A valve assembly having a position control characteristic that is represented by an N-th order polynomial equation includes a valve housing a valve element, and a valve characterization circuit. The valve housing has at least a fluid inlet, a fluid outlet, and a flow passage between the fluid inlet and fluid outlet. The valve element is mounted on the valve housing, is disposed at least partially within the valve housing flow passage, and is movable between a closed position and an open position. The valve characteristic circuit is mounted on the valve housing, and includes a plurality of resistors. Each resistor has a resistance value representative of at least one digit in the N-th order polynomial equation.