Capacitor Self Resonant Frequency

A capacitor has no self resonant frequency. This is because it has no internal series inductance.

The L-C-R model for a capacitor is false.

A capacitor is a two conductor transmission line in the manner of a 50 ohm coaxial cable (slit down the side and opened out flat), but with extremely small characteristic impedance [Note 1.]. Like the coaxial cable, the transient, initial impedance of a capacitor when presented with a voltage step is resistive, not reactive.

The so-called self resonant frequency results from the inclusion of a capacitor’s legs as part of the component. The formula for self resonant frequency is ω = 1/√LC , where the L is the inductance of the single loop made up of the capacitor’s legs, external to the component. [Note 2.]

The idea that low value capacitors have a better high frequency performance came from the fact that the above formula for self resonant frequency ω = 1/√LC gives a higher value if either L or C are reduced. If the legs stay the same, L stays the same. So change in self resonant frequency results from reducing the value of C. Ergo, low value capacitors have a higher self resonant frequency. The worst capacitors are the best.

Note 1. For the Zo of a transmission line, see http://www.ivorcatt.org/image/page95xtra-large.gif

A number of factors combine to give a capacitor a very low characteristic impedance Zo, and thus a very low transient resistance when addressed by a voltage step. First, the thickness of the dielectric d is very small. Second, the width of the top and bottom plates w which make up the capacitor is relatively very large. Thirdly, the dielectric constant of the dielectric is very high indeed.

Note 2. The following pages may help you to grasp the real physical make-up of a capacitor, as opposed to the conventional, false, LRC model.

http://www.ivorcatt.org/icrwiworld78dec1.htm . Actually, Figure 2 on page 2 is a more accurate depiction of a real capacitor than is Figure 1. A capacitor is a parallel plate transmission line with connections at one end. This is represented in Figure 2 by the two lines to the right of the resistor and battery.

http://www.ivorcatt.co.uk/4_5.htm . Here we see the true nature of the oscillation when an inductor is connected to a capacitor. It is not a sine wave, but rather a series of steps.

Ivor Catt. June 2002

“A capacitor is a two conductor transmission line in the manner of a 50 ohm coaxial cable (slit down the side and opened out flat), but with extremely small characteristic impedance [Note 1.]. Like the coaxial cable, the transient, initial impedance of a capacitor when presented with a voltage step is resistive, not reactive.”

This was an unfortunate statement (above) in 2002, and missed the key point. The key statement is that when a demand is made on a charged capacitor, charged to 5v, it initially behaves like a 5v battery with a source impedance of (say) 0.1 ohms. So if the initial current demanded is 100ma, the voltage output will drop by IR = 0.1 amps x 0.1 ohms = 0.1 x 0.1 = 10mv, from 5v to 4.99v. There will be no limiting series inductance.

This situation lasts for the time it takes for a signal to travel from end to end in the capacitor and back, similar to the charging situation in my article , at which time the 5v will drop a little more, to slightly over 4.98v. This time delay may be 5 nsec, because the speed of propagation of a signal in the very high permittivity Ɛ between the plates of a capacitor is very slow. It will be slowest (best for us) in the supposedly worst type of hi value capacitor, electrolytic.

Ivor Catt     October 2012