30 BELL SYSTEM TECHNICAL JOURNAL 



ponents and differ only in the constant factors involving the network 

 parameters. These corresponding factors in the two expressions 

 are then equated to make the two impedances identical at all fre- 

 quencies and it is this set of equations which leads to the relations 

 between the parameters of the two networks. The list of structures 

 given in Appendix III covers the usual transformations in practice 

 and could be extended by adding more and more elements. 



Among other types of possible substitutions are obviously those 

 involving a change from three star-connected (T) to three delta- 

 connected (n) similar impedances, or vice versa, and from three 

 star- or delta-connected inductances to a transformer with mutual 

 impedance. As a simple illustration consider the mid-series band 

 pass wave-filter VI 1 having series inductance and capacity and shunt 

 capacity which can be put in the form of series inductances connect- 

 ing a series of three star-connected capacities. Changing these 

 capacities into the delta form gives a recurrent structure in which 

 inductances alternate with capacities for the series impedances and 

 capacities form the shunt impedances. Similarly Vi may be changed 

 to a structure in which inductances alternate with capacities for the 

 series impedances and inductances form the shunt impedances. 

 Another structure for the latter is a series of transformers connected 

 by series capacities. 



Composite Band Pass Wave- Filter Illustration 



A band pass wave-filter has been chosen to show what can be 

 accomplished by means of a composite structure towards realizing the 

 ideal of attenuation and impedance characteristics. The transmit- 

 ting band and impedance are specified by 



/, = 4,000 «*, 

 f 2 = 7,000 co, 

 and R = 600 ohms. 



The sections arbitrarily taken to make up the structure are one each 

 of the following: 



IV U M-type, m = .6, (f lm =3739 ~ , f 2 « = 7489~), 

 Zi,/2* = 8300~, 

 and Z7i,/i«=3300~ > 



where a half section of the M-type is placed at each end so as to give 

 the network a symmetrical terminal characteristic impedance of 



