6-2] BASIC PRINCIPLES 295 



of angular coverage in 2 seconds; and an ability to separate targets with 

 radial velocities of from to 2000 knots in 40-knot increments, we find: 



,V 150 ,^ 360 ^^ 2000 ,n r ^ -,r,2 ^ i 



A^ = -Tpj- X . ry X ^7^ = 13.5 X 102 elements/sec. 



which is a very large number even though the radar is providing only three 

 dimensions — range, one angle, and velocity. This answer implies a system 

 bandwidth requirement of at least 13.5 Mc even if it were possible 

 (which as the reader shall soon see, it is not) to apportion this bandwidth 

 between range, angle, and velocity coordinates in the desired manner. 



In the case of a passive system the information matrix is usually only 

 two-dimensional (angle only) since passive systems do not ordinarily have 

 range and velocity measuring capabilities.^ 



System Sampling Frequencies. The system sampling frequencies 

 govern the minimum resolution element size and the total unambiguous 

 measurement interval of each coordinate — range, angles, and velocities. 

 In general, there are three basic sampling frequencies which are important 

 in determining the character of the signal entering the receiver: (1) trans- 

 mitted bandwidth, (2) transmission periodicity, and (3) angular scanning 

 frequency. 



1. The transmitted bandwidth I^ft determines the rate at which the radar 

 system can collect pieces of range information. It represents, in effect, the 

 rate at which successive range elements of space can be interrogated. This 

 principle is easily seen for the case of a pulse radar. In this case the trans- 

 mitted bandwidth is the reciprocal of pulse length (A/^ = l/r). At any 

 instant of time following transmission, the received pulse information 

 originates from a range interval Ai? which has the width 



Ai^ = f = ^; (6-3) 



Thus every r seconds, information is received from a new range interval. 

 The same principles hold whether the transmitted bandwidth is created 

 by pulsing or by other means such as "FM-ing." That is, the minimum 

 range resolution element is defined by Equation 6-3 and the rate Nr at 

 which the system collects pieces of range information is: 



Nr = ^ft. (6-4) 



If the transmitted bandwidth is large relative to the maximum doppler 

 shift and all the other sampling frequencies, then the transmitted band- 

 width also defines the maximum rate at which the radar may collect all 



^A passive system designed to collect and classify radiation sources according to their 

 frequency, bandwidth, polarization, and angular location can encounter bandwidth problems 

 similar to those of an active three- or four-dimensional radar system. 



