... updated 27 August 2003
I had thought that Ivor had deleted this section from his website as it is clearly erroneous.
Given that electromagnetism is evidently a subject of great interest to engineers, Ivor's site attracts a respectable volume of readers. It is therefore worthwhile correcting one of the most blatant and demonstrable errors on the website.
Ivor claims that capacitors do not have self-inductance if measured without their leads. He makes this claim on purely theoretical grounds. The problem with this assertion is that it relates to no known real-world components! The application note from American Technical Ceramics (ATC), rubbished by Ivor, is actually excellent, and is well worth reading.
A capacitor has capacitance. It also has parasitic inductance and resistance. These are measurable and quantifiable. Nowadays electronics designers working on high density or high frequency designs use surface mount components almost exclusively. There are no lead wires to worry about, and the inductance is then due to the path length within the body of the part. The inductances are quite small, of the order of 2nH, but are nevertheless important in RF designs.
Good text books make the distinction between low frequency capacitance and high frequency capacitance. Why? Capacitance changes with frequency, even for solid dielectric capacitors! Now I am not just talking about rubbish dielectrics such as X7R and Z5U. These Class II and Class III dielectrics are no use at all for any sort of "analog" applications because the capacitance changes with temperature, time and frequency by extraordinarily ridiculous amounts (see manufacturer's data sheets).
Even for good dielectrics like NP0 ceramic, polyester and air, the capacitance INCREASES with frequency. Now you know that the impedance of a capacitor decreases with frequency You learnt this at school. Well using complex arithmetic, by which I mean maths in the form of a+jb, where j is the square root of minus one, you can work out what the measured value of a capacitor would be if you consider a real world device to have a small parasitic inductance in series with the capacitive element. The maths shows that the measured capacitance actually increases with frequency until the capacitor hits its first self-resonant frequency.
If you are unwilling or unable to do the maths, then you can look up the measured impedance curves given by all volume manufacturers of capacitors. The impedance curves drop at 20dB/decade initially, but as they approach the self-resonant point, the curve slope increases slightly, showing a rising capacitance!
The theory is explained in detail in this excellent application note from American Technical Ceramics. Effective Capacitance vs Frequency by Richard Fiore of ATC.
Impedance measurements on capacitors have been an essential part of the traceability of resistance to national standards and the inter-relationship between the various SI electrical units. You would therefore expect that national metrology institutes such as the UK National Physical Laboratory (NPL) and the USA equivalent (NIST, formerly National Bureau of Standards, NBS) would have expert knowledge on the subject. Such impedance measurements are done using "four terminal pair" connections. An Internet search on "four terminal pair" will reveal some interesting and relevant papers on the subject. NBS impedance measurements on capacitors
Whether the parasitic inductance of a surface mount capacitor is identically equal to a body-length sized wire is a debatable point. It is also true that making the capacitor body shorter, as for example used in microwave capacitors, is an important way of increasing the self-resonant frequency of a capacitor. But in the real world the capacitor does have a finite amount of self-inductance which does adversely affect its performance in real-world applications.
Ivor has made a test using 1µF coupling capacitors well above their self-resonant frequency with apparently no ill effects. This is an interesting observation and deserves a response. With increasing frequency a capacitor first becomes self-resonant and attains a minimal impedance. As the frequency is further increased, the capacitor looks like an inductor. Further increase of frequency causes the inductance to become self-resonant and an impedance maximum is reached. The impedance then starts to fall again with increasing frequency. This pattern of peaks and troughs in the impedance continues as the frequency is increased, but all of this behaviour is remarkably uncontrolled, undefined and unpredictable in its detail. With increasing frequency it is likely that the impedance peaks will be lower and the troughs higher, the resonant Q factors getting lower with increasing frequency.
When used as a coupling capacitor, you can get away with a lot more series impedance than is tolerable for a decoupling capacitor. If the capacitor looked like 1 ohm for example, it would only serve to give additional insertion loss. I have done a simulation of Ivor’s experiment using SIMetrix. Using a 1 ohm impedance to represent the loss in the capacitors the output signal is only reduced by 2%. You should understand that getting accurate voltage readings on a 150ps pulse with a sampling scope based on 1965 technology is not an easy thing to do. It is not at all clear whether Ivor would have been able to see a 1% or 2% reduction in the signal amplitude or indeed whether such a loss would have been seen as important enough to record at the time. There is also no guarantee that the sampling scope would have been accurate to better than 5% when comparing a positive going pulse to a negative going pulse at these edge speeds.
As a matter of practical experience when working on a DC to 1GHz oscilloscope amplifier, I have had to prevent 700MHz oscillations by changing an 0603 10nF decoupling capacitor to a 100pF 0603 decoupling capacitor.
Ivor has got himself a bit confused about transmission lines and real components. Ivor says that capacitors are really transmissions lines and should be treated as such. This is a bit backwards. According to electromagnetic theory, everything is based on Maxwell's theory, transmission lines, waves, fields and so forth. All very complicated. Rather than confront the huge mass of differential equations necessary to solve even simple problems, practical engineers have come up with "lumped element models". Rather than consider a coil of wire as a transmission line, it is easier to consider it as "an inductor". This approximation is only valid up to a certain limiting frequency where the phase shift of the current in the wire becomes too great. When the phase shift is relatively small the system is described as "quasi-static" and the simple lumped element approximation is used. We know it is not exact, but it is good enough for engineering purposes. Thus Ivor has "invented" non-quasi-static systems, something known about for over a century! It has to be said in Ivor's defence, however, that such descriptions are not usually seen in modern electronics books, but were published in some good text books between say 1930 and 1955.
REFERENCESLow frequency capacitance versus high frequency capacitance: 1) "Radio Engineering" by F.E.Terman, 3rd edition, 1947. section 2.5 page 28. 2) "Radio Engineers' Handbook" by F.E.Terman, First Edition 1943 (1950) para 32, page 120.
Distinction between distributed and lumped impedances: 3) "Communication Networks", vol II, "The classical theory of long lines, filters and related networks" by E.A. Guillemin. 1935, pages 1-6.
Maths involved for low frequency vs. high frequency inductance: 4) "RF-inductor modelling for the 21st century" by L.O.Green. EDN magazine, Sep 27th 2001.