The Correct Equation for the Current Through Voltage-Dependent Capacitors

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: ${\it dQ/dt=d[C(V)V]/dt=C(V)[dV/dt]+V[dC(V)/dt].}$ In the second equation, the term ${\it V[dC(V)/dt]}$ does not exist: ${\it dQ/dt=} {\it C(V)[dV/dt]}$ . 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 ${\it V[dC(V)/dt]}$ in the first equation with the measured capacitance. We also perform a theoretical analysis, which shows that the differential capacitance, ${\it C(V)=dQ/dV}$ , in the correct current equation corresponds to the physical parameters of the diode capacitance.