07-11-2012, 11:35 AM
Circuit Analysis Techniques
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We learned that KVLs, KCLs, and i-v characteristics equations results in a set of linear
equations for the circuit variables (typically 2E equations in 2E circuit variables where E is
number of elements).W e learned that we can use i-v characteristics equations when we are
marking the circuit variables and reduce the number of equation to be solved to E equations
in E unknowns (which is the same as number of KCLs plus KVLs).In this section, we
learn two methods, node-voltage and mesh-current, which reduce the number of equations
to either number of KCLs or number of KVLs.These are node-voltage and mesh-current
methods.T hey also form the basis to deduce certain properties of linear circuits.
Node-Voltage Method
The node-voltage method is based on following idea.Instead of solving for circuit variables,
i and v of each element, we solve for a different set of parameters, node voltages in this case,
which automatically satisfy KVLs.As such, we do not need to write KVLs and only need
to solve KCLs.
Recipe for Node Voltage Method
1.Iden tify nodes and supernodes.
a) Choose the reference node as the one with maximum number of voltage sources
attached to it.
b) Use i-v characteristic equations of IVS to find node voltage values and reduce the
number of unknowns
2.W rite KCL at each node or supernode.
3.Solv e node-voltage equations.
4.Calculate problem unknowns from node voltages. If you need to calculate the current
in a voltage source you may have to write KCL at a node connected to that voltage
source.