MAXIMALLY-FLA T FILTERS IN WA VEGUIDE 685 



ripples in the pass-band than on maximally-flat structures. The work of 

 Bennett will be followed closely not only because it came first, but also be- 

 cause it is easy to understand. 



Bennett expresses the values of the filter branches in terms of their cutoff 

 frequencies, which in turn bear a relationship to the cutoff frequencies of the 

 total filter. In the language of one who is familiar with microwave tech- 

 nique,^ , 10 , 11 , 12 |-j^g values of the filter branches can be expressed in terms of 

 the loaded Q's of the cavities, which in turn bear a relationship to the loaded 

 Q of the total filter. A simple mathematical expression connects the loaded 

 Q to the cutoff wavelengths. 



At low frequencies the band-pass maximally-flat filter is .made up of 

 resonant branches connected alternately in series and in parallel. The 

 microwave analogue of this configuration is obtained by the use of shunt 

 resonant cavities that are spaced approximately a quarter wavelength apart 

 in the waveguide. Use is made of the impedance inverting property of a 

 quarter wave Hne, thereby eliminating the necessity of using both series and 

 parallel branches. 



The resonant cavity in the waveguide resembles a shunt resonant tuned 

 circuit,^^ but is different in several minor respects. An analysis of these 

 differences reveals the corrective measures that are necessary in order that 

 the simulation shall be sufficiently accurately attained. 



The first part of the paper deals with the concepts of loaded Q and reso- 

 nant filter branches of both the series and the parallel types. Admittance 

 and impedance functions, as well as expressions for the insertion loss, are 

 given using these terms, and the relationship between loaded Q and cutoff 

 frequencies is stated. This concept of loaded Q is then introduced to de- 

 scribe the performance of a complete maximally-flat filter in terms of its 

 cutoff frequencies. The insertion loss is then given as a simple expression 

 containing the total Q and the resonant frequency. The ^'s of all the 

 branches are derived from the total Q in simple terms. The connection be- 

 tween the insertion loss and the input standing wave ratio is then discussed 

 before turning to the actual design problem. 



Next the paper deals with the application of the filter theory to wave- 

 guide technique. The limitations of the quarter-wave coupling lines are 

 pointed out and the added selectivity due to them is derived. 



Then the paper compares microwave resonant cavities with parallel- 

 tuned circuits. Formulas are given which relate the geometrical configura- 

 tion to the loaded Q, the resonant frequency and the excess phase of the 

 cavities. Three types of cavities are treated: those using inductive posts, 

 inductive irises and capacitive irises. 



Finally, the measured results on a four-cavity maximally-flat filter in 1" X 

 2" waveguide are presented and compared with the original design points. 



