318 BELL SYSTEM TECHNICAL JOURNAL 



and xvc is made up of one positive branch. 

 II.— High Pass 



U, = -ij) ^ (^4) 



and Xik consists of one negative branch. 

 III. — Low-and-High Pass 



Uk — 7~1 77 7~T2 ' (^^) 



/O/I //la / 



where j\a = y/o/i, the anti-resonant frequency where Uu = <» and 

 xifc = CO , For this class xu: has a positive branch from to fxa and a 

 negative branch from fu to oo . 



IV. — Band Pass 



C/, = M_ l^-^ - -^ V, (36) 



(/2-/l)n f UrI ' 



where /ir = V/i/o, the mid-frequency or resonant frequency where 

 Uk = and xu- = 0. Here xik is made up of a negative branch in the 

 frequency range from to/i,- and a positive branch from/ir to oo . 



2.5 Equivalent Structures 



Many structures can be obtained which are externally equivalent to 

 each of the above transducers ; in fact, an infinite number is possible. 

 That this is so can be seen from a consideration of the general trans- 

 ducers of Fig. 11, for example. It will not even be necessary to 

 include the entire networks in this discussion but only the branches 

 containing three impedances of two kinds, Zik and Zofc- The branch 

 containing one of Zn- in parallel with the series combination of one of 0u- 

 and one of Zok may be transformed completely by a well-known formula 

 into one of Zn in series with a parallel combination of one of z^ and one 

 of Z'2K- No change in the number of impedance elements results and the 

 magnitudes are fixed. If, however, an arbitrary part of the original 

 parallel Zik branch is kept out of the above transformation the final 

 equivalent structure would have one more Zik impedance and one more 

 mesh than the original. The proportions of each impedance may 

 obviously be varied continuously as the arbitrary division is so varied, 

 thereby giving an infinite variety of magnitudes. This four impedance 

 structure, equivalent to the original one, reduces at the limits to the 

 two structures each having three fixed impedances, as we know. A 

 similar process can be carried out with the shunt branch in the shunt 



