THE TRANSISTOR AS A NETWORK ELEMENT 



345 



High Pass 



Consider next a high pass filter with cut-off at coo- The transmission is 



e = 



cco^p^ 



(1 + Wo V + '^o V)(l + «o V) 



o^oY 



1 -j- ap 



_(1 + cooV)(l + apJLl + cooV + WoV. 



The complex plane plot in Fig. 12(b) shows exactly the same pattern of 

 singularities as the low pass case with the addition of three zeros at 

 the origin. To realize this function the feedback network remains un- 

 changed, whereas the input network becomes a ladder in which the 

 positions of the resistances and capacitances are interchanged. 



Band Pass 



A series resonant branch inserted in series between resistive termina- 

 tions is a simple form of band pass filter having the following trans- 

 mission : 



e = 



V 



r -1/^-1 



1 + ^mOr^v + t^mV Li«+ «P_ 



Qv 



I + ap 



Ll + co-iQ-ip + 



OmY. 



where Wm is the radian frequency of the peak and Q is a measure of the 

 sharpness of the peak. 



The singularities shown in Fig. 12(c) consist of a zero at the origin and 

 two complex conjugate poles. Once again the complex poles are obtained 

 b}' a bridge circuit in the feedback path. The usual penalty is incurred 

 by the appearance of a real zero which must be cancelled by a real pole. 

 Therefore the admittance function must supply a zero at the origin and 

 one real pole. This is done by a series combination of resistance and 

 capacitance in the input circuit. 



Band Elimination 



A parallel resonant branch inserted in series between resistive ter- 

 minations is a simple form of band elimination filter having the following 

 transmission: 



2 



e = 



II -2 2 

 1 + w,„ p 



1 + <^m^QV + <^inV~ 



1 



+ 



co,„ p 



I -\- ap 1 + ap. 



1 -f ap 



_\ + oiJQp + oiJp-_ 



The singularities consist of two conjugate zeros on the real freciucncy 

 axis and two complex conjugate poles. A bridge circuit in the feedback 



