Talk:Nodal analysis

Untitled
some example with an image would be useful

Here's a circuit that's useful for explaining nodal analysis. To be truly useful though, it needs to have some nodes labeled. Then the article can be updated with an actual example of solving this circuit. TheAmigo42 (talk) 22:31, 22 April 2008 (UTC)

Dubious
only for linear circuits? according to academicearth.org/lectures/nonlinear-analysis node analysis is suitable for non-linear circuits. the lecture use word "node" instead of "nodal" but it seems approach is the same? can some expert verify this.


 * You're right, nonlinear circuits can be solved by nodal analysis. The trick is using Newton's method to turn the nonlinear problem into a series of linear problems, but the nodal equations certainly apply. I've added a mention of this. YoungGeezer (talk) 21:51, 15 August 2009 (UTC)

Flawed image
The image showing the currents entering and leaving the node is in error because one of the currents is entering via a simple wire. Wherever it is coming from would be part ofnthe same node. — Preceding unsigned comment added by 68.116.10.119 (talk) 03:23, 18 September 2011 (UTC)

KVL?
In item 7 the article states:

"The KCL and KVL equations form a system of simultaneous equations that can be solved for the voltage at each node."

As far as I know, the KVL equations don't appear explicitly because they are automatically fulfilled by this method (which is one of its great advantages). I think the words "and KVL" should be removed from this sentence. (ezander) 89.183.29.180 (talk) 15:33, 12 August 2008 (UTC)


 * You're right, KVL doesn't enter into it. I think what the original writer was trying to say was that KCL and branch admittance relations, I=F(V), are used. Hopefully my edit clarifies this. YoungGeezer (talk) 21:49, 15 August 2009 (UTC)

A note about the big exclamation point and note stating that Wikipedia is not for presenting ' instructions, advice, or how-to content', nodal analysis is a process and is easiest to convey by listing the steps involved. —Preceding unsigned comment added by 24.30.129.175 (talk) 22:29, 8 February 2009 (UTC)

The matrix equation
I am thinking of add a new sub-section on the matrix form for the node-voltage equation for nodal analysis, as discussed in section 3.6 "Nodal and Mesh Analyses by Inspection" in the textbook by Alexander and Sadiku. In the book, the equation is only presented, here I added a brief derivation and a discussion on its singularity. Gamebm (talk) 15:17, 1 August 2017 (UTC)

Matrix form for the node-voltage equation
In general, for a circuit with $$N$$ nodes, the node-voltage equations obtained by nodal analysis can be written in a matrix form as derived in the following. For any node $$k$$, KCL states $$\sum_{j\ne k}G_{jk}(v_k-v_j)=0$$ where $$G_{kj}=G_{jk}$$ is the negative of the sum of the conductances between nodes $$k$$ and $$j$$, and $$v_k$$ is the voltage of node $$k$$. This implies $$0=\sum_{j\ne k}G_{jk}(v_k-v_j)=\sum_{j\ne k}G_{jk}v_k-\sum_{j\ne k}G_{jk}v_j=G_{kk}v_k-\sum_{j\ne k}G_{jk}v_j$$ where $$G_{kk}$$ is the sum of conductances connected to node $$k$$. We note that the first term contributes linearly to the node $$k$$ via $$G_{kk}$$, while the second term contributes linearly to each node $$j$$ connected to the node $$k$$ via $$G_{jk}$$ with a minus sign. If an independent current source/input $$i_k$$ is also attached to node $$k$$, the above expression is generalized to $$i_k=G_{kk}v_k-\sum_{j\ne k}G_{jk}v_j$$. It is readily to show that one can combine the above node-voltage equations for all $$N$$ nodes, and write them down in the following matrix form

\begin{pmatrix} G_{11} &G_{12} &\cdots  &G_{1N} \\ G_{21} &G_{22} &\cdots  &G_{2N} \\ \vdots &\vdots &\ddots  & \vdots\\ G_{N1} &G_{N2} &\cdots  &G_{NN} \end{pmatrix} \begin{pmatrix} v_1\\ v_2\\ \vdots\\ v_N \end{pmatrix}= \begin{pmatrix} i_1\\ i_2\\ \vdots\\ i_N \end{pmatrix} $$ or simply
 * $$Gv=i$$

It is worth noting that the matrix $$G$$ on the left hand side of the equation is singular since it satisfies $$G 1=0$$ where $$1$$ is a $$1\times N$$ column matrix. This corresponds to the fact of current conservation, namely, $$\sum_{k}i_k=0$$, and the freedom to choose a reference node (ground).


 * It might be interesting to cite Alexander & Sadiku as a reference for this section. I was a little confused by it but found no references for further clarification... Lucky I found this in the talk page. 2804:14D:4CDC:A0C1:C98D:E7E5:205E:546D (talk) 01:00, 11 March 2020 (UTC)

Changing the reference node DOES change the results
In section Procedure, the second step says "Select one node as the ground reference. The choice does not affect the result and is just a matter of convention." Well, whether the results change when a difference node is selected as ground depends on what "results" mean here.

If "results" mean the node voltages, which what actually you first compute in nodal analysis, then it's false that changing the ground node doesn't change the results.

If "results" mean the element voltages and/or branch currents, then it's true that changing the ground node doesn't change the results.

Regardless, I think it should be specified. For example, the second step should say "Select one node as the ground reference. The choice does not affect the element voltages and branch currents and is just a matter of convention, though it changes the node voltages." --Alej27 (talk) 00:38, 20 November 2020 (UTC)