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06-Circuit Theorems I

# 06-Circuit Theorems I - Circuit Theorems Circuit Theorems...

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ircuit Theorems Circuit Theorems © Fred Terry all, 2008 Fall, 2008 1

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Key Concepts from A&S Chapter 4 • Linearity uperposition Superposition • Equivalent Circuits – Source Transformations – Thevenin & Norton Equivalents • Maximum Power Transfer Theorem 2
Definition: Linearity • A function f(x) is linear if f(ax)=af(x) • Almost All Circuit Elements In 215 are Linear – Resistors V=IR • V(I) is linear, I(V) is linear – Linearly Dependent Sources – Capacitors – Inductors + v c i c c c v iC = v L i L L L i vL = 3 - t - t

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Linearity • With A Circuit Made Up of All Linear Elements, All I-V Results Are Linear • Later, We Will Take A Brief Look at Some on- near Elements but in Most Cases Non linear Elements, but in Most Cases Will Show How to Use Piecewise Linear odels to Analyze These Circuits Models to Analyze These Circuits 4
Superposition Superposition Principle: The voltage drop across and current through an element in any linear circuit are the algebraic sums of the voltages ross and currents through that element due to across and currents through that element due to each independent source acting alone. Step by step procedure: 1) Turn off all all independent sources except 1. Find the output voltage and/or current due to that source using nodal or mesh analysis 2) Repeat step (1) for all independent sources 3) Add all these results to obtain the actual voltage d/or current of interest 5 and/or current of interest

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Superposition example Find v x i t W Will D N d l 0 First We Will Do Nodal Analysis hen We Will Do 20 Ω + Then We Will Do Superposition +- 0.1v x 4 Ω V s v x I s - 6
Nodal 20 Ω + +- 0.1v x 4 Ω V s v x I s - 7

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Superposition Step 1: Turn off 2A Source urrent Source with I=0 is an OPEN CIRCUIT 20 Ω Current Source with I=0 is an OPEN CIRCUIT +- 0.1v x1 4 Ω V s + v - CL: KCL: () 1 1 1 0.1 0 0 4 sx x x Vv v v ++ = Ω Note that we leave the ependent urce in the 8 1 20 0.25 4 xs s vV V ΩΩ →= + = dependent source in the reduced circuit!
Superposition Step 2: Turn off 10V Source oltage Source with V=0 is an SHORT CIRCUIT Voltage Source with V=0 is an SHORT CIRCUIT 20 Ω 1v 4 Ω I + v 2 0.1v x2 s - Note, again, that we leave e ependent urce in the 9 the dependent source in the reduced circuit!

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ittle Trick: 20&4 esistors are in Little Trick: 20&4 Ω Resistors are in Parallel in Reduced Circuit CL: .1v 2 10/3 Ω I s + v x2
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06-Circuit Theorems I - Circuit Theorems Circuit Theorems...

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