Circuit Nodal Analysis: Writing Node Equations

In summary: There are two possible interpretations of Vo as the potential at opposing ends of R1. This is a minor detail but, when you're first learning this stuff, it can make a difference.In summary, the conversation discusses setting up node equations in terms of literal variables and the potential and current values associated with different resistors in a circuit. The concept of "literal variables" is defined and the approach for setting up node equations is explained. The question also raises a potential ambiguity in the polarities of the potentials across the resistors.
  • #1
Celostrophus
5
0

Homework Statement



34sgdp0.png

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
 
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  • #2
Hi Celostrophus! Welcome to Physics Forums. :smile:

What is meant by a "literal variable"?
 
  • #3
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...
 
  • #4
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
 
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  • #5
Celostrophus said:
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.
 
  • #6
Celostrophus said:

Homework Statement



34sgdp0.png

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.
 

FAQ: Circuit Nodal Analysis: Writing Node Equations

What is circuit nodal analysis?

Circuit nodal analysis is a method used to analyze electrical circuits by writing node equations. It involves identifying and labeling the nodes (points where three or more components connect) in a circuit and using Kirchhoff's Current Law (KCL) to write equations at each node. These equations can then be solved to find the unknown node voltages.

How do I write node equations in circuit nodal analysis?

To write node equations, you first need to identify all the nodes in the circuit and label them. Then, at each node, apply KCL to write an equation in terms of the node voltages and the currents entering and leaving the node. Finally, solve the equations simultaneously to find the node voltages.

What is Kirchhoff's Current Law (KCL)?

Kirchhoff's Current Law (KCL) states that the sum of currents entering a node in a circuit must be equal to the sum of currents leaving the node. This law is based on the principle of conservation of charge and is a fundamental concept in circuit analysis.

Can circuit nodal analysis be used for both DC and AC circuits?

Yes, circuit nodal analysis can be used for both DC (direct current) and AC (alternating current) circuits. However, for AC circuits, additional considerations need to be made for the frequency and phase of the currents and voltages.

What are the advantages of using circuit nodal analysis?

Circuit nodal analysis is a powerful and versatile method for analyzing electrical circuits. It allows for the analysis of complex circuits with multiple nodes and components. It also provides a systematic approach for solving circuit problems and can be used for both DC and AC circuits. Additionally, it can be easily extended to include more advanced circuit elements, such as dependent sources and non-linear components.

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