Telecom Fundamentals and Signal Theory
This domain tests the physical-layer maths behind every telecom link: decibels, bandwidth, noise, sampling and analogue/digital modulation. Expect numerical questions and definitions rather than history.
Core rules
- Power ratio in decibels: dB = 10 log10(Pout/Pin). Voltage or current ratio uses 20 log10 when impedance is unchanged. +3 dB is double power, +10 dB is ten times, −3 dB is half.
- Absolute power uses dBm, referenced to 1 mW: 0 dBm = 1 mW, 10 dBm = 10 mW, 30 dBm = 1 W. A gain or loss in dB is added to dBm, but dBm must never be added to dBm.
- Nyquist gives the maximum symbol rate for a noiseless channel, C = 2B log2 M; Shannon gives capacity with noise, C = B log2(1 + S/N). SNR in dB = 10 log10(S/N).
- Sampling theorem: fs ≥ 2fmax. PCM bit rate = fs × bits per sample × channels.
- AM varies carrier amplitude and needs about 2fm bandwidth; FM varies frequency, needs more bandwidth but resists noise better.
Worked example
A 2 mW signal enters an amplifier and leaves at 200 mW. Gain = 10 log10(200/2) = 10 log10 100 = 20 dB. A 3 dB cable loss follows: 200 mW ÷ 2 = 100 mW, or in dBm, input 3 dBm + 20 dB − 3 dB = 20 dBm = 100 mW. The final answer is 20 dBm, not 23 dBm: the 3 dB loss is subtracted.
Traps
Using 10 log10 on a voltage ratio; adding dBm to dBm; treating dB as an absolute unit; forgetting that −3 dB halves power; confusing signal bandwidth with carrier frequency; using Shannon when the question says noiseless.