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# Chapter 4 - Chapter 4 Circuit Theorems SJTU 1 Linearity...

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SJTU 1 Chapter 4 Circuit Theorems

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SJTU 2 Linearity Property Linearity is the property of an element describing a linear relationship between cause and effect. A linear circuit is one whose output is linearly ( or directly proportional) to its input.
SJTU 3 Fig. 4.4 For Example 4.2 . 1 , 5 ; 3 , 15 A Io then A Is if A Io then A Is if = = = =

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SJTU 4 Superposition(1) The superposition principle states that voltage across (or current through) an element in a linear circuit is the algebraic sum of the voltages across (or currents through) that element due to each independent source acting alone.
SJTU 5 Steps to Apply Superposition Principle: 1. Turn off all independent source except one source. Find the output(voltage or current) due to that active source using nodal or mesh analysis. 2. Repeat step 1 for each of the other independent sources. 3. Find the total contribution by adding algebraically all the contributions due to the independent sources. Superposition(2)

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SJTU 6 j R1 V e + - L N i j + - V1 R1 i1 L N i2 - L N + V2 e R1 2 1 ; 2 1 i i i V V V + = + =
SJTU 7 Fig. 4.6 For Example 4.3 2 1 v v v + = V v V v V v 10 8 2 ; 2 1 = = =

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SJTU 8 Source Transformation(1) A source transformation is the process of replacing a voltage source V s in series with a resistor R by a current source i s in parallel with a resistor R, or vice versa. V s =i s R or i s =V s /R
SJTU 9 Source Transformation(2) It also applies to dependent sources:

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SJTU 10 Fig. 4.17 for Example, find out Vo
SJTU 11 So, we get v o =3.2V

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SJTU 12 7 2A 6V 2A I Example: find out I (use source transformation ) A I 5 . 0 =
SJTU 13 Substitution Theorem 20V + 6 I2 4V 4 - 8 I3 V3 I1 20V 8V - I3 V3 6 I1 + 8 I2 V3 6 + - 20V I1 1A 8 I3 I2 I1=2A, I2=1A, I3=1A, V3=8V I1=2A, I2=1A, I3=1A, V3=8V I1=2A, I2=1A, I3=1A, V3=8V

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Chapter 4 - Chapter 4 Circuit Theorems SJTU 1 Linearity...

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