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The basic physical laws are given for each system, and the associated parameters are defined. Examples are included to show the application of the basic laws to physical equipment. The result is a differential equation, or a set of differential equations, that describes the system. The equations derived are limited to linear systems or to systems that can be represented by linear equations over their useful operating range. The important concepts of system and of state variables are also introduced.
The source voltage va ¼ e is known; therefore, there is only one unknown voltage, vb, and only one node equation is necessary. Kirchhoff ’s second law, that the algebraic sum of the currents entering (or leaving) a node must equal zero, is applied to node b. The current from node b to node a, through the resistor R, is ðvb À va Þ=R. The sum of these currents must equal zero: vb À va 1 v ¼0 þ R LD b Rearranging terms gives 1 1 1 þ vb À va ¼ 0 R LD R ð2:8Þ ð2:9Þ Except for the use of different symbols for the voltages, this is the same as Eq.
28 Chapter 1 REFERENCES 1. IEEE Standard Dictionary of Electrical and Electronics Terms, Wiley-Interscience, New York, 1972. 2. Bossert, D. : ‘‘Design of Pseudo-Continuous-Time Quantitative Feedback Theory Robot Controllers,’’ MS thesis, AFIT/GE/ENG/89D-2, Graduate School of Engineering, Air Force Institute of Technology, Wright-Patterson AFB, Ohio, December 1989. 3. Houpis, C. , and S. J. Rasmussen: Quantitative Feedback Theory Fundamentals and Applications, Marcel Dekker, New York, 1999. 4. Hamilton, G.