130 SAMPLED-DATA CONTROL SYSTEMS 
6.4 Design by the Use of the Most Important Sidebands Due to 
Sampling. Method 2 
As was mentioned in Sec. 6.2, method 2, which was first proposed by 
W. K. Linvill,** lends itself most easily to the use of the polar plot or 
Nyquist diagram as a design tool. Application of the design steps out- 


Sampled system 

Continuous system 
0 i 2 3h AT ST Cf 7h) Sf oF i0n 
Time. 
Fic. 6.12. Step responses of systems of Fig. 6.11. 
lined in See. 6.2 is straightforward and will be illustrated shortly by the 
same example used for method 1. Method 2 has two principal advan- 
tages over method 1. The first of these is the fact that by using more and 
more sidebands it is possible in a perfectly straightforward manner to 
improve the accuracy of the method. Obviously, there is a limit, deter- 
mined by the amount of labor involved, to how far this process can be 
carried, but the fact remains that if a particular part of the frequency 
response is critical, an improvement in the approximate plot of those 
frequencies can be made. The second advantage of this method is that a 
measure of the validity of the approximation can be made relatively 
quickly by plotting the exact polar plot for the loop transfer function from 
the pulse transfer function of the system. This check procedure is simple 
to apply on a polar plot but rather obscure on the Bode diagram. 
The basic idea of this method is the approximation of 
Grae = » CENA are) (6.12) 
by a few terms of the summation. The construction of the approximate 
plot of (6.12) can be considerably simplified by the observation of the 
