The Approximate Networks of Acoustic Filters

HE original theory of acoustic filters given by Stewart 1 is based upon the representation of such filters by means of lumped constants in the form of a T network. More recently, the writer 2 has presented a theory of acoustic filters, showing that they are equivalent to a combination of electric lines. Lines, as an approximation, 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. 2 , 3 This first approximation represents the low pass filter well at low frequencies, 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 FILTERS N E T W O R K S OF ACOUSTIC 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 / V MAIN CONDUCTING TUBE Fig. 1 Stewart, Phys. Rev., 20, pp. 528-551, 1922. Phys. Rev., 25, pp. 90-98, 1925. s Mason, Bell System Technical Journal, 6, pp.