D. G. Tucker 33 
RESPONSE 
t TO PEAK OF 7:5 
1 AT X =277 
PLAIN LINEAR 
ARRAY 
SUPERDIRECTIVE 
o:5 ARRAY 
(e) >=+—=—_—* 
7° 30 
7 2 
; Oe 
Arse MULTIPLICATIVE 
a ARRAY 
OPS = 
Fig. 2.2, Comparison of (a) normal additive, (b) multiplicative, and 
(c) superdirective directional responses for the same array. 
with a similar receiver; they just cannot work together. There is not space to 
deal with this question here (a full account is being published elsewhere [9]), 
and we must accept multifrequency two-element receivers as a special kind of 
array to be studied separately. Nevertheless, with care, some of the methods 
of ordinary arrays, e.g., the synthesis of superdirective directional responses, 
can be applied. 
The practical form of this kind of receiving array is based on the multipli- 
cative system, in which the outputs of thetwo multifrequency receiving elements 
are multiplied together, as shown in Fig. 2.3. The multifrequency signal sent 
from the transmitter comprises a group of r harmonics. On reception at the 
two elements, these harmonics contain directional information in the form of 
the phase angles +md, where ¢=(md/\) sin 0, dis the spacing between the ele- 
ments, and A is the wavelength at the fundamental angular frequency p. On mul- 
tiplication (and ignoring the "special filter" for the moment), the de output 
becomes a function of signal direction, thus 
vy, ye E2 cos 2m¢ 
m=1 
If only odd values of m are used, and all E,, (for m odd) are equal, this becomes 
Y, E* sin(r + 1) Co) 
sing 
which is the well-known form of directional response for a linear array of uni- 
form sensitivity, with r+1 elements (which is an even number), except for a 
factor of 2 in the angular scale. 
