Mason's Rule Solver
===================
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.
Theory
------
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.
Specifying the Network
----------------------
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)```
Using the Program
-----------------
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)
```
File Details
------------
```mason.m``` -- the mason's rule function. Type help mason for arguments.
```example.net``` -- the example network described in the theory section.
About the program
-----------------
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.
Update from 2016
----------------
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.)
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