. The Bell System technical journal . ationship between capacitance and frequency in the as derived in Section , we find . [-/-a where, MPi () () (■ - f) If Pi » 2 then the expression between Re and Ri may be written R, = i?x (l + |j () The restriction that Ci > Co may be removed if the error between ()and () is taken into account. This error may be expressed as Per Cent Error in R. = 100 [^] [i + Vf+VPf] ^^^^^^ The resonant resistance, i^i, together with () provides a means ofchecking the meter. The magnitude of Ri may be determined by thes
. The Bell System technical journal . ationship between capacitance and frequency in the as derived in Section , we find . [-/-a where, MPi () () (■ - f) If Pi » 2 then the expression between Re and Ri may be written R, = i?x (l + |j () The restriction that Ci > Co may be removed if the error between ()and () is taken into account. This error may be expressed as Per Cent Error in R. = 100 [^] [i + Vf+VPf] ^^^^^^ The resonant resistance, i^i, together with () provides a means ofchecking the meter. The magnitude of Ri may be determined by thesubstitution method and from this, the value of Re calculated. Fig. the agreement between the meter and those expected fromresonant frequency measurements. The remaining crystal constants Li and Ci (Fig. ) may be evaluatedfrom the measurement of wi, wo and Co. The resonant frequency, coi,is defined as col = ^ () The anti-resonant frequency, C02, is defined as 234 BELL SYSTEM TECHNICAL JOURNAL CALCULATED. MEASURED 50 40 25 ua. 20 10 - 5 ANTI-RESONANCE Fig. —Typical characteristic of a quartz crystal measured by the Performance Index meter. Solving these equations simultaneously, it is found that 1 1 u = Ci = Co(c02 — COi) 2ciJeCo(c02 — COi) ^0(^2 — cci) 2Co(a)2 — ooi) () Experimental DataThe performance of the meter may best be illustrated by experi-mental data. The following data indicate the correlation which may beobtained between the meter and various types of oscillator considerations are extended to (1) Frequency and ampUtude correlation with a Pierce and Tuned-Plate oscillator PERFORMANCE INDEX OF QUARTZ PLATES 235 (2) The measurement of the effective capacitance, Ct, of an oscillator as afunction of tuning, and (3) The variation of as a function of voltage across the crystal. The results presented are not to be considered as generalized data, but areintended only to show a se
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