1• Modified Nodal AnalysisECE 201: Lecture 7Borja PeleatoMotivation2• 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 currentsModified Nodal Analysis3• 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 nowModified Nodal Analysis41. Identify the nodes in the circuit, set a reference and define a voltage variable for each node.2. Decide which auxiliary currents we are taking as variables– At least, we have to define one for each floating voltage source and another for each controlling current3. Replace element whose current has been identified as a variable by an independent current source (value is a variable)– 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 variables4. For each element replaced by a current source, write its constitutive relationship– Floating voltage sources: V+ - V-= Vs– Resistors: V+ - V-= I*R5. Now we have as many equations as unknowns. Solve.Example 15Example 26Alternative to MNA7• 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
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