  Studies of cold atom collisions and few-body interactions often require the
energy dependence of the scattering phase shift, which is usually expressed in
terms of an effective-range expansion. We use accurate coupled-channel
calculations on $^{6}$Li, $^{39}$K and $^{133}$Cs to explore the behavior of
the effective range in the vicinity of both broad and narrow Feshbach
resonances. We show that commonly used expressions for the effective range
break down dramatically for narrow resonances and near the zero-crossings of
broad resonances. We present an alternative parametrization of the effective
range that is accurate through both the pole and the zero-crossing for both
broad and narrow resonances. However, the effective range expansion can still
fail at quite low collision energies, particularly around narrow resonances. We
demonstrate that an analytical form of an energy and magnetic field-dependent
phase shift, based on multichannel quantum defect theory, gives accurate
results for the energy-dependent scattering length.
