. The Bell System technical journal . ncy. In terms of the image parameters of the coupling networks, the valueof ju/3 becomes o ^ :^jaR2^KiK2 ^.^. ^^ {KxKi + R1R2) sinh e + {R1K2 + R2KO cosh 6 ^ ^ If it be assumed that the network is dissipative, the transfer constanthas an attenuation component and may be represented by e = A +71/ STABILIZED FEEDBACK OSCILLATORS 473 as in equation (34). When the phase constant \p has the value ± 90degrees, equation (40) becomes ± aR2^K,K, ^^ (KiK. + R1R2) sinh A + (R,K2 + R2K,) cosh A (41) When the feedback network is purely reactive, stabilization of thefre
. The Bell System technical journal . ncy. In terms of the image parameters of the coupling networks, the valueof ju/3 becomes o ^ :^jaR2^KiK2 ^.^. ^^ {KxKi + R1R2) sinh e + {R1K2 + R2KO cosh 6 ^ ^ If it be assumed that the network is dissipative, the transfer constanthas an attenuation component and may be represented by e = A +71/ STABILIZED FEEDBACK OSCILLATORS 473 as in equation (34). When the phase constant \p has the value ± 90degrees, equation (40) becomes ± aR2^K,K, ^^ (KiK. + R1R2) sinh A + (R,K2 + R2K,) cosh A (41) When the feedback network is purely reactive, stabilization of thefrequency requires that the phase shift component of the image trans-fer constant have a value ± 90 degrees within a transmission this condition the attenuation component of the transfer con-stant is zero and equation (41) is simplified by the reduction of sinh A tozero and cosh A to unity. A simple example of an oscillator stabilized in the above manner isshown in Fig. 8. The two vacuum tubes are coupled by a simple shunt. Fig. 8—Stabilized two-stage oscillator. inductance of relatively low magnitude and low dissipation. With thehigh resistance of the screen-grid tube in the first stage this shunt re-actance coupling provides a substantially constant phase shift of 90degrees. A low-impedance transformer might also be used for couplingthe stages or, if desired, a four-terminal dissipative network designedto provide the required phase shift in a moderately wide frequencyrange. The feedback network is required to produce a phase shift of only 90degrees and may therefore have a relatively simple configuration. Thedirection of the phase shift should, of course, be opposite to that of theamplifier. In the example illustrated the feedback network corre-sponds to that of a simple Colpitts oscillator. The condition forstabilization is that the two shunt capacitances be equal and theoscillation frequency is that of the resonance of the inductance withone of the two equal co
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