1• Mesh (or loop) analysisECE 201: Lecture 8Borja PeleatoMain Idea2• Nodal analysis solved a circuit by finding the voltage at every node, currents could be found later using Ohm’s law and KCL.• Loop analysis tries to find all the currents instead, voltages can be found later using Ohm’s law or KVL.Mesh analysis31. Chose a few loops to apply KVL on– Not a unique way of doing it. – Try to avoid having current sources involved in multiple loops– Make sure that every element belongs to at least one loop2. Define an unknown current for each loop– Direction is arbitrary, but you can be smart about it (more on this later)3. For each loop, apply KVL using Ohm’s law to write voltages as I*R– WATCH OUT FOR OVERLAPPING CURRENTS!!!– WATCH OUT FOR THE POLARITY OF VOLTAGE SOURCES!!!4. Solve the system of equationsExample 14Pros & Cons5• Pros:– Often requires fewer equations or variables– More intuitive– If only one of the unknown currents goes through a current source, you can trivially find its value to be equal to that of the source (sign depends on relative direction). Try to define the loops this way.• Cons:– Choosing the loops is more of an art than a science… that is why computers always go for Nodal Analysis.– It cannot handle two loops sharing a current source. Loops should be chosen to avoid that scenario. If it is unavoidable, use Nodal AnalysisNodal vs Mesh analysis6• Both methods solve the circuit, but sometimes one is much simpler than the other. With practice, you will learn to identify the best method to use in each case.• Some general tips that you can use:– Grounded voltage sources are good for Nodal Analysis, since they tell us the voltage of a node– Floating voltage sources are bad for Nodal Analysis, since they introduce additional unknowns– Current sources are good for Mesh analysis, since they tell us the current on a loop (if the loops are well picked)– In the end, nodal analysis will tell us the voltages at the nodes, and mesh analysis the currents at the branches.– Nodal analysis will have as many equations as nodes in the circuit, Mesh will have as many equations as loops in the circuit• You can use one method to solve the circuit and the other to verify your resultExample 27Example
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