APPROXIMATE NETWORKS OF ACOUSTIC FILTERS 



335 



on Fig. 4. These representations follow directly from the T or ir 



2S2V 2 



— wwv — 



PL 

 2S 



SL 

 -OC2 



Fig. 4 



yOL 



s2 V 2 



rVWW — O^MXIS 



SL 

 20C2 



network representation shown on Fig. 3, by open or short circuiting 

 the T and tt networks, respectively. 



B. Lumped-Constant Representation oj an Acoustic Filter 



In his theory of acoustic filters, Stewart has represented an acoustic 

 filter by the network shown on Fig. 5, where Z^ is the impedance of the 



/PL 



s, 



PL 



Fig. 5 



side branch. Stewart has represented the side branch impedance, by 

 either one or two elements, depending on the side branch, and the main 

 branch by a single inductance, equal to the sum of the distributed 

 inductances of the tube. This corresponds to the first approximation 

 of the representation of a line by lumped constants. This repre- 

 sentation gives good results for the low pass filter, but does not repre- 

 sent, very adequately, the band-pass filters. 



The best second approximation for an acoustic filter, employing two 

 elements to represent the main conducting tube, is shown on Fig. 6. 





PL 

 S| 



■ S|L 

 PC2 



;z2 



■ S|L 

 "PC2 



Fig. 6 



