The Correct Equation for the Current Through Voltage-Dependent Capacitors
Utkarsh Jadli, Faisal Mohd-Yasin, Hamid Amini Moghadam, Jordan R. Nicholls, Peyush Pande, Sima Dimitrijev
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: <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\it dQ/dt=d[C(V)V]/dt=C(V)[dV/dt]+V[dC(V)/dt].}$ </tex-math></inline-formula> In the second equation, the term <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\it V[dC(V)/dt]}$ </tex-math></inline-formula> does not exist: <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\it dQ/dt=} {\it C(V)[dV/dt]}$ </tex-math></inline-formula> . 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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\it V[dC(V)/dt]}$ </tex-math></inline-formula> in the first equation with the measured capacitance. We also perform a theoretical analysis, which shows that the differential capacitance, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\it C(V)=dQ/dV}$ </tex-math></inline-formula> , in the correct current equation corresponds to the physical parameters of the diode capacitance.