transmit array vector (magnitude and phase for each
element in the transmit array). The magnitude and phase
of the radiated field were then computed over and beyond
the bounds of the desired planewave regions, these values
are shown in Figure 7a (field amplitude) and Figure 7b
(field phase). The field T-factor, shown in Figure 7c, was
also computed and is > 0.8 over the extent of the desired
planewave region. Returning to the table of T-factor
values, one sees this means that the magnitude of the field
variation will be < 3-dB, and the phase variation < 20degrees over the planewave region. The figures below
show the resulting field satisfies both conditions.
1.5
phase - degrees
field magnitude
200
1.0
0.5
-200
-600
Specified Planewave
Region
-1000
Specified Planewave
Region
-1400
0.0
-15
-10
-5
0
5
10
15
20
z/l
field T-factor
(a)
-15
-10
-5
(b)
0
5
10
15
20
1.0
8. REFERENCES
0.8
[1] Spherical Near-Field Antenna Measurements, ed. J.
Hansen, Peter Peregrinus Ltd., UK, 1988.
[2] R. Haupt, “An Introduction to Genetic Algorithms for
Electromagnetics,” IEEE Antennas Propagat. Mag,
vol. 37, pp. 7-15, Apr. 1995.
[3] Practical Genetic Algorithms, R. Haupt and S. Haupt,
John Wiley and Sons, Inc., NY, 1998.
[4] Antenna Theory, W. Stutzman and G. Thiele, J. Wiley
and Sons, Inc., 2nd edition, NY, 1997.
[5] http://www.generalmicrowave.com
[6] M. Timmons, C. Courtney and D. Voss, “Practical
Architecture and Simulated Performance of a PseudoPlane Wave Generator,” EURO-Electromagnetics
2000, Edinburgh, Scotland, 2000.
[7] “Development of a dynamic precision phase /
amplitude controller: Final Report,” Herley Micro.
Products, General Microwave, 425 Smith St.,
Farmingdale, NY 11735-1198.
0.6
Specified Planewave
Region
0.4
0.2
0.0
-15
(c)
Figure 8 – Future Planewave Generator Concept
z/l
-10
-5
0
5
10
15
20
z/l
Figure 7 – PWG simulation results.
7. SUMMARY
This paper has described a system approach to the
generation of planewave-like EM fields over limited
regions for the purpose of testing the in-situ response of
integrated aircraft electronics coupled to the external
environment though distributed, spatially limited, EM
apertures. The approach proposes the use of a transmit
phased array, with operation in the nearfield region of the
transmit array, but in the farfield of the radiators of the
array. It employs an optimizing algorithm to determine
the transmit array’s excitation vector, and seeks to
generate planewave-like regions only over limited extents
of a large asset. Clearly, the departures from true
planewave behavior of the transmit array’s radiated field
will produce some second-order effects, and these may
limit the capability of the PWG in some respects. But, the
proposed concept will permit the in-situ test and
evaluation of avionics systems that occupy limited extents
on large SUTS, and will permit the simulation of their
responses to a wide variety of EM field engagement
scenarios in both static and dynamic test modes. In
addition, due to the modular and distributed nature of the
proposed PWG, the system should exhibit scaling
properties that will permit the system to expand in concert
with the desired performance parameters (size of
planewave zone, maximum angle of arrival simulation,
etc.). A highly integrated PWG concept is shown in
Figure 8.
9. ACKNOWLEDGMENTS
This work was supported in part by the United States Air
Force under the Small Business (SBIR) Innovation
Research program. The authors wish to thank the
following individuals for their contributions to the
development of this technology:
Mr. Abraham
Atachbarian (EAFB SBIR Program Manager), Ms. Joanne
M. Eldredge (EAFB Contracting Office), Mr. Mark
Timmons and Mr. Ged Bluzas (EAFB, former Project
Officers), Mr. David Slemp (Agilent Technologies), and
Dr. Bill Swartz, Mr. Frank Elwood, and Mr. Philip Critelli
(Voss Scientific).