14 



BELL SYSTEM TECHNICAL JOURNAL 



Further increase in the frequency cannot make any change in the 

 absolute difference in phase between the two ends of the other section, 

 since opposition is the greatest possible difiference in phase; the wave 

 now adapts itself to increasing frequency by altering its attenuation. 



Upon continuing the increase of frequency, so as to reduce the 

 ratio to — 00 , we arrive at either anti-resonance corresponding to 

 Zi = 00 or resonance corresponding to Z2 = 0; the artificial line has 

 now degenerated into a row of isolated impedances Z2, or into a series 

 of impedances Zi short-circuited to the return wire; in either case 

 the attenuation is infinite since no wave is transmitted. Passing 

 beyond this critical frequency the ratio becomes positive, according 

 to our assumption, and we are again in a stop (-f ) band. 



While in this rapid survey of what happens during this frequency 

 cycle little has been actually proven, it should have been made 

 physically clear why abrupt changes in the character of the trans- 

 mission occur at the frequencies making the ratio equal to 0, — 1 or 

 00 , since the line degenerates into a simpler structure, or the phase 

 change reaches its absolute maximum, on account of resonance, at 

 these particular frequencies. 



500 Cycles 1000 



Fig. 7 — Graph for Locating the Pass Bands and Stop Bands of Fig. 4 

 Z, = -i(P - x2)(62 - .r2)/8.v(32 - .r^), 



-4Z2 = -t4x(4=' - x2)/(22 - x2)(52 - -v^) and x = cycles/100 



