Im currently reading through the classic book on electrical network theory Balabanian and Bickarts electrical network theory. And Im getting confused on page 101, and the set of equations their... Eq's 67-72 dealing with accompanied sources and what exactly hes trying to imply with these equations... Im thinking from the direction he goes afterwards that these equations are dealing with the seperation 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
I dont 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 seperated 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 Notes/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