Digital_Communications_Part_A

SSB - Phasing Method
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types_phasing_map.png

Another way of generating SSB is called phasing method. This uses a technique called phase discrimination to cancel out one of the sidebands at the generation stage (instead of filtering it out afterwards).

Block Diagram
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ssb_phasing_method_block_diagram.png

The phasing method uses complex IQ processing to resolve the superposition of lower and upper sidebands at audio frequencies.

The complex mixer creates an I and Q component by splitting the signal into two DSBSC mixers that are modulated by a sine and cosine local oscillator (e.g. implemented by a phase shift of 90°). An Hilbert transformer shifts the Q component by 90° before entering the DSBSC mixer. The I and Q component are then added together to form the SSB signal.

I think just by looking at the block diagram, it is not too intuitive on how we cancel one of the sidebands by using complex numbers, but let's build this block diagram first, see it working and then validate the answer mathematically.

Lab Bench
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Probe 1 - Baseband Quadrature Generation
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We first start by generating a quadrature baseband signal by shifting by

  • Orange Line: baseband signal
  • Blue Line: quadrature signal

ssb_phasing_method_block_diagram_probe1.png

Time Domain Waveforms
ssb_phasing_time_probe1.gif

Probe 2 - IQ DSBSC Generation
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Second, we generate two DSBSC signals in quadrature to each other by multiplying with the respective carrier.

  • Orange Line: DSBSC signal
  • Blue Line: DSBSC signal

ssb_phasing_method_block_diagram_probe2.png

Time Domain Waveforms
ssb_phasing_time_probe2.png

Note

Notice on how we have two DSBSC signals with a modulation index in quadrature.

Frequency Domain Spectrum

  • Orange Line: DSBSC signal
  • Blue Line: DSBSC signal

ssb_phasing_spectrum_probe2.gif

Note

Looking at the spectrum we see that both DSBSC signals have the same sidebands, which makes sense because the spectrum makes all magnitudes positive.

However, if I was able to plot the Fourier Transform, I would see the DSBSC sidebands slightly different than what we see here.

If we plot the Fourier Transform, we get the following graphs:

ssb_phasing_fourier_probe2.png

Probe 3 - SSB Phasing Generation
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On the last step, we can see the final result by probing and confirm that one of the sidebands will cancel out and the other sideband will become the double in magnitude.

The cool part with this last step is that we can validate the Fourier Transform graphs 🙂

ssb_phasing_method_block_diagram_probe3.png

Frequency Domain Spectrum

  • Orange Line: DSBSC signal
  • Blue Line: DSBSC signal

ssb_phasing_spectrum_probe3.png

The cool part about this is, if I play around with the phase shifter that generates the signal that goes into the second DSBSC, we can choose which sideband we want to cancel out.

ssb_phasing_animation_probe3.gif

Or we could subtract the signals instead of adding to reverse the sidebands result.

Time Domain Analysis
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  • Baseband:
  • Carrier:

The good news about the theory is that we covered pretty much all of it already, we just need to formalize it.

Probe 1 - Baseband Quadrature Generation
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Generate a quadrature baseband signal by shifting by

Probe 2 - IQ DSBSC Generation
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Generate two DSBSC signals in quadrature to each other by multiplying with the respective carrier.
Quadrature carrier

Probe 3 - SSB Phasing Generation
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Last step, add or subtract with to get the SSB

Addition
Subtraction

Frequency Domain Analysis
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To make our life easier and this process a bit faster we can use the knowledge from the DSBSC section and from the Fourier Analysis Support Knowledge section.

Addition
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Recall that we can eliminate the frequencies that are negative from ():

Subtraction
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ssb_phasing_theory.png

Summary
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  • We get easier suppression results using the phasing method compared with the filtering method.

References
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Table Of Contents

SSB - Phasing Method

Block Diagram

Lab Bench

Probe 1 - Baseband Quadrature Generation

Probe 2 - IQ DSBSC Generation

Probe 3 - SSB Phasing Generation

Time Domain Analysis

Probe 1 - Baseband Quadrature Generation

Probe 2 - IQ DSBSC Generation

Probe 3 - SSB Phasing Generation

Frequency Domain Analysis

Addition

Subtraction

Summary

References