  We discuss a model for studying the statistical properties of the impedance
($Z$) and scattering ($S$) matrices of open electromagnetic cavities with
several transmission lines or waveguides connected to the cavity. In this
paper, we mainly discuss the single port case. The generalization to multiple
ports is treated in a companion paper. The model is based on assumed properties
of chaotic eigenfunctions for the closed system. Analysis of the model
successfully reproduces features of the random matrix model believed to be
universal, while at the same time incorporating features which are specific to
individual systems. Statistical properties of the cavity impedance $Z$ are
obtained in terms of the radiation impedance (i.e., the impedance seen at a
port with the cavity walls moved to infinity). Effects of wall absorption are
discussed. Theoretical predictions are tested by direct comparison with
numerical solutions for a specific system. (Here the word universal is used to
denote high frequency statistical properties that are shared by the members of
the general class of systems whose corresponding ray trajectories are chaotic.
These universal properties are, by definition, independent of system-specific
details.)
