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Learn Nodal Analysis, Super Nodes, and Mesh Analysis techniques for solving electric circuits efficiently and accurately in this comprehensive lecture. Understand the step-by-step process, including converting voltage sources to current sources, and applying Kirchhoff's current law. Practice writing nodal equations for complex networks and solving for unknown voltages with practical examples. Enhance your understanding of electrical circuit analysis methods today!
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ELECTRIC CIRCUIT ANALYSIS - I Chapter 8 – Methods of Analysis Lecture 10 by MoeenGhiyas
TODAY’S LESSON CONTENTS • Nodal Analysis (General Approach) • Super Nodes • Nodal Analysis (Format Approach)
Nodal Analysis (General Approach) • Mesh Analysis employs KVL • While Nodal Analysis uses KCL for solution • A node is defined as a junction of two or more branches • Define one node of any network as a reference (that is, a point of zero potential or ground), the remaining nodes of the network will all have a fixed potential relative to this reference • For a network of N nodes, therefore, there will exist (N – 1) nodes with a fixed potential relative to the assigned reference node
Nodal Analysis (General Approach) • Steps • Determine the number of nodes within the network • Pick a reference node, and label each remaining node with a subscripted value of voltage: V1, V2, and so on • Apply Kirchhoff’s current law at each node except the reference • Assume that all unknown currents leave the node for each application of KCL. • Solve resulting equations for nodal voltages
Nodal Analysis (General Approach) • Apply nodal analysis to the network of Fig • Step 1 – The network has two nodes • Step 2 – The lower node is defined as the reference node at ground potential (zero volts), and the other node as V1, the voltage from node 1 to ground.
Nodal Analysis (General Approach) • Step 3: Applying KCL - I1 and I2 are defined as leaving node ------- eq (1) • By Ohm’s law, where • and • . Putting above in KCL eq (1)
Nodal Analysis (General Approach) • Putting above in KCL eq (1) • Re-arranging we have • . Substituting values
Nodal Analysis (General Approach) • Now • But from Ohm’s law we already know
Super Node • In nodal analysis technique, if voltage source is found in the circuit, it is better to convert it to current source and apply nodal analysis method • Concept of super node becomes applicable when voltage sources (without series resistance) are present in the network
Super Node • Steps • Assign a nodal voltage to each independent node, including the voltage sources, as if they were resistors or voltage sources • Remove the voltage sources (replace with short-circuit ) • Apply KCL to all the remaining independent nodes • Relate the chosen node to the independent node voltages of the network, and solve for the nodal voltages • Any node including the effect of elements tied only to other nodes is referred to as a super-node (since it has an additional number of terms)
Super Node • Example – Determine the nodal voltages V1 and V2 of Fig (using the concept of a super-node) • Step 1 - Assign Nodal Voltages • (All unknown currents leave node) • Step 2 – Replace Voltage source with short circuit
Super Node • Step 3 – Apply KCL at all nodes (here only one remaining super-node) • Note that the current I3 will leave the super-node at V1 and then enter the same super-node at V2. 0.25V1+ 0.5V2 = 2
Super Node • Step 4 – Relating the defined nodal voltages to the independent voltage source (initially removed), we have V1 – V2 = E = 12 V (Note why not V2 – V1 ??) • Step 5 – Solve resulting two equations for two unknowns: 0.25V1 + 0.5V2 = 2 V1 – V2 = 12
Super Node • Step 5 – Solve resulting two equations for two unknowns: 0.25V1 + 0.5V2 = 2 & V1 – 1V2 = 12 • Here by substitution method,
Super Node • Now, and • The currents can be determined as
Nodal Analysis (Format Approach) • This technique allows us to write nodal eqns rapidly • A major requirement, however, is that all voltage sources must first be converted to current sources before the procedure is applied • Quite similar to mesh analysis (format approach)
Nodal Analysis (Format Approach) • Choose a reference node and assign a subscripted voltage label to (N - 1) remaining nodes of the network • Column 1 of each eqn is summing the conductances with node of interest and multiplying the result by that node voltage • Each mutual term is the product of the mutual conductance and the other nodal voltage and are always subtracted from the first column • The column to the right of the equality sign is the algebraic sum of the current sources tied to the node of interest. A current source is assigned a positive sign if it supplies current to a node and a negative sign if it draws current from the node • Solve the resulting simultaneous equations for the desired voltages
Nodal Analysis (Format Approach) • Example – Write the nodal equations for the given network • Step 1 – Choose ref node & assign voltage labels • Step 2 to 4 as below
Nodal Analysis (Format Approach) • Example – Write the nodal equations for the given network • Similarly for V2 ,
Nodal Analysis (Format Approach) • Example – Using nodal analysis, determine the potential across the 4Ω resistor • Step 1 – Choose ref node & Assign voltage labels, and redraw the network
Nodal Analysis (Format Approach) • Steps 2 to 4 as below:
Nodal Analysis (Format Approach) • Check Solution
Summary / Conclusion • Nodal Analysis (General Approach) • Super Nodes • Nodal Analysis (Format Approach)