Understanding Pole/Zero Analysis

In pole/zero analysis, a network is described by its network transfer function which, for any linear time-invariant network, can be written in the general form:

In the factorized form, the general function is:

The roots of the numerator N(s) (that is, z i ) are called the zeros of the network function, and the roots of the denominator D(s) (that is, p j ) are called the poles of the network function. S is a complex frequencyDesoer, Charles A. and Kuh, Ernest S. Basic Circuit Theory. New York: McGraw-Hill.1969. Chapter 15..

The dynamic behavior of the network depends upon the location of the poles and zeros on the network function curve. The poles are called the natural frequencies of the network. In general, you can graphically deduce the magnitude and phase curve of any network function from the location of its poles and zerosVan Valkenburg, M. E. Network Analysis. Englewood Cliffs, New Jersey: Prentice Hall, Inc., 1974, chapters 10 & 13..

The section ReferencesReferences, lists a variety of source material addressing transfer functions of physical systems R.H. Canon, Jr. Dynamics of Physical Systems. New York: McGraw-Hill, 1967. This text describes electrical, mechanical, pneumatic, hydraulic, and mixed systems. , design of systems and physical modelingB.C. Kuo. Automatic Control Systems. Englewood Cliffs, New Jersey: Prentice-Hall, 1975. This source discusses control system design, and provides background material on physical modeling., and interconnect transfer function modelingL.T. Pillage, and R.A. Rohrer. Asymptotic Waveform Evaluation for Timing Analysis, IEEE Trans CAD. Apr. 1990, pp. 352 - 366. This paper is a good references on interconnect transfer function modeling which deals with transfer function extraction for timing analysis. ,S. Lin, and E.S. Kuh. Transient Simulation of Lossy Interconnects Based on the Recursive Convolution Formulation, IEEE Trans CAS. Nov. 1992, pp. 879 - 892. This paper provides another source of interconnect transfer function modeling. .