252 BELL SYSTEM TECHNICAL JOURNAL 



By the same procedure just described for evaluating Z from the im- 

 pedance expression Zab , the value of Z corresponding to the minimum 

 impedance operating point, Pi , (Fig. 15.10) must be determined. For 

 this operating condition Zi may be expressed by (15.65). The coefficients 

 of this operating point are given by (15.67) with the above values of a and 

 7] (Equation 15.101). Utilizing (15.68) to solve for Z, we get 



M [1 + 4/^ + If] 

 Zi = —j / 7TT ^ —- — (minimum impedance) (15.102) 



Zi - Z\ = ^' (Ac) 



where Aco = the difference in radian frequency between the frequency of 

 oscillation in the generalized oscillator (anti-resonant frequency of the im- 

 pedance, Zab) and the frequency of oscillation in the PI meter (minimum 

 impedance frequency of the impedance, Zj) 



Aco 



CO2 — 0)1 



.^ + t)[: + ^r7±]"''^'""('^^») 



(15.51) 



It is of interest to note that (15.102) becomes (15.44) when the value of 

 Z (15.69) is introduced. 



