244 



BELL SYSTEM TECHNICAL JOURNAL 



The numerator remains the same; however, the denominator has an addi- 

 tional term added to both 7 and 5. 



Fig. 15.11 — Various crj'stal circuit combinations. 



In the same way, a series element, S, may be added as shown in Fig. 15.11. 

 The impedance of this combination is similarly modified and the input im- 

 pedance may be expressed as 



S -f 



WT 



W + T 



[« + 5(7 + |)] + [/3 + 5(5-t-|)] 



^ Z 



7 + ;. + 



T 



(15.75) 



a" -h ^"Z 

 1" + h"Z 



The addition of a series element leaves the denominator unchanged but adds 

 a term to the numerator. The form of (15.75) is exactly the same as (15.52) 

 except that the magnitudes of the constants, a, |8, 7 and 5 have been modified. 

 As an example, apply (15.74) to obtain an expression for the impedance 

 Zab (Fig. 15.2). This expression for impedance may be written directly 

 if the following values are substituted in (15.74). 



T + jMt \ 



/3 



7 = 5 = y 

 1 



(15.76) 



T = 



Zab — 



WT 



W + T 



jccCt J 



[r + JMt] + [t]Z 



- 



M^'+i( 



Co 



1 + 



:)]-['(-i)]^ 



(15.77) 



