Once we know the nodal voltages we can find anything in the circuit eg voltage

Once we know the nodal voltages we can find anything

This preview shows page 44 - 49 out of 49 pages.

Once we know the nodal voltages, we can find anything in the circuit! e.g., voltage across the 5Ω resistor in the middle is equal to V 1 V 2 ; voltage across the 3A source is V 1 ; voltage across the 2A source is V 2 ; and currents can be found via Ohm’s law. Prof. C.K. Tse: Circuit Analysis Review
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45 Nodal analysis In general, we formulate the solution in terms of unknown nodal voltages: [ G ] [ V ] = [ I ] nodal equation where [ G ] is the conductance matrix [ V ] is the unknown node voltage vector [ I ] is the source vector For a short cut in setting up the above matrix equation, see Sec. 3.3.1.2 of the textbook . This may be picked up in the tutorial. Prof. C.K. Tse: Circuit Analysis Review
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46 Nodal analysis — observing superposition Consider the previous example. The nodal equation is given by: Thus, the solution can be written as Remember what 3 and 2 are? They are the sources! The above solution can also be written as or SUPERPOSITION of two sources Prof. C.K. Tse: Circuit Analysis Review
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47 Problem with voltage sources The nodal method may run into trouble if the circuit has voltage source(s). Suppose we define the unknowns in the same way, i.e., V 1 , V 2 and V 3 . The trouble is that we don’t know what current is flowing through the 2V source! How can we set up the KCL equation for nodes 2 and 3? One solution is to ignore nodes 1 and 3. Instead we look at the supernode merging 2 and 3. So, we set up KCL equations for node 1 and the supernode: One more equation: V 3 V 2 = 2 Finally, solve the equations. Prof. C.K. Tse: Circuit Analysis Review
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48 In all cases, we see that the mesh method ends up with N equations and N unknowns, where N is the number of nodes of the circuit minus 1. One important point: The nodal method is over-complex when applied to circuits with voltage source(s). WHY? We don’t need N equations for circuits with voltage source(s) because the node voltages are partly known! In the previous example, it seems unnecessary to solve for both V 2 and V 3 because their difference is known to be 2! This is a waste of efforts! Can we improve it? Complexity of nodal method Prof. C.K. Tse: Circuit Analysis Review
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49 Final note on superposition Superposition is a consequence of linearity. We may conclude that for any linear circuit, any voltage or current can be written as linear combination of the sources. Suppose we have a circuit which contains two voltage sources V 1 , V 2 and I 3 . And, suppose we wish to find I x . Without doing anything, we know for sure that the following is correct: I x = a V 1 + b V 2 + c I 3 where a, b and c are some constants. Is this property useful? Can we use this property for analysis? We may pick this up in the tutorial. I x V 1 V 2 I 3 Prof. C.K. Tse: Circuit Analysis Review
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  • Summer '16
  • Martin Chow
  • Thévenin's theorem, Voltage source, Norton's theorem, Current Source, Series and parallel circuits, Voltage drop

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