Lecture Notes (4)

# Vs vs impedance zs resistance inductance capacitance

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Unformatted text preview: rops around any The loop is =0. V(s) V(s) Impedance Z(s) Resistance Inductance Capacitance Memorize! 13 Kirchhoff’s Current Law (KCL) 14 Impedance computation V1(s) Series connection Series The algebraic sum of currents into any junction The is zero. I(s) I(s) V2(s) Z1(s) Z2(s) V(s) V(s) Proof (Ohm’s law) Proof (Ohm’ 15 16 Impedance computation Modeling example R1 i(t) i(t) Parallel connection Parallel I1(s) Input v1(t) Z1(s) I(s) I(s) R2 v2(t) Output C Z2(s) I2(s) Proof (Ohm’s law) Proof (Ohm’ Kirchhoff voltage law (with zero initial conditions) Kirchhoff V(s) V(s) KCL KCL By Laplace transform, By 17 Modeling example (cont’d) i(t) i(t) Input v1(t) 18 Example: Modeling of op amp R1 Zf(s) (s) R2 I(s) I(s) v2(t) Output - Zi(s) (s) C Input Vi(s) (s) i vd + If(s) (s) - Rule1: i =0 Rule2: vd=0 Vo(s) Output (s) Transfer function Transfer Impedance Z(s): V(s)=Z(s)I(s) Impedance Transfer function of the above op amp: Transfer (first-order system) (first19 20 Modeling example: op amp R2 i(t) R1 i(t) Input vi(t) (t) C - i =0 - i vd + Modeling exercise: op amp C2 C1 Vd=0 R2 vo(t) Output (t) R1 By the formula in previous two pages, By + Vd=0 - - i vd Input vi(t) (t) i =0 vo(t) Output (t) Find the transfer function! (first-order system) (first21 22 Summary & Exercises More exercises in the textbook Find a transfer function from v1 to v2. Find Modeling Modeling Modeling is an important task! Modeling Mathematical model Mathematical Transfer function Transfer Modeling of electrical systems Modeling Find a transfer function from vi to vo. Find Next, modeling of mechanical systems Next, Exercises Exercises Do the problems in page 23 of this lecture note. Do 23 24...
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