Nodal Analysis (KCL): Correct My Equations

In summary, the person is unsure about the equations and is looking for guidance. The equations are correct, but the dependent sources are throwing him off.
  • #1
magnifik
360
0
For the following circuit, can someone please correct my equations for nodal analysis (KCL)
9i5w11.png


I am especially unsure about my second equation because of the dependent voltage source to the left of the node.

1) I1 = (V1 - 3I2)/1
2) 0 = V3/2 + (V3 -V2)/2
3) I2 = (V2-V3)/2 + 2V3
 
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  • #2
(1) and (2) are wrong.

N.B., current flows though every element in the circuit.
 
  • #3
NascentOxygen said:
(1) and (2) are wrong.

N.B., current flows though every element in the circuit.

the dependent sources are throwing me off. are the equations at least partially correct?
 
  • #4
magnifik said:
the dependent sources are throwing me off. are the equations at least partially correct?

Your third equation is okay. The first equation is ignoring the fact that the controlled voltage source 3I2 is connected to V3, not ground. The second equation is ignoring any current that may be flowing into the V3 node via the 3I2 source.

What is it you are expected to solve for? Is it the three voltages in terms of currents I1 and I2?

You might find it beneficial to write an equation in terms of the supernode (as indicated by the line breaks):

attachment.php?attachmentid=40509&stc=1&d=1320006593.gif
 

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  • #5
gneill said:
Your third equation is okay. The first equation is ignoring the fact that the controlled voltage source 3I2 is connected to V3, not ground. The second equation is ignoring any current that may be flowing into the V3 node via the 3I2 source.

What is it you are expected to solve for? Is it the three voltages in terms of currents I1 and I2?

ultimately, i will be solving for y-param. i was able to do so using mesh analysis instead, but i was hoping to try and obtain the nodal equations to double check my answers.
 
  • #6
magnifik said:
ultimately, i will be solving for y-param. i was able to do so using mesh analysis instead, but i was hoping to try and obtain the nodal equations to double check my answers.

Are you wanting the Y parameters only for the two-port? That is, just for V1-I1 as the input and V2-I2 as the output, in effect reducing the whole circuit to just a two-port?
 

1. What is nodal analysis (KCL)?

Nodal analysis, also known as Kirchhoff's Current Law (KCL), is a method used to analyze and solve electrical circuits by applying the principle of conservation of charge. It involves identifying and analyzing the voltage and current at each node (connection point) in a circuit.

2. How do you apply KCL in nodal analysis?

To apply KCL in nodal analysis, you need to follow these steps:

  • Choose a reference node (usually the node with the most connections) and assign it a reference voltage of 0V.
  • Write down the Kirchhoff's Current Law equation for each node, which states that the sum of currents entering a node is equal to the sum of currents leaving that node.
  • Substitute the known and unknown currents into the equations, using Ohm's Law (V=IR) to calculate any unknown currents.
  • Solve the resulting system of equations to find the unknown currents and voltages at each node.

3. What are some common mistakes to avoid in nodal analysis?

Some common mistakes to avoid in nodal analysis include:

  • Forgetting to include a voltage source in the equations.
  • Mixing up the signs (positive or negative) of the currents.
  • Not using the correct reference node.
  • Using the wrong units (e.g. forgetting to convert mA to A).
  • Not including all the nodes in the circuit.

4. Can KCL be used in any type of circuit?

Yes, KCL can be used in any type of circuit, as long as the circuit is linear (i.e. follows Ohm's Law) and has a constant voltage source. It can be applied to both DC and AC circuits, and is a fundamental tool for analyzing and solving electrical circuits.

5. How is nodal analysis (KCL) different from other circuit analysis methods?

Nodal analysis (KCL) is different from other circuit analysis methods, such as mesh analysis and Thevenin's theorem, in that it is based on the principle of conservation of charge. It focuses on analyzing the currents at each node in a circuit, while other methods may focus on voltage drops or power calculations. Nodal analysis can also be used to solve more complex circuits that may be difficult to solve using other methods.

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