DISTORTION CORRECTION 453 



of propagation these two ladder sections have the same iterative 

 impedance and propagation constant. In the full-series section ter- 

 minated by R the junction point between R of the section and Z21 is 

 short-circuited with the point at the receiving side of Zn, while in the 

 corresponding full-shunt network the structure is the same except that 

 these two points are open-circuited. Because of the identity of 

 propagation constants this can be possible only if the two points are 

 at the same potential whence they can be connected by any impedance 

 without altering propagation in the one direction. This being the 

 case, a branch of resistance R, conjugate with the sending branch, 

 can be connected across these points, and this results in giving the 

 symmetrical bridged-T (I) type (where c = 1), or the equivalent net- 

 work of Fig. 7 terminated by R. Thus the receiving-side series 

 resistance R in the limiting case (c = 1) of the bridged-T (I) section 

 plays no role and is superfluous for this direction of transmission, but 

 it makes the section symmetrical and ensures similar propagation 

 and impedance characteristics when transmitting in the opposite 

 direction. ^^ 



If, in the network of Fig. 7, Zn is made resonant and anti-resonant 

 at different frequencies, selective maximum energy transmission can 

 be obtained at these frequencies between pairs of the four different 

 resistance branches which might also be considered as different lines. 

 The propagation constant between any pair of resistances can be 

 determined from the relationships established above. 



As an aid in obtaining an approximate value of the propagation 

 constant for any of these types when its impedance elements are known, 

 a simple chart may be drawn up if desired. This could be obtained 

 in the following manner. The formulae (12) to (15) are all of the form 



gr = ^A+iB — ^ _|_ ^-^j 



whence 



qA _ -^^2 j^ ^2^ Q5^ 



and 



tan B = film. 



Thus, it is evident that any locus of uniform attenuation constant, A, 

 is represented in the m, n plane by a circle of radius, e^, with center 

 at the origin. Also, any locus of uniform phase constant, B, is a 

 straight line of slope, tan B, starting from the origin. 



" Another method of deriving the section having directly the form given by putting 

 c = 1 in the bridged-T (I) type was used by G. H. Stevenson, U. S. Patent No. 

 1,606,817, November 16, 1926. 



