Impedance measurements were made on SPRITE (signal processing in the element) detectors. The resistive contributions were found to contain a contact resistance term, along with a term proportional to the semiconductor material length between terminals. The capacitive contributions were strongly frequency dependent and were largely independent of material length. This behavior would appear to be caused by nonohmic contacts at the metal-semiconductor interfaces where the SPRITE is bonded to its external electrical connections. When the SPRITEs were illuminated, the resistance decreased as expected, but the capacitance showed a sizable increase as well. A T-network model is developed that is consistent with the set of two-terminal impedance measurements. A model of this type should provide a useful starting point for electronics optimizations in SPRITE systems, including the design of the bias source, the readout mechanism, and the preamplifier.