Why do some books use dQ/dV for capacitance?

[Rib5]

Hi guys,

Today was the second time in a textbook that they calculated capacitance using $$C = \frac{dQ}{dV}$$. In my electromagnetics book and any sources I find online they use $$C = \frac{Q}{V}$$.

Can anyone help me understand why they can do it like this? This type of calculation was done to calculate the zero bias junction capacitance of a pn junction diode.

 

[phyzguy]

For a linear capacitor, it doesn't make any difference, but for devices like diodes and transistors where Q is not a linear function of V, then it matters. For these non-linear devices, the differential capacitance dQ/dV is typically referred to as the "capacitance". This confused me also when I first started studying devices, but it is just a matter of convention. I think it arose because people were using these devices in small signal circuits where what mattered was the response of the capacitor to a small change in voltage. In any case, if you look up a "C-V diagram" for a diode, MOS capacitor, or some other non-linear device, what is actually being plotted is dQ/dV vs V.

 

[Rib5]

Thanks for the reply, that explains a lot. It seems like in a lot of books they leave out a lot of the conclusions or assumptions that they make.

So basically it can be treated the same as a regular capacitance as long as the change in differential capacitance over the voltage range used isn't very big and mostly linear.