418 



BELL SYSTEM TECHNICAL JOURNAL 



resistances in such a way as to make a constant resistance attenuator of 

 essentially the same impedance as the filter. For a series coil, this 

 can be done by putting a shunt resistance between sections, while for a 

 shunt coil it can be done by putting series resistances between sections. 

 If this is done the whole effect of the dissipation is to add a constant 

 loss to the dissipationless filter characteristic, this loss being independ- 

 ent of the frequency. 



Since the lattice type network provides the most general type of 

 filter network, attention will first be directed to this type of section 

 employing inductances. It is easily proved that if any impedance is in 

 series with both sides of a lattice network, as shown by Fig. 10^, then 



A c 



-*^AAAA/ ^AAAA 



•-AAAA/— 



Fig. 10 — Two network equivalences. 



this is equivalent to placing this impedance in series with each arm of 

 the lattice network as shown. Similarly, if a given impedance shunts 

 the two ends of a lattice network, as shown by Fig. lOB, a lattice net- 

 work equivalent to this is obtained by placing the impedance in shunt 

 with all arms of the lattice. We are then led to consider a lattice net- 

 work which contains coils either in series or in shunt with the arms of a 

 lattice network, these arms containing only crystals and condensers, 

 since the dissipation will then be effectively either in series or in shunt 

 with the lattice network section. 



If an inductance is added in series with a crystal the resulting re- 



