Capacitors are the most interesting electrically in the same way that the sickest person in an emergency room is the most interesting medically. They have more fine details than the resistors and inductors, so I will try to attack the problem in four sections: device parasitics, dielectric absorption, dissipation and temperature effects.

As for parasitics, we first take an ideal capacitor (C) and put a resistor in series, this will be the leakage resistance (RL), then we add a series RC circuit (DA), which will be due to dielectric properties, then we put in a series resistance (ESR) and inductance (ESL), which will be due to the packaging. Starting from the simplest part first, the capacitor is a real device and the conductors have real resistances, so the sum of all of these ohmic losses can be described as the ESR. Next, we have the ESL. This is a physical property of a real device and is heavily dependant on capacitor construction. Capacitors that are radially wrapped, like some electrolytics, have the highest ESL while parallel plate chip capacitors have the lowest. For this reason some datasheets recommend two bypass capacitors of different sizes for fast ICs. That is, due to the series LC, each capacitor has a frequency at which they have the lowest impedance, so the bypass capacitors are tuned in such a way that they have lowest impedances at frequencies at which other components operate. This way one IC can decouple from other ICs running at different frequencies etc. The leakage resistance is due to the finite resistance of the dielectric material as well as the finite resistance of the packaging material.

Dielectric absorption deserves a long essay, but will get a mere paragraph. The best description of the phenomenon is an analog memory in a capacitor. That is, if a capacitor is charged to a voltage V1, then disconnected from the voltage and the leads are shorted for a brief period of time, and then opened again, the capacitor will show a slight voltage across the terminals when the device should be discharged and the voltage should be zero. This voltage depends non-linearly on the input voltage and can create errors in sample-and-hold circuits and integrators. Not all capacitors exhibit DA on the same scale: electrolytic are the worse while polystyrene and polypropylene are the best.

The dissipation factor describes the various finite resistances in the non-ideal capacitor model. It is effectively a measure of how long a capacitor can hold its charge after the charging voltage is disconnected. The leakage parameter is often specified as a megaohm-microfarad product which describes self-discharge time in seconds. This can be anywhere from 1 second in electrolytic capacitors to 1,000,000 seconds in Teflon and film devices. The leakage, ESL and ESR are lumped together to define the dissipation factor (DF), where DF is inversely proportional to the Q factor.

As far as temperature effects go, capacitors suffer from all of the problems that inductors and resistors suffer from along with non-linear changes in dielectric properties due to change in temperature. These are often specified in ppm around a certain temperature where they are linear-like. It is also important to note that the capacitors maximum working temperature is heavily dependant on the manufacturing technology. Polystyrene capacitors have a upper working limit of about 80C while Teflon capacitors can be used all the way up to 200C.

This is by no means a comprehensive overview of non-ideal capacitor properties, merely an introduction.

 
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