THE ELECTRIC WAVE-FILTER 13 



It is not necessary to check the table item by item, many of which 

 have already been proven, but it will be instructive to check some of 

 the items by assuming that Z1/4Z2, called the ratio for brevity, is 

 positive to begin with, and that a continuous increase in frequency 

 reduces the ratio to zero and back through =f 00 to its original posi- 

 ti\e value. This cycle starts with a stop ( + ) band since the artificial 

 line is in effect a network of reactances, all of which have the same 

 sign ; there is attenuation and the iterative impedances are imaginary. 

 When the ratio decreases to zero, there must be either resonance 

 which makes Z\ = 0, or anti-resonance which makes Z2 = 00 ; in 

 either case the artificial line has degenerated into a much simpler cir- 

 cuit; it is a shunt made up of all Z2's combined in parallel, or a simple 

 series circuit made up of all Zi's, respectively; the iterative imped- 

 ances are and ^ , respectively ; there is no attenuation in either case. 



With a somewhat further increase of the frequency the ratio will 

 assume a small negative value with the result that the artificial line 

 will have both kinetic and potential energy. An analogy now exists 

 between the artificial line and an ordinary uniform transmission line, 

 which possesses both kinetic and potential energy, and is ordinarily 

 visualized as being equivalent to many small positive reactances, in 

 series, bridged, to the return conductor, by large negative reactances. 

 The fact that uniform lines do freely transmit waves is a well-known 

 physical principle, and it is not necessary to repeat here the physical 

 theory of such transmission merely to show that the same phenomenon 

 occurs with the identical structure when it is called an artificial line 

 or wave-filter. 



In order to determine just how far the ratio may depart from zero, 

 on the negative side, without losing the property of free transmission, 

 we look for any change in the action of the individual section of the 

 artificial line which is fundamental ; nothing less than a fundamental 

 change in the behavior of the individual section can produce such a 

 radical change in the line as an abrupt transition from the free trans- 

 mission of a pass band to the to-and-fro surging of energy in a stop 

 band. Now as the ratio is made more and more negative by the 

 assumed increase of frequency, the value —1 is reached, at which 

 frequency the symmetrical section (Fig. 6) of the artificial line is 

 capable of free oscillation by itself. This is well recognized as a 

 most fundamental change in the properties of any network, and it 

 afifords grounds for expecting a complete change in the character of 

 the propagation over the artificial line. The change must be to a 

 stop band with currents in opposite phase, since at resonance the 

 potentials at the two ends of a section are in opposite phase. 



