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From: David Jefferies
Date: 11 Jan 2002
Time: 16:55:27
Remote Name: 195.92.168.165
Hello Taworri,
I've finally got around to this one. I read Langford Smith as you suggested. He quotes the characteristic impedance of a straight wire of diameter d as 138 log10(lambda/d) - 104 ohms, which is equivalent to 138 log10 (0.1764 lambda/d) which is the same as that of a coax cable whose inside sheath radius is 0.1764 lambda or lambda/5.67. This is understandable in terms of the fact that a standing wave of wavelength lambda goes from maximum to zero in a distance lambda/4.....you get the idea. Thus if field lines start from the wire surface, they will have fallen to zero about this distance away from the wire.
The same kind of considerations apply to the capacitance of your disk, which is [4 epsilon d] for a disk or diameter d metres, where epsilon for free space is 8.857E-12 Farads/metre. This comes out at your 0.9pF per inch, quoted from Terman (Ugh! imperial measures cause crashes on Mars - a personal bete noir). Thus, if the dish is of radius greater than lambda/6 you might find the value 0.9pF/inch diameter grossly in error.
It all has to do with the phase shift as light at wavelength lambda propagates across the structure. The transmission line formula allows for this; the electrostatic formla doesn't.
I don't think a transmission line formed from two circular plates, with the generator at the centre and the load at the circumference of the plates, has a constant Zo and so the method wouldn't work.
Hope some of this helps
regards
David.