Transmission Characteristics of 

 Electric Wave-Filters 



By OTTO J. ZOBEL 



SvNOPsis: The tr.insmi^iun loss characteristic of a transmitting network 

 .IS a function of frc<|uency is an index of the network's stea<ly-state selective 

 properties. Methods of calculation heretofore employed to determine 

 these characteristics for composite wave-filters are long and tedious. This 

 iviper gives a methtxl for such determinations which greatly simplilies 

 .ind shortens the calculations by the intro<liiction of a system of charts. 

 .\ccount is taken of the effects of both wave-filter <lissipation ami terminal 

 conditions. The mcthoti is Ixisetl upon formulae containing new para- 

 meters, calletl "image parameters," which are the natural ones to use with 

 composite wave-filters. 



A detailed illustration of the use of this chart calculation method is given 

 and the transmission losses so obtained are found to agree, except for dif- 

 ferences which in practice are negligible, with those obtained by long direct 

 computation. 



In the .Appendix are derived two sets of corresponding formulae which 

 arc applicable to a linear transducer of the most general type, namely, an 

 active, dissymmetrical one; the one set contains image parameters and 

 the other set recurrent parameters. .•\n impe<lance relation is found to 

 exist between the four open-circuit and short-circuit impedances of a linear 

 transducer even in the most general case. Reduction of these formulae to 

 the more usual case of a passive linear transducer is also made, those con- 

 taining the image parameters being especially applicable to the case of 

 composite wave-filters. 



I. I.NTRODICTION 



ELECTRIC \va\c-filtcr characteristics and systematic methods 

 of deriving them have been considered in previous numbers 

 of this Journal.' This paper deals with a simple and rapid method 

 of calculating the steady-state transmission losses of vva\e-filter net- 

 works over both the transmitting and attenuating frequency bands, 

 including the effects of dissipation and wave-filter terminal condi- 

 tions. Such transmission loss determinations are essential in showing 

 the selective characteristics of these networks and serve as important 

 guides in meeting given design requirements. 



General formulae for any dissymmetrical linear transducer are 

 derived in terms of new parameters, called image parameters. One of 

 the formulae is fundamental to the solution of the present problem 

 and is particularly well adapted to calculations in composite wave- 

 filter structures. These parameters of such a composite structure, 

 being readily obtainable from those of its parts, are the natural 

 parameters to use in this case. The formula possesses, among others, 



' Physical Theory of the Electric Wave-Filter, G. A. Campbell, B. S. T. J., 

 .Nov., 1922; Theory- and Design of Uniform and Composite Electric Wave-I'ilters, 

 O. J. Zobel, B. S. t. J., Jan., 1923; Transient Oscillations in Electric Wave-Kilters, 

 J. R. Carson and O. J. Zobel, B. S. T. J., July. 1923. 



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