THE ELECTRIC WAVE-FILTER 7 



cross-connections the propagation still remains unchanged. We have 

 again obtained Fig. 4 with no circuit difference except the inter- 

 change of terminals 8 and 7 with terminals 4 and 8; or, if this is ignored, 

 a reversal in the sign of the current at alternate pairs of terminals. 

 This shows that the reveisal of the current in alternate sections of 

 Fig. 4 may not be of primary significance, since networks which are 

 essentially equivalent have reversed currents. 



In order to deal, at the start, with only the simpler terminal con- 

 ditions, we may consider the line to begin with only one-half of the 

 series impedance Zi, or only one-half of the bridged admittance 

 1 'Zo. These mid-points are called the mid-series and mid-shunt 

 points; knowing the results of termination at either of these points, 

 the effect of termination at any other point may be readily deter- 

 mined. For Fig. 4 termination at mid-shunt has been chosen so 

 that each section of the line adds a complete symmetrical mesh to 

 the network. 



An alternator, introducing an impedance Z^, is shown as the source 

 of the steady-state sinusoidal current in Fig. 4. Assume that the 

 impedance Z^ is variable at pleasure, and that it is gradually adjusted 

 to make the total impedance in the generator circuit vanish, — in this 

 case no e.m.f. will be required to maintain the forced steady-state 

 which becomes a free oscillation. If, in addition, it is assumed that 

 the line has an infinite number of sections, this required value of Z^ 

 will be the negative of the mid-shunt iterative impedance^ of the ar- 

 tificial line, which will be designated as K^. The first shunt on the 

 line now includes — X2 in parallel with 2Z2 so that its total impedance 

 is, say, Z'= —2ZiK-i.l(^Zi — K'^. The infinite line with its first 

 shunt given the special value Z' is thus capable of free oscillation. 



It is possible to simplify this infinite oscillating circuit by cutting 



off any part of it which has the same free period as the whole circuit. 



The entire infinite line beyond the second shunt 3, 4 certainly has 



this same free period, provided its first shunt also has the impedance 



Z'. Conceive the shunt Zi at 3, 4 as replaced by the four impedances 



2Z2, 2Z2, + X2 and —Ki all in parallel; the first and last, which 



together make the Z' required by the infinite line, leave 2Z2 and 



^ The "iterative impedance" of an artificial line is the impedance which repeats 

 itself when one or more sections of the artificial line are inserted between this im- 

 pedance and the point ot measurement. It is thus the impedance of an infinite 

 length of any actual artificial" line, regardless of the termination of the remote end 

 of the line. In general, its value is different for the two directions of propagation, 

 but not when the line is symmetrical, as at mid-series and mid-shunt. The values 

 at these points are denoted by Kx and Ki. "Iterative impedance" is employed 

 because it is a convenient term which is distinctive and describes the most essential 

 property of this impedance; it seems to be more appropriate than "characteristic 

 impedance," "surge impedance" and the other synonyms in use. 



