APPLICATION OF CONVENTIONAL TECHNIQUES 123 
Design step 5.1. Represent the pulse transfer function HG(z) in the 
form (polar plot or root locus) which is most familiar to the designer. 
Design step 5.2. A pulse transfer function of a form realizable by 
practical networks (to be discussed in detail later) is selected and the new 
plot or locus drawn for N(z)HG(z) and evaluated directly or by time- 
response calculation. 
Design step 5.3. The selected network is realized by a continuous net- 
work (RC) separated from the plant and hold by a switch. 
This method, which was also proposed by Sklansky,*? truly applies con- 
ventional methods to sampled-data systems. 
The fundamental procedure of plotting frequency data and shaping by 
forming the product of the plant and network pulse transfer functions is 
exactly analogous to conventional continuous-design techniques. One 
may even apply constant magnitude ‘‘M circles’’ to the design to ensure 
a specific maximum response for real frequencies. In terms of the root 
locus, the rules* for loci construction are exactly the same as in the con- 
tinuous case, although for sampled-data systems the unit circle replaces 
the imaginary axis as the boundary of stability and the negative real axis 
and origin in the z plane have significance not ordinarily found in the 
s plane. 
6.3 Design by Continuous Approximation of Sample and Hold. 
Method 1 
The fundamental step in the application of this method lies in determin- 
ing a useful and realistic continuous approximation to the sample and 
hold operation. Such an approximation may be derived and evaluated 
either by time- or frequency-domain considerations, but it is essential 
that the approximation be as simple as possible. The first application of 
the method will be made to the most common hold circuit, which is the 
clamp, or zero-order hold. This circuit was discussed in some detail in 
Chap. 3 and is described by the transfer function 
sin wT/2 
a es Gitano SBE We Ie 
EIGics) i — ane! oT? 
(6.4) 
If this element is followed by a plant with the transfer function G(jw), then 
the over-all loop pulse transfer function is 
Ps 5 @ + N09 
ie 1 Does) sin] ( 2 )2| 
Gi) TP > Te 5) a (Ci IOI 
—o Rae 
G(jw + jnwo) (6.5) 
