574 BF.LL SYSTEM TECHMCAL JOURNAL 



transfer constant and image impedances of a single section, and tlu' 

 propagation constant and mid-point characteristic impedances ol the 

 corresponding ladder network. 



3. The transfer constant of a symmetrical mid-series or mid-shunt 

 section is equal to the propagation constant of the corresponding ladder 

 type; that of a dissymmetrical mid-half section {having mid-series and 

 mid-shunt terminations) is equal to one-half the above propagation 

 constant. 



4. The image impedance of a mid-point section at a mid-series or 

 mid-shunt point termination is equal to the mid-series, Ki, or mid-shunt, 

 K2, characteristic impedance, respectively, of the corresponding ladder 

 network. 



Formula (3) is for the present purpose superior to the well known 

 formula for transmitted current (derived for comparison in the Ap- 

 pendix) which contains the transducer recurrent parameters in the 

 form of its propagation constant, T, and characteristic impedances, 

 Ka and Kt,. The reason for this is that in a dissymmetrical com- 

 posite wave-filter where Ka differs from Kb, the usual case, no simple 

 relations exist between these latter parameters of the transducer 

 and the corresponding [jarameters of the individual sections com- 

 prising the network. In the special case of symmetrical networks, 

 however, the latter formula becomes identical with (3) which follows 

 from what has already been said. 



Another method of obtaining the transmitted current, which may 

 be termed the "section-by-section elimination method," consists in 

 calculating by the aid of the KirchholT laws the current ratios and 

 total impedances from section to section back through the entire 

 network beginning at the receiving impedance. From the standjioint 

 of time economy certain objections may be raised to the possible use 

 here of this general long hand method of calculation. The melliod 

 carries with it the determination of the phase as well as the amiitiliide 

 of the transmitted current; but since the amplitude only is rctjuired 

 in the transmission loss formula, this method does more than is 

 necessary. Again, an alteration in the composite network structure 

 re(|uires a more or less complete recalculation when this method is 

 emi)loyed, whereas by the application of (3) it will be found that this 

 is not necessary. However, this method is useful where irregularities 

 exist in the network, f)r where the particular method of design which 

 had been followed in obtaining the composite structure cannot readily 

 be found, but ils impedance elements and R are known. 



