Circuit Nodal Analysis: Writing Node Equations

[Celostrophus]

Homework Statement

a)Write two node equations in terms of the literal variables.

I1 = Is1
I2 = gm2Vo
I3 = gm1Va
I4 = Is2

Va = Voltage across R2
Vo = Voltage across R1
Vb = Voltage across R3

Homework Equations

The Attempt at a Solution

I tried setting up nodes right above R2 and Right above R3 but it didn't work. I'm really unsure how to approach this problem as our professor only gave us basic examples and our textbook doesn't really have good examples...

Va(G1 + G3 - gm1) - VoG3 = -Is1
Va(-gm1 - G3) + VbG2 + Vo(G3 - gm2) = -Is2

 

[NascentOxygen]

Hi Celostrophus! Welcome to Physics Forums.

What is meant by a "literal variable"?

 

[Celostrophus]

I have no idea. It's not explained or defined anywhere in the textbook which is one of the reasons I was having trouble solving the problem. Poor wording by the writers I guess...

 

[Ratch]

Celostrophus,

You seem to have trouble setting up node equations. So why don't you try again by writing the equations with all components that touch each node on the left side of the equation, and the voltage/current sources plus the voltages from the other nodes on the right side of the equations. I will give you the first one.

Va(G1+G2)= I1-I3+VoG1

Now, you do the second equation for Vo. We can fill in the dependent current sources later. By the way, are you sure that I2 and I3 are defined correctly?

Ratch

 

[The Electrician]

I have no idea. It's not explained or defined anywhere in the textbook which is one of the reasons I was having trouble solving the problem. Poor wording by the writers I guess...

"Literal variable", or "Literal coefficient", or just "Literal", is a concept from your first algebra class:

http://www.blurtit.com/q7030015.html

http://www.calculatoredge.com/math/advmath/advans28.htm

The question just wants a symbolic solution which is your only option anyway since no numerical values are given.

 

[gneill]

Homework Statement

a)Write two node equations in terms of the literal variables.

I1 = Is1
I2 = gm2Vo
I3 = gm1Va
I4 = Is2

Va = Voltage across R2
Vo = Voltage across R1
Vb = Voltage across R3

Are there particular polarities associated with these potentials across resistors?

While it may be only slightly dubious to assume that Va and Vb are associated with the node voltages at the top of R2 and R3 respectively where, by convention, the bottom rail is assumed to be the common (ground) node, we're not given any such 'hints' for the potential across R1.