We present progress in the development of a dynamic force reference instrument (KDFR) based on the Kibble principle. We describe the operating principle and design of the KDFR and discuss how the design for alternating current (AC) force measurements contrasts with Kibble balances for mass measurement and necessitates additional corrections to the force calculation. We further analyze the coil impedance, a critical factor for correcting the measured voltage in a single-mode AC Kibble measurement and illustrate a scheme for calibrating its temperature dependence.