1. SIMULINK EXAMPLE
transmitter
Receiver
Channel
Lets assume we would like to represent a channel
by using SIMULINK.
Lets define a channel as a low-pass filter. R
Y(t)
X(t) C

2. In the time domain we get :

3. Simulation goals H(z) source scope In Out
Definitions before we start to build the model:
1 - Drawing the icon picture
X(t)
Y(t) R C
F cut-off = [Hz]

4. 2 – User guide window
T-sample R C
3 -Look under mask
T-sample In R C
4 – S function

5. METHOD 1

6. Step – 1 -Setup the working environment
1) Define the relevant path
2) Building the block model by:
File
new
model

7. Step – 2 -input ports
Build input ports
system in
out
S-function

8. Connecting the block constant
Step Operation with Mask editor called “Edit Mask ”
Icon on the Block
Click right mouth
This is the frame where you build the windows guide
ICON
PARAMETERS
Init..
Documentation
Prompt Variable Type
Tsample edit
R edit
C edit
Connecting the block constant
to the real parameters
Mask type
Mask description

9. fprintf(‘Fcutoff=%1.2f’,1/RC) %plot([x],[y]) plot([0,0.2],[0.8,0.8])
Step – 3-1 – draw icon 01 11 00 10
Units “Normalized
0.85
0.80
0.75 R C
fprintf(‘Fcutoff=%1.2f’,1/RC)
%plot([x],[y])
plot([0,0.2],[0.8,0.8])
plot ([0.2, 0.2, 0.5, 0.5, 0.2],[0.75,0.85,0.85,0.75,0.75])
Plot([0.5,1],[0.8,0.8])

10. Step – 3-2 - Operation with Mask editor called “Edit Mask ”

13. The model should look like :

14. Step – 4 -Start with S - function
S – function contains the name of the program and
users parameters
Choose the S-Function from the “User Define function” library
S-function name should be the same as the name of the file.m

15. Function(sys, xo, str, ts)=s_function_name(t,x,u,flag,parameters)
Step – 4-1: S-function
returns
inputs
Function(sys, xo, str, ts)=s_function_name(t,x,u,flag,parameters)
s_function_name
Gets:
t- running time
x – state variable
u- input signal
flag – s_function status flag
Returns
sys – model parament array
x0 – initial state conditions
str – state ordering string
ts – sampling time
Model_name <> S-Function name
function [sys,x0,str,ts] = sfunc_DiffequLPF(t,x,u,flag,Tsample,R,C)

16. The model should look like :
Double
click

17. Step – 4:1 – Defining the S-function
a) Initialization – setup number of input and outputs
function [sys,x0,str,ts]=mdlInitializeSizes
% call simsizes for a sizes structure, fill it in and convert it to a
% sizes array.
% Note that in this example, the values are hard coded. This is not a
% recommended practice as the characteristics of the block are typically
% defined by the S-function parameters.
sizes = simsizes;
sizes.NumContStates = 0;
sizes.NumDiscStates = 1; represent the Number of delay units in the iir
sizes.NumOutputs = 1; dynamic size allocation
sizes.NumInputs = -1; dynamic size allocation
sizes.DirFeedthrough = 1; input dependency
sizes.NumSampleTimes = 1; % at least one sample time is needed
sys = simsizes(sizes);

18. function sys=mdlDerivatives(t,x,u) Stay without changes
% initialize the initial conditions
x0 = []; x0 = [0]; Initial conditions
% str is always an empty matrix
str = [];
% initialize the array of sample times
ts = [0 0];
function sys=mdlDerivatives(t,x,u) Stay without changes
sys = [];
% end mdlDerivatives

19. TS = An m-by-2 matrix containing the sample time
% (period, offset) information. Where m = number of sample times. The ordering of the sample times must be:
% TS = [ , : Continuous sample time.
% , : Continuous, but fixed in minor step sample time.
% PERIOD OFFSET, : Discrete sample time where PERIOD > 0 & OFFSET < PERIOD.
% ]; : Variable step discrete sample time where FLAG=4 is used to get time of next hit.
% There can be more than one sample time providing they are ordered such that they are monotonically increasing. Only the needed sample times should be specified in TS. When specifying than one sample time, you must check for sample hits explicitly by eeing if
abs(round((T-OFFSET)/PERIOD) - (T-OFFSET)/PERIOD)
is within a specified tolerance, generally 1e-8. This tolerance is dependent upon your model's sampling times and simulation time.
You can also specify that the sample time of the S-function is inherited from the driving block. For functions which change during minor steps, this is done by specifying SYS(7) = 1 and TS = [-1 0]. For functions which
are held during minor steps, this is done by specifying SYS(7) = 1 and TS = [-1 1].

20. function sys=mdlUpdate(t,x,u,Tsample,R,C)
% This is where the discrete state is updated
% Yo(n+1) = Yo(n)*(1-a) + a*Yi(n).
% The state x corresponds to the state at the previous time step,
% which is Yo(n-1)
% uri
tau = R*C;
alpha = tau/Tsample;
sys = x*alpha/(1 + alpha) + u/(alpha+1);
% end mdlUpdate
=========================================
% mdlOutputs
% Return the block outputs.
function sys=mdlOutputs(t,x,u,Tsample)
sys = x; % The x state now is Yo(n), which is the same as sys from
% the mdlUpdate function
% end mdlOutputs

21. METHOD 2

22. Step – 1 -Setup the working environment
1) Define the relevant path
2) Building the block model by:
File
new
model
Step – 2 -Start with the lowest hierarchy
Choose the “constant” block from the source simulink library as the number of the parameter needed to be installed
Select “input port” from the sources sub library
Select “output port” from the sink sub library
Drag each to the model frame work and you may get:

23. Untitled window 1
system in
out
S-function
constant
S – function may contains the program to be executed

24. Step – S Function
Choose the S-Function from the “User Define function” library
Step – 4 -Combining the MUX
Choose the “MUX” block from the signal routing library
Press double click
Select 4 inputs
The connections order should be according –
Input - should port one
Other - constants

25. Step – 5 : connecting the following and getting the picture
Tsample
sfunc_DiffequLPF
Constant 1
Out^^ R
S-function
Constant 2 C
Constant 3
Create sub-system
In**
Out^^

26. Connecting the block constant
Step Operation with Mask editor called “Edit Mask ”
Icon on the Block
Click right mouth
This is the frame where you build the windows guide
ICON
PARAMETERS
Init..
Documentation
Prompt Variable Type
Tsample edit
R edit
C edit
Connecting the block constant
to the real parameters
Mask type
Mask description

27. fprintf(‘Fcutoff=%1.2f’,1/RC) %plot([x],[y]) plot([0,0.2],[0.8,0.8])
Step – 6-1 – draw icon 01 11 00 10
Units “Normalized
0.85
0.80
0.75 R C
fprintf(‘Fcutoff=%1.2f’,1/RC)
%plot([x],[y])
plot([0,0.2],[0.8,0.8])
plot ([0.2, 0.2, 0.5, 0.5, 0.2],[0.75,0.85,0.85,0.75,0.75])
Plot([0.5,1],[0.8,0.8])

28. Step - 6 - Operation with Mask editor called “Edit Mask ”

31. The model should look like :

32. Function(sys, xo, str, ts)=s_function_name(t,x,u,flag)
Step - 7 – s-function
returns
inputs
Function(sys, xo, str, ts)=s_function_name(t,x,u,flag)
s_function_name
Gets:
t- running time
x – state variable
u- input signal
flag – s_function status flag
Returns
sys – model parament array
x0 – initial state conditions
str – state ordering string
ts – sampling time
Model_name <> S-Function name

33. Step – 7:1 – Defining the S-function
a) Initialization – setup number of input and outputs
function [sys,x0,str,ts]=mdlInitializeSizes
% call simsizes for a sizes structure, fill it in and convert it to a
% sizes array.
% Note that in this example, the values are hard coded. This is not a
% recommended practice as the characteristics of the block are typically
% defined by the S-function parameters.
sizes = simsizes;
sizes.NumContStates = 0;
sizes.NumDiscStates = 1; represent the Number of delay units in the iir
sizes.NumOutputs = 1; dynamic size allocation
sizes.NumInputs = -1; dynamic size allocation
sizes.DirFeedthrough = 1; input dependency
sizes.NumSampleTimes = 1; % at least one sample time is needed
sys = simsizes(sizes);

34. function sys=mdlDerivatives(t,x,u) Stay without changes
% initialize the initial conditions
x0 = []; x0 = [0]; Initial conditions
% str is always an empty matrix
str = [];
% initialize the array of sample times
ts = [0 0];
function sys=mdlDerivatives(t,x,u) Stay without changes
sys = [];
% end mdlDerivatives

35. function sys=mdlUpdate(t,x,u)
% This is where the discrete state is updated
% Yo(n+1) = Yo(n)*(1-a) + a*Yi(n).
% The state x corresponds to the state at the previous time step,
% which is Yo(n-1)
% uri
Tsample = u(2); R = u(3); C = u(4);
tau = R*C;
alpha = tau/Tsample;
sys = x*alpha/(1 + alpha) + u(1)/(alpha+1);
% end mdlUpdate
=========================================
% mdlOutputs
% Return the block outputs.
function sys=mdlOutputs(t,x,u)
sys = x; % The x state now is Yo(n), which is the same as sys from
% the mdlUpdate function
% end mdlOutputs