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Physics 2% exam weight

Communication Systems

Part of the MDCAT study roadmap. Physics topic phy-19 of Physics.

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Communication Systems

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

A communication system transfers information (voice, data, video) from a source to a destination using three elements: a transmitter, a transmission channel, and a receiver. The information signal (low-frequency audio) cannot be sent directly because it would require an antenna thousands of kilometres long. Modulation overcomes this by superimposing the information on a high-frequency carrier wave, shrinking the required antenna to roughly λ/2, where λ = c/f.

  • Amplitude Modulation (AM): carrier amplitude changes with the modulating signal; frequency stays constant. Bandwidth BW = 2 f_m.
  • Frequency Modulation (FM): carrier frequency changes; amplitude stays constant. Bandwidth uses Carson’s rule: BW = 2(Δf + f_m).
  • AM power: P_t = P_c (1 + m²/2), where m = modulation index = (A_max − A_min)/(A_max + A_min).

MDCAT tip: only 1 MCQ (≈2% weight) — focus on AM vs FM differences and the reason modulation is needed.

🟡 Standard — Regular Study (2d–2mo)

Standard content for students with a few days to months.

Why Modulation Is Necessary

Audio signals lie between 20 Hz and 20 kHz. Transmitting them directly would need an antenna of length λ/2 = c/(2f). At 1 kHz this gives 150 km — physically impossible. Shifting the signal onto a carrier of frequency f_c around the MHz band reduces the antenna to a few metres, avoids low-frequency mixing between stations, and lifts the signal above most atmospheric noise.

Amplitude Modulation

The instantaneous carrier amplitude follows the modulating waveform: A_c(1 + m sin ω_m t)·sin ω_c t. The modulation index m must stay ≤ 1; values above 1 cause envelope distortion and interference. The transmitted AM signal contains three frequency components: f_c − f_m, f_c, and f_c + f_m, giving a bandwidth of BW_AM = 2 f_m (twice the highest audio frequency).

Frequency Modulation

Here the carrier frequency swings around f_c by a peak deviation Δf, while amplitude remains constant. FM is far more noise-resistant because atmospheric and electrical disturbances are mostly amplitude-based and are rejected by the FM limiter. Bandwidth is given by Carson’s rule: BW_FM = 2(Δf + f_m) — substantially wider than AM, which is why FM stations are spaced ~200 kHz apart while AM stations use 10 kHz.

PropertyAMFM
Carrier property variedAmplitudeFrequency
Bandwidth formula2 f_m2(Δf + f_m)
Noise immunityLowerHigher
Typical bandwidth~10 kHz~200 kHz
Total power P_tP_c(1 + m²/2)Constant

Wave Propagation

Ground waves (≤ 2 MHz) follow Earth’s curvature, sky waves (2–30 MHz) reflect off the ionosphere for long-range broadcast, and space waves (> 30 MHz) travel line-of-sight for TV, satellites, and mobile links.

Common trap: students swap AM and FM bandwidth formulas. Remember — AM bandwidth = 2 f_m, FM uses Carson’s rule.

🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Modulation Index and Power Distribution

For an AM transmitter with carrier power P_c and modulation index m, the total radiated power is P_t = P_c(1 + m²/2). The sidebands each carry P_c m²/4, so useful information power is only P_c m²/2 — roughly one-third of P_t at m = 1. Operating below m = 1 wastes transmitter power in the carrier, while m > 1 produces over-modulation, where the envelope flattens and the recovered audio distorts.

Worked Example

A 1 MHz carrier is amplitude-modulated by a 5 kHz audio signal with m = 0.8.

  • Sideband frequencies: 995 kHz and 1005 kHz.
  • Bandwidth: BW = 2 × 5 kHz = 10 kHz.
  • If P_c = 9 kW, then P_t = 9 × (1 + 0.32) = 11.88 kW, with each sideband radiating 9 × (0.64)/4 = 1.44 kW.
  • Antenna length: minimum practical size is λ/4; the textbook λ/2 is the fundamental dipole. Higher carrier frequency → shorter antenna.
  • SNR trade-off: FM’s wider bandwidth improves SNR roughly as (Δf/f_m)² (Carson’s insight), at the cost of occupying more spectrum.
  • Digital successors: pulse-code modulation (PCM) and QAM extend these analogue principles; the bandwidth–noise trade-off persists in Shannon’s channel capacity theorem.
  • Propagation linkage: ground-wave absorption rises with frequency; sky-wave skip depends on the ionospheric critical frequency, set by solar activity — important when comparing AM radio ranges day vs night.

Common Mistakes

  • Forgetting that modulation index is dimensionless and capped at 1.
  • Using f_m instead of 2 f_m for AM bandwidth.
  • Assuming FM uses less spectrum than AM — usually the opposite.
  • Treating decibels as a unit of power instead of a ratio (10 log₁₀ P/P₀).

Practice Prompts

  1. An AM broadcast at 600 kHz uses a 4 kHz audio signal with m = 0.75. Compute the bandwidth and the fraction of total power carried by the sidebands.
  2. An FM station has Δf = 75 kHz and f_m = 15 kHz. Apply Carson’s rule and compare the result with an equivalent AM station’s bandwidth.

Exam strategy: one MCQ in 90 minutes — spend under 60 seconds. Eliminate options by checking AM vs FM property and the bandwidth formula.

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