26 BELL SYSTEM TECHNICAL JOURNAL 



propagation constant. It has now been shown with complete gener- 

 ality that: 



The lattice artificial line, with physically realizable branch impedances , 

 is identically equivalent in propagation constant and mean iterative 

 impedance to the chain of identical physically realizable networks con- 

 nected, together in sequence through tivo pairs of terminals. 



To complete this simplification of the generalized artificial line it is 

 necessary to know the simplest possible form of the one-point im- 

 pedances employed in the branches of the lattice network. The 

 discussion of the most general one-point impedance obtainable by 

 means of any network of resistances, self and mutual inductances, 

 leakages and capacities will find its natural place, together with 

 allied theorems, in a paper on the subject of impedances. For the 

 present purpose it is sufficient to state: 



The most general branch impedance of the lattice network may he 

 constructed by combining, in parallel, resonant circuits having im- 

 pedances of the form R-\-iLp-\-{G-{-iCp)~^; or they may equally 

 well be constructed by combining, in series, anti-resonant circuits having 

 impedances of the form \G-\-iCp-\-{R-^iLp)~^Y~^ 



Summary of Physical Theory 



The wave-filter under discussion approximates to a resistanceless 

 artificial line, and such an ideal artificial line is capable of two, and 

 only two, fundamentally distinct states of motion. In one state the 

 disturbance is attenuated along the line, and there is no flow of energy 

 other than a back and forth surging of energy, the intensity of which 

 rapidly dies out along the line. In the other state there is a free 

 flow of energy, without loss, from section to section along the line, 

 with no surge of energy between symmetrical sections. Each state 

 holds for one or more continuous bands of frequencies; these bands 

 have been distinguished as stop bands and pass bands. 



A high degree of discrimination, between different frequencies, 

 may be obtained, even if each section, taken alone, gives only a 

 moderate difference in attenuation, by the use of a sufificient number 

 of sections in the wave-filter, since the attenuation factors vary in 

 geometrical progression with the number of sections. 



Any number of arbitrarily located pass bands may be realized by 

 means of the lattice artificial line; furthermore, the propagation 

 constant at one frequency, and the iterative impedance at one fre- 

 quency may both be assigned, while the location of zero phase con- 



