Analysis of Electrical Circuits with Variable Load Regime by A. Penin

By A. Penin

This publication introduces electrical circuits with variable rather a lot and voltage regulators. It permits to outline invariant relationships for numerous parameters of regime and circuit sections and to turn out the ideas characterizing those circuits. Generalized identical circuits are brought. Projective geometry is used for the translation of adjustments of working regime parameters. Expressions of normalized regime parameters and their alterations are provided. 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 law features of quite a bit with constrained energy of voltage resource is taken into account. The publication offers the basics of electrical circuits and develops circuit theorems. it's helpful to engineers, researchers and graduate scholars who're attracted to the fundamental electrical circuit thought and the legislation and tracking of energy offer systems.

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15 Two-port with loss and a variable load conductivity ð1:28Þ 18 1 V0 I0 ! a ¼ 11 a21 ! " Y11 a12 V1 Á ¼ YD10Y a22 I1 Y 10 1 Y10 Y00 Y10 # Á ! V1 : I1 Introduction ð1:29Þ Using the attenuation coefficient c [2], we may rewrite Eq. 29) V0 I0 YIN:C ! # ! " pYL:C ffi V1 ffiffiffiffi chc shc DY ¼ Á : 1 ffi pIffiffiffiffi shc chc D ð1:30Þ Y In turn, the admittance transformation has the view YL YIN Y þ thc ¼ L:C YL : YIN:C 1 þ Y thc L:C ð1:31Þ We have the relative values YIN =YIN:C , YL =YL:C . 31) is not a pure relative because contains the value thc.

21. We may note that values YL , Yi have not any scales also. The above mentioned arguments make it possible to confront regimes of compared circuits and give the basis for analysis of the general case of circuit. 3 Regime Symmetry for a Load Power 47 Fig. 3 Regime Symmetry for a Load Power In the above Sect. 23) and have projective properties. 6) and determines a parabola in Fig. 6. This quadratic curve has similar projective properties that permit to compare the regime of different circuits, to determine the deviation from the power matching [11, 12, 15].

12 Active circuit with the voltage stabilization of two loads In case of two loads (without conductivity yN ), the two equations turns out y0N þ y1N ¼ ðV0 À V1 Þy0N À I2 ; y1N y0N þ y2N ¼ ðV0 À V2 Þy0N À I1 : I2 y2N I1 It is possible to carry out the normalization by the SC current of the voltage source. These expressions contain six normalized values. If regimes differ, we have the set of twelve different values. On the other hand, the normalization by the maximum load currents I1M ¼ y0N ðV0 À V1 Þ, I2M ¼ y0N ðV0 À V2 Þ leads to the reciprocal components I2 =I1M ; I1 =I2M .

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