696 



BELL SYSTEM TECHNICAL JOURNAL 



From equation 7, the admittance of the circuit is expressed in terms of its 

 selectivity, thus 





ii-% 



(29) 



Solving for the selectivity of this circuit, from Equations 28 and 29: 



Q = ^ 



(30) 



The selectivity of the coupling line can hence be counteracted by sub- 

 tracting - from the selectivities of the branches associated with it, provided 



Fig. 8— Schematic diagram illustrating that the selectivity of a quarter wavelength 

 of line can be represented by adding a tuned circuit to each end of an ideally inverting 

 impedance transformer. 



the coupling Une is a quarter wavelength long. If it becomes necessary to 



use f wavelength coupUng lines, the selectivity of the line is tripled and — - 



o 



is subtracted from the selectivities of the associated branches. 



Resonant Cavities 



The foregoing analysis reviews the principles of the design of filters which 

 use lumped-constant circuits distributed along a transmission line. These 

 principles can be applied to the design of filters in waveguides, coaxial lines, 

 or any other types of transmission lines, provided that these lines are suffi- 

 ciently lossless, the band is sufficiently narrow and the branches themselves 

 are realizable. In the microwave region the first two provisions are usually 

 met without difficulty, as is also the third provision when circuits with dis- 

 tributed constants are used. It may be difficult to construct a coil and a 

 condenser circuit for microwaves, but easy to construct a resonant cavity 

 which displays some of the desirable properties of the tuned circuit. Reso- 

 nant cavities are similar to lumped tuned circuits in two respects. ^^ • ^^ They 

 transmit a band of frequencies and they introduce a phase shift. An ap- 

 proximate equivalence is demonstrated in Appendix I, and is illustrated in 

 Fig. 9, which depicts a resonant cavity as being nearly identical with a 



