Mason.m uses mason's rule to simplify signal flow graphs. It takes a file describing the network and produces a symbolic equation relating a dependent output node to an independent input node.
Mason's rule is traditionally used for control system analysis but has applications in microwave circuit design, filter design and many other areas.
This program crunches down a signal flow graph to generate a symbolic equation for the equivalent phaser relating an output node and an input node. For example:
1 s21 2
*------>------*------------.
| | |
| | |
s11 v ^ s22 v R2
| | |
| | |
*------<------*------------'
3 s12 4
There are four nodes 1,2,3 and 4, and there are 5 Coefficients S11,S21, S12,S22 and R2. If we set node 1 as an independent input node, and choose node 3 as a dependent node we get the following simplification:
1
a ---> *
|
| R2
v b/a= s11+s21* -------- *s12
| 1-s22*R2
|
b <--- *
3
If we set node 1 as the independent input node, and node 2 as the dependent output node we get:
1 2
a ---> *------>------* ---> b
s21
b/a = --------
1-s22*R2
This program generates these equations for a given network and pair of nodes.
A network description file is used to specify the topology of the flow diagram. Each node is assigned a number, and each branch is defined a coefficient number. Each branch is described as one line in a file, defined as follows:
[Coefficient #] [Start Node #] [Stop Node #] [Coefficient Name]
The Coefficient numbers must be in order (starting at 1 not 0). For example, to describe the following diagram (where coefficient numbers are in brackets),
1 (1) s21 2
*------>------*------------.
| | |
| | |
(4) s11 v ^ (2) s22 v (5) R2
| | |
| | |
*------<------*------------'
3 (3) s12 4
we can use this file (where the white space are tabs, but any white space should suffice):
1 1 2 s21
2 4 2 s22
3 4 3 s12
4 1 3 s11
5 2 4 R2
This is saved as 'example.net' in this directory
The coefficient name can be any valid symbolic expression used in Maple. If the expression has multiple terms then enclose them in brackets. For example:
(-D*z^(-1)) or (1+B)
It is important that the lines in the net file be ordered so that the coefficient numbers count from 1 up. Don't use 0 to number the coefficients or nodes! Once you have made the net file, run 'mason.m' from Matlab, as described below:
USAGE:
[Numerator,Denominator] = mason(Netfile,StartNode,StopNode)
Netfile - is a string with the name of the netfile to load
StartNode - is the integer number describing the independent input node
StopNode - is the integer number describing the dependent output node
Numerator - is a string containing the equation for the Numerator
Denominator - is a string containing the equation for the Denominator
Try out the example network! To recreate the above examples use:
[Numerator,Denominator] = mason('example.net',1,3)
[Numerator,Denominator] = mason('example.net',1,2)
mason.m -- the mason's rule function. Type help mason for arguments.
example.net -- the example network described in the theory section.
I have tested this program with many different networks, and used it a lot in my research. However don't assume it is perfect! If you find any bugs, or if you find this program useful, give me a shout.
Rob Walton --- 2000
Written at TRLabs, Calgary, Alberta, Canada.
Original code is here: http://www.mathworks.com/matlabcentral/fileexchange/22-mason-m .
Mathworks recently asked me to update the license file on this. While doing this I thought I might put it up here on github where someone might find it useful. It is not beautiful but seems to have withstood the tests of time.
(Only this readme file differs from the code on mathworks.)