Understanding VCCS Circuit Analysis: Solving for Vo in terms of Vi

[Jarvis323]

I solved for Vo in terms of Vi and I get the negative of the correct answer according to the book. Someone told me that the TA set the node to the left of Vo = to -Vo, and this explains why my answer is the negative, but I don't understand why the node adjacent to Vo is -Vo instead of just Vo.

 

[railgundoc]

I think I know why it becomes -Vo. Draw out the flow of current on the left side and it should be going upwards right?

When you do the analysis, you would do (ground-Vo)/2 = gm*vx, giving the -Vo

 

[Jarvis323]

But if you do the KCL that way, then you are defining the current (ground - Vo) / 2 going into the node, and the other current is going out, so they must be defined to be of opposite sign. So you would instead subtract and you would get the same thing

gmVx + (Vo - 0) = 0
or
gmVx - (0 - Vo) = 0

either way it's the same thing.

 

[rude man]

But if you do the KCL that way, then you are defining the current (ground - Vo) / 2 going into the node, and the other current is going out, so they must be defined to be of opposite sign. So you would instead subtract and you would get the same thing

gmVx + (Vo - 0) = 0
or
gmVx - (0 - Vo) = 0

.

These equations are dimensionally inconsistent.

Summing currents at Vo to zero one obtains
gmVx + Vo/2K = 0

 

[Jarvis323]

These equations are dimensionally inconsistent.

Summing currents at Vo to zero one obtains
gmVx + Vo/2K = 0

Your right, I accidentally left out the / 2k on the post. But I still don't see why it should be the negative.

 

[rude man]

Your right, I accidentally left out the / 2k on the post. But I still don't see why it should be the negative.

Look at the equation summing currents to zero!

 

[Jarvis323]

The equation summing currents to 0 gives Vo = -gmVx. In the problem, gm is 2m / 1 ohm. I solve the left side using mesh analysis, or voltage division and get Vx = .5 Vi, then with node analysis on the right side, you get Vo = -2Vx, Vo = -Vi. But the book gets Vo = Vi.

So rude man also gets the wrong answer. But why?

 

[rude man]

The equation summing currents to 0 gives Vo = -gmVx. In the problem, gm is 2m / 1 ohm. I solve the left side using mesh analysis and get Vx = .5 Vi, then with node analysis on the right side, you get Vo = -2Vx, Vo = -Vi. But the book gets Vo = Vi.

So rude man also gets the wrong answer. But why?

Rude man doesn't get the wrong answer, neither do you. The book gets the wrong answer.

PS what does "gm is 2m / 1 ohm" mean? I assume it means gm = 1 mA/V. Otherwise you don't get Vo = - Vi for an answer.

 

[Jarvis323]

You're right, sorry, I meant that the book gets Vo = 2 Vi, and I get Vo = -2Vi.

But are you sure the book is wrong? On another forum, I got one person agreeing with me that the book is wrong, and another person said this,

the circuit shown equals the classical equivalent small-signal ac circuit diagram for a common emitter transistor amplifier. As you will know, this amplifier has inverting gain characteristics.
Thus, for a positive input voltage, the output is negative, indeed.

 

[rude man]

You're right, sorry, I meant that the book gets Vo = 2 Vi, and I get Vo = -2Vi.

But are you sure the book is wrong? On another forum, I got one person agreeing with me that the book is wrong, and another person said this,

OK, then the VCCS gm = 2mA/V. But Vo is still negative.

Unless you have the polarity of gm wrong too. If gm = -2mA/V then Vo = +2Vi.

Try to get all the parameters stated right ... would be helpful ...

 

[rude man]

You're right, sorry, I meant that the book gets Vo = 2 Vi, and I get Vo = -2Vi.

But are you sure the book is wrong? On another forum, I got one person agreeing with me that the book is wrong, and another person said this,

What's the problem? This statement ALSO says the output is negative!
We all agree the book is wrong!