. The Bell System technical journal . e of Cs that has been calibrated in terms of Ct. To facilitate still further the operation of the PI meter, the voltage Ci isproduced as shown in Fig. by arranging for the oscillator to have itsfrequency controlled by the crystal through feedback from capacitor, Ck .Automatic volume control is provided such that the amplitude of d isessentially constant at all times and at all frequencies. The circuit is con-structed to oscillate at the desired frequency, and adjustment for insuringthis operation is provided in the form of a phase shifting circuit wit
. The Bell System technical journal . e of Cs that has been calibrated in terms of Ct. To facilitate still further the operation of the PI meter, the voltage Ci isproduced as shown in Fig. by arranging for the oscillator to have itsfrequency controlled by the crystal through feedback from capacitor, Ck .Automatic volume control is provided such that the amplitude of d isessentially constant at all times and at all frequencies. The circuit is con-structed to oscillate at the desired frequency, and adjustment for insuringthis operation is provided in the form of a phase shifting circuit with variable 224 BELL SYSTEM TECHNICAL JOURNAL capacitor, Cr. After a crystal has been inserted in its proper place, oscilla-tions will begin, but may be slightly above or below the resonant frequencyof the crystal plus Ct. By adjustment of Cr the frequency can be shiftedthe slight amount necessary for resonance. This is observed by placingswitch 5 in the PI position and making the adjustment to give maximumdeflection of e„. SWITCH S. Fig. —Diagram of Performance Index meter. Derivation of PI Circuit Equation The following circuit relations derived from Figure show first, thatthe ratio of Cp to Ci is a function of the Performance Index of the crystal,and second, that the calibration circuit permits an absolute evaluation ofits magnitude. At resonance, the effective circuit Q, designated as Qo, is determined from Q2 = Cc + «0 (-S () Since the circuit Q includes the capacitance of Cx as a part of the crystal, it isnecessary to express Q2 in terms of the crystals properties (see Fig. ). Since QA = -^ ) of the crystal is independent of Cx, the relationship between Qiand Q2 is readily obtained by equating the expressions for the anti-resonantimpedance first, when Cx is considered to be in shunt with the series capac-itor, Ct, and second, when Cx is considered as part of the crystal. This re-sults in Q2 =Qi Ct — CxCt () PERFORM A.\CE IXDEX OF
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