THE TRANSISTOR AS A NETWORK ELEMENT 



347 



\i(les ii total change in phase of 1S()° and is characterized b.y a sinf>;le 

 pole-zero pair symmetrically located on the a axis as shown in Fig. 13(a). 

 Only one parametei-, the distance from the origin can l)e chosen. The 

 second degree structure provides a maximum phase shift of 'M\()° and 

 is characterized by two conjugate poles in the left half plane and two 

 symmetrically located zeros in the right half plane shown in Fig. 13(c). 

 The two parameters which can be selected are the rectangular coordinates 

 of one singularity. 



It has been suggested that these functions can be realized without 

 benefit of inductance. Here again numerous arrangements are possible, 

 but onl}^ a few examples will be given. The basic operation is to perform 

 one division on the original transmission function resulting in a quotient 

 of unit}^ and a fractional remainder of opposite sign. The fractional re- 

 mainder is then synthesized by a RC network in conjunction with an 

 amplifier. 



Single 180° Section 



The transmission of a single 180° section is 



1 



COo p 



iiCOo 



- 1 



1 + OJo 'p COo + p 



In this case the fractional remainder consists of only one real pole 

 which is realized by the R-C structure shown in Fig. 13(a). 



Two 180° Sections 



The overall transmission of two 180° sections in tandem is the product 

 of each transmission 



e = 



1 



coi'p 



_1 + ^i^pj Ll + ^-i^P 



1 



W2 P 



2(cOi + 0)2 )p 



(1 -\- Vp)(l + co7ip) 



- 1 



In this case the fractional remainder consists of one real zero and two 

 real poles which are realized by the R-C structure shown in Fig. 13(b). 



Single 360° Section 



By far the most common phase corrector is the 360° section whose 

 transmission is 



€ = — 



_1 + Q-Wp + co-Y: 



= 9 



Q OOmP 



_1 + ap_ 



1 + ^ p 



_1 + Q-^U-^P + U^n-P-- 



- 1 



