Understanding Electrical Network Theory Equations: Confusion on Pg 101

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Discussion Overview

The discussion centers around confusion regarding specific equations presented in the book "Electrical Network Theory" by Balabanian and Bickart, particularly on page 101. Participants are trying to understand the implications of equations 67-72, which relate to the treatment of sources and passive elements in electrical networks, within the context of network topology and analysis.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant expresses confusion about the equations AI=AIg and BV=BVg, suggesting they relate to separating sources from passive elements in a network.
  • Another participant requests a visual reference of the page to facilitate understanding.
  • A participant elaborates that the author discusses a generalized network branch and the treatment of sources as accompanied for analysis purposes, mentioning that A is a node graph matrix and B is a loop matrix.
  • One participant speculates that if Ai=0 (KCL), then the current can be separated into currents through passive elements and sources, but finds the notation unclear regarding the branch current column matrix.
  • A participant references external class notes that discuss generalized network branches and nodal analysis, noting differences in notation that may affect understanding.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the interpretation of the equations or the author's intent. Multiple viewpoints and interpretations are presented, indicating ongoing confusion and debate.

Contextual Notes

There are limitations in the discussion, including missing visual references, incomplete external resources, and potential differences in notation that may affect clarity and understanding of the equations.

jesse7771
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Im currently reading through the classic book on electrical network theory Balabanian and Bickarts electrical network theory. And I am getting confused on page 101, and the set of equations their... Eq's 67-72 dealing with accompanied sources and what exactly he's trying to imply with these equations... I am thinking from the direction he goes afterwards that these equations are dealing with the separation of sources from the passive elements in the network, but the way they are written in giving me a hard time.

The equations are:
AI=AIg
BV=BVg

And I-Ig=B'Im
V-Vg=A'Vn

Thanks for any input
 
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Can you provide a picture of the page in question? It might help generate some responses.
 
I don't have a smart phone or scanner sorry... The author going over a generalized network branch, and how you can treat all sources as accompanied for the sake of dealing with sources and passive elements seperatly in a network. This whole chapter is going over topology in network analysis, and where A is a node graph matrix and B is a loop matrix and ig and vg are source column matrixes.
 
Sorry for this oddly specific question, the author is using it to formulate nodal and loop analysis for circuits. My only thought would be that if Ai=0 (KCL) and I can be separated into a current though the passive element and a current through the source in a generalized branch then A(ip-ig)=0 then Aip=Aig, where ip would be the current through the parrallel passive element in the branch and ig would be the parrallel branch. But from the notation it is clear that i in the would be the branch current column matrix, meaning simply the current through the branches which seems natural to assume all the current through the branches. The 3rd equation would follow where i-ig=B'im, but this is not what the equations are saying at all.

The only discussion I could find of this was in a graduate level network theory class's notes but they are incomplete in this section... http://classes.engr.oregonstate.edu/eecs/fall2013/ece580/Lecture%20Notes/p1-21.pdf The generalized network branch is on page 17 and page 18 goes into nodal analysis but uses a slightly different notation which seems to be more consistent with KCL and KVL