Communication Systems (Analog and Digital)
This domain covers AM, FM and PM, noise performance, sampling and quantization, digital modulation, and multiple-access and coding basics.
Core rules
- AM: total power Pt = Pc(1 + m²/2); bandwidth is 2fm; DSB-SC and SSB trade bandwidth against receiver complexity.
- FM: Carson's rule BW ≈ 2(Δf + fm). FM trades bandwidth for SNR, with an improvement factor of roughly 3β²(β + 1) over baseband at high modulation index; below threshold, performance collapses.
- PCM: bit rate = n·fs; quantization SNR ≈ 6.02n + 1.76 dB for a full-scale sinusoid.
- Digital: BPSK and QPSK need the same Eb/N0 for a given error probability, but QPSK sends two bits per symbol and so doubles bit rate in the same bandwidth; a matched filter maximises SNR at the sampling instant.
Worked example
A commercial FM broadcast uses Δf = 75 kHz with fm = 15 kHz. Carson's rule gives BW = 2(75 + 15) = 180 kHz, and the modulation index is β = 75/15 = 5, giving about six significant sideband pairs - hence the 200 kHz channel spacing. If the channel instead carried PCM at 8 kHz sampling with 8 bits, the bit rate would be 64 kbit/s and quantization SNR about 6.02(8) + 1.76 ≈ 49.9 dB.
Traps
Using 2fm instead of Carson's rule for wideband FM; omitting the 1 + m²/2 term in AM power; confusing bit rate with baud rate for multilevel signalling; and using Eb/N0 and SNR interchangeably without bandwidth bookkeeping.