Introduction to Analog Communication Systems

Every communication system requires a source (origin of the message), a channel (the physical medium the message travels through), and a destination (the intended recipient). The other options list useful building blocks, but only source–channel–destination is universal.

In the Shannon–Weaver model the transmitter converts/encodes the message into a signal suitable for the channel (e.g., via a transducer and modulator). The receiver performs the reverse operation at the destination end.

Noise is random, unwanted energy (thermal, shot, atmospheric, man-made) added to the signal. Attenuation is loss of signal strength; distortion is alteration of the waveform; multiplexing is a technique for sharing a channel, not an impairment.

Broadcasting is simplex: information flows in one direction only, from the transmitter to many receive-only receivers. Walkie-talkies are half-duplex; telephones are full-duplex.

Telephone-quality speech occupies roughly 300 Hz – 3.4 kHz (about 3.1 kHz of bandwidth). 20 Hz – 20 kHz is the full high-fidelity audio range, not the telephone band.

AM broadcasting uses the MF band (530–1700 kHz). FM broadcasting uses VHF (88–108 MHz); HF is shortwave; UHF hosts cellular and TV services.

Coaxial cable is a guided medium — the signal is physically contained within the cable. Sky wave, satellite links, and line-of-sight microwave are all unguided (wireless) channels.

The envelope of an AM wave is A_c[1 + μ·m(t)]. If μ > 1 the envelope crosses zero and the carrier undergoes phase reversals — the message is no longer contained in the envelope, so an envelope detector recovers a severely distorted signal and splatters interference into adjacent channels.

The detector requires 1/f_c ≪ RC ≪ 1/W. If RC is too large, the capacitor holds its charge and its voltage "cuts diagonally" across the tips of the RF cycles instead of following the envelope downward — producing distortion, especially at high modulation index and high audio frequencies.

The product detector multiplies the incoming wave by a locally generated carrier. The demodulated output scales by cos φ: a phase error attenuates the message (90° error nulls it completely) and a frequency error produces a beat tone. Hence a PLL must lock the local oscillator to the incoming carrier. The envelope detector simply follows the amplitude envelope and needs no reference.

Speech spans roughly 30–40 dB of dynamic range, but peaks are infrequent (average μ ≈ 0.3). Without a limiter, loud peaks would over-modulate the carrier (μ > 1), causing distortion and adjacent-channel splatter, while most of the time the signal would be under-modulated with poor SNR. The compressor raises quiet parts and clips peaks, keeping μ near its optimum.

Expanding i_C = a₀ + a₁v + a₂v² + … with v = c(t) + m(t), the square-law term yields a₂c²(t) + 2a₂c(t)m(t) + a₂m²(t). The cross-product 2a₂c(t)m(t) is exactly a DSB component at f_c ± f_m; the tuned tank then selects the carrier-plus-sideband group, completing the AM spectrum.

Propagation physics favors low frequencies: ground waves follow the Earth's curvature (LF/MF), and HF sky waves reflect from the ionosphere for intercontinental coverage. UHF/SHF signals travel essentially line-of-sight with little diffraction. The trade-off is that lower frequencies offer far less available bandwidth.

The defining feature of half-duplex is bidirectional capability with alternating, non-simultaneous use of a shared channel. Push-to-talk forces turn-taking: while A transmits, B can only receive, and vice versa. Simplex would mean a station could never transmit (or never receive).

AM bandwidth = 2 f_m = 2 × 4 kHz = 8 kHz (upper and lower sidebands each extend f_m above and below the carrier). This is why AM broadcast stations are spaced 10 kHz apart.

μ = A_m/A_c = 6/10 = 0.6. This is under-modulation, so the envelope faithfully carries the message and can be demodulated with an envelope detector.

The bounds are 1/f_c = 1 μs and 1/W = 200 μs, so RC should lie comfortably between (a few μs up to ~50–100 μs). 10 μs satisfies this: it smooths the 1 MHz carrier yet discharges fast enough to follow a 5 kHz envelope. RC = 1 ms ≈ 1/W causes diagonal clipping; 0.5–1 μs leaves heavy carrier ripple.

C = B log₂(1 + S/N) = 4000 × log₂(16) = 4000 × 4 = 32 kbps. (log₂16 = 4 since 2⁴ = 16.) This is the theoretical maximum error-free rate — a cornerstone result of information theory.

SSB transmits only one sideband, so its bandwidth equals the message bandwidth: 3 kHz — half that of DSB-AM (2f_m = 6 kHz). This spectral efficiency is why SSB dominates amateur radio and analog multiplex telephony.

P_t = P_c(1 + μ²/2) = 500 × (1 + 0.64/2) = 500 × 1.32 = 660 W. Of this, 500 W sits in the carrier (which carries no information) and only 160 W in the sidebands — illustrating AM's power inefficiency.