IH.I\S\llsSI(>.\ Cll.lh!.U I IKISIICS CI- ll.irr.-III.II.NS oil 

 AI'I'INDIX 



Dl Kl\ \TliiN Ol- I.IM AK rKANM>l(i:K I'oKNH lAl. 



riu- lormiil.i iisi'd in tlu- li-xt for a (lissymiiiftriral rompositi' wa\i- 

 tilltT slnirturi' rontains tho iniase parameters '' and is a special case 

 i>f a general iDrnuiia which is applicable m any linear transducer, 

 acti\e or passi\e. This ^t'licral formula is derixed liere together 

 with other useful ones. 



A linear transducer will lie detineil as an electrical network which 

 has two input and two output terminals and a structure such that so 

 far as these terminals are concerned the currents are linear functions 

 of the potential differences and therefore the principle of superposi- 

 tion holds. The structure may contain sources as well as sinks of 

 enerjiy; that is, the transducer may be acti\e or passive. In the 

 most general case, that of an active dissymmetrical linear transducer, 

 four in<lependent parameters are necessary to specify its electrical 

 properties. Two sets of such parameters will be considered in deri\- 

 in.;; correspondiiii; foriiuilae. the imat;e parameters and the recurrent 

 parameters. 



I. Ima(.i-: F\\k.\.\ii;ti;ks 



1. iicnrrdl I. incur Transducer. The parameters in this case are 

 defined with reference to the single transducer in Fig. 3. Let the 

 terminal impedances in this figure be so chosen that the impedances 

 in the two directions from terminals a are equal, that is, the latter 

 itni)edances are the "image" of each other, and at the same time a 

 similar "image condition" holds with reference to terminals b. With 

 the transducer so terminated, its directional transfer constants are here 

 defined as T.,h = \oiiAh Ih) when transmitting from terminals a to 

 terminals b. and 'J'ha = \i>gAh I,,) when transmitting from terminals b 

 to terminals a. The image impedance \Va of the transducer is the 

 impetlance across terminals a in either direction, and the image im- 

 pedance W'l, is similarly defined at terminals h. In general. Tab and 

 Th,, are difTerent, as are also 11',, and U'^. 



The transducer is now to be terminated by the general impedances 

 Z„ and Zh with an electromotive force £j a|)plied in series with Za- 



'The relarions among five other distinct sets of parameters for a transdiircr 

 (such as a (lassivc onei which can be specified liy three complex parameters were 

 given 1)V <<. .\. t"anipl)ell in ("isftidal Oscillations, Trans. .-X. I. K. K.. \'ol. XXX. 

 Part li; Table I, (). .S85, fJU. The different sets correspond to the four normal 

 networks designated ,is the T, the 11, the transformer, and the artificial line, and 

 to the simple circuit onc-[>oint and two-point im()e'lances. -A sixth set, one-p<imt 

 and two-(x)int admittances, was used in .Appendix 1 of my pa|XT in the H. S. T. J., 

 Jan. l')2.<. 



