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Why do some books use dQ/dV for capacitance?

  1. Aug 28, 2010 #1
    Hi guys,

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

    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.
  2. jcsd
  3. Aug 28, 2010 #2


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    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.
  4. Aug 28, 2010 #3
    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.
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