Electronic – Why is capacitor a linear element


Why is a capacitor a linear device?

One property for linearity is that the capacitance or some such parameter must not change with voltage or current. Is this enough to make a device linear?

A few sources say that the \$Q=CU\$ has a linear characteristic with voltage and so it is a linear device but wouldn't there be at least one such parameter in a MOSFET/diode that does change with respect to voltage or current in a linear manner – for example the voltage of a diode decreases linearly with the temperature.

So what should I exactly consider for linearity?

Best Answer

First of all, an I-V curve does not make any sense for a capacitor. This is because a capacitor follows the following equation: $$i = C \frac{dV}{dt}$$

Note that the current depends on the rate of change of voltage. So you can have the same current at two different voltages, if the rate of change is the same.

The reason a capacitor is a linear device is because differentiation is linear. Superposition becomes: $$i_1 +i_2 = \frac{d}{dt}(v_1 + v_2) = \frac{dv_1}{dt} + \frac{dv_2}{dt}$$