MAXIMALLY-FLAT FILTERS IN WAVEGUIDE 



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T Thickness of iris. 



Vynax Maximum voltage on transmission line. 



Vmin Minimum voltage on transmission line. 



0) Angular frequency. 



12 Frequency parameter. 



Y Admittance. 



Fo Surge admittance of transmission line. 



Z Impedance. 



Zq Surge impedance of transmission line. 



THE Y'S ARE USED TO DENOTE 

 GENERALIZED ADMITTANCE FUNCTIONS 



Fig. 1^ — Block diagram of a filter consisting of a ladder network. 



Fig. 2 — ^Schematic diagram of a low-pass filter. 



General 



The art of designing filters which utilize lumped elements is well known. 

 Desirable characteristics may be obtained by means of a ladder network of 

 generalized admittances, such as is illustrated in Fig. 1. In particular a 

 low-pass filter takes the configuration shown in Fig. 2, and a band-pass filter 

 that of Fig. 3. In either case, certain frequency selectivity characteristics 

 can be obtained when the individual branches are assigned definite values. 

 The individual branches, LiCi , L2C2 , in the bandpass filter consist of an 

 inductance, Lr , and capacity, Cr , in series or shunt. For the specific case 

 to be discussed in this paper, namely a filter consisting of lossless elements 

 intended for insertion between a source having an internal resistance R 

 and a receiver having the same resistance, analysis is simplified if a branch 

 is described in terms of its resonant frequency and its loaded Q* The 



* The loaded Q of a resonant branch in such a filter is the reciprocal of its percentage 

 band width measured to the half power points when that branch alone is fed by the same 

 generator and has the same load resistance as that of the total filter. 



