By A. Penin
This ebook introduces electrical circuits with variable a lot and voltage regulators. It permits to outline invariant relationships for varied parameters of regime and circuit sections and to end up the innovations characterizing those circuits. Generalized similar circuits are brought. Projective geometry is used for the translation of alterations of working regime parameters. Expressions of normalized regime parameters and their alterations are awarded. handy formulation for the calculation of currents are given. Parallel voltage resources and the cascade connection of multi-port networks are defined. The two-value voltage legislation features of quite a bit with restricted energy of voltage resource is taken into account. The ebook offers the basics of electrical circuits and develops circuit theorems. it truly is valuable to engineers, researchers and graduate scholars who're drawn to the fundamental electrical circuit conception and the legislation and tracking of strength provide systems.
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Extra info for Analysis of Electrical Circuits with Variable Load Regime Parameters: Projective Geometry Method
For their ﬁnding, Eq. 31) is solved as VL1 ¼ VL2 . It turns out the two real roots, VL ¼ 0; VL ¼ V0 , which deﬁne the hyperbolic transformation of hyperbolic (Lobachevski) geometry. Physically, the ﬁxed point means such a regime when a variable VL does not depend on the initial or subsequent value RL . It is evident for SC; OC regimes. If the roots of equation coincide, the ﬁxed point deﬁnes the parabolic transformation and, respectively, parabolic (Euclidean) geometry. If the roots are imaginary, geometry is elliptic (Riemannian).
This case is considered in the next section. 3 Boost Converter Let us consider a boost converter in Fig. 20a. 37), we offer an equation of the known static regulation characteristic VL n ¼ ; V0 1 þ ðrÞ2 ðnÞ2 ð1:40Þ 1 where n ¼ 1ÀD ! 1 is the inverse relative pause width. 36). The regulation characteristics for various values ðrÞ2 are shown in Fig. 20b. It is obviously that the maximum values VL correspond to the various values n. The characteristic value is also n = 1. The solid arrows show the correspondence of the characteristic points and dash arrow conﬁrms to running points.
22) as ( 1 10 1 0 I11 ¼ ÀY11 DR10 L1 I1 þ Y12 DRL2 I2 þ I1 1 10 1 0 I21 ¼ Y12 DR10 L1 I1 À Y22 DRL2 I2 þ I2 : Then, we get ( À Á1 10 1 0 1 þ Y11 DR10 L1 I1 À Y12 DRL2 I2 ¼ I1 À Á : 1 10 1 0 ÀY12 DR10 L1 I1 þ 1 þ Y22 DRL2 I2 ¼ I2 ð1:23Þ The solution of Eq. 23) gives the subsequent currents À Á 0 0 I10 þ DR10 L2 Y22 I1 þ Y12 I2 ¼ ; D10 À Á 0 0 I 0 þ DR10 L1 Y11 I2 þ Y12 I1 I21 ¼ 2 D10 I11 ð1:24Þ where the determinant 2 10 10 10 D10 ¼ ð1 þ Y11 DR10 L1 Þð1 þ Y22 DRL2 Þ À ðY12 Þ DRL1 DRL2 : Let us carry out the analysis of these relationships.
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