For the practical tank circuit examined in Section 12.14, the Data from Figure 12-32 Y-locus may be

For the practical “tank” circuit examined in Section 12.14, the

Data from Figure 12-32

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Y-locus may be constructed by combining the C-branch locus and the RL-branch locus. To illustrate the addition, the points corresponding to frequencies 00, < ₂ <3 are marked on the individual loci and on the sum, shown in Fig. 12-31(c). It is seen that Ymin occurs at a frequency greater than ; that is, the resonance is high-impedance but not maximum-impedance. This comes about because G varies with @ (see Section 12.14), and varies in such a way that forcing B = 0 does not automatically minimize G² + B². The separation of the resonance and minimum- admittance frequencies is governed by the Q of the coil. Higher Qind corresponds to lower values of R. It is seen from Fig. 12-31(b) that low R results in a larger semicircle, which when combined with the Y-locus, gives a higher and a lower minimum-admittance frequency. When Qind 210, the two frequencies may be taken as coincident. The case of the two-branch RC and RL circuit shown in Fig. 12-32(a) can be examined by adding the admit- tance loci of the two branches. For fixed V = V/0°, this amounts to adding the loci of the two branch currents. Consider the C variable to be without limit, and R₁, R₂, L, and was constant. Then current I, is fixed as shown in Fig. 12-32(b). The semicircular locus of Ic is added to I, to result in the locus of IT. Resonance of the circuit corresponds to 0 = 0. This may occur for two values of the real, positive parameter C [the case illustrated in Fig. 12-32(b)], for one value, or for no value-depending on the number of real positive roots of the equation Im Y,(C) = 0.