7-7] 



IF AMPLIFIER DESIGN 



363 



The values of s for which the denominator vanishes (j = si; s = Si* . . . 

 etc.) are the zeroes of the denominator. At these values of s, the transfer 

 function becomes infinite, so they are called the po/es oj the network function. 

 The synthesis of an IF amplifier is facilitated by use of a potential analogy.* 

 By considering each pole to represent the position of positive line charge 

 normal to the complex frequency plane, and each zero to represent the 

 position of a negative line charge normal to the plane, it can be shown that 

 the potential measured along theyco axis resulting from the pole-zero array 

 is equivalent to the logarithm of the magnitude of the normalized transfer 

 function. 



When the transfer function consists of poles which are very far removed 

 from the origin and near thej'co axis (as in Fig. 7-4), an arrangement of the 





C^+JW, 



Transmission 

 Band 



Z(a)) 



Due to cr3+jco3 

 Due to cTi+jcOj 

 ■Due to cTj+jcOg 



Fig. 7-4 S-Plane and Z-Plane Representations of IF Amplifier Characteristics. 



poles at each interval about a semicircle having the jw axis as diameter 

 produces an approximate constant potential on the jco axis. The networks 

 that are used, however, have zeroes at the origin and conjugate poles in 

 the third quadrant of the plane. When the ratio of bandwidth of the overall 

 receiver to the IF frequency becomes large, the contribution of these zeroes 

 and poles to the transfer function in the passband region becomes significant. 

 A conformal transformation 



Z = s' 



(-9 



(7-20) 



is used to obtain an exact low-pass transformation, where 



_ number of zeroes at origin of s plane 

 ^ number of poles in upper left s plane 



for the individual network elements employed. This transformation moves 

 the zeroes to infinity in the z plane, and results in coincidence of the s plane 



*W. H. Huggins, The Potential Analogue in Network Synthesis and Analysis, Air Force, 

 Cambridge Research Lab. Report, March 195L 



