Egerton University — Faculty of Engineering

Virtual Laboratory: Amplitude Modulation

EEEN 462 — Analog Communication  |  4th Year B.Sc. Electrical Engineering
Experiments: Full-Carrier DSB • DSB-SC • SSB • VSB  |  fc = 38 kHz, Ac = 1 V

1. Laboratory Objectives

By the end of this virtual laboratory, the student should be able to:

  1. Generate and analyse four amplitude-modulation schemes: full-carrier DSB (DSB-FC / conventional AM), suppressed-carrier DSB (DSB-SC), single-sideband (SSB) and vestigial-sideband (VSB).
  2. Compare the time-domain waveforms and frequency spectra of the four schemes for the same message signal (fc = 38 kHz, Ac = 1 V, 0 ≤ m ≤ 1.5).
  3. Investigate the effect of the modulation index on each scheme, including overmodulation distortion in DSB-FC.
  4. Determine and compare the transmission bandwidths: 2fm (DSB-FC, DSB-SC), fm (SSB) and fm + fv (VSB).
  5. Evaluate the power efficiency of each scheme and relate it to the presence or absence of the carrier.
  6. Recommend an appropriate AM scheme for a given application (broadcast, carrier telephony, TV video).

2. Theory

Let the message be m(t) = Amcos(2πfmt) and the carrier c(t) = Accos(2πfct), with fc = 38 kHz, Ac = 1 V and modulation index m = Am/Ac varied from 0 to 1.5.

2.1 Experiment 1 — Full-Carrier Double-Sideband AM (DSB-FC, Conventional AM)

s(t) = Ac[1 + m·cos(2πfmt)]cos(2πfct)
s(t) = Accos(2πfct) + (mAc/2)cos[2π(fc+fm)t] + (mAc/2)cos[2π(fc−fm)t]

The spectrum contains a carrier at fc plus upper and lower sidebands at fc ± fm, each of amplitude mAc/2. Bandwidth BT = 2fm. Total power PT = Pc(1 + m2/2) with Pc = Ac2/2, giving a maximum efficiency of only 33% at m = 1. For m > 1 (overmodulation) the envelope crosses zero and envelope detection fails.

2.2 Experiment 2 — Double-Sideband Suppressed-Carrier AM (DSB-SC)

s(t) = mAccos(2πfmt)cos(2πfct) = (mAc/2)cos[2π(fc+fm)t] + (mAc/2)cos[2π(fc−fm)t]

The carrier is suppressed (by a balanced modulator); only the two sidebands are transmitted. Bandwidth BT = 2fm, but 100% of the transmitted power now carries information. There is no envelope proportional to the message — the waveform exhibits phase reversals at each message zero-crossing — so coherent (synchronous) detection is required.

2.3 Experiment 3 — Single-Sideband AM (SSB)

sUSB(t) = (mAc/2)cos[2π(fc+fm)t]

One sideband (here the upper) is transmitted and the carrier and the other sideband are removed, e.g. by a sharp band-pass filter or the phase-shift method. Bandwidth BT = fm (half that of DSB), giving excellent spectral economy; power P = m2Ac2/8. SSB is used in long-distance telephony and HF radio. Demodulation requires carrier re-insertion (BFO) at the receiver.

2.4 Experiment 4 — Vestigial-Sideband AM (VSB)

s(t) = (mAc/2)cos[2π(fc+fm)t] + α(mAc/2)cos[2π(fc−fm)t],   α = 0.25

VSB transmits one sideband in full plus a vestige (a controlled fraction α) of the other. With the vestige, a simple gradual-cut filter suffices, and the vestige component compensates the sideband so that the demodulated baseband response is flat. Bandwidth BT = fm + fv, where fv is the vestige width (here fv = 0.25fm for demonstration). VSB is the standard for analogue television video.

2.5 Comparison of the Four Schemes

PropertyDSB-FCDSB-SCSSBVSB
Carrier transmittedYes (full power)SuppressedSuppressedSuppressed
Sidebands transmittedBothBothOneOne + vestige
Bandwidth2fm2fmfmfm + fv
Max. efficiency33% (m = 1)100%100%≈ 94%
DetectionEnvelope (simple)CoherentCoherent / BFOCoherent / envelope + filter
Typical useAM broadcastingCarrier telephonyHF radio, telephonyTV video
Key insight: Moving from DSB-FC to SSB saves 3/4 of the bandwidth, while suppressing the carrier saves up to two-thirds of the power. The price is increased transmitter/receiver complexity.
Display note: A 38 kHz carrier is far too fast to draw on screen, so time-domain plots show a fixed 4 ms window with a display carrier scaled to 20 kHz (y-axis fixed at −2 V to +2 V); the displayed message frequency therefore visibly changes as fm changes. All frequency-spectrum plots use the true 38 kHz carrier with a fixed ±15 kHz window.

3. Procedure

3.1 Pre-Lab

  1. Review the theory for all four schemes and write the equations for s(t), BT and PT in each case.
  2. For fm = 1 kHz and m = 0.5, pre-calculate the sideband frequencies and bandwidths for Experiments 1–4.

3.2 Experiment 1 — DSB-FC

  1. Select the DSB-FC tab. Set fm = 1 kHz, m = 0.5.
  2. Observe the message, envelope and AM waveform; sketch Amax and Amin in your notebook.
  3. Sweep m = 0, 0.5, 0.8, 1.0, 1.2, 1.5. Record the modulation status and observe envelope zero-crossings for m > 1.
  4. Record sideband amplitudes and positions from the spectrum; verify BT = 2fm for fm = 0.5, 1, 2, 3 kHz.
  5. Record Pc, PSB, PT and η for m = 0.3, 0.5, 0.7, 0.9, 1.0.

3.3 Experiment 2 — DSB-SC

  1. Select the DSB-SC tab with fm = 1 kHz, m = 0.5.
  2. Observe the waveform: confirm the phase reversals at message zero-crossings and the absence of a faithful envelope.
  3. Sweep m from 0 to 1.5 and note how the whole waveform scales. Explain why "overmodulation distortion" does not apply here.
  4. From the spectrum, confirm that the carrier component at 38 kHz is absent and verify BT = 2fm.
  5. Record the total power and efficiency and compare with DSB-FC at the same m.

3.4 Experiment 3 — SSB

  1. Select the SSB (USB) tab with fm = 1 kHz, m = 0.5.
  2. Observe the single-tone waveform and the single spectral line at fc + fm.
  3. Vary fm over 0.5, 1, 2, 3 kHz and record the sideband position; verify BT = fm.
  4. Sweep m from 0 to 1.5 and record the transmitted power. Compare the SSB power and bandwidth with DSB-SC at the same m.

3.5 Experiment 4 — VSB

  1. Select the VSB tab (vestige factor α = 0.25) with fm = 1 kHz, m = 0.5.
  2. Observe the main sideband at fc + fm and the vestige at fc − fm (25% amplitude). Sketch the spectrum.
  3. Vary fm and record the occupied bandwidth BT = fm + fv, fv = 0.25fm.
  4. Sweep m from 0 to 1.5; record power and efficiency and compare with SSB and DSB-SC.

3.6 Wrap-Up

  1. Construct a summary table of bandwidth, power and efficiency for the four schemes at m = 1.0, fm = 1 kHz.
  2. Answer the discussion questions in Section 5 and write your report.

4. Interactive Simulation

Fixed parameters: carrier frequency fc = 38 kHz, carrier amplitude Ac = 1 V. Select an experiment tab and vary fm and m. Time-domain plots show a fixed 4 ms window (0–4 ms) with the y-axis fixed at −2 V to +2 V, so the displayed message frequency changes as fm changes; spectra use the true 38 kHz carrier over a fixed ±15 kHz window.

Scheme
DSB-FC
Status
m < 1
Sideband(s)
—
Bandwidth BT
—
Total power PT
—
Efficiency η
—

4.1 Waveforms

4.2 Frequency Spectrum (true carrier at 38 kHz)

5. Guidelines for Report Writing

Your report should be a formal, individually written, typed A4 document with the following structure:

  1. Title Page: Egerton University; Faculty of Engineering; EEEN 462 — Analog Communication; experiment title (Amplitude Modulation Virtual Laboratory: DSB-FC, DSB-SC, SSB and VSB); your name and registration number; date; lecturer's name.
  2. Abstract: A short paragraph (5–8 lines) summarising the four experiments and the main comparative findings.
  3. Objectives: As listed in Section 1.
  4. Theory: In your own words, the time-domain and frequency-domain descriptions of the four schemes, including bandwidth and power expressions.
  5. Procedure: A concise account of what you actually did, with the simulator settings for each experiment.
  6. Results:
    • Tables of measurements for each experiment (fm, m, spectral components, BT, PT, η).
    • Waveform and spectrum screenshots for each scheme at m = 0.5 and m = 1.0 (and m = 1.3 for DSB-FC to show overmodulation).
    • A single summary table comparing all four schemes at m = 1.0, fm = 1 kHz.
    • Graphs of PT and η versus m (0–1.5) for DSB-FC and DSB-SC on one set of axes.
  7. Analysis / Discussion: Answer:
    1. Verify from your data that BT = 2fm for DSB, fm for SSB and fm + fv for VSB.
    2. Using your DSB-FC plots at m > 1, explain why an envelope detector produces distortion during overmodulation.
    3. Explain why DSB-SC has no envelope, and state the consequence for receiver design.
    4. Why is SSB preferred over DSB-SC for HF radio links, and what is the trade-off?
    5. Compare the power efficiency of DSB-FC (m = 1) with DSB-SC at the same m. Where does the wasted power go in DSB-FC?
    6. Why is VSB (rather than SSB) used for analogue TV video transmission?
  8. Conclusion: Relate your findings to the objectives; state which scheme you would select for (i) AM broadcasting, (ii) long-haul telephony, and (iii) TV video, with justification.
  9. References: Cite the course textbook and this virtual laboratory (IEEE style).
Presentation: Typically 10–15 pages including figures. All figures must be numbered, captioned and referenced in the text. Indicative marking: Theory 15%, Procedure 10%, Results 35%, Discussion 30%, Presentation 10%.

6. References

  1. L. W. Couch II, Digital and Analog Communication Systems, 8th ed., Pearson, 2013.
  2. S. Haykin and M. Moher, Communication Systems, 5th ed., Wiley, 2009.
  3. B. P. Lathi and Z. Ding, Modern Digital and Analog Communication Systems, 4th ed., Oxford University Press, 2009.
  4. EEEN 462 Course Notes, Department of Electrical and Electronic Engineering, Egerton University.