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## CIRCUIT ANALYSIS METHODS

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**CIRCUIT ANALYSIS METHODS**Chapter 3 Mr. Muhamad Sani Mustafa**CIRCUIT ANALYSIS METHODS**• Node-Voltage method • Mesh-current method • Source transformation • Thevenin equivalent circuit • Norton equivalent circuit • Maximum power transfer • Superposition principle**INTRODUCTION OF NODE-VOLTAGE METHOD**• Use KCL. • Important step: select one of the node as reference node • Then define the node voltage in the circuit diagram.**In the diagram, node 3 is define as reference node and node**1 and 2 as node voltage V1 and V2. • The node-voltage equation for node 1 is,**In the diagram, node 3 is define as reference node and node**1 and 2 as node voltage V1 and V2. • The node-voltage equation for node 1 is,**THE NODE-VOLTAGE METHOD AND DEPENDENT SOURCES**• If the circuit contains dependent sources, the node-voltage equations must be supplemented with the constraint equation imposed by the presence of the dependent sources.**example…**Use the node-voltage method to find the power dissipated in the 5Ω resistor.**The circuit has 3 node.**• Thus there must be 2 node-voltage equation. • Summing the currents away from node 1 generates the equation,**As written, these two equations contain three unknowns**namely V1, V2 and iØ. • To eliminate iØ, express the current in terms of node-voltage,**SPECIAL CASE**• When a voltage source is the only element between two essential nodes, the node-voltage method is simplified.**There is three essential nodes, so two simultaneous equation**are needed. • Only one unknown node voltage, V2 where as V1=100V. • Therefore, only a single node-voltage equation is needed which is at node 2.**SUPERNODE**• When a voltage source is between two essential nodes, those nodes can be combine to form a supernode (voltage sourse is assume as open circuit).**Summing both equation,**Above equation can be generates directly using supernode approach**Starting with resistor 5Ω branch and moving**counterclockwise around the supernode,**CIRCUIT ANALYSIS METHODS**• Node-Voltage method • Mesh-current method • Source transformation • Thevenin equivalent circuit • Norton equivalent circuit • Maximum power transfer • Superposition principle**INTRODUCTION OF MESH-CURRENT METHOD**• A mesh is a loop with no loop inside it. • A mesh current is the current that exist only in the perimeter of a mesh. • Mesh-current method use KVL to generates equation for each mesh.**Solving for ia and ib, and you can compute any voltages or**powers of interest.**THE MESH-CURRENT METHOD AND DEPENDENT SOURCES**• If the circuit contains dependent sources, the mesh-current equations must be supplemented by the appropriate constraint equations.**Use the mesh-current method to determine the power**dissipated in the 4Ω resistor.**But**• Substituting into the mesh-current equation,**Using Cramer rule, the values of i2 and i3 can be determine,****SPECIAL CASE (SUPERMESH)**• When a branch includes a current source, the mesh-current method can be simplified. • To create a supermesh, remove the current source from the circuit by simply avoiding the branch when writing the mesh-current equations.