Capacitor Behaviour at Radio Frequencies

We tend to think of components as individual elements in a circuit. At DC and low AC frequencies, this assumption is very nearly true. Those kinds of circuits will behave very close to mathematically derived performance. As the frequency of operation increases, inductance and resistance increase in importance, becoming significant at RF.
The equivalent circuit of a capacitor is shown here. Co is the nominal capacitance value, ESL is the effective series inductance contributed by the capacitor's wire leads and the body of the device, and ESR is the equivalent series resistance. ESL and ESR are frequency dependent, and along with Co, are also temperature dependant. The magnitudes of ESR and ESL depend on the configuration of the capacitor(SMT chip, disc,etc.), the material it is made from (mica, ceramic, porcelain, etc.), and the method of contruction (multilayer, single layer, etc.).

Effective Series Inductance

All wire leads are small inductors. Although components with wire leads are being rapidly replaced by surface mount types, there still is plenty around. The inductance of a straight round wire is:
L= 0.0002b[ln(2 b/a) - 0.75]
where L is the inductance in uH, a is the wire radius in mm, b is the wire length in mm. These values are for a wire in free space. More complex analysis might be more accurate in representing a particular installation, the above equation is sufficient to give us an idea of the magnitude of the leads inductance. For example, a 1/4"(6.3mm) length of #20 AWG (0.8mm diameter) wire has an inductance of 3.4nH.
A chip capacitor may have a series inductance in the range of 1nH or more, depending on its size. A capacitor with leads must include this value in addition to the inductance of the wires.

Effective Series Resistance

ESR consists of the combination of ohmic losses, such as contacts , fingers, leads, and bonded joints, plus dielectric losses. ESR is frequency dependent and will generally be in the range of 0.1 ohm to a few ohms.In some cases, ESR can be as high as a hundred ohms or more. Capacitor manufacturers provide specifications of ESR for various styles of their devices. A very low ESR is needed for a resonant circuit or matching network in order to keep th Q high and losses low. In a bypass or coupling application, ESR is less important.

Series Resonance

Whenever inductors and capacitors are present in the same circuit, they create one or more resonant frequencies. At high frequencies, the effect of resonance on the impedance of a capacitor can be dramatic. A 100pf capacitor with 3.4 nH of lead inductance will have a resonant frequency of 240MHz.
The series inductive reactance is combined with the capacitive reactance, and as frequency increases, the apparent capacitance value increases. The series resonant frequency makes the capacitor actually behave as an inductor, see table for the effect of a 100pf capacitor.

Performance of a typical 100pf capacitor vs frequency

Q Factor

Q factor relates stored energy (pure capacitance) to dissipated energy (loss):
Q = (Xco - X esl)/ ESR
Q is the total reactance over the resistance at the frequency of interest. Q specifications for a capacitor are of little value unless the frequency at which the Q is determined coincides with the desired operating frequency. Don't use manufacturs' Q data without understanding how it was measured. Q is a necessary specificatioon in the design of practical oscillators or filters.

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