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BELL SYSTEM TECHNICAL JOURNAL 



the frequency, and hence the discrimination obtainable will not be 

 affected. This follows from the network equivalences shown in Fig. 8 

 which were first proved in a previous paper.^ Even if this resistance 

 compensation cannot be completely obtained it can often be obtained 

 over a limited range near the cutoff and the peak frequencies by adding 

 resistances to some of the crystal or electrical elements of such a 

 value that the resistive components of the two arms are nearly equal 

 over a limited frequency range. This results in cutting down the 

 distortion near the cutoff and increasing the loss in the attenuated 

 regions. 



The lattice filters of Figs. 2 to 6 can be realized in ladder or bridge 

 T forms in certain cases. If the two arms have two common series 

 elements, then by the first equivalence of Fig. 8 they can be taken 

 outside the lattice. Similarly, if two common shunt elements can be 

 found in the two arms, then, by the second theorem of Fig. 8, the 



ABC 



Fig. 9 — Method for reducing a lattice filter to a tt network filter. 



elements can be placed in shunt on the ends of the filter. For example, 

 suppose that we consider filter No. 1 of Fig. 2 and shunt the crystal 

 by a capacitance Ci which is equal to the capacitance of the lattice 

 arm as shown in Fig. 9A. Then the two capacitances can be taken 

 out in shunt leaving a crystal in the series arm of a tt network as 

 shown in Fig. 9C. This has the same type of characteristic as the 

 lattice but considerably greater limitations. 



A somewhat more general transformation can be made to a bridge 

 T network of the type shown in Fig. lOA. This network is equivalent 

 to the lattice network shown in Fig. lOB. As is evident, if we have 

 an impedance in parallel with one arm and in series with the other, 

 the resulting lattice can be transformed into a bridge T network. 

 For example, in Fig. 3, filter No. 2, if we reverse the lattice and series 

 arms, which can be done without changing the characteristics except 

 for a 180° phase reversal, the filter can easily be reduced to a bridge 



