284 



BELL SYSTEM TECHNICAL JOURNAL 



The filter discussed above shows some of the possibilities and limita- 

 tions of filters constructed from transmission lines. Many other types 

 are also possible. Figure 4 lists a number of these and the types of 

 filter characteristics they give. The design equations for a number of 

 them are considered in detail in the patent referred to above and hence 

 will not be worked out here. 



IV. Impedance Transforming Band-Pass Filters Employing 

 Transmission Lines as Elements 



In a good many cases it is desirable to transform from one impedance 

 to another over a wide range of frequencies. Examples of such uses 

 are when antennas are connected to transmission lines, or when trans- 

 mission lines are to be connected to vacuum tubes, etc. Transforming 

 band-pass filters constructed out of transmission lines which will 

 transform over wide frequency ranges are therefore of practical interest. 

 Previously two types of single-frequency transformers, constructed 



-rrrrj'/j'////7// 



Fig. 5— A wide-band transformer — constructed from coaxial conductors. 



from transmission lines, have been suggested ^ but these differ from the 

 types investigated here in that they have a specified ratio of impedances 

 for a single frequency only. 



One of the simplest types of band transforming filters is shown by 

 Fig. 5. It consists of a series transmission line of characteristic im- 

 pedance Zoi and a shunt line having the characteristic impedance Zog. 

 Since the impedance of the short-circuited line is 



• ^ . C0/2 

 JZ02 tan — , 



the equations for the structure are 

 ei = ei cos-^ 7*/Zoi sm — ; 



ti — ti cos 



V 

 CjoIi 



V 



tl 



ei 



0)1 1 



J 7- sm — 

 Zoi V 



t2 = — 



12 + H ; 



>0 



ei 



eo; 



(19) 



Z02 tan 



wh 



' See reference 1, pages 430 and 431 . 



