Page 23 - Jan2013
P. 23

Martin L. Smith
Blindgoat Geophysics 2022 Quimby Mountain Road Sharon, Vermont 05065
Michael R. Roddewig
Department of Electrical Engineering, Montana State University Bozeman, Montana 59717
Kurt M. Strovink
Department of Physics, Colorado School of Mines Golden, Colorado 80401
John A. Scales
Department of Physics, Colorado School of Mines Golden, Colorado 80401
  IPntroduction to phased arrays “A field-programmable gate rewards the development of sophisti-
hased source arrays are physical- ly-distributed arrays of radiators (source transducers) driven by
time-delayed copies of a common sig-
nal. The time delays are chosen so that
the net antenna pattern of the array is
focused on either a particular target or
lies in a particular direction. A simple
example is an array of broadcast anten-
nae with an individual element's time
delay determined by the length of its
feed cable. By switching among sets of
feed cables the composite antenna may
be made to have major lobes in differ-
ent directions, in terms of both elevation and azimuth, as needed to meet the varying requirements of daytime and nighttime operation. These arrays have either fixed delays or a few, selectable sets of fixed delays.
Phased receiver arrays are based on exactly the same principles as their source counterparts—a correspondence that is spelled out in a little more detail in the implementa- tion section of this article. In all other respects, the term phased array will mean phased source array.
We are interested here in electronically-steerable phased arrays, that is, phased arrays with electronically- controlled time delays. These systems are capable of rapid shifts over many antenna patterns which make it practical to quickly scan the major lobe of the outgoing signal over a range of azimuths and elevations. One application of this technology is military target-tracking radar systems, which may have to (nearly) simultaneously track many potential threats much more rapidly than would be feasible with a physically steered antenna. Perhaps the most active area of the application of phased-array technology is in bio-med- ical devices which image the body with ultrasound. This field is driven by the needs of medical diagnosis and treat- ment; it is fortunate that the human body represents a rela- tively homogeneous environment of acoustic speeds which
22 Acoustics Today, January 2013
array (FPGA) is a complex, miraculously versatile piece of field-configurable hardware comprising hundreds of thousands of logical units of various types...”
cated imaging methods. For discussion of the basic technologies and a number of examples, see, for example, Cobbold (2007) and Azhari (2010).
Phase-shift versus time-shift
There are two basic modes of
phased-array implementation. In the first, the driving signal is sinusoidal and the signal routed to each element is given a prescribed phase shift. In the second more general, case the driving signal is an arbitrary function of time and the signal routed to each element is
time-delayed by a prescribed amount. Note that the time- shift case includes the phase-shift case as a particular instance. We will focus on time-shifted systems which accept an arbitrary function of time as input.
Planar wavefield versus time-on-target
There are also two philosophically distinct ways of com- puting the pattern of element time delays. In the planar wave- field method, time delays are chosen so that the radiated field approximates a plane wave moving in a prescribed direction. Figure 1 schematizes the quasi-planar wavefront formed by the time-shifted circular wavefronts from an array of sources. Note that the approximation to a plane wave degrades to the right of the figure where the desired plane wave is closer to the array. At distances that are large compared to the array dimension the array appears as a point source and the wave- front is circular (in two dimensions, spherical in three). Of course spreading waveforms at large distances look locally like plane wavefronts.
In the time-on-target method, delays are chosen so that signals from all of the individual elements arrive at a pre- scribed location in space at the same time (the name derives from a practice in artillery management). Figure 2 shows the circular wavefronts from the five-element array arriving

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