APPLICATION OF CONVENTIONAL TECHNIQUES 139 
The necessary values are, for 7’ = 1 sec, 
a=1 
IK SS Ni 
With the compensating network so chosen, the loop pulse transfer 
function reduces to 
MOEe) = = (6.27) 
z—1 
and, from elementary root-locus considerations, it may be seen that 
increasing the forward gain by a factor of 2.72 to unity moves the pole 
of the closed loop to the origin. The over-all pulse transfer function 
K(g) is thus reduced to ; 
GB) 
Re) 

zg! (6.28) 
which describes a system which, at sampling instants, represents a pure 
delay of one sampling period and no transient beyond one sampling 
period. The extension of these ideas of cancellation compensation and 
the limitations on the method will be developed in some detail in the 
next chapter. 
The use of pulsed RC networks to provide the necessary compensating 
transfer functions for sampled-data systems is considerably more general 
and more flexible than is indicated by the special examples worked out in 
Fig. 6.17. As a matter of fact, Sklansky®? has shown that any linear 
realizable pulse transfer function may be realized by a pulsed RC network, 
of the general form shown in Fig. 6.16. The proof of this important 
result follows from a consideration of the characteristics of the basic pulse 
network transfer function and the general form of the realizable pulse 
transfer function of a finite system. The latter is 
Ms 
8 
" 
2 
X 
Ve 
T 
? 
ll 
Oo 

(6.29) 
ih» 
o 
ce 
4 
S 
where the a; and b; are real and bb) # 0. As shown in Chap. 4, the restric- 
tion on bo is necessary to ensure that the linear system described by (6.29) 
operates only on present and past and not on future samples. The sys- 
tem is finite (stores a finite number of past-input and past-output data 
values) if p and q are finite. From an elementary analysis of the pulsed 
