Figuie 6. A transmission line resonator (as described by Tesla in US Patent # 593,138 ■ November 2, 1897)
It is noteworthy that, in the days of Breit, Tuve, Cockioft, Walton and Van Dc Graaff, a complaint against spark gap transmiiters and high voltage RF generation by distributed resonance transformers was that their output was too broadband! (These early pioneers of nuclear science merely required high energy —not high power.)
The relevant physical processes by which high voltage is produced on microwave resonators is common knowledge.37 Consider the generic transmission line shown in Figure (i. The coordinate origin is taken at the load and a time harmonic generator drives the input end at x = - (. The voltage at any point along die line is then given by the expression
where x=0 at the load and x -- - f at the generator end. Physically, Equation (26) expresses the fact that the voltage at any point aiong the transmission line is the superposition of a forward travelling wave and a backward travelling wave. The resultant analytical expression describes □ spatially distributed interference pattern called a standing wave. As usual, y is ihe complex propagation constant y^et+jP The complex constants V+ and V_ follow from the second order partial dif-
■ <rntinl equation of which equation (16) 1» * solu-a-« (the "transmission line equation"), ind depend ■cut the boundary conditions (the generator and fcr load).
' i, .n the load end one may define the complex Lkl reflection coefficient T:
(27) r=vyv.=jri Ifi h" »n open circuited liner=I|D .
I r. m equation (26) we have, at the input end of Cm line, re, again, F is a complex quantity. Also from i ution (26), we may write the voltage at the load rod as:
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