We introduce a simplified effective-range function for charged nuclei, related to the modified $K$ matrix but differing from it in several respects. Negative-energy zeros of this function correspond to bound states. Positive-energy zeros correspond to resonances and ``echo poles'' appearing in elastic-scattering phase-shifts, while its poles correspond to multiple-of-$\ensuremath{\pi}$ phase shifts. Pad\'e expansions of this function allow one to parametrize phase shifts on large energy ranges and to calculate resonance and bound-state properties in a very simple way, independently of any potential model. The method is first tested on a $d$-wave $^{12}\mathrm{C}+\ensuremath{\alpha}$ potential model. It is shown to lead to a correct estimate of the subthreshold-bound-state asymptotic normalization constant (ANC) starting from the elastic-scattering phase shifts only. Next, the $^{12}\mathrm{C}+\ensuremath{\alpha}$ experimental $p$-wave and $d$-wave phase shifts are analyzed. For the $d$ wave, the relatively large error bars on the phase shifts do not allow one to improve the ANC estimate with respect to existing methods. For the $p$ wave, a value agreeing with the $^{12}\mathrm{C}(^{6}\mathrm{Li},d)^{16}\mathrm{O}$ transfer-reaction measurement and with the recent remeasurement of the $^{16}\mathrm{N}\phantom{\rule{4pt}{0ex}}\ensuremath{\beta}$-delayed $\ensuremath{\alpha}$ decay is obtained, with improved accuracy. However, the method displays two difficulties: the results are sensitive to the Pad\'e-expansion order and the simplest fits correspond to an imaginary ANC, i.e., to a negative-energy ``echo pole,'' the physical meaning of which is still debatable.