This work describes the modeling and analysis of a low power electronics converter for piezoelectric energy harvesting. The proposed converter consists of a diode bridge rectifier, a MOSFET switch driven by a PWM signal, and a rechargeable battery as the storage device. The circuit is used to convert mechanical vibration energy into electric charge stored in a battery using piezoelectric transducers mounted on a flexible structure. By utilizing an averaging scheme, it is shown that the converter exhibits a pseudo-resistive behavior across its input terminals. An analytical expression for the input resistance of the converter is derived and further evaluated by simulations and experiments. A self-powered converter is utilized to convert vibration energy into electric charge whose input resistance can be set to a prescribed value depending on the input source resistance. It is also shown that by applying a feedback controller to the circuit, the input resistance of the converter can be regulated to a desired value. This feature may be utilized to achieve impedance matching in applications requiring maximum power transfer. Experimental studies are conducted to verify the performance of the self-powered circuit and the feedback control scheme.