344 BELL SYSTEM TE.CHNICAL JOURNAL 



ingly and their outputs are "received" by conventional receivers, with 

 common automatic gain control. The demodulated audio outputs are 

 equalized for difference in transmission time and then combined. 

 A cathode-ray oscilloscope displays the output of the exploring or 

 monitoring branch. It plots amplrtude (provided by a linear rectifier) 

 as the ordinate, against phase shift 02 (corresponding to in Fig. 1). 

 The screen of the oscilloscope is of the retentive type and thus displays 

 several consecutive sweeps at once. A pattern corresponding to two 

 waves is illustrated. The other cathode-ray oscilloscope is used in the 

 adjustment which equalizes the delay of the two waves. Delay is 

 added to the low angle branch until the oscilloscope shows a line (or 

 compact elongated figure) which oscillates between the two axes as the 

 two waves fade differently. This means that all of the audio fre- 

 quencies of one branch are combining in phase with those of the other. 



The above brief description was introduced to acquaint the reader 

 with the essentially simple features of the MUSA system. Before de- 

 scribing the details and the results obtained with the experimental 

 system, a more comprehensive analysis of steering principles will be 

 given. 



Returning to Fig. 1, it is assumed, of course, that the transmission 

 lines are terminated in their characteristic impedance at the receiving 

 terminal " (the phase shifters of Fig. 1) so that the phase is distributed 

 linearly along the lines. Neglecting line loss (or equalizing it), the N 

 currents, equal in magnitude and different in phase, are 



^2 = /gj{a,<+0-27ra(u-cos 8)) 

 jg = /^j{c>.^+2[0-27ro(u-cos 8)1! 



j\. = /g?{u<+(A'-l)[0-27ra(<;^cos 8)11 



XI) 



where i = instantaneous current in exponential notation 

 CO = angular frequency 

 N = total number of unit antennas 

 a = spacing in free space wave-lengths 



V = c/v = the ratio of the velocity of light to that of the trans- 

 mission line. 



The sum of the N currents is 



A = /e'"'(l + ^;[0-27ra(i'-cos 8] _|_ ... _|_ ^/(Ar-l) [<^-2ra(i'-eos 8)] 1 ('2') 



1' Non-characteristic terminations at the receiving ends of the lines are per- 

 missible if all terminations are identical and if the antennas are matched to the 

 characteristic line impedance. Conversely, characteristic terminations at the re- 

 ceiving ends suffice if the antenna impedances are merely identical. 



