Digital_Communications_Part_A

DSBSC
...

Double Sideband Suppressed Carrier
...

types_dsbsc_map.png

The first type of AM modulation is the most simple one, but probably one the most used one 🙂

Important

Make sure that you fully understand the DSBSC.

  • The other types of AM modulation built from this one
  • Later, during the digital modulation techniques (Part B of this course), a lot of the knowledge from the DSBSC will be useful to understand digital modulations concepts.

Block Diagram
...

design_icon.png
DSBSC_block_diagram.png

Lab Bench
...

lab_icon.png

Using the lab equipment, I connect an analog carrier signal at 100 kHz to input 1 of a multiplication module, and an analog baseband signal at 2 kHz to input 2 on that same multiplication module.

Carrier and Baseband Signals
...

  • Orange Line: baseband signal
  • Blue Line: carrier signal

Time Domain Waveform
dsbsc_carrier_baseband_time.png

dsbsc_carrier_baseband_time_zoom.png

Frequency Spectrum
dsbsc_carrier_baseband_spectrum.png

Modulated Signal
...

  • Orange Line: baseband signal
  • Blue Line: modulation output

Time Domain Waveform
dsbsc_modulation_baseband_time.png

dsbsc_modulation_baseband_time_zoom.png

Note
  • We can see the amplitude of the carrier being modulated by the baseband signal generating the modulation output .
  • We see the envelope of the carrier changing accordingly
Important

There is a small thing that we need to know about the hardware multiplication module that I am using:

  • The output of the multiplication module is equal to , with k approximately equal to 1/2.
  • That is why we don't see the maximum amplitude of the modulation output signal (in the time domain) equal to but rather .
  • That k factor is 1/2 so that, with standard level inputs, later stages of the BiSKIT are not overloaded.

Frequency Spectrum
dsbsc_modulation_spectrum.png

dsbsc_modulation_spectrum_zoom.png

Note
  • We can observe that the modulated signal (in blue) contains two sidebands around the suppressed carrier .
  • Those sidebands are at frequencies

Time Domain Analysis
...

theory_icon.png

  • Baseband:
  • Carrier:

The modulation output is the following:
We can use Desmos (or similar mathematical toolboxes) to validate the mathematical expressions.

Important

In order to match the results from the Lab section, we need to adjust the modulation output by 1/2, which is the k factor present on the hardware multiplication module.

  • The theoretical equation doesn't reflect that but the equation on Desmos does.

Frequency Domain Analysis
...

Now it is time to verify the spectrum domain starting from the time domain equation.
There are two ways to get the spectrum, and they give the same answer.

Option 1
...

We apply the following trigonometric identity to :
And then apply the following Fourier Transform pair:

Option 2
...

We apply directly the modulation Fourier Transform property:

  • where the carrier is the modulator
  • and is the baseband signal
    Since is the following Fourier Transform pair:
    We get to the same result as option 1:

Frequency Spectrum
...

Waveforms software only shows the positive side of the spectrum. With that in mind we can eliminate the frequencies that are negative from () and rewrite the equation as:

Note

If we sketch we get the spectrum below, which complies with what we observed.

  • Suppressed carrier on the modulated signal
  • Two sidebands at frequencies

fourier_spectrum_icon.pngSpectrum
dsbsc_modulation_spectrum_math.png
However, the magnitudes from the graph above are not equal to what we observed in the lab bench spectrum:

Info

A couple more things to get the spectrum magnitude correct:

  • Don't forget to divide by 1/2 due to the k factor of the hardware multiplication module.
  • We don't need to worry about the value because on the Waveforms software, if we compute the FFT using the Vpeak which is relative to 1V amplitude sine wave, cancels out.
    waveforms_vpeak_parameter.png

With these adjustments, the magnitudes are now the same.

Summary
...

  • In DSBSC the carrier signal is completely suppressed from the AM signal.

  • The two sidebands contain complete contents of the modulating signal.

  • It is a power efficient method compared with other AM types.

  • One disadvantage of using DSBSC is that the resultant envelope is not a faithful representation of the modulating signal. This is more noticeable when complex waveforms such as speech are used.

  • Because there is no carrier, the receiver side or demodulator will have a harder time synchronizing with the carrier.

  • DSBSC AM is not often used in analog communication systems. However, it forms the basis for generating another AM type signal, the single-sideband suppressed-carrier (SSBSC), or just single-sideband (SSB) signals.

References
...

Table Of Contents

DSBSC

Double Sideband Suppressed Carrier

Block Diagram

Lab Bench

Carrier and Baseband Signals

Modulated Signal

Time Domain Analysis

Frequency Domain Analysis

Option 1

Option 2

Frequency Spectrum

Summary

References