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Chapter 7 Transient regime o f linear circuits

Chapter 7 Transient regime o f linear circuits. http://users.utcluj.ro/~ lcret. Chapter 7. Transient regime. THE LAPLACE TRANSFORM. Laplace transform definition: where (complex quantity) The unit step function The impulse function. Chapter 7. Transient regime.

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Chapter 7 Transient regime o f linear circuits

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  1. Chapter 7 Transient regime of linear circuits http://users.utcluj.ro/~lcret

  2. Chapter 7. Transient regime. • THE LAPLACE TRANSFORM. • Laplace transform definition: • where (complex quantity) • The unit step function • The impulse function

  3. Chapter 7. Transient regime. 3) The transform of the first derivativeof f(t) : L Integrating by parts: L Assuming that the integrated term vanishes at the upper limit: L represents the initial condition.

  4. Chapter 7. Transient regime. 4) The transform of the integralof f(t) : Changing f(t) with in the formula of the Laplacetransform of the first derivativeof f(t), for a function with zero initial conditions leads to:

  5. Chapter 7. Transient regime. • Properties of the Laplace transform: • linearity : • superposition:

  6. Chapter 7. Transient regime. • Network analysis by Laplace transform. • the voltage-current relationship for an inductance carrying initial current i0 • the transform corresponding to the voltage-current relationship for capacitance, charged to an initial voltage u0

  7. Chapter 7. Transient regime. Example of circuit transformation. Applying Kirchhoff's voltage law to the s-domain circuit: or

  8. Chapter 7. Transient regime. Inverse Laplace transform : where are the roots of (poles !) - the original function:

  9. Chapter 7. Transient regime. Ohm’s Law and Kirchhoff’s Laws (using the Laplace transform): where: Applying the Laplace transform it results the Ohm’s law:

  10. Chapter 7. Transient regime. The corresponding circuit is:

  11. Chapter 7. Transient regime. Kirchhoff’s Laws (using the Laplace transform): 1) Kirchhoff’s Current Law (KCL) 2) Kirchhoff’s Voltage Law (KVL)

  12. 12/62 References [1] Charlews K. Alexander, Matthew N.O.Sadiku, Fundamentals of Electric Circuits (Fifth Edition), published by McGraw-Hill, 2013 [2] Radu V. Ciupa, Vasile Topa, The Theory of Electric Circuits, published by Casa Cartii de Stiinta, 111118 [3] Dan. D Micu, Laura Darabant, Denisa Stet et al., Teoria circuitelor electrice. Probleme, published by UTPress, 2016

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