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Mesh analysis of circuit

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Using mesh analysis, find the voltage gain Av = V2/V1 in the circuit. See attached file for full problem description.

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This solution looks at a mesh analysis of a circuit.

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Using mesh analysis for each of the loops:
1: -V1 + i1 + 2i1 - 2i2 = 0 and V = 2i1 - 2i2
2: -2i1 + 2i2 + 4i2 + 4i2 - 4i3 - 2V = 0
Substituting V = 2i1 - 2i2 loop 2 becomes:
2: -2i1 + 2i2 + 4i2 ...

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