328 



THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 



6. Filters or Selective Networks 



Filters offer another particularly simple illustration of the potential 

 analogy. The object of a filter is to transmit all frequencies in a prescribed 

 range and to block all other frequencies. This means that the potential 

 must be substantially constant in the pass-band, and large and negative 

 in the stop-band. Now the potential inside a conductor is constant, hence 

 charge distributions on conductors should yield transmission functions of 

 filters. 



POSITIVE CHARGE 



DISTRIBUTED ON A 



CONDUCTING SHIELD 



'FIELD OUTSIDE 

 SHIELD 



DOUBLED DENSITY 

 ON HALF CONTOUR 





X 



\ 



SYMMETRY RELATIVE 

 TO EACH AXIS 



LUMPED 'charge 

 APPROXIMATION 



\ 



GAIN 



UNCHANGED 



AT REAL OJ 



RFAL D 



(a) CLOSED CONTOUR 



(b) 



HALF CONTOUR 



Fig. 6 — Analogy between filters and conducting shields; (a) positive charge distributed 

 on symmetric shield, (b) lumped charge distribution on half of contour. 



Figure 6 illustrates the analogy between filters and conductors, or shields. 

 The first condition in the set (28) requires that the shield must be symmetric 

 in the real />-axis. Symmetry about the co-axis is not necessary, but it i^ 

 usually advantageous. The third condition of (28) requires that the charge 

 on the shield should be positive, in the absence of external charges. Positive 

 charges determine the poles of F(p), and must therefore he in the left half 

 of the />-plane if the network is to be physically realizable. In the shield, 

 on the other hand, there are positive charges in both halves of the />-plane, 

 so that we cannot use the charge distribution on the shield without modi- 



