Dominant Zero and Excess Phase of a Hurwitz Polynomial

In the analysis and design of linear electronic circuits, it is often necessary and desirable to restrict attention to first-order effects only. Simplifications of the circuit may take the form of a dominant natural frequency (or time-constant) description. That is, of the total natural frequencies of the circuit, one may be found to be dominant over a frequency or time interval of interest. For the low-pass situation, necessary conditions are presented in this paper to establish the dominant zero of a polynomial in terms of the coefficients of the polynomial. Simple expressions are also given to estimate the second-order effect of excess phase (or dead time). A simple transistor amplifier is used as an example.