Capacitor self resonance




A capacitor does not have a self resonant frequency


The ridiculous story about the self resonant frequency in a capacitor.

The legless capacitor

Today, 15th September 2009, the first Google hit out of 400,000 for "self resonant frequency" is the Wikipedia entry. Ivor Catt web pages are hits no. 2, 5, 8 and 35.

Wikipedia nonchalantly discusses the internal series inductance of a capacitor and the self resonant frequency of a capacitor. It elegantly links this with the internal capacitance of an inductor.

Returning to the capacitor, Catt's article in Wireless World, December 1978, says; "Series inductance does not exist. Pace the many documented values for series inductance in a capacitor, this confirms experience that when the so-called series inductance of a capacitor is measured it turns out to be no more than the series inductance of the wires connected to the capacitor. No mechanism has ever been proposed for an internal series inductance in a capacitor."

Now, 30 years later, still no such mechanism has ever been proposed.

If you look at the Wikipedia entry for "self resonant frequency" [now removed. Ivor Catt January 2012] and then click onto "history", you will see the many attempts by me to add a short pointer to my web page, Google hit no. 2, which contradicts the Wikipedia message. You will see that every time, my edit to Wikipedia has been rapidly removed. Once, the comment by whoever removed it was "(Removed self-serving statement that does not have independent support.)". In another case, "Page author linked to own webpage. Webpage was poorly written and inflammatory.)"

In a similar situation, we have to agree that the statement by the small boy that the emperor had no clothes was inflammatory.

We should ponder the arrogance of the person or persons who persistently remove the link between a Google hit no. 1 (out of 400,000) and hit no. 2.


The false idea that a capacitor has series inductance leads designers round the world to wastefully back up each large capacitor decoupling (smoothing) a voltage supply with a so-called "high frequency" capacitor, thought to have a high self resonant frequency. This always has very low capacitance, and I have pointed out why elsewhere. When measuring the so-called self resonant frequency, the experimenter leaves long leads on the capacitor, and so leaves a single turn inductor outside the capacitor. This inductor is generally much the same in val;ue for each experiment. Now the reason why it is thought that a low capacitance capacitance has a higher self resonant frequency is, not that it has a lesser inductance, but that it has lower capacitance. This is buried in the formula for self resonant frequency. The square of the self resonant frequency equals 1/(inductance x capacitance). The capacitor is thought to have a higher self resonant frequency because it has lower capacitance, not lower inductance!

The proper way to reduce the inductance and therefore increase the self resonant frequency (up to infinity), is to cut off the capacitor's legs. Now in no other component is it thought that the component's legs are part of the component.

40 years ago I found a book which listed the self resonant frequency of 20 capacitors of various types - tantalum etc. Extraordinarily, it gave the length of the leads for each capacitor. I found that without reading the capacitor type or make, I could work out its self resonant frequency from its stated capacitance and the stated length of the leads. To calculate the inductance of the leads, I used the formulae now in my book.


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Ivor Catt 22apr02

In 1963 I bought the EH-125 pulse generator. This delivered a –10v step with a 100picosecond fall time into a 50 ohm load (e.g. 50 ohm coax.).

The pulse generator could also deliver a –ve 10v spike with a width of 150psec. I decided to try to create a positive 10v spike. I cut into the 50 ohm coax, and joined the incoming inner to the outgoing outer via a red 1uF tantalum capacitor. I also joined the incoming outer to the outgoing inner via another 1uF tantalum capacitor. Further downstream I found that I had a positive 150psec spike with no discernable degradation (in rise time or pulse width) compared with the initial –ve spike. That is, I had a +ve 10v spike with a width of 150psec.

It is interesting to calculate the physical width of a 150 psec wide spike travelling down normal coax, which has a dielectric with a dielectric constant of 2. Whereas light travels one foot in vacuo in one nsec, it would travel 8 inches in material with a dielectric constant of 2. Thus, a 150psec spike in the coax has a width of about one inch. So I sent a TEM spike with a width of 1 inch through these 1uF capacitors. [Note 1] Obviously, I kept their legs short. It is sad that during the ensuing 40 years the New York IEEE and the London IEE prevented me from informing electronic engineers that they did not have to add “high frequency” decoupling capacitors to their logic boards, that the 1uF would do perfectly well on its own. This obstruction has cost the industry many millions of pounds. However, a bolshie IEEE and a bolshie IEE cost us a lot more than that in other ways. Ivor Catt 22apr02

Note 1.

Anyone who wants to play with frequencies can be told that the fundamental of the 150psec spike will be around 3GHz. Put that in your “self-resonant” pipe and smoke it! IC

Note 2.

As the spike passes the capacitors placed to each side, the situation is as in Figure 14. The characteristic impedance of each capacitor is very small, less than 1% of 50 ohms. Thus, the mismatch is less than 2%, causing a minimal reflection of less than 1%.

At the same time, if the legs of the capacitors are kept down to a total of one quarter of an inch in length, and the two parallel legs represent a quarter inch transmission line of characteristic impedance 150 ohms, then the mismatch will cause a reflection of 50%, see Figure 11 and the reflection formula. This will be reduced by the fact that the 150psec spike covers a distance of one inch and a half, so that the reflections on entering the 150 ohms region tends to be masked by the opposite mismatch on re-entering the 50 ohm impedance of the next section of coax. This reduces the reflection to one sixth, i.e. 8%.


It all began in Phoenix, Arizona in 1964. We had received a split contract (the other. competing company being Texas Instruments) to deliver a (partially populated) 64 word memory, 8 bits per word, in nine months. Access time, write time and cycle time to be 20 nsec. We could achieved this with chips which contained two bits of memory and had an access time of 2 nsec (as I remember) . Our logic gates, ECL, has a switching time of 1.35 nsec - I am sure of that figure.

In the event, we delivered on time, as did TI. However, since our access time etc. was 14 nsec and theirs was (I think) 17 nsec, we got the follow-on contract.

I decided to have a voltage plane, 5v or 0v, between asignal layers, with the result that the mother board, something less than one foot cube, had thirteen layers.

I had to determine what was the source impedance at a point between two voltage planes, the one at 0v and the other at 5v. How much of the two panes word help to decouple 5v in the first fraction of a nanosecond, when I knew that any signal travelling in the epoxy glass dielectric only went 6 inches in a nanosecond. Bill Herndon told me; "It's a transmission line". (See Figure 1 in our December 1978 article. .) He told me that it was not his idea, it was Stopper's, whom I never met.

It is not clear how long after this that I realised that a capacitor was also a transmission line with two parallel planes. It was then clear that a capacitor could not have internal series inductance, and also that the transient impedance of a capacitor was resistive, not reactive. Also, this resistance, or actually characteristic impedance between the two capacitor planes must be very small. That meant that the alleged series inductance in all capacitors, which was rearing its ugly head and indicating that the voltage supply to even faster logic could not be decoupled - that our logic was the fastest possible - was not a problem,

Today, 40 years later, it is still falsely believed that a capacitor has internal series inductance and thus a self resonant frequency. It I try to point out the error into the Wikipedia entry for "self resonant frequency", my comment is immediately removed.

Ivor Catt 15.9.2009






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