610 



BELL SYSTEM TECHNICAL JOURNAL 



former are adjusted to resonate at the same frequency. The determi- 

 nation of the constants for the circuit so that it conforms not only to 

 the requirements relating to the band selectivity and to the voltage 

 transformation ratio, but also to requirements of transmission effi- 

 ciency, is explained in the following mathematical analysis. 



For convenience in analyzing the essential parts of Fig. 1 they are 

 shown in a simplified schematic form in Fig. 2. In this schematic, 



I \NW^ 



E,(a^ 



P-M 



S-M 



:C2 



Fig. 2 — "T" network of a transformer coupling circuit. 



the sending-end impedance Zo corresponds to the effective plate 

 impedance of the first vacuum tube and the electromotive force Ei 

 corresponds to the internal plate voltage of this tube. The trans- 

 former formed by inductances P and 5 is replaced by the well known 

 "r" network.^ The capacity Ci is provided by a separate condenser, 

 while that of G is equal to the effective distributed capacity of winding 

 S plus the effective input capacity of the second vacuum tube. 



The method used in computing the output voltage of a transmission 

 circuit such as is shown in Fig. 2 consists in determing the "image" 

 impedances corresponding to each pair of terminals. These image 

 impedances are determined from the open and short-circuit imped- 

 ances, measured at the terminals of the network,^ by the following 

 relationships: 



Zi, 2 = ^z7z7, (1) 



and 



Z3. 4 = VZo"Zs", (2) 



where Zo' and Zs equal respectively the open and short-circuit 

 impedances and Zi, 2 the image impedance at terminals 1, 2 and Zo" 

 and Zs" equal the open and short-circuit impedances and Z3, 4 the 

 image impedance at terminals 3, 4. 



Since the resistance elements of a transformer of this type can be 

 made very small in comparison to the reactance elements, it is practical 

 to eliminate them in computing the open and short-circuit impedances. 



1 "Telephone Transformers," by W. L. Casper, A. I. E. E. Jour., March, 1924, 

 Vol. XLIII, No. 3. 



^"Transmission Characteristics of Electrical Wave Filters," by O. J. Zobel. 

 Bell Sys. Tech. Jour., October, 1924, Vol. Ill, No. 4. 



