. The Bell System technical journal . oscillation, detection, amplification, or other usesof the thermionic vacuum tube. In treating the oscillator problem we consider the amplificationterm of the general equations; namely tp= ^ {rp-\-Zn) L ^ ^ V rp-\-z„J The oscillating conditions require that current shall flow witiiout adriving voltage. Hence, as e is zero, ip can be finite only if one ofthe factors in the denominator is zero. Thus either rp+zn = 0 (54) or r,+gnil-^-~^=0 (55) V rp-\-z„ 458 BELL SYSTEM TECHNICAL JOURNAL gives the conditions for oscillation. Fig. 5 and the relations of (45),(
. The Bell System technical journal . oscillation, detection, amplification, or other usesof the thermionic vacuum tube. In treating the oscillator problem we consider the amplificationterm of the general equations; namely tp= ^ {rp-\-Zn) L ^ ^ V rp-\-z„J The oscillating conditions require that current shall flow witiiout adriving voltage. Hence, as e is zero, ip can be finite only if one ofthe factors in the denominator is zero. Thus either rp+zn = 0 (54) or r,+gnil-^-~^=0 (55) V rp-\-z„ 458 BELL SYSTEM TECHNICAL JOURNAL gives the conditions for oscillation. Fig. 5 and the relations of (45),(46), (47), (48) and (49) are applicable here. The condition of (54)requires a negative value of rp, and hence is not the usual oscillationcondition. The condition of (55) therefore gives the criterion for 1the oscillation condition. As before, neglecting quantities in ywe may write (55) in the following form rg-{-qn=()zi{Zg-\-rg or r,+ = 0. (56) When applied to a hypothetical Hartley oscillator, Fig. 9, with thecircuit constants. Fig. 9—Hartley oscillator S2 =jc^Lp 1 _• T equation (56) gives as the conditions for oscillation 1 1 [ LpL^~\ {Lp-\-Lg) C Eh -\- Ea J (nearly), (57) Lt [-a]^ IxL^ (nearly (58) OPERATION OF THERMIONIC VACUUM TUBE CIRCUITS 459 The relations of (57) and (58) have been given many times, and areincluded here only in order to illustrate the ease with which simpleproblems may be solved from fundamental relations. Application of the Theory The illustrations will serve to give a sufficiently comprehensive viewof the methods of applying the general equations to special cases. Inasmuch as the derivation of the equations requires no assump-tions other than that the static curves of grid current-grid potential,and plate current-plate potential of the tube remain constant, theaccuracy with which a given problem may be calculated dependsonly upon the ability to determine the effective differential coefficientsrequired by the Taylors series expansions, and the
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