Experiment 2 : DSB-SC Modulation and Demodulation

Objective: DSB-SC Modulation and Demodulation

Description: In this experiment you will design an analog modulator and an analog demodulator. Both simple multiplier type and nonlinear element type Modulators/Demodulators will be constructed. You will compare the received signal with the transmitted signal and also study the effect of phase shift at the demodulator.

The carrier frequency will be 500kHz, which is in the commercial AM radio frequency range. The signal bandwidth will be 20kHz, which is the bandwidth needed for high quality music. (Actual systems may use a smaller bandwidth.)

Instructions

• 0. Recall:
  1. Recall that you need to set the simulation parameters T_SIM and T_SAMPLE (as you did in the first experiment).
  2. It would be a good idea to read the instructions for experiment 1 before starting.
  3. Save your models in separate .mdl files as you finish each part of the experiment.

• I. Initialization: Copy the initialization files for the experiment into your Matlab working directory. Note: You have to do the initialization again since the initialization files are different from those used in Experiment 1.

  The following constants should be set by the startup file. Use who in the matlab workspace to check if the constants are all there. Some additional constants may also be set, but you can ignore them.

  • F_CARR = 2*pi*5e05 ----------Carrier Frequency, rad/sec
  • T_PERIOD = 2*pi/F_CARR --------Time period of carrier
  • T_SAMPLE = T_PERIOD/4.01 ----Sampling period used in Simulink
  • FFT_NUM_PTS = 4096 ----------Number of points used for FFT
  • T_SIM = FFT_NUM_PTS*T_SAMPLE ------Time of simulation
  • NUM_SAMPLES = T_SIM/T_SAMPLE ------Total number of samples
  • BW_MESSAGE = 2*pi*2e04 ------Message Bandwidth.
  • F_CUTOFF = BW_MESSAGE*2 -----Cutoff frequency of lowpass Butterworth filter
  • F_BAND_LOW = F_CARR-F_CUTOFF -----Lower cutoff of bandpass Butterworth filter
  • F_BAND_HIGH = F_CARR+F_CUTOFF ----Higher cutoff of bandpass Butterworth filter
  • a_NONLIN = 2 ----------Linear component of Nonlinear Device.
  • b_NONLIN = 1 ----------Quadratic component of Nonlinear Device.

  To speed up your block selection, the library ece359lib also has standard blocks from the simulink menu.

• II. Multiplier Modulator/Demodulator: As in Figure 4.1 of the book
  1. Select the Message Signal block form the ece359lib library. This block produces a signal m(t) band-limited to BW_MESSAGE.
  2. Multiply this signal by a unit magnitude sinusoid at frequency F_CARR (rad/sec). It's okay to use a sine wave rather than a cosine wave (that we used in class), as long as you use the same sinusoid at the demodulator. The multiplier output is the modulated signal s(t) (the greek symbol phi(t) was used in class, but here s(t) is used instead).
  3. Now construct a multiplier demodulator. Use a Butterworth lowpass filter with cutoff F_CUTOFF, and order 5 for the demodulator.
  4. Adjust the demodulator oscillator amplitude (i.e. use a factor of 2) to make the demodulator output v(t) equal in amplitude to the input m(t).
  5. Look at the Fourier transforms of m(t), s(t), v(t). Use the scope block to see the time characteristics of the signals.

• III. Nonlinear Modulator/Demodulator Figure 4.3 of text. (You need to design the demodulator structure using the same nonlinear device.) This might be a big simulink model, refer to this link for additional help.

  1. For the same input signal m(t) as in II, implement the nonlinear device based modulator of Figure 4.3 of the text.
  2. Use a Butterworth order 3 band-pass filter with the parameters F_BAND_LOW, F_BAND_HIGH for the modulator. The nonlinear device may be obtained from ece359lib/Nonlinear Block. It has parameters a_NONLIN and b_NONLIN which have been preset to 2 and 1, respectively.
  3. Implement a nonlinear device based demodulator without using any multipliers. Hint: The demodulator has a structure very similar to that of the modulator, except that it has a lowpass filter at the end. Use the lowpass filter of II.
  4. Obtain the Fourier transforms of m(t), s(t), v(t). Use the scope block to see the time characteristics of the signals.

• IV. Phase Offset: Study the effect of phase offset between the carrier and the receiver.

  1. Use the setup of part II, but for m(t), use a sinusoid with frequency BW_MESSAGE/5 instead of the random Message Signal. You do not need the Fourier transform blocks for this part.
  2. Give the receiver oscillator phase offsets with respect to the transmit oscillator in the range from 0 to pi in steps of pi/4. Reminder Matlab accepts the pi symbol, no need to give the decimal approximation 3.14.
  3. Observe time domain characteristics of the received signal. Note the level of attenuation (with sign) of the received signal for different phase shifts. You must measure the attenuation using the scope. The Fourier transformer does not preserve the sign. (A rough estimate of the attenuation, obtained by looking at the scope will suffice).
  4. Plot the attenuation vs. phase shift. (Note the attenuation in a table and feed the data into Matlab to make a plot.) Take more phase offset values if needed.

Questions

1. Write the equations relating m(t), s(t), v(t). in II. (that is write the other two in terms of m(t) ) Verify your simulation results. You do not need to submit any plots for this part.
2. Submit a block diagram of II.
3. Submit a block diagram of III. Label any ambiguous components.
4. Write the equations relating m(t), s(t), v(t) in III. Your equations should explain the working of the demodulator.
5. Give plots of both m(t) and v(t) for III. Also give plots of the Fourier transforms of m(t), s(t) and v(t).
6. Explain with equations the phase-attenuation plot obtained in IV. Submit this plot.
7. Print the Fourier transform of the demodulated signal of part IV when phase shift is pi/2. Do you see anything unusual? Explain what you see.
8. Using the setup of part IV, and phase offset zero, show the transmitted signal with a solid line and the received one with a dashed line on the same plot. See scope for details. Comment on the delay between the two signals. Extra credit - Can you justify the value of this delay?