Addendum to Ivor Catt,
Addendum written and uploaded on 24feb04
Charge spreading out across the plate of a capacitor
Maxwell and later Heaviside did not realise that a capacitor is a transmission line, along with all lecturers and text book writers worldwide up to the present day. Looking at the conventional way a capacitor is drawn, it appears that the problem the electric charge has, entering the capacitor at only one point and then having to spread out over the capacitor plate, is a trivial one. The distance the charge has to travel looks small. Also, the way it is then distributed seems complicated, but fast. This will lead to some readers of my letter in Electronics World in April 2004 dismissing me as pedantic.
Heaviside’s failure to notice that a capacitor is a transmission line was not the only reason why he failed to notice the flaw in what is said to be Maxwell’s greatest achievement, the “invention” of “The Extra Current”, now called “Displacement Current”. Heaviside described Maxwell a “The heaven-sent Maxwell, a man whose fame, great as it is now, has, comparatively speaking, yet to come.” – O. Heaviside, Electrical Papers, vol. 1, p438.
Failing to notice that a capacitor is a transmission line would have led Heaviside to fail to realise that the electric charge spreads out across the capacitor plate very slowly. Whereas the speed of light, or of a TEM step in a transmission line with vacuum dielectric, is one foot per nanosecond, this speed depends on the dielectric constant of the dielectric. If a capacitor’s dielectric has a dielectric constant of 10,000, the speed of travel for the TEM wave and therefore the speed with which charge spreads out across the plate of a capacitor will be reduced by the square root of 10,000, down to one foot in 10 nanoseconds. 10nsec relates to a frequency of 100MHz. Thus, if a capacitor’s width is one tenth of an inch but it has a dielectric constant of 10,000, a signal will not traverse it in 100 picoseconds. The delay would increase to 10 nsec. When you look at a tiny capacitor, you should try to regard it as very large with difficulty in handling inputs of 100MHz.
I have posted web pages ridiculing the false idea of a capacitor’s “self resonant frequency”. Our December 1978 article asserted that series inductance does not exist in a capacitor. No physical mechanism has ever been proposed for the mechanism of unwanted series inductance, which I attribute to the capacitor’s legs, not to its insides. At this point I need to point out that the time delay in traversing the insides of a capacitor has nothing to do with the phoney idea of self resonant frequency. That is, the round trip across a capacitor and back does not relate to all the nonsense published about “self resonant frequency”. If you investigate someone’s experiment when he thought he was finding the “self resonant frequency” of his capacitor, you will find that his result will depend on the length of the legs he left on his capacitor, and will have had nothing do with the capacitor’s insides, including the delay across the inside of a capacitor.
Ivor Catt 24feb04
Theory of Flight.
The Heaviside Signal http://www.ivorcatt.com/2604.htm
http://www.ivorcatt.com/1_1.htm figures 4, 5.