More on a capacitor’s self resonant frequency.

Some of those discussing “self resonant frequency” resort to mentioning the inductance of a capacitor’s external leads, in order to hedge their bets under onslaught by me at my web page http://www.ivorcatt.co.uk/26031.htm . I have also had people argue with me that regardless of whether there is internal inductance, the external inductance of its leads still makes the idea that a capacitor has self resonant frequency reasonable.

Berkeley ; “This inductance is exacerbated by the leads of the capacitor, which often dominate the inductance.”

However, it is untrue that even including external leads gives a capacitor a self resonant frequency, for the following reason. When I had a 10v negative 150psec pulse, or spike, travelling down a coaxial cable and wanted a positive one, I connected upstream inner to downstream outer via a 1uF electrolytic, and upstream outer to downstream inner via a second electrolytic. An identical positive pulse emerged. No inductance impeded the flow of the spike, because the leads merely formed a very small segment of the 50 ohm coax cable, admittedly more like 100 ohm “twisted pair”. In my case, as is usual, the two leads to the capacitor entered it at the same end, so there was no inductive loop. The initial impedance presented by each capacitor was resistive, not reactive. The capacitor represented a parallel plate transmission line with very low characteristic impedance.

Introducing a 0.2 inch section of 100 ohm into a 50 ohm coaxial cable has the following effect on a step with 100 psec risetime. The signal is travelling in air at one foot per nsec, so the rising slope of 100 psec has a length of one inch. At the change from 50 ohm to 100 ohm, the reflection coefficient if 1/3. However, an opposite reflection returns at the next change, from 100 to 50 ohms, only 20 psec later, more or less cancelling the first reflection. The result is a reflection of only 1/3 x 1/5, or 7% of the voltage, or 3% of the energy. As to the capacitors, they probably have a characteristic impedance of perhaps 0.01 ohm, causing a reflection of less than 1% since they are in series with a 50 ohm coax cable.

Ivor Catt 18 January 2012