  A Feshbach resonance arises in cold atom scattering due to the complex
interplay between several coupled channels. However, the essential physics of
the resonance may be encapsulated in a simplified model consisting of just two
coupled channels. In this paper we describe in detail how such an effective
Feshbach model can be constructed from knowledge of a few key parameters,
characterizing the atomic Born-Oppenheimer potentials and the low energy
scattering near the resonance. These parameters may be obtained either from
experiment or full coupled channels calculations. Using R-matrix theory we
analyze the bound state spectrum and the scattering properties of the
two-channel model, and find it to be in good agreement with exact calculations.
