Synchronous and Asynchronous Demodulation of AM, Exponential Carriers, Envelope Detection

Objective

The objective of this lab is to deepen students understanding of synchronous and asynchronous demodulation principles for amplitude modulation.

AM-DSB/SC, Synchronous Demodulation, Complex Exponential Carrier

1. Build a complex exponential modulator and the corresponding synchronous demodulator.  A block diagram of these systems is shown below.
   



2. Use the same input signal as before (in Lab 2a).
3. Note that modulating a real signal x(t) by a complex exponential actually requires multiplication by cos and sin. This yields a real (cos) and an imaginary (sin) channel. Demodulation by multiplication with a complex exponential will require four real multiplies and two adds.  The imaginary part of the result should be zero. Therefore, you only need to compute the real part and simply let w(t) be the real part of the complex multiplication.  However, compute the imaginary part also and show that it is zero or very small.
   
4. Use To Workspace blocks to export the signals y(t) and w(t) to the workspace.
5. Make spectral plots of the three signals x(t), y(t), and w(t).  Write an explanation and turn it in to the lab TA.

AM-DSB/WC, Asynchronous Demodulation, Sinusoidal Carrier

1. An asynchronous demodulator for AM-DSB/WC looks like



2. The first task is to design the envelope detector shown below.



3. Roughly the operation of this circuit is as follows.  When the input voltage is greater than the output voltage, the output voltage tracks the input.  When the input voltage falls below the output voltage, the output voltage decays exponentially with time constant 1/RC.  This functionality is easy to build into a Simulink model shown below.



4. The parameters for the MATLAB Fcn block are as shown here.



5. The value 0.05 in the exponential is the value of T/RC where T is the time between samples.  In this case T=1 because we are assuming a sample rate of one sample per second.  The matlab function implements the logic described above--output the input if the input is greater than the output otherwise output a decayed version of the previous output.  This was described in step 3 above.
6. Note that the operation of the diode has been replaced by the Abs function.  This means that we are tracking the envelope of the absolute value of the signal rather than the positive part of the signal.
7. Add the rest of the blocks as shown below and run the simulation to see the operation of the envelope detector.



8. Set the frequency of the Sine Wave block to 0.04 and set the Simulation Parameters as shown here.



9. Double click the scope display and you will see this.



10. The cyan line is the sine wave source, the magenta line is the rectified signal, and the yellow line is the envelope detected signal.  Change the 1/RC (see step 5 above) constant and the frequency of the sine wave source and see how the envelope changes.
11. Now you are ready to build the AM-DSB/WC modulator and the synchronous demodulator in Simulink.  Use a carrier frequency of 0.3.  Use a Sine Wave block as the modulating signal x(t). Let the frequency of this signal be 0.003.  Remember that envelope detectors need the carrier frequency to be much greater than the highest frequency in the modulating signal.
12. Before you add the final low pass filter, use To Workspace blocks to extract the modulating signal x(t) and the envelope detector output z(t).  Plot the spectra of x(t) and z(t)-A using the function you wrote for Lab 1. When I did this, I got the following.





13. The lower figure is a zoom of the upper figure around DC.  You can see that the envelope detector output z(t)-A differs from the modulating signal x(t) by some extra high frequency components and component at DC.  These spectral plots should give you some ideas on how to design the low pass filter to remove the high frequency components in z(t)-A.  For illustration, the following figure shows x(t) and z(t)-A.  Which one is which?



14. Complete the asynchronous demodulator by designing the low pass filter and filtering z(t)-A to produce w(t).  The following figure shows x(t) and w(t).  Which one is which?  Is w(t) close enough to x(t) to be acceptable?



15. Print and turn in plots of the signals x(t), y(t), z(t), and w(t).  Also print and plots of the spectra of x(t) and z(t)-A. Plot the magnitude response of the low pass filter you applied to z(t)-A to produce w(t).  Explain how you selected the filter parameters (cut off frequency, gain, etc.).  Turn all of this in to the lab TA.