EE40 Summer 2006: Lecture 8 Instructor: Octavian Florescu 1 Announcements Midterm Review session this Thursday in Cory 277 from 5pm-8pm Midterm #1 Next.

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Presentation transcript:

EE40 Summer 2006: Lecture 8 Instructor: Octavian Florescu 1 Announcements Midterm Review session this Thursday in Cory 277 from 5pm-8pm Midterm #1 Next Tuesday in Dwinelle 145 from 12pm-1:30pm  You are allowed on 8½ x 11 cheat sheet (front and back) but must be hand written  You are not permitted the use of a graphing calculator  Past Midterms posted online 1 st lab slot is cancelled next week. Only attend your second lab slot. For those of you that have your second lab slot on Tuesday, the prelab is due at the end of the lab. HW #3 online

EE40 Summer 2006: Lecture 8 Instructor: Octavian Florescu 2 Lecture #8 OUTLINE Review and examples  1 st and 2 nd Order Circuits  Phasors  Complex impedence  Misc. Problems

EE40 Summer 2006: Lecture 8 Instructor: Octavian Florescu 3 Equivalent inductance L1L1 L eq = ? Z eq = ? L2L2 L3L3

EE40 Summer 2006: Lecture 8 Instructor: Octavian Florescu 4 Equivalent Capacitance and Voltage Division C1C1 C eq = ? Z eq = ? ΔV o = ? C2C2 C3C3 +ΔVi-+ΔVi- +ΔVo-+ΔVo-

EE40 Summer 2006: Lecture 8 Instructor: Octavian Florescu 5 Charge Sharing C1C1 V final = ? C2C2 +V1-+V1- +V2-+V2-

EE40 Summer 2006: Lecture 8 Instructor: Octavian Florescu 6 KCL/KVL Solve for all the electrical characteristics.

EE40 Summer 2006: Lecture 8 Instructor: Octavian Florescu 7 1 st Order Circuit Example 1 Find Vo(t) knowing i(t) = 2+3u(t), the unity step function using a source transformation. Plot the Vo(t), i(t), E capacitor (t). How long does it take Vo(t) to reach 4V? i (t) 11 + - 1F Vo(t)

EE40 Summer 2006: Lecture 8 Instructor: Octavian Florescu 8 1 st Order Circuit Example 2 Find Vo(t) knowing i(t) = u(t) Plot the Vo(t), i(t), E capacitor (t) How long does it take Vo(t) to reach 4V? i (t) 10  + - 1F Vo(t)

EE40 Summer 2006: Lecture 8 Instructor: Octavian Florescu 9 One Last 1 st Order Find Vo(t) if V 1 =u(t) + Vo -

EE40 Summer 2006: Lecture 8 Instructor: Octavian Florescu 10 2 nd Order Circuit Example 1 Find the damping factor and the natural frequency of this circuit. i (t) R + - C L Vo(t)

EE40 Summer 2006: Lecture 8 Instructor: Octavian Florescu 11 2 nd Order Circuit Example 2 i(t) = 1+u(t)+Acos(ω o t+Ф) Find Vo(t) knowing L=10uH, C=1nF, R=50Ω i (t) R + - C L Vo(t)

EE40 Summer 2006: Lecture 8 Instructor: Octavian Florescu 12 Phasor Example Find the total equivalent impedance Z of the circuit. At what frequency is the impedance purely real? i (t) R + - C L Vo(t) Z

EE40 Summer 2006: Lecture 8 Instructor: Octavian Florescu 13 Complex Impedence Example 1 + Vi(t) Vo(t) Z1Z1 Z2Z2 -Find V o (jω)/ V i (jω) -Knowing Z 2, choose Z 1 such that maximum power is delivered to the load.

EE40 Summer 2006: Lecture 8 Instructor: Octavian Florescu 14 2 nd Order Circuits Find the Bode Plot for Vc/Vs C +–+– VSVS R L + V C --