Source Transformation Fakulti Kejuruteraan Elektrik CIRCUIT THEOREMS Superposition Thevenin’s Norton’s Source Transformation

Fakulti Kejuruteraan Elektrik CIRCUIT THEOREMS Circuits can be analysed using Kirchhoff’s laws without tampering with their original configurations. However, for complex and large circuits, using kirchhoff’s laws will be tedious. Thus circuit theorems can be used to simplify circuit analysis.

LINEARITY PROPERTY

Linearity Property It is the property of an element describing a linear relationship between cause and effect. A linear circuit is one whose output is linearly related (or directly proportional) to its input. A circuit is said to be linear if it is both additive and homogenous. A linear circuit consists of only linear elements, linear dependent sources and independent sources.

Linearity Property Homogeneity property requires that if an input is multiplied by a constant, then the output is multiplied by the same constant v = i R → k v = k i R Additivity property requires that the response to a sum of inputs is the sum of the responses to each input applied separately. v1 = i1 R and v2 = i2 R → v = (i1 + i2) R = v1 + v2

Linearity Property Example 4.1 Find I0 when vs = 12 V and vs = 24 V

Linearity Property Example 4.1 Assume I0 = 1 A, use linearity to find the actual value of I0

Linearity Property Practice Problem 4.1 Find vo when is = 15 A and is = 30 A

Linearity Property Practice Problem 4.2 Assume that V0 = 1 V and use linearity to calculate the actual value of V0 in the circuit below

Linearity Property Problem 4.4 Use Linearity to determine i0

Linearity Property Problem 4.5 Assume V0 = 1 V, use linearity to find the actual value of V0

SUPERPOSITION THEOREM

Superposition Theorem It states that the voltage across (or current through) an element in a linear circuit is the algebraic sum of the voltage across (or currents through) that element due to EACH independent source acting alone. The principle of superposition helps us to analyze a linear circuit with more than one independent source by calculating the contribution of each independent source separately.

Superposition Theorem Steps to apply superposition principle Turn off all independent sources except one source. Find the output (voltage or current) due to that active source using nodal or mesh analysis. Repeat step 1 for each of the other independent sources. Find the total contribution by adding algebraically all the contributions due to the independent sources.

Superposition Theorem Two things have to be kept in mind: When we say turn off all other independent sources: Independent voltage sources are replaced by 0 V (short circuit) and Independent current sources are replaced by 0 A (open circuit). Dependent sources are left intact because they are controlled by circuit variables.

Superposition Theorem Example 4.3 Use the superposition theorem to find v in the circuit shown below. 3A is discarded by open-circuit 6V is discarded by short-circuit

Superposition Theorem Practice Problem 4.3 Use the superposition theorem to find v0 in the circuit shown below.

Superposition Theorem Example 4.4 Use the superposition theorem to find i0 in the circuit shown below.

Superposition Theorem Practice Problem 4.4 Use the superposition theorem to find Vx in the circuit shown below.

Example 4.5 Use the superposition theorem to find i in the circuit shown below.

Superposition Theorem Practice Problem 4.5 Find I in the circuit below using superposition

Tutorial (Superposition Theorem) Problem 4.11 Use superposition principle to find i0 and v0 in the circuit below

Tutorial (Superposition Theorem) Practice Problem 4.15 Use superposition to find i. Calculate the power delivered to the 3-ohm resistor

Tutorial (Superposition Theorem) Practice Problem 4.16 Find io in the circuit below using superposition