COAXIAL AND BALANCED TRANSMISSION LINES 



281 



case the filter parameters take on the simple form 

 cosh r = 



. C0(2/i + /2) 



sm 



sm 



aji2 



and K = Zo, J - tan — ^ tan '^i^^i±Al . (16) 



For this case the lower side of the pass band occurs when cosh F = + 1 

 and the upper side when cosh T = — 1. Hence the frequency limits 



50 



y 30 



3TT 

 4 



5TT 

 4 



3TT 



2 



7-rT 

 4 



VALUE OF -^^ IN RADIANS 



Fig. 2— Attenuation characteristic of band-pass filter. 



of the first pass band can be obtained by solving the transcendental 

 equation 



. o)(2li -\- h) ^ . wh „ 

 sm T sm — = 0, 



V V 



which has the solutions 



/i = 



V 



4(/i + h) ' 



h = 



V 



4/r 



(17: 



Hence by making the shunting line very short, it is possible to obtain 

 a narrow band with this type of filter. The mid-frequency of the 

 band occurs when 



. o^{2k + h) . 

 sm = 



or when 



Jm -r- 



V - All + 2/2 ' 



The characteristic impedance of this type of filter becomes very high 

 for narrow-band filters as is shown by equation (16). At the mean 



