11 Pages

 1 1 

(5.51) The responses due to input 1, obtained from Eq. (5.51), are:

Since the relative phases of the τ's are not known and not required for m.p. systems, then to ensure the achievement of the desired performance specifications Eq. (5.60) is expressed as follows:


bound largest the -- )(jb11cr ωττ ≤+ |||| 1111 (5.62)

These represent an over design since they result in a more restrictive performance. A pictorial representation of Eqs. (5.61) and (5.62), for ω = ωi, is shown in Fig. 5.15. Note that the τ's in this figure and in the remaining discussion in this section represent only magnitudes. From this figure the following expression is obtained:

In the "low frequency range" the bandwidth (BW) of concern, 0 < ω < ωh, ∆τ is split up based upon the desired performance specifications. As is discussed later, for the high frequency range only an upper bound is of concern; thus, there is no need to be concerned with a “split.”