THE TRANSISTOR AS A NETWORK ELEMENT 343 



N'on-inductive Filters 

 Low Pass 



Consider first an iinaj>;t' parameter, constaiit-A', low pa.ss filter which 

 is usually built as a ladder-type structure of series iiiductaiice and shunt 

 capacitance. A full section contains three reacti\-e arms and jii'oduces an 

 asymptotic loss that increases 18 db per octa^•e. 



The transmission is given by the following expression 



(1 + coo V + ^0 V) (1 + '^o V) 



where coo = cut-off frecjuenc}^ in radians per second. 



The function has three poles, one real and two complex conjugate. 

 The cjuestion now arises how this function can be divided between the 

 input and feedback networks so as to be physically realizable. Since we 

 know that a passive R-C structure cannot have complex poles in the 

 short circuit transfer admittance, there is no choice but to use the 

 impedance function in the feedback circuit for this purpose. It is now 

 found that any R-C structure which will provide the complex poles insists 

 on providing a real zero for good measure. This unwelcome zero can be 

 nullified by supplying its counterpart as a pole in the admittance func- 

 tion. The transmission is now rewritten, as follows: 



e-' = 



1 



_(1 + co^V) (1 + ap)_ 



1 + ap 



I -\- coo^p -{- 0)0 y. 



and the singularities are shown in Fig. 12(a). Since the original transmis- 

 sion function also rec[uires a real pole, the admittance function must now 

 suppl}^ two real poles. A simple ladder structure having three seiies 

 resistances and two shunt capacitances meets this requirement. The 

 complex poles cannot be supplied by a ladder structure, but require some 

 sort of l)ridge such as shown in Fig. 12(a). 



At low freciuencies the transmission through the filter depends on the 

 ratio of the total series input resistance to the total resistance in the 

 bridge arm of the feedback network. Therefore any amount of flat loss 

 or a moderate flat gain through the filter can be obtained simph' by 

 adjusting the ratio of impedance levels of the input and feedl)ack net- 

 works. 



Simulation of functions by this technique does not provide a unique 

 solution since there is considerable freedom in choice of configuration 

 and location of the cancelling pole and zero. 



