ECE 201 Lecture 7 Borja Peleato Modified Nodal Analysis 1 Motivation The main step in Nodal Analysis step 4 told us to apply KCL in every node using Ohm s law to replace currents by voltage difference divided by R This works for resistors but what about sources Current sources we already know current plug it into KCL Grounded voltage sources We already know voltage of that node no need to apply KCL Floating voltage sources Also what can we do if we have current controlled dependent sources None of our variables are currents 2 Modified Nodal Analysis Same as Nodal Analysis with some additional unknowns representing currents and some additional equations needed to find them You can add as many unknown currents as you like with arbitrary directions but the minimum are For each floating voltage source dependent or independent we define an auxiliary current going through it We take currents controlling dependent sources as unknowns If we are interested in finding any other current in the circuit e g solution of the problem we might as well add it now 3 Modified Nodal Analysis 1 2 Identify the nodes in the circuit set a reference and define a voltage variable for each node Decide which auxiliary currents we are taking as variables 3 Replace element whose current has been identified as a variable by an independent current source value is a variable 4 At this point we have a circuit with resistors independent current sources and grounded voltage sources only Apply Nodal analysis to this circuit to get one equation for each of the voltage variables For each element replaced by a current source write its constitutive relationship 5 At least we have to define one for each floating voltage source and another for each controlling current Floating voltage sources V V Vs Resistors V V I R Now we have as many equations as unknowns Solve 4 Example 1 5 Example 2 6 Alternative to MNA Some texts propose a different method for dealing with floating voltage sources Enclose both nodes as well as the floating voltage source between them into a supernode Write constitutive relationship equations just like in MNA Apply KCL to this supernode be careful the supernode has different voltages In 201 we prefer MNA but you are free to use whatever method you prefer 7
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