  We use the dressed potentials obtained in the adiabatic representation of two
coupled channels to calculate s-wave Feshbach resonances in a 3D spherically
symmetric potential with an open channel interacting with a closed channel.
Analytic expressions for the s-wave scattering length $a$ and number of
resonances are obtained for a piecewise constant model with a piecewise
constant interaction of the open and closed channels near the origin. We show
analytically and numerically that, for strong enough coupling strength,
Feshbach resonances can exist even when the closed channel does {\em not} have
a bound state.
