Self-resonant frequency of a capacitor
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
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
Scandals in Electromagnetic Theory http://www.ivorcatt.com/28scan.htm
8june03 Google Hits no. 4 and 5 (out of a total of 1,200) for "self resonant frequency" + capacitor . (My contradicting hits were 1 and 2 .)
Power Supply Bypassing
How can the voltage spikes be reduced? The solution is in a statement of wishful thinking: if only the fast current changes could be supplied to the circuit locally instead of remotely through LS1 and LS2. This local current source can be in the form of a capacitor CB between VCC and GND.
HANDS-ON DESIGN Add a 0.1uF bypass capacitor by removing the comment character "*" from the CB 3 0 0.1UF statement. Run a simulation and plot Q1 output V(12) and local supply voltage V(3). What happened to the voltage spikes? They should be dramatically reduced. Why? Capacitor CB now supplies the current transient; there are no fast current changes through LS1 and LS2 to create voltage spikes. Add trace I(LS1) in a new plot window to see how the current changes in LS1 have been slowed significantly.
If you increased CB from 0.1 uF to 1.0 uF, CB supplies even more of the current demand locally, requiring even less from VS. At first it seems too good to be true; the larger the value of CB, the smaller the magnitude of the voltage spikes. However, real world capacitors have some disturbing similarities to the power supply leads as will be discussed in the next section.
The bad news is that all real world capacitors have parasitic components similar to the power supply leads: inductance and resistance. What this means is that capacitors can actually be modeled by a series RLC circuit (See Capacitor Model for a review http://www.ecircuitcenter.com/Circuits/cmodel1/cmodel1.htm ). The unexpected result is that the capacitor looks inductive at high frequencies! The switch over from capacitive to inductive behavior happens at its self-resonant frequency. Your circuit may perform poorly if operating above the capacitor's self-resonant frequency. (The good news is you can usually choose a capacitor whose reactance is still capacitive in your frequencies of interest.)
Power Supply Bypassing
(above) is totally wrong. It is particularly damaging because it writes about power supply decoupling, when the truth is, the bigger the capacitor, the better. As I point out below, he is drawing the reader into a trap;
SMALLER IS SOMETIMES BETTER
What we need is a capacitor with a higher self-resonant frequency. And the truth about capacitors is this: for a given capacitor type, smaller capacitor values generally have higher self resonant frequencies.
As I show below, the reason why a smaller value capacitor appears to be better is not because it has lower L, but because it has lower C. We need good decoupling, not a low value for C x L, which means a low value for C.
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 b and separation a. See http://www.ivorcatt.com/2_2.htm “We now calculate the characteristic impedance Zo …..”. The (resistive) impedance is very low because the dielectric constant is very high indeed, and the separation b is tiny. Ivor Catt 18may02
Practical confirmation of my assertion is given below at ****
Google hit no. 9 on 8june03 for "self resonant frequency" + capacitor .
The frequency at which both impedances
Here we see the truth muddled up with old wives’ tales. The writer does not of course realise that the primary reason why the “self resonant frequency” is lower for a large C is that the formula includes the value of C. The “culprit” is a larger C, not a larger L.
Ivor Catt. 18june02
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
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
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
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%.
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.
http://www.ivorcatt.com/em_test04.htm Ivor Catt 18may02
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. http://www.ivorcatt.com/em_test04.htm 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.
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.
Ivor Catt. 18june02
Scandals in electromagnetic theory http://www.ivorcatt.com/28scan.htm
(Possibly we need a standard word for this. I suggest "Riposte", or the symbol [R] .) Ivor Catt, 30june02. firstname.lastname@example.org