FREQUENCY RESPONSE, FILTERS, AND RESONANCE
For the RLC series circuit, the Y-locus, with ! as the variable, may be determined by writing Y ¼ G þ jB ¼ whence
R R2 þ X 2
1 R jX ¼ R þ jX R2 þ X 2 X B¼ 2 R þ X2
Both G and B depend on ! via X. Eliminating X between the two expressions yields the equation of the locus in the form 2 G 1 2 2 1 G2 þ B2 ¼ or G þB ¼ R 2R 2R which is the circle shown in Fig. 12-30. and ! ¼ !h .
Note the points on the locus corresponding to ! ¼ !l , ! ¼ !0 ,
For the practical ‘‘tank’’ circuit examined in Section 12.14, the 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 !1 < !2 < !3 are marked on the individual loci and on the sum, shown in Fig. 12-31(c). It is seen that jYjmin occurs at a frequency greater than !a ; that is, the resonance is highimpedance but not maximum-impedance. This comes about because G varies with ! (see Section 12.14), and varies in such a way that forcing B ¼ 0 does not automatically minimize G2 þ B2 . The separation of
Published on May 10, 2013