TABLE OF CONTENTS Having learned to plot the basic functional building blocks, we are now ready to sketch the piecewise-linear Bode plots of arbitrary gain functions. These plots are most useful when the roots are well separated from each other, say, by at least a decade. Even when this is not the case, these plots still provide a good starting point for a basic understanding of a frequency response.
In general, a gain function can be expressed as
where K is a suitable scaling factor, and the numerator terms N 1( s) through N k( s) and the denominator terms D 1( s) through D ?( s) have one of the following standard forms:
The last form is used only if ? < 1. If ? ? 1, the roots are real and the quadratic term can be factored into the product of two terms of the type of Equation (14.105b). By Equations (14.76) and (14.77),
indicating that the Bode plots of H can be obtained by first sketching the Bode plots of its individual terms and then adding them up geometrically. The procedure is summarized as follows:
Given a gain function H( s), factor it into the standard form of Equation (14.104), with each numerator and denominator term having one of the forms of Equation (14.105).
Separately sketch the linearized plots of the numerator terms as well as...
