Project Cyclops, A Design... - Department of Earth and Planetary ...

stripline. For 2 _< k _< 6, appropriate lengths of coaxial
line may be used. For 7 _< k _< 14, it is probably more
economical to use the acoustic surface wave delay units.
Figure I0-11 is a block diagram of an acoustic delay
unit. The entire IF signal (825-1175 MHz) is amplified
by the input amplifier #o and drives the lithium niobate
delay line. The wave launched propagates in both
directions and is absorbed at both ends of the crystal.
The wave propagating to the left is picked up after some
convenient minimum delay ro - el. This signal is
amplified by the amplifier/zi and is given an additional
small trimming delay el in a loop of stripline. By adjusting
el we can set the delay via this path at Zo. The wave
propagating to the right is picked up after a delay
ro + r - e2, amplified in amplifier/a2, and trimmed by
the additional delay e2, and arrives at the switch with
the precise delay ro + r.
When the switch S is thrown by the computer, a
delay r = 2k nanoseconds is inserted or removed. In
either position of the switch, the signal is introduced and
picked up from the acoustic line. Thus, switching the
delay in or out does not affect any phase shift (or
dispersion) caused by the transducer electrodes. Regardless
of the delay, the total number of transducers
through which every IF signal passes always remains the
same. Hence any dispersion caused by these elements is
common to all lines and does not interfere with the
constructive addition of the signals.
To hold the switched delay of each unit at precisely
an integer number (2 k) of nanoseconds, ro is adjusted to
be an odd number of quarter nanoseconds. Then the
phase of the 1 GHz pilot should be 90 ° different at all
times at the input and output. To assure this, the pilot is
stripped at the input and output, and the two signals are
applied to a phase detector whose output drives a
heating element attached to the acoustic line. We thus
make use of the temperature coefficient of the line to
hold the delay precisely constant. This compensation
may not be needed on the units having short delays; it is
not expensive and may be included on all units to
standardize them and to obviate the need for precise
control of ambient temperature.
If further study reveals that indeed there is some
dispersion in the acoustic wave propagation, frequencydependent
delay compensation may be added in the
shorter units. The longer delay units may be divided into
two equal parts (two of the next shorter delay units) and
a spectrum inverting repeater introduced between the
two halves. By combining these techniques we feel
confident that the required delay can be obtained to the
required high accuracy and stability.
As the Earth turns, the fine delay units associated
with the antennas at the rim are switched rather rapidly.
The maximum switching rate is
f - (23)
Crmi n
where _2 = 2_r/86164 is the angular rotation rate of the
Earth, a is the array radius, c is the velocity of light and
rmi n is the minimum delay step. For a lO-km diameter
array and r = 114 nanosecond f= 4.86 switch operations
per second. For reliability and to minimize switching
times it is recommended that all switching be done with
diode gates.
With the digital delay switching described above the
required delay slope across the array is approximated at
all times by a series of steps. The delay error is therefore
a sawtooth function. As a result the probability density
function for the phase error,/frO), is a constant 1/20o
between the limits --00 and 0o where 0o = nfmaxrmi n.
Here/'max is the maximum demodualted IF frequency
and rmi n is the minimum delay step. As a result, the
array efficiency is reduced by the factor
in 0 2
r_= p(O) cosO d = L--_o J
(24)
Taking fmax = 175 MHz and rmi n = 1/4 nsec we find
0o = 0.1375 radian and r/= 0.994. Clearly, the discrete
delay steps do not degrade the performance appreciably.
To save central computer storage and time, it is
suggested that the delay system for each 1F line have
associated with it a delay register, an increment register,
and an adder. At the outset, the proper delay and
increment (positive or negative) are computed for each
line. (Both are stored to several more digits of accuracy
than used by the delay units.)Periodically-say every
1]10 sec-the increments are added, thus updating the
delays. Occasionally, perhaps once a minute, the computer
makes its rounds, and updates each delay to the
right absolute value and corrects the increment. (The
same technique, incidentally, can be used to drive the
antennas in azimuth and elevation.)
It is estimated that the cost of the IF delay system
should not exceed $8000 per line. Since the number of
delay bits increases only logarithmically with array
radius we may, to the present accuracy of estimation,
assume the cost per line to be independent of array size.
EFFECT OF GAIN AND PHASE DISPERSION
Equation (24) gives the reduction in array efficiency
117