ES442 Final Project AM & FM De/Modulation Using SIMULINK Goal: 1. Understand the basics of SIMULINK and how it works within MATLAB. 2. Be able to create, configure and run a simple model. 3. Create a subsystem. 4. Utilize variables between the MATLAB workspace and the SIMULINK model space. 5. Apply and investigate AM and FM modulation within SIMULINK. Background: SIMULINK is a model based difference or differential equation solver using simulation time/time steps as a fundamental basis for the simulation's construction and evaluation. A model consists of sources and sinks and intermediate blocks that represent basic dynamical system elements. These elements can be as basic as passive elements such as power supplies, sine waves, resistors, capacitors etc. to complex enigmatic entities like neural networks and image processing engines. Each entity within the model contains properties that control the function and the characteristics of each block. These properties need to be configured to represent the system being modeled. In addition to the model elements the equation solver that governs the simulation needs to be configured as well. SIMULINK enables quick evaluation of simple to complex systems and can shed insight into system behavior in a fraction of the time of physical prototypes. While the suggested reading and activity will only scratch the surface of SIMULINK it is intended to bring the reader up to a basic understanding of SIMULINK and its interaction within MATLAB. A typical SIMULINK work flow session will consist of the following steps 1. Type ">>simulink" at MATLAB prompt 2. Create new model from the SIMULINK library browser menu pull downs: FILE- >New Model 3. Add blocks that correspond to model dynamics/functions: Sine waveforms, constants, filters, ramps, scopes, user functions etc. 4. Define the blocks; add details about sources, sinks, operators. There are many resources to construct model topologies As previously mentioned each block needs to be defined with appropriate model parameters. If it's a spring model, an appropriate "K" value needs to be defined. If it's a sine waveform: Amplitude, frequency, phase need to be defined. 5. Save the Model. 6. Set simulation Options/ Solver options: The type of solver to use ODE45, ODE3, etc. These are provided with MATLAB The time step and various differential equation boundary conditions should be defined. 7. Run the model 8. Configure the output either with outputs within SIMULINK or export data to the MATLAB workspace for more control over the plotting, or additional post processing. Ver.1 1
Read the provided handout in PIAZZA for details on how to work with SIMULINK and create models. The following link provide valuable resources for how to create basic models using SIMULINK: https://www.mathworks.com/academia/student_center/tutorials/sltutorial_launchpad.html?confirmation_page# Lab Activity It is important to go through the handout. This project is based on the examples in the handout. AM Modulation 1. Create a DSB- SC AM modulator model. See Pg 128 of the handout. The model should look similar to the figure below: M(t) and Carrier are sine waveforms. The product, gain, and SCOPE blocks can be found by searching "product", "gain" and "SCOPE", respectively within the library browser: Note that the frequency for the carrier is set to 10 Hz. The frequency for the modulating frequency is set to 1 Hz. Tips to construct the model using SIMULINK: Ver.1 2
Left click to pull signals from output to input of blocks. Right click to create a branch from an existing signal path. To create a SCOPE with more than one input modify the "Number of axes" property within the SCOPE properties window double click on the SCOPE and then click on the gear to get to the SCOPE parameters. Any variable defined in the MATLAB workspace can be used within SIMULINK. Try typing >>fc = 10 >>fm = 1 In the Main MATLAB window use fc and fm instead of 1 and 10 within the sine waveform properties. This will come in handy to experiment with different model parameters in more complex models. 2. We now need to configure the solver. See the following configurations: Ver.1 3
Form the SIMULINK window run the simulation. The SCOPE should be able to be configured to show something similar to what is shown below. Double click on the SCOPE block after running the simulation to view the SCOPE traces. Ver.1 4
If the output is only a portion of the recorded waveform the "history" of samples recorded may need to be modified, or the waveform needs to be set to AUTO scale (shown below). 3. Condense the two blocks in the AM modulation model (the gain block and the multiplier block) into a subsystem as shown below. This can be done by selecting the two blocks and then right clicking and selecting "create subsystem". Run the simulation again confirm that the system still works. Take a snapshot of the output of the SCOPE. Answer the following questions: a. What happens if you change the GAIN value to unity? b. Why do we call this type of modulation SC (suppressed carrier)? Ver.1 5
FM Modulation Use a new file and create the FM modulation model shown below. Read page 130 of the handout for more details. The mathematical expression of the FM modulated signal will be In our model we assume: kf = 5Hz/V, fc = 10Hz and modulating waveform is s(t) = cos(2*pi*t). The VCO block is actually a user defined function, search "Fcn." Double click on the "Fcn" block and add desired function with "U" representing the input to the function. Ver.1 6
Configure the blocks to suit the system. The Discrete- Time Integrator should have a sample time of 0.01 (the same as the simulation sample time, previously set in the AM Modulation portion). Configure the solver. Refer to the AM modulation solver configuration. Run the simulation. The SCOPE should be able to be configured to show something similar to what is shown below: If the output is only a portion of the recorded waveform the "history" of samples record may need to be modified, or the waveform needs to be set to auto scale. Ver.1 7
Condense the two FM modulation blocks into one FM modulation subsystem as shown below. Run the simulation again confirm that the system still works. Take a snapshot of the output of the SCOPE. Using MATLAB Code Within SIMULINK In this section we would like to modify the "ADD" block with a user provided MATLAB function. 1. Copy your previously created FM modulator subsystem. Enter into the subsystem and delete the "ADD" block. Search for "MATLAB Function" and add it to your model subsystem. Double click on the MATLAB Function Block and enter in the code below in the MATLAB block. Save the function. Ver.1 8
Add the block into the location where the ADD block used to be: Run the simulation, confirm that the simulation provides the same output. Change the GAIN to 15. Take a snapshot of the SCOPE results. NOTE: If there is any problem with this section please report it! Ver.1 9
Using SIMULINK to Display Signal Spectrum In this section you need to model a complete FM modulator/demodulator and analyze the output of each section. Download the FM_Mod_Dem file and unzip it. Open the following file in the folder and run it using MATLAB: Setup_FM_Mod_Dem_Partial.m. You should see the following: Note that the FM modulator is similar to the modulator you created in the previous section. 1. Take snapshots of the spectrum of the message signal and FM signal. Elaborate on the results. What is the carrier frequency? What is the bandwidth? 2. Pay attention to how the Spectrum Analyzers are setup; click on and check the setting. 3. Click on different tabs and observe the setting for SCOPE Properties, Display Properties, Axis Properties, and Line Properties. 4. Modify the model (circuit) as shown below and rename the mdl file. Note that the block represents a LPF. The characteristics of the filter is defined as follow: This is specified in the Setup_FM_Mod_Dem_Partial.m file. Ver.1 10
5. Run the simulator and observe the output. Take a snapshot of the FOUR signals captured by the SCOPE. 6. Explain briefly how the demodulator operates. Ver.1 11