Chapter 4Circuit TheoremsSJTU
SJTU 1 Chapter 4 Circuit Theorems
Linearity Property: Linearity is the property of an elementdescribing a linear relationship betweencause and effect: A linear circuit is one whose output islinearly ( or directly proportional) to itsinput.2SJTU
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
Fig. 4.4 For Example 4.23262222 V2/21VI14A1111.172421,=15A52ifIs =15A, then Io = 3A;if Is =5A, then lo=1A.3SJTU
SJTU 3 Fig. 4.4 For Example 4.2 5 , 1 . 15 , 3 ; if Is A then Io A if Is A then Io A = = = =
Superposition(1): The superposition principle states thatvoltage across (or current through) anelement in a linear circuit is the algebraicsum of the voltages across (or currentsthrough) that element due to eachindependent source acting aloneSJTU
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
Superposition(2)Steps to Apply Superposition Principle:1.Turn off all independent source except one source. Findthe output(voltage or current) due to that active sourceusing nodal or mesh analysis.2.Repeat step 1 for each of the other independent sources3.Find the total contribution by adding algebraically all thecontributions due to the independent sources5SJTU
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)
i十R1LNVi1i2X+R1R1LNLNV1V2V=V1+V2: i=il+i2SJTU6
SJTU 6 j R1 V e + - L N i j + - V1 R1 i1 L N i2 - L N + V2 e R1 V =V1+V 2; i = i1+ i2
Fig. 4.6 For Example 4.382V=vl+v2十3A426Vvl= 2V: v2 =8V.. v = 10V821282M3+十V2i42423A6VV1(a)(b)7SJTU
SJTU 7 Fig. 4.6 For Example 4.3 v = v1+v2 v V v V v V 10 1 2 ; 2 8 = = =
Source Transformation(1): A source transformation is the process of replacinga voltage source V. in series with a resistor R by acurrent source i, in parallel with a resistor R, orV,=i,R or i=Vs/Rvice versa.Roa0RVob68SJTU
SJTU 8 Source Transformation(1) • A source transformation is the process of replacing a voltage source Vs in series with a resistor R by a current source is in parallel with a resistor R, or vice versa. Vs=isR or is=Vs /R
Source Transformation(2): It also applies to dependent sources:RWaa2SS66O9SJTU
SJTU 9 Source Transformation(2) • It also applies to dependent sources:
Fig. 4.17 for Example, find out Vo2232+428212V3A2O10SJTU
SJTU 10 Fig. 4.17 for Example, find out Vo