TABLE OF CONTENTS We now develop a systematic method for realization (or implementation) of an arbitrary Nth-order transfer function. The most general transfer function with M = N is given by
Since realization is basically a synthesis problem, there is no unique way of realizing a system. A given transfer function can be realized in many different ways. A transfer function H( s) can be realized by using integrators or differentiators along with adders and multipliers. We avoid use of differentiators for practical reasons discussed in Sections 2.1 and 4.3-2. Hence, in our implementation, we shall use integrators along with scalar multipliers and adders. We are already familiar with representation of all these elements except the integrator. The integrator can be represented by a box with integral sign (time-domain representation, Fig. 4.19a) or by a box with transfer function 1/ s (frequency-domain representation, 4.19b).
Rather than realize the general Nth-order system described by Eq. (4.60), we begin with a specific case of the following third-order system and then extend the results to the Nth-order case
We can express H ( s) as
We can realize H( s) as a cascade of transfer function H 1( s) followed by H 2( s), as depicted in Fig. 4.20a, where the output of H 1( s) is...
