The Approximate Networks of Acoustic Filters 



By W. P. MASON 



The approximate equivalent electrical networks of acoustic filters are 

 developed in this paper, from the lumped-constant approximation networks 

 for electric lines. In terms of this network, design formulae have been 

 developed for all single band pass filters. It is possible, from these formulae, 

 to determine the physical dimensions of an acoustic filter necessary to have 

 a given attenuation and impedance characteristic. 



THE original theory of acoustic filters given by Stewart ^ is based 

 upon the representation of such filters by means of lumped 

 constants in the form of a 7" network. More recently, the writer ^ 

 has presented a theory of acoustic filters, showing that they are 

 equivalent to a combination of electric lines. Lines, as an approxi- 

 mation, can be represented by networks with lumped constants, and 

 hence an acoustic filter has a lumped-constant approximation network, 

 which should represent the filter well at low frequencies. It is here 

 shown that the network proposed by Stewart is a first approximation 

 to the network of electric lines given in the former paper.^-^ This 

 first approximation represents the low pass filter well at low fre- 

 quencies, but does not very adequately represent the band-pass filters. 

 Accordingly, a second approximation is developed. All of the single 

 band-pass filters have been analyzed and design formulae are given 

 for them in terms of the second approximation network. 



The Approximate Lumped-Constant 

 Networks of Acoustic Filters 



An acoustic filter, as developed so far, consists of a main conducting 

 tube, and a side branch. In a symmetrical filter, the side branch is 

 connected to the main conducting tube half-way between the two ends, 

 as shown on Fig. 1 . The type of filter obtained depends primarily on 



SIDE BRANCH 



/ 



^MAIN CONDUCTING TUBE 



Fig. 1 



1 Stewart, Phys. Rev., 20, pp. 528-551, 1922. Phys. Rev., 25, pp. 90-98, 1925. 

 * Mason, Bell System Technical Journal, 6, pp. 258-294, 1927. 

 ^ This fact has also been pointed out by Stewart, Journal of the Optical Society, 

 July 1929, and by Lindsay, Phys. Rev., 25, pp. 652-655, 1929. 



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