Performing Mesh analysis with current sources...?

Question

Someone told me I need a positive voltage source to perform mesh analysis on this circuit:

http://img260.imageshack.us/img260/4665/deletemecircuituz9.jpg

Is this true?

I don't see how the voltages in the outer loop can add to 0.

I've solved this with nodal analysis but have not been able to with mesh analysis yet. The equations I've come up with are:

(both currents assumed clockwise)

i2 - i1 = Va/4
i2 = -1

I was thinking a Supermesh would provide the third equation I need but all I see from that is:

i1*2 + i2*3 = 0 but from the PSpice analysis I know this isn't going to lead to a solution.

Thanks

In case anyone is unfamiliar with PSpice, the current source in the middle of the circuit is a voltage controlled current source. The reference voltage is from nodes above and below the other current source.

The gain is set to .25.

I was able to solve the problem by using the VCCS to determine the potential
across the constant current source. I'm not sure what rule I am using
though.

When creating a supermesh around the entire circuit it seems to me like the
constant current source should be the loop current. I don't see why I
should have thought to calculate the voltage across the current source in
the first place...

Here are the final equations I've used:

i1 - i2 = Vab/4 -constraint from VCCS
i2 = -1 -known loop current
2(i1) - 3 = (i1 + 1)4 -supermesh


If anyone can help me understand what rules state to do this or what logic should have led me to the solution in the first place, please respond!

Jared-

But I thought I did use a supermesh in the end, by adding the voltage drops across both resistors and then the voltage drop across the current source.... That is not a supermesh?

Joa-

Things are looking clearer the more I look at this but I do not follow your calculations...

You mention V several times- what voltage does this refer to?

You said i2 = .25V. I know i2 is 3.5A so this would require V = 14V. There isn't a 14V node in this circuit though...

Answer 1

A super mesh isn't going to help you - you only have 2 meshes so a supermesh will include the entire circuit.

First, stop trying to understand it. With dependant sources the answer is usually counter-intuitive unless you have seen that exact problem 100 times before (like with a MOSFET or something). Second, the laws of physics will always hold true, whether or not it is intuitive to you.

The sum of the voltages around the mesh will be zero. Remmember, i1 and i2 are unique quanties to that mesh so the border will be i1-i2 or i2-i1. Just write the equations down without rationalizing in your head what you think can and can't happen, and the answer will pop out.

Answer 2

You can't use the supermesh. Well maybe you don't need to at any rate. They seem to work well when a node has a "naked" current source. And while that may look to be the case, the dependent source is paired with the 2 ohm resistor. And because the source is dependent, I think only one loop equation results:

V - 3*i1 - 2*(i1+i2) = 0 (V across the 1 A source)

but clearly i1 = 1 and i2 = 0.25*V, so it is easy to solve for V and then the two voltages.

Another approach would be to convert the dependent source to Thevenin Equivelent. That would give you a the voltage source that you mention. It was just hidden as current source. In the end, it's all the same.

As for the total loop not appearing to sum to zero volts, the current sources do have a voltage across them. It is easy to forget that because theoretically they have an infinite resistance. In this circuit, that is why the currents from either source do not flow into the other source's leg, and ultimately, cause the the loop voltages to sum to zero.