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Mason's rule

We can use Mason's rule to solve for the relationship between of any two nodes in the network.

Let T be the transfer ratio between two nodes

where 		 text_wrap_inline2889, text_wrap_inline2891, ... are the various paths connecting the nodes,

text_wrap_inline2893 is a first order loop,

text_wrap_inline2895 is a second order loop,

text_wrap_inline2897 is a first order loop that does not touch path text_wrap_inline2889,

text_wrap_inline2901 is a second order loop that does not touch path text_wrap_inline2889.

A first order loop is defined as the product of the branches encounter starting from a node and moving in the direction of the arrows back to its origin.

A second order loop is the product of two non-touching first order loops.

Example 1 We want to find the ratio text_wrap_inline2905.


Similarly, we can also find

Example 2 We want to find the power delivered from a source to a load as shown in Figure 14. The power delivered is

Figure 14: Flow graph for a load connected to a source


If the load is conjugately matched to the source, i.e., text_wrap_inline2907, P becomes the available power from the source