This paper explores using electrically induced damping (electrical damping) as a dual indicator to power output and harvesting bandwidth in vibration-based piezoelectric energy harvesting. It evaluates electrical damping's impact on bandwidth and power using an impedance-based unified model. Analytical formulas are systematically developed to quantify the electrical damping and change in system stiffness for harvesters interfaced with various circuit topologies. The relationship between the electrical damping and power is elucidated through both analytical analysis and numerical examples. This electrical damping approach allows for analyzing power and bandwidth simultaneously.