THEORY AND DESIGN OF WAVE-FILTERS 25 



together and are numbered. The subscripts i and 2 on these num- 

 bers refer, respectively, to the mid-series and mid-shunt equivalent 

 wave-filters. The quantities with brackets occurring in some of the 

 formulae are included merely to indicate the origin of their equivalents 

 from the low-and-band pass wave-filters. 



Low Pass Wave- Filters 



These are some of the simplest wave-filters and are here obtained 

 by considering 



/o=/ico=/i = 0. (39) 



In general these wave-filters have three elements per section and are 

 identical with the M-types since there is but a single coefficient 

 m\~m. The "constant k " structure, series inductance and shunt 

 capacity, results when / 2 «, = oo . 



High Pass Wave- Filters 



These wave-filters which are complementary to the low pass wave- 

 filters also have simple structures, in general three elements per 

 section, the M-types. To derive them assume in the general formulae 



/o = 0, 



(40) 



and ji =/ 2 « = oo . 



The additional condition, / loo =0, gives the "constant k" wave- 

 filter of series capacity and shunt inductance. 



Low-and-High Pass Wave- Filters 

 For the low-and-high pass transmission characteristic put 



/!=/*. -00. (41) 



Here some simplifications in notation may be made, as is indicated 

 in the formulae by the quantities in brackets. The general struct- 

 ures, M-types, require six elements per section. A limiting case, the 

 " constant k " wave-filter, having four elements per section, results 

 when /i» = V/o/i =/ 1 » . 



Band Pass Wave- Filters 



With the condition 



/o = (42) 



an internal transmitting band is retained and also the two independent 

 frequencies of infinite attenuation, /i« and / 2 ». Depending upon 



