# Self resonant frequency of a capacitor

When will this nonsense end? When will  Dr. Mike Blewett , late of Surrey University, stop teaching nonsense? Since I mentioned him, he has slipped from no. 2 to no. 9.

Searching “self resonant frequency”, I have Google hit no. 1, and three hits out of the first five out of 6 million. Mine have been there for years. Yet no professor or text book writer has approached me. They continue to “teach” their students how to measure this non-existent “self resonant frequency of a capacitor”    Ivor Catt  6 April 2014

Electrical resonance occurs in an ceramic capacitor at a particular resonance frequency where the imaginary parts of the capacitor impedance and admittances cancel each other.

Since a capacitor is a transmission line, it has no series inductance and so no self resonant frequency. Although Google for “self resonant frequency” puts Catt’s observation above Wikipedia’s at the front of two million hits, any link to Catt’s hit put in Wikipedia is removed.

[September 2013 update. In Google, Catt is still no. 1 hit out of 4 million for “self resonant frequency”. Wikipedia have removed their web page for “self resonant frequency”! Yet Wikipedia does not ban entries on what does not exist. See http://en.wikipedia.org/wiki/Ghost . Ghosts does better with 70 million hits.]

In 2014, Google continue the nonsense here . Note;The smaller the capacitance C and the inductance L the higher is the resonance frequency.” The “best” capacitor is the worst capacitor.

Most of the web pages criticised below have disappeared. I suggest you do a Google search for “capacitor self resonant frequency” to read today’s culprits. IC 2011

Self-resonant frequency of a capacitor

Unfortunately, most of the web pages hyperlinked to below have disappeared

Nonsense about so-called “self-resonant frequency” of a capacitor.

If you cut off a capacitor’s legs at the knees, you will double its self-resonant frequency – Ivor Catt

Charge spreading out across the plate of a capacitor

My 1994 book Electromagnetism 1 is at http://www.ivorcatt.com/em.htm

Nigel Cook on Ivor Catt’s ideas, (London) Electronics World (was Wireless World), aug02, pp46-49

More nonsense is at http://www.ivorcatt.com/2605.htm

#### Yet more nonsense

Scandals in Electromagnetic Theory  http://www.ivorcatt.com/28scan.htm

# RIPOSTE Ivor Catt's view of Capacitors, by Leslie Green CEng MIEE

http://www.atceramics.com/pdf/technotes/effective_capacitance_vs_fr.pdf     talks about self-resonant frequency.   The “parasitic inductance” does not exist inside the capacitor. However, the article is very primitive, because the graphs go in the wrong direction, with C increasing with frequency, anyway. The alleged L reduces the C, not increasing it as the author seems to think.

“the capacitor can be used up to the natural self-resonant frequency or”

Unfortunate students are made to measure the “self-resonant frequency” of a capacitor. Tell them to cut off the poor capacitor’s legs!

http://www.capacitors.com/consider/consider.htm

This guy is stumbling in the right direction, but he gets his number wrong. Inductance caused by the legs should be proportional to the length of the legs.

“Lead length alters a capacitor's range of operating frequency. Here a 2 uf capacitor's self-resonance decreases from 490 kHz to 290 kHz when its leads are lengthened from 3/8 inch to 3 inches. In other words, the capacitor's usable operating range is reduced by almost half.”

More nonsense;

http://www.qsl.net/kf4trd/varactor.htm

your poor capacitor behaves just like an inductor! The frequency at which both impedances
are equal is known as the self-resonant frequency. This frequency is
set by the materials used and the construction of the capacitor.

http://www.emf-emi.com/dosanddonts.shtm

Ensure that the SRF (self-resonant frequency) of capacitors is above the highest frequency to be bypassed.

…. 10.) Select and mount decoupling capacitors having self-resonance (SRF) above logic band-width (1/)

http://www.cypress.com/pub/appnotes/decouple.pdf

This writer is in a bad way. Pure fantasy.   – IC

What a pity this poor fellow has been pulled from the www by his paymasters. The hyperlink now jumps straight to another page, bypassing the nonsense I saw on 30jan02. Perhaps I have influence! Ivor Catt. 5may02

http://www.benchmarkmedia.com/appnotes-a/caig/caig06.asp

However, all capacitors have their own self-resonant frequency

To avoid series inductance, a well behaved capacitor keeps its legs together – Ivor Catt

Update 12 years later on 14 February 2014. All but one of the above web pages have been removed!

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The amount of nonsense drifting around the world, of which the above are examples, is vast.

See my 1978 article at http://www.electromagnetism.demon.co.uk/z001.htm ; 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.”

The key point in my article is that No mechanism has ever been proposed for an internal series inductance in a capacitor.”

The IEE and IEEE have helped to cause the confusion to escalate by suppressing my 1978 article http://www.electromagnetism.demon.co.uk/z001.htm , which puts an end to a capacitor’s series inductance. Also, competent experimentation will show that a capacitor has no internal series inductance.  http://www.ivorcatt.com/em_test04.htm

Ivor Catt, 30jan02

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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 http://www.ivorcatt.com/2_1.htm 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 http://www.ivorcatt.com/1_4.htm 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%.

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18may02   More drivel. Fig. 2 at  http://www.ultracad.com/seminar_caps.htm

Google Hit no. 7 for   “self resonant frequency” + capacitor

This article high on the Google hit list has row of capacitors, and each one decouples (digital electronic equipment for) its particular frequency range.

This farce is obvious if one realises that a 2uF capacitor is made by glueing together two 1uF capacitors. Thus, a supposedly “high frequency capacitor” is merely the front little bit of a 1uF capacitor. Of course, you can ruin the performance of either by leaving it with long legs, making a series one-turn inductor to stifle its performance. However, the idea that a 10pF capacitor has shorter legs than a 1uF capacitor is based on nothing at all.

Since a capacitor is a two-conductor transmission line with very low characteristic impedance, the transient impedance that it presents to a step is resistive, not reactive. This is the way it behaves when decoupling digital circuits; as a local energy store for the 5v supply with a very low resistive source impedance, not a reactive source impedance. Calculation of the impedance is made by using the normal formula for the characteristic impedance of a transmission line made up of two parallel plates with width a and separation b. See p73 of my book “Electromagnetics 1”, pub. Westfields 1975. The (resistive) impedance is very low because the dielectric constant is very high indeed, and the separation b is tiny.   Ivor Catt   18may02

In the surreal world created with inappropriate mathematical stunts by physically ignorant operators, a capacitor is looked on with disdain, not because it has more L, but because it has more C.

Ivor Catt  18may02

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Recap. Take the formula for the resonant frequency for an inductor-capacitor tank circuit.

The frequency (in radians per sec.) squared equals (1/ inductance x capacitance)

Thus, either increase in inductance or increase in capacitance reduces the resonant frequency. This has led physically ignorant mathematical mugwumps to think, not that the best capacitor has the least capacitance, which even they might realise is ridiculous, but that the best capacitor has the least inductance, making it able to perform to a much higher frequency up to its higher resonant frequency. They have failed to realise that they would realise their dream, of a high self resonant frequency, by reducing the capacitance just as well as by reducing the inductance. They think that it is an accident that lo value capacitors have the highest self resonant frequency. They think it is because of the difference in inductance, which it is not.

However, all this is nonsense when decoupling digital logic. What matters with digital logic is the transient performance of a decoupling capacitor, when some switching logic wants to grab as much charge as possible to launch down a transmission line  towards the next logic gate. The true model, which should have replaced the series L C R model for a capacitor, was already published in 1978, http://www.electromagnetism.demon.co.uk/z001.htm  , and has been ignored for 24 years by radio men who continue to teach and publish the old model which is inappropriate and damaging in digital electronics. Note that today, most capacitors are used in DC voltage decoupling.

The only way out of this impasse is for students to create problems during the lecture when lecturers continue to pump out the old, wrong drivel. Otherwise these lecturers and text book writers will continue to copy and repeat each other from a bygone age when electronics was about radio, and such a misconception about the physical nature of a capacitor was not so damaging.  Students have much to gain by disrupting their lectures. It is probably more difficult to learn and be examined in material which is false. Ivor Catt.   18may02.

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In 1965, living in the USA, I telephoned the design engineers in Sprague, who manufactured capacitors. They told me that they tested for the high frequency performance of a capacitor by testing at 5kHz and 50kHz, and deduced its performance at 1MHz and above using the series L C R model. Thus, the published self-resonant frequency of a capacitor is the result of lo frequency testing extrapolated using the L C R model.

By making this error, engineers in the capacitor manufacturers might have doubled their companies’ sales, ensuring that a second “high frequency” capacitor would be added to every 1uF decoupling capacitor in every digital system.          Ivor Catt   18may02.

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In the Wikipedia case below the legs were left the same, so L was constant. So-called “self resonant frequency” duly increased by a factor of 3 each time C was reduced by a factor 10. Resonance is when ὡ=1/√LC. So with L constant, ὡ increases by a factor 3 when C falls by a factor 9. The capacitor has nothing to do with this “self resonant frequency”, which depends on its external legs. The capacitor itself has no internal series inductance.

Sample self-resonant frequencies for one set of C0G and one set of X7R ceramic capacitors are:

 10 pF 100 pF 1 nF 10 nF 100 nF 1 µF C0G (Class 1) 1550 MHz 460 MHz 160 MHz 55 MHz X7R (Class 2) 190 MHz 56 MHz 22 MHz 10 MHz

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Source of a Capacitor’s so-called “ self resonant frequency

Riposte
I make the commitment that anyone wishing to counter any assertion made on this site will be guaranteed a hyperlink to a website of their choosing at the point where the disputed assertion is made.    ivor@ivorcatt.com

Ivor Catt. 18june02

Scandals in electromagnetic theory  http://www.ivorcatt.com/28scan.htm

x

(Possibly we need a standard word for this. I suggest "Riposte", or the symbol [R] .) Ivor Catt, 30june02.   ivor@ivorcatt.com