The Correct Equation for the Current through Voltage-Dependent Capacitors

Abstract

Two different equations for the current through voltage-dependent capacitances are used in the literature. One equation is obtained from the time derivative of charge that is considered as capacitance–voltage product: dQ/dt=d[C(V)V]/dt=C(V)[dV/dt]+V[dC(V)/dt]. In the second equation, the term V[dC(V)/dt] does not exist: dQ/dt= C(V)[dV/dt]. This paper clears the ongoing confusion caused by the difference between these two equations. We use the voltage-dependent parasitic capacitance of a commercial Schottky diode in reverse bias mode to test experimentally both equations. The result is that it is incorrect to add the term V[dC(V)/dt] in the first equation with the measured capacitance. We also perform a theoretical analysis, which shows that the differential capacitance, C(V)=dQ/dV, in the correct current equation corresponds to the physical parameters of the diode capacitance.