Equivalent Branch Reduction

If an electrical branch contains more than one series element, then this branch will be 'collapsed' into an equivalent resistance and current source, effectively removing unnecessary nodes (i.e. decreasing the size of the network conductance matrix) and enhancing solution speed.

 

By the time the network is solved, the branch will be seen as an equivalent conductance.  This technique is illustrated below:

 

 

 

Figure 3-2 - Equivalent Branch Reduction

 

In this convenient form, other branches of the same type may be paralleled between the same nodes, simply by adding the equivalent branch conductance and current sources.