circuit analysisnortonthevenin
In the following diagram, the Thévenin equivalent of the circuit on the left is shown on the right:
simulate this circuit – Schematic created using CircuitLab
However, it appears that there is no Norton equivalent for this circuit.
Similarly, the following diagram shows a circuit whose Norton equivalent exists, but there appears to be no Thévenin equivalent for it:
Since \$i_x \$ is not associated in any way with the output port AB, \$i_x\$ is an independent variable and thus, as seen from the port AB, the CCVS is an independent source. The Thevenin equivalent is:
simulate this circuit – Schematic created using CircuitLab
The difference in the signs of the solutions lies in the directions chosen for the current. So, the answers are equivalent, the current is just flowing in the opposite direction to which you have selected.
Best Answer
A Thevenin or Norton equivalent is a circuit that has the same I-V curve as some more complex linear network, but itself contains only two elements: a source and a resistor or conductor.
In your first circuit, resistor R1 is irrelevant to finding the Thevening equivalent. Since R1 is in parallel with a voltage source, the overall I-V curve is just a vertical line through 1 V, as if you had only a voltage source. Which is exactly what your Thevenin equivalent circuit shows.
The reason you can't find a Norton equivalent circuit is because a Norton circuit can't produce a vertical line I-V curve with finite element values. You could create (or at least think about) a Norton equivalent circuit in limit as \$I\to\infty\$, if you maintain \$G=\frac{I}{1\mathrm{V}}\$ as you increase I.
The second circuit is just the dual. It has a horizontal I-V curve, and a Thevenin circuit can't have a horizontal curve with finite values.