The goal of this research is to increase the bandwidth (BW) over which substantial energy can be harvested using a piezoelectric energy harvester (PEH). The key innovation is the use of bias-flip (BF) electronics at the output of a PEH having a large electromechanical coupling coefficient $κ_{e}^{2}$. For a PEH with large $κ_{e}^{2}$, the open-circuit resonance frequency $f_{oc}$ is substantially larger than the short-circuit resonance frequency $f_{sc}$. Over the intervening range, the reactive part of the conjugate matched load impedance is small, and can be approximated using BF electronics in which the BF voltage is sufficiently small and the BF losses are small. This results in a large BW over which substantial energy can be harvested. Experimental results using a commercially available PEH are presented to demonstrate this concept. Design guidelines are provided for achieving PEHs having increased $κ_{e}^{2}$.