Timeline for Why is the capacitance calculated with small-signal variables the same as the capacitance from the basic steady-state formula?
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| when toggle format | what | by | license | comment | |
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| Nov 5, 2022 at 12:08 | vote | accept | zraibra | ||
| Nov 3, 2022 at 18:01 | comment | added | hyportnex | yes, that "C" is the linearized capacitance while the ratio of the integrals as you wrote it correctly now represents the static operating ("large signal")point representing the average $V$ or $E$ around which the tangent is the linearized ("small signal") capacitance. Is it clearer now? | |
| Nov 3, 2022 at 17:53 | comment | added | zraibra | That means, that the "small signal capacitance" from $C=\frac{Im(\underline Y)}{\omega}$ is the linearized version of a nonlinear (changing) capacitance in that specific operation point. That's why it can be compared to the static or linear version, only for that operation point, right? Also then the equation should be $\frac{\oint_S Dds}{\int_L Edl}$ | |
| Nov 3, 2022 at 14:37 | comment | added | hyportnex | Also, in a capacitor, $Q$ is the surface integral of the $D$ field over one of the plates, while $V$ is the line integral of the $E$ field from one plate to the other; the ratio you wrote is above not the definition of these quantities. | |
| Nov 3, 2022 at 14:30 | comment | added | hyportnex | There is no meaningful way to have a "general" capacitance if the $D=D(E)$ relationship is nonlinear just as the amplification or gain of nonlinear amplifier is not meaningful. The function $y=f(x)$ with $f(0)=0$ can be written as Taylor expansion $y(x)=K_1x+K_2x^2+K_3x^3...$ but unless $|x| \ll 1$ you do not have a useful linear approximation such as $y \approx K_1x$ and the concept of capacitance is a linear approximation to the function $Q=Q(V)$ or $D=D(E)$. | |
| Nov 3, 2022 at 14:14 | comment | added | zraibra | So what would be the generalized definition of the capacitance then? Or do I just have to use a more generalized formula like: $$ \frac QV=\frac{dD/dv}{\int_A^B Ddl} $$ | |
| Nov 1, 2022 at 14:42 | history | answered | hyportnex | CC BY-SA 4.0 |