CONSTANT RESISTANCE NETWORKS 



183 



The second network, which when connected in parallel with Fig. 3 

 will give a constant resistance, is obtained from the first by replacing 

 X by 1/X. It is shown in Fig. 4. 



These structures have been designed on the basis of X being a pure 

 imaginary. Note, however, that the two structures will have a 

 constant resistance provided that X is any function realizable by a 

 combination of resistances and reactances. Equations (8) and (9) 

 will still hold but (3) and (7) will no longer be true. Note, too, that 

 for the simplest case of w = 1 the structures reduce to the usual form 

 for constant resistance networks as shown in Fig. 1. 



-iAW-1 — W\ — T 



•AAAr 



■AA/V- 



. a2>v 



'R=l 



Fig. 3 



an 



AM — T- 



33 ajL 



-AAAri VW 



.-i 





'R=l 



Fig. 4 

 Figs. 3-4 — A pair of constant resistance networks of "constant K" configuration. 



If X is taken of the form i(f/fo), the structure of Fig. 3 will be made 

 up of series coils and shunt condensers in the form of a low-pass filter. 

 The structure of Fig. 4 will be of the form of a high-pass filter with 

 series condensers and shunt inductances. The loss of the first network 



IS 



e2«i = 1 + 



/o 



and of the second 



e2a, = 1 ^ i^j^"' 



With / < /o the loss of the first network will be small and the loss of 

 the second network large. With / > /o the reverse is true. At/ = /o 

 each of the networks takes half of the available power, illustrating a 



