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*fe is the critical frequency of the numerator or denominator term in question, t The correction is positive for a numerator term (zero) and negative for a denominator term (pole).

*fe is the critical frequency of the numerator or denominator term in question, t The correction is positive for a numerator term (zero) and negative for a denominator term (pole).

term in Eq. (3-8c), is modified by the tabulated correction terms, and the new curves summed up. In the case of higher-order terms, such as the second-order third term in Eq. (3-8c), the gain correction is multiplied by the order of the term.

The phase shift of the gain function can also be approximated as before,

The result is shown in Fig. 3-9, using the same principle employed in the construction of Fig. 3-7. Note that numerator terms in the gain function [Eq. (3-8)] contribute a leading phase, while denominator terms contribute a phase lag. A second-order term gives twice the phase shift, as though it were two first-order terms.

A more accurate phase curve can be obtained by substituting for the straight-line plot of Fig. 3-9 the true phase values of Table 3-1 for each term in the gain function. For the second-order term the phase values are merely doubled.

3-2 The Geometric Interpretation of Gain Functions. It is appropriate now to introduce a further generalization which will have great value throughout most of the later portions of the book. It consists

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