EE 351 · Interactive laboratory
Analog amplitude modulation
One message. Choose which spectral components to transmit.
Build on Week 1 spectra and Week 3 mixing. SSB and receiver operation are a preview beyond Week 3.
Time domain
Shared time axis; amplitudes in peak volts. All plots start at t = 0.
Solid: transmitted waveform. Dashed: ± analytic envelope magnitude. For overmodulated DSB-TC, dotted: signed modulation factor.
Under-modulated DSB-TC: the envelope follows the message and stays above zero.
100% DSB-TC modulation: the envelope just touches zero.
OVERMODULATION: the signed modulation factor crosses zero. The physical envelope folds upward, distorting envelope detection.
DSB-SC: carrier phase reverses at message zero crossings. The magnitude envelope follows |m(t)|, losing the message sign.
SSB with carrier: carrier and one sideband beat together. Its envelope is generally not a scaled copy of the message.
Single-tone SSB-SC is one shifted cosine with constant envelope. Its frequency carries the tone offset; it need not look like conventional AM.
μ = 0: no message-bearing sidebands. With a transmitted carrier only the carrier remains; with suppression the output is zero.
Frequency domain
- m(t) × kc(t): two sidebands
- Add carrier for TC
- Remove one sideband for SSB
A cosine of peak amplitude a contributes weight a/2 at each of ±f. Dashed outlines and × marks show removed lines; these are not transmitted energy. L = LSB, C = carrier, U = USB, named relative to +fc.
| Component | ±f (kHz) | Peak (V) | Each ± weight (V) |
|---|---|---|---|
| LSB | |||
| Carrier | |||
| USB |
The bracket shows the channel span for a baseband occupying 0…Bm, with Bm = fm. An ideal single spectral line has zero width; B for SSB is the general-message channel requirement, not a claim that this tone fills that band.
Bandwidth & power
- Message Bm
- Transmission BT
- Carrier power
- LSB / USB power
- Total power
- Information-bearing power
R = 1 Ω. Each cosine contributes a²/(2R). Carrier baseline Pc0 = Ac²/(2R); each retained sideband contributes Pc0μ²/4. DSB-TC: PT = Pc0(1 + μ²/2). Information fraction = retained sideband power / total power, not a measure of receiver performance.
Can this receiver recover the message?
Appropriate in the ideal model for DSB-TC with 0 < μ ≤ 1. Remove the envelope DC to recover a scaled message. A practical RC detector also needs suitable time constants.
Appropriate with exact carrier frequency and phase: s(t) × 2cos(2πfct) → ideal low-pass filter → DC removal → scaled message. SSB-SC needs carrier insertion/recovery; transmitted carrier can provide a reference.
Not appropriate: overmodulated DSB-TC produces a folded envelope. Coherent detection can still recover the ideal, unclipped signal.
Not appropriate: envelope detection loses sign in DSB-SC and yields a constant for this SSB-SC tone. Use synchronized coherent detection.
Generally distorted for SSB with a transmitted carrier. A dominant carrier and a weak sideband allow an approximation, not exact recovery. Reduced-carrier operation needs greater care; use coherent detection for faithful recovery.
No message is transmitted at μ = 0, so there is nothing to recover.
Solid: detector output. Dashed: expected scaled message (gain V/V). No automatic gain correction. Ideal noiseless channel, phase-aligned oscillator and ideal filtering; no PLL simulation.
Compare all four modes at these parameters
| Quantity | DSB-TC | DSB-SC | SSB-TC | SSB-SC |
|---|---|---|---|---|
| Carrier | Transmitted | Suppressed | Transmitted | Suppressed |
| Selected sidebands | LSB + USB | LSB + USB | USB | USB |
| Bandwidth | ||||
| Total power | ||||
| Envelope detection | Exact ideal recovery for 0 < μ ≤ 1 | No | Weak-sideband approximation only; generally distorted | No |
Suppression saves transmitted power at fixed component amplitudes. This is not an equal-output or equal-SNR comparison. At μ = 0 all sideband amplitudes are zero.
Think before you change it
- Hold fc fixed and predict both sideband frequencies when fm doubles. What happens to BT?
- Suppress the carrier. Which lines disappear, and how much power do you save?
- Keep only USB, then only LSB. Explain why their powers match but their waveform frequencies differ.
- Set μ = 1, then 1.3. Which detector still recovers a scaled message, and why?
- Which mode sends the fewest components? What receiver capability makes that possible?
Predict, change one parameter, then explain the result using both plots. These prompts are ungraded.
Learning outcomes
After working with this visualization, you should be able to:
- Explain AM schemes using waveforms and spectra.
- Determine carrier and sideband frequencies and transmitted bandwidth.
- Explain the effects of transmitting or suppressing the carrier and either sideband.
- Select an appropriate basic demodulation approach.
- Evaluate bandwidth and power trade-offs among AM schemes.
Model assumptions & equations
m(t) = Amcos(2πfmt), c(t) = Accos(2πfct). The multiplier sensitivity k has units V⁻¹, and μ = kAm. Thus k m(t)c(t) has units V. With k = 1 V⁻¹, DSB-SC matches the numerical multiplication convention in Week 3.
Define b = Acμ/2 and f± = fc ± fm. All four forms retain the same b:
- DSB-TC: s(t) = Ac[1 + μ cos(2πfmt)]cos(2πfct).
- DSB-SC: s(t) = k m(t)c(t) = b cos(2πf−t) + b cos(2πf+t).
- SSB-TC: s(t) = Accos(2πfct) + b cos(2πf±t).
- SSB-SC: s(t) = b cos(2πf±t). Choose + for USB or − for LSB.
For SSB-TC, the envelope is √[Ac² + b² + 2Acb cos(2πfmt)]. It is approximately Ac + b cos(2πfmt) only when b ≪ Ac. An exact envelope detector is therefore not a general SSB receiver.
Frequencies are in Hz internally. Voltages are peak amplitudes across a normalized 1 Ω load. Signals are infinite-duration ideal cosines with zero initial phase. Spectra are analytical line weights, not sampled FFT magnitudes or power spectral densities. SSB filtering is ideal component removal; practical filters and carrier recovery are outside this model.
Time traces are sampled densely for drawing; resizing changes neither calculations nor signal parameters. A suppressed carrier control still sets the multiplier reference amplitude Ac. μ remains the original DSB reference depth after suppression.