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Circuits and Systems Theory MEH237 Yrd. Doç. Dr. Sibel ÇİMEN 26.09.2011

Circuits and Systems Theory MEH237 Yrd. Doç. Dr. Sibel ÇİMEN 26.09.2011. Books. Course Book : Fund amentals of Electric Circuits, by Charles K. Alexander and Matthew N. O. Sadiku , McGraw Hill; 3rd edition (2007) Reference Books:

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Circuits and Systems Theory MEH237 Yrd. Doç. Dr. Sibel ÇİMEN 26.09.2011

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  1. Circuits and Systems TheoryMEH237 Yrd. Doç. Dr. Sibel ÇİMEN 26.09.2011

  2. Books Course Book : • Fundamentals of Electric Circuits, by Charles K. Alexander and Matthew N. O. Sadiku, McGraw Hill; 3rd edition (2007) Reference Books: 1) Electric Circuits, by James W. Nilsson and Susan Riedel, Prentice Hall; 8th edition (2007) 2) Schaum's Outline of Electric Circuits, by MahmoodNahvi and Joseph Edminister, McGraw-Hill; 4th edition (2002) 3) Introduction to Electric Circuits, by Richard C. Dorf and James A. Svoboda, Wiley, 7th edition (2006) 4) Schaum's Outline of Basic Circuit Analysis, by John O'Malley and John O'Malley, McGraw-Hill; 2nd edition (1992)

  3. Course Outline 1) Second Order DC Circuits (Fund. of Electric Circuits, CH 8) 2) Sinusoids and Phasors (Fund. of Electric Circuits, CH 9) 3) Sinusoidal Steady-State Analysis (Fund. of Electric Circuits, CH 10) 4) AC Power Analysis (Fund. of Electric Circuits, CH 11) 5) Frequency Response (Fund. of Electric Circuits, CH 14) 6) Laplace Transform (Fund. of Electric Circuits, CH 15

  4. Second Order Circuits

  5. 1.1. Introduction

  6. 1.2. Finding Initial and Final Values • Keep in mind; • Capacitor voltage always continuous… • Inductor current always continuous…

  7. EXAMPLE 1.1. The switch in Figure has been closed for a long time. İt is open at t=0. Find; )/dt, )/dt,

  8. EXAMPLE 1.2. In figurecalculate; , )/dt, )/dt

  9. 1.3. The Source-Free Series RLC Circuits (1.a) (1.b)

  10. 1.3. The Source-Free Series RLC Circuits • Applying KVL aroundtheloop; (2) • To eliminate the integral, we differentiate with respect to t and rearrange terms:…. (3)

  11. 1.3. The Source-Free Series RLC Circuits • with initial values equation (2)… (4) or Bobinin uçlarından akan akımın exp. Karakteristiği olduğunu biliyoruz… • equation (3)becomes… or i 0

  12. 1.3. The Source-Free Series RLC Circuits Known as characteristic equation (5) İt’sroots; Where;

  13. 1.3. The Source-Free Series RLC Circuits resonant frequency or undamped natural frequency (rad/s) neperfrequencyor damping factor (Np/s) İn terms of equation (5) gets… (6) The two values of s in Eq. (5) indicate that there are two possible solutions in Eq. (6); that is, Natural response of series RLC;

  14. 1.3. The Source-Free Series RLC Circuits There are three types of solutions; Overdamped Case ( İn this situation; negative and real

  15. 1.3. The Source-Free Series RLC Circuits Critically Damped Case (

  16. 1.3. The Source-Free Series RLC Circuits Under Damped Case (

  17. EXAMPLE 1.3. R=40 Ω, L=4H and C=1/4 F. Calculate the characteristic roots of the circuit. Is the natural response overdamped, underdamped, or critically damped?

  18. EXAMPLE 1.4. Find i(t) in the circuit. Assume that the circuit has reached steady state at t=.

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