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By J. H. Gridley, P. Hammond

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D. at the sending end to be unaffected by the circuit connected to it, the source must be regarded as having zero internal impedance, the consequent current doubl­ ing effect on the wave k'^VJZ^) ύηω{ί-2χ) adding to the original current an increment Ik^VJZQ) sin ω ( ί - 2 τ ) . Clear­ ly, the next term corresponds to the arrival at the source of a wave which started a time 4r before the instant we consider, and which has been reflected from the far end, source, and far end again. Now there is a well-known identity between exponential and circular functions e>i = cos ωί-^j sin ωί FINITE LOSS-FREE LINES 55 or sin ωί = 3(e>0> where the symbol 3 denotes "imaginary part of".

V and current VJZQ travels towards the load end. In time t = //c, say r = r, these waves impinge on the load resistance, 50 FINITE LOSS-FREE LINES 51 F I G . 1. P . D . Kapplied to loss-free line terminated in resistance R. raising its potential from zero to = where, from eqn. 6), {2RI[R-\-Zo])V. d. d. v^j^ impinging on the source, but opposite in sign. d. d. d. reflected from the source travels towards the load, arriv­ ing there after time τ from the incidence of on the source. d. -v^j at the load raises its potential by an amount -k^v^j^ or, since v^i = k^V, by an amount —ktk^v^^.

At termination of line of Fig. 1. 3. d. F volts to a loss-free hne terminated in resistance R resulted eventually in a sensibly steady flow of current V/R amps, the steady state being approached by a series of reflec­ tions of diminishing amplitude. The exercise was primarily undertaken to bridge the gap between the distributed circuit theory of the present study and the lumped circuit theory familiar to the reader. The latter theory should now be regarded as a limiting case of the former, to be used directly when line lengths are short compared with the time of wave propagation.

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