§ 8.1Amplitude Modulation & Demodulation
AM signal & modulation index
$$ s(t) = A_c[1 + m\cos\omega_mt]\cos\omega_ct, \qquad m = \frac{A_m}{A_c} = \frac{V_{max} - V_{min}}{V_{max} + V_{min}} $$
- Spectrum: carrier f_c + two sidebands f_c ± f_m → BW = 2f_m; m > 1 = overmodulation (envelope distortion, splatter).
AM power bookkeeping (the most-asked block)
$$ P_t = P_c\left(1 + \frac{m^{2}}{2}\right); \quad P_{SB,each} = \frac{m^2P_c}{4}; \quad \eta = \frac{m^{2}}{2 + m^{2}} \le 33.3\%\ (m = 1); \quad I_t = I_c\sqrt{1 + \tfrac{m^2}{2}} $$
- Multiple tones: \( m_{eff} = \sqrt{m_1^2 + m_2^2 + \cdots} \).
- Efficient variants: DSB-SC (suppress carrier — balanced/ring modulator; saves ⅔ power, BW still 2f_m, needs coherent detection); SSB (one sideband — filter or phase-shift method; BW = f_m, best power/BW economy; needs precise carrier reinsertion — voice, HF); VSB (partial sideband — analog TV video compromise).
- Generation: low-level (multiplier/collector modulation then linear PA) vs high-level (modulate the final PA — efficient, broadcast).
- Demodulation: envelope detector (diode + RC) for standard AM — design window:
Envelope-detector RC condition $$ \frac{1}{f_c} \ll RC \ll \frac{1}{f_m}\quad\big(\text{precisely } RC \le \frac{\sqrt{1-m^2}}{m\,\omega_m}\big) $$Too large RC → diagonal clipping; too small → ripple. Coherent (synchronous) detection for SC systems — multiply by recovered carrier + LPF; Costas loop/pilot recovers phase.
UGC NET focus
P_t = P_c(1 + m²/2) numericals (also via antenna-current ratio); m from V_max/V_min; 33.3% ceiling; SSB bandwidth halving; envelope-detector RC window and diagonal clipping.
§ 8.2Frequency & Phase Modulation
Angle modulation essentials
$$ s(t) = A_c\cos\!\big(\omega_ct + \beta\sin\omega_mt\big); \qquad \beta_{FM} = \frac{\Delta f}{f_m}, \qquad \beta_{PM} = k_pA_m $$
- FM: instantaneous frequency deviation Δf ∝ message amplitude (deviation independent of f_m); PM: phase ∝ message. PM ≡ FM of the differentiated message; FM via integrator + PM (Armstrong).
- Spectrum: Bessel-function sidebands at f_c ± nf_m (infinite, but negligible beyond β+1); carrier vanishes at β = 2.405 (J₀ null — deviation calibration). Constant envelope → constant power = A_c²/2 regardless of modulation (class-C friendly).
Carson's rule
$$ BW \approx 2(\Delta f + f_m) = 2f_m(\beta + 1) $$
- NBFM (β ≪ 1): BW ≈ 2f_m (AM-like); WBFM: broadcast Δf = 75 kHz, f_m = 15 kHz → β = 5, BW = 180 kHz (200 kHz channels).
- Generation: direct (varactor-tuned VCO — drift) vs indirect Armstrong (crystal-stable NBFM → frequency multipliers ×n multiply β and Δf).
- Demodulation: slope detector → balanced (Foster–Seeley) discriminator → ratio detector (built-in AM rejection) → quadrature detector → PLL (§4.18 — VCO control voltage is the message); FM needs a hard limiter first (kills AM noise).
- FM noise advantages: SNR improvement 3β²(β+1) over AM (capture effect — stronger signal wins); noise ∝ f² triangle → pre-emphasis/de-emphasis (75 µs networks boost/restore highs).
- FM vs AM: better noise immunity and constant power vs much wider bandwidth and complex circuits.
UGC NET focus
Carson numericals (β = 5 → 180 kHz); Δf independent of f_m (FM) — index changes, deviation doesn't; β = 2.405 carrier null; Armstrong = NBFM + multipliers; pre-emphasis 75 µs; constant-envelope property.
§ 8.3Superheterodyne Receiver
Convert every station to one fixed intermediate frequency where gain/selectivity are optimized once. Chain: antenna → RF amplifier (preselection) → mixer + local oscillator (ganged tuning: f_LO = f_s + f_IF, high-side) → IF amplifier (the gain/selectivity workhorse) → detector → AF amplifier; AGC closes the loop.
- Standard IFs: 455 kHz (AM broadcast), 10.7 MHz (FM), 38–45 MHz (TV).
- Image frequency: the other input that mixes to the same IF:
Image frequency & rejection $$ f_{im} = f_s + 2f_{IF}\ \ (\text{high-side LO}); \qquad \text{IFRR} = \sqrt{1 + Q^{2}\rho^{2}},\ \ \rho = \frac{f_{im}}{f_s} - \frac{f_s}{f_{im}} $$Image must be rejected before the mixer (RF stage tuning) — once mixed, IF filtering cannot separate it. Higher IF eases image rejection but hardens adjacent-channel selectivity → double-conversion receivers use both.
- Receiver metrics: sensitivity (minimum usable signal — set by noise figure), selectivity (adjacent-channel rejection — IF filter shape), fidelity (faithful reproduction — overall bandwidth), image rejection, dynamic range. Tracking error from imperfect ganged tuning (three-point tracking).
- Why superhet beats TRF: constant gain/selectivity over the band, stable high gain at fixed IF, simpler tuning — the universal receiver architecture (radio → radar → SDR front ends).
UGC NET focus
f_im = f_s + 2f_IF numericals (AM: station 1000 kHz → image 1910 kHz); 455 kHz/10.7 MHz constants; image rejected only before mixing; sensitivity vs selectivity vs fidelity definitions; LO tracking f_s + f_IF.
§ 8.4Random Signals & Noise
- Random signal: described statistically (mean, autocorrelation R_x(τ), power spectral density S_x(f) — Wiener–Khinchin pair); ergodic/stationary vocabulary; Gaussian PDF dominates (central-limit theorem).
- External noise: atmospheric (lightning, < 30 MHz), extraterrestrial (solar/cosmic), industrial/man-made. Internal:
- Thermal (Johnson–Nyquist): resistor agitation —
Thermal noise (the anchor formula) $$ P_n = kT B; \qquad \overline{v_n^{2}} = 4kTRB \quad (k = 1.38\times10^{-23}\ \text{J/K};\ kT_0 \approx 4\times10^{-21}\ \text{W/Hz} = -174\ \text{dBm/Hz}) $$White (flat PSD), Gaussian; available power independent of R.
- Shot noise: discrete charge crossing junctions — \( \overline{i_n^2} = 2qI_{DC}B \); white.
- Flicker (1/f): dominates at low f (corner frequency); partition noise (current splitting); burst noise.
- Thermal (Johnson–Nyquist): resistor agitation —
- Noise adds in power (uncorrelated): σ² sums; noise bandwidth ≈ equivalent rectangular BW of the filter.
- SNR = P_signal/P_noise (dB = 10 log); the figure that all link design protects; SNR_out vs SNR_in leads into §8.5.
UGC NET focus
kTB numericals (−174 dBm/Hz + 10 log B); 4kTRB vs kTB (open-circuit voltage vs available power); shot 2qIB; which noise dominates where (1/f at audio, thermal at RF); noise powers add.
§ 8.5Noise Figure & Noise Temperature
Definitions
$$ F = \frac{(S/N)_{in}}{(S/N)_{out}} \ge 1 \quad (\text{NF dB} = 10\log F); \qquad T_e = (F - 1)T_0,\ \ T_0 = 290\ \text{K} \ \Leftrightarrow\ F = 1 + \frac{T_e}{T_0} $$
- F measures SNR degradation; ideal noiseless network F = 1 (0 dB). Noise temperature suits very-low-noise devices (LNAs, radio astronomy: T_e of tens of K reads finer than NF tenths of dB).
- Friis cascade formula (the certain numerical):
Cascaded stages $$ F_{total} = F_1 + \frac{F_2 - 1}{G_1} + \frac{F_3 - 1}{G_1G_2} + \cdots; \qquad T_{e,total} = T_1 + \frac{T_2}{G_1} + \frac{T_3}{G_1G_2} + \cdots $$The first stage dominates — put a high-gain low-noise amplifier first (why the LNA sits at the antenna/dish feed). Use ratios, not dB, inside the formula!
- Lossy (passive attenuator) line: F = L (its loss ratio), T_e = (L−1)T_phys — feeder loss before the LNA adds dB-for-dB to system NF.
- System noise: P_n = kT_sysB with T_sys = T_antenna + T_e,RX; receiver sensitivity = −174 dBm + 10 log B + NF + SNR_req.
- Measurement: Y-factor method (hot/cold loads).
UGC NET focus
Friis cascade computations (convert dB→ratio first!); T_e = (F−1)290; first-stage dominance reasoning; attenuator F = L; sensitivity-floor arithmetic from −174 dBm/Hz.
§ 8.6Information Theory
Information & entropy (Shannon, 1948)
$$ I(x_i) = \log_2\frac{1}{p_i}\ \text{bits}; \qquad H(X) = -\sum_i p_i\log_2 p_i \ \text{bits/symbol} $$
- Rarer events carry more information; H = average information. H maximum for equiprobable symbols: H_max = log₂M (binary fair coin → 1 bit; biased → less). Information rate \( R = r_sH \) bits/s (r_s = symbol rate).
- Source-coding theorem: average codeword length \( \bar{L} \ge H \); efficiency η = H/L̄. Huffman coding (optimal prefix-free): merge two least-probable repeatedly — variable length, no codeword a prefix of another (instantaneous decoding); Shannon–Fano as the simpler cousin. Kraft inequality Σ2^{−l_i} ≤ 1.
- Channel measures: mutual information I(X;Y) = H(X) − H(X|Y); capacity C = max I; BSC capacity C = 1 − H(p).
Shannon–Hartley channel capacity (the unit's flagship)
$$ C = B\log_2\left(1 + \frac{S}{N}\right)\ \text{bits/s} $$
- Worked anchor: 3 kHz, SNR 30 dB (=1000) → C ≈ 3000 × 9.97 ≈ 30 kbps.
- Trade-off: bandwidth ↔ SNR exchange; infinite-bandwidth limit C∞ = (S/N₀)log₂e → the Shannon limit E_b/N₀ ≥ −1.6 dB for error-free communication.
- Channel-coding theorem: rates below C achievable with arbitrarily small error (existence, not construction) — the license for §8.7's codes.
UGC NET focus
Entropy computations for given p_i (and the equiprobable maximum); Huffman tree construction + average length; C = B log₂(1+SNR) numericals (SNR in dB → ratio!); −1.6 dB Shannon limit; prefix-free property.
§ 8.7Error Detection & Correction
- Redundancy buys reliability: code rate R = k/n for (n, k) codes; ARQ (detect + retransmit: stop-and-wait, go-back-N, selective-repeat) vs FEC (correct without return channel).
- Detection schemes: single parity (detects odd # errors), 2-D parity (corrects 1), checksum (Internet), CRC — message ×2^r ÷ generator polynomial, remainder appended; receiver re-divides → zero remainder = clean; catches all bursts ≤ r bits (CRC-16/32 standards).
- Hamming distance d_min — the geometry of codes:
Detection/correction capability $$ \text{detect } s \text{ errors: } d_{min} \ge s + 1; \qquad \text{correct } t: d_{min} \ge 2t + 1 \ \ (d_{min} = 3 \to \text{SEC}) $$
- Hamming (7,4) SEC code: r parity bits cover \( 2^r \ge n + 1 = k + r + 1 \) (k = 4 → r = 3); parity at positions 1, 2, 4, …; the syndrome (recomputed checks) reads out the error position in binary — flip that bit. Extended Hamming (8,4) = SEC-DED (ECC memory).
- Family map (recognition level): linear block codes (generator/parity-check matrices, syndrome decoding), cyclic codes (shift of a codeword is a codeword — CRC hardware = LFSR §5.8), BCH/Reed–Solomon (burst correction — CDs, QR, DVB), convolutional codes + Viterbi decoding, modern turbo/LDPC approaching the Shannon limit.
- Burst errors → interleaving spreads them into correctable sprinkles.
UGC NET focus
d_min rules (2t+1); Hamming (7,4) syndrome-locates-the-error mechanics and 2^r ≥ k+r+1 sizing; CRC division concept; parity's odd-error limitation; RS = burst champion; code rate arithmetic.
§ 8.8Pulse Code Modulation (PCM), DPCM & DM
PCM = digitize the waveform: sample (≥ Nyquist, §3.17) → quantize (n bits, 2ⁿ levels) → encode; receiver: regenerate → decode → reconstruct LPF. Regenerative repeaters make noise non-accumulating — digital's decisive advantage.
PCM design set
$$ R_b = n f_s \ \text{bits/s}; \qquad BW_{min} \approx \frac{R_b}{2}; \qquad \Delta = \frac{V_{FS}}{2^{n}},\ \ \sigma_q^2 = \frac{\Delta^2}{12}; \qquad SQNR = 6.02\,n + 1.76\ \text{dB} $$
- Anchors: telephony 8 kHz × 8 bits = 64 kbps (DS0); CD 44.1 kHz × 16 bits × 2 ch ≈ 1.41 Mbps. Each extra bit: +6 dB SQNR, +f_s bps.
- Companding (non-uniform quantization): compress before, expand after — constant SQNR across levels for speech; µ-law (µ = 255, North America/Japan) and A-law (A = 87.6, Europe/India).
- DPCM: transmit the prediction error (sample-to-sample correlation) → fewer bits at equal quality (speech ~4 bits); predictor + quantizer loop.
- Delta modulation (DM): 1-bit DPCM — staircase chases the signal. Two failure modes:
Slope-overload condition $$ \text{avoid overload: } \frac{\Delta}{T_s} \ge \left|\frac{dm(t)}{dt}\right|_{max} = 2\pi f_mA_m \ \ (\text{sine}) $$small Δ → slope overload (can't keep up); large Δ → granular noise (idle hunting). ADM/CVSD adapts Δ to fix both; sigma-delta (§5.12) = DM + oversampling + noise shaping.
- Cousins for contrast: PAM/PWM/PPM are analog pulse modulations (no quantization) — only PCM is truly digital.
UGC NET focus
R_b = nf_s and the 64 kbps anchor; 6 dB/bit; slope-overload inequality numericals (find Δ or f_s); µ-law vs A-law region map; DM's two noise types and the Δ trade; why repeaters beat amplifiers.
§ 8.9Digital Modulation: ASK, FSK, PSK, BPSK, QPSK, QAM
| Scheme | Carrier parameter keyed | BW (main lobe) | BER (coherent) | Notes |
|---|---|---|---|---|
| ASK / OOK | amplitude (on–off) | 2R_b | \( Q\!\left(\sqrt{E_b/N_0}\right) \) | simplest; worst noise immunity; envelope-detectable; optical OOK |
| FSK | frequency (f₁/f₂) | 2Δf + 2R_b | \( Q\!\left(\sqrt{E_b/N_0}\right) \) | constant envelope; non-coherent easy; MSK = minimum-shift refinement |
| BPSK | phase 0°/180° | 2R_b | \( Q\!\left(\sqrt{2E_b/N_0}\right) \) — best binary | antipodal; needs carrier recovery (Costas); DPSK avoids it (~1 dB penalty) |
- BER ranking at fixed E_b/N₀: BPSK best; coherent ASK/FSK 3 dB worse; non-coherent slightly worse again. \( Q(x) = \frac12\,\mathrm{erfc}(x/\sqrt2) \).
- M-ary trade: k = log₂M bits/symbol → symbol rate R_s = R_b/k → bandwidth ÷ k; constellation points crowd → more SNR needed. Bandwidth efficiency η = R_b/B (bps/Hz).
- QPSK: 4 phases (±45°, ±135°), 2 bits/symbol — same BER as BPSK but half the bandwidth (the headline fact); I/Q modulator = two BPSKs in quadrature; offset-QPSK and π/4-QPSK tame envelope transitions; Gray mapping makes adjacent symbols differ by 1 bit.
- QAM: amplitude and phase → square constellations 16/64/256-QAM (4/6/8 bits per symbol) — cable, Wi-Fi, LTE/5G adaptive modulation; needs linear PAs and high SNR (~+6 dB per 4× constellation).
- Matched filter/correlator reception maximizes SNR; eye diagram quality check; raised-cosine pulse shaping (roll-off α): BW = R_s(1+α)/... occupied = (1+α)R_s for baseband symmetry — controls ISI (Nyquist criterion).
UGC NET focus
BER ordering and the BPSK 3 dB edge; QPSK = BPSK BER at half BW; bits/symbol log₂M and bandwidth division; constant-envelope schemes (FSK/PSK) vs QAM linearity demand; Gray coding purpose; 16-QAM = 4 bits/symbol arithmetic.
§ 8.10TDM & FDM
| FDM | TDM | |
|---|---|---|
| Sharing dimension | frequency slices, simultaneous | time slots, sequential |
| Signal type | analog heritage | natural for digital/PCM |
| Separation hardware | bandpass filters + SSB stacks | synchronized commutators |
| Guard provision | guard bands | guard times + frame sync bit |
| Impairments | crosstalk via filter skirts, intermod | timing jitter, sync loss |
| Examples | radio/TV broadcast bands, analog telephony groups (12 ch × 4 kHz = 48 kHz group), OFDM as the modern digital descendant | E1/T1 telephony, GSM slots, SONET/SDH |
- TDM frame arithmetic (the standard numerical): N channels each sampled at f_s with n bits → \( R_b = N n f_s \) + framing. E1 (India/Europe): 32 slots × 8 bits × 8 kHz = 2.048 Mbps (30 voice + 2 signalling/sync); T1: 24 × 8 × 8k + 1 framing bit/frame = 1.544 Mbps.
- Synchronous vs statistical (asynchronous) TDM — stat-mux assigns slots on demand (packet precursor).
- FDM needs linear amplification (intermodulation); TDM needs accurate clocks — the dual weaknesses.
UGC NET focus
E1 = 2.048 Mbps / T1 = 1.544 Mbps build-ups; composite-rate computations Nnf_s; guard bands vs guard times; FDM-intermod / TDM-sync weakness pairing.
§ 8.11Multiple Access: FDMA, TDMA, CDMA
| FDMA | TDMA | CDMA | |
|---|---|---|---|
| Resource per user | own frequency band, all the time | own time slot, full band | own spreading code, full band & time |
| Separation | filters | time sync | code correlation (orthogonal/PN) |
| Guard need | guard bands | guard times | — |
| Systems | 1G AMPS, satellite | GSM (+FDMA), DECT | IS-95, 3G UMTS/WCDMA |
- CDMA / spread spectrum: message × high-rate PN code spreads bandwidth (processing gain \( G_p = B_{spread}/B_{message} = R_{chip}/R_{bit} \)); receiver correlates with the same code to despread; other users look like noise → soft capacity, inherent security/anti-jam, multipath RAKE combining, frequency reuse = 1. DSSS (direct-sequence) vs FHSS (frequency-hopping, Bluetooth). Near–far problem → tight power control.
- OFDMA (4G/5G, Wi-Fi): many orthogonal subcarriers (IFFT/FFT, §3.19) assigned in time–frequency resource blocks → ISI immunity via cyclic prefix, scheduler flexibility; SC-FDMA uplink (lower PAPR). SDMA (spatial, beamforming/MIMO) overlays all of the above.
- Duplexing (separate, often confused with access): FDD (paired up/down bands) vs TDD (same band, time-split — asymmetric-traffic friendly).
UGC NET focus
Resource-axis matching (frequency/time/code); processing gain G_p = R_chip/R_bit; CDMA reuse-1 and near–far; OFDMA = orthogonal subcarriers + cyclic prefix; FDMA/TDMA/CDMA ↔ generation mapping; access vs duplex distinction.
§ 8.12Data Communications: Modems & Codes
- Modem (modulator–demodulator): digital ↔ analog for band-limited channels (telephone/cable/DSL). Baud (symbol rate) ≠ bit rate:
The classic baud trap $$ R_b = R_{baud}\times\log_2 M \quad (\text{bits/symbol}) $$e.g., 2400 baud × 16-QAM (4 bits) = 9600 bps. Evolution: FSK (300 bps) → PSK/QAM → V.34 (33.6 k) → V.90 (56 k) → ADSL/cable (Mbps via many QAM subcarriers).
- Transmission modes: simplex / half-duplex / full-duplex; serial vs parallel; asynchronous (start/stop bits per character, cheap) vs synchronous (block + clock, efficient).
- Codes: ASCII (7-bit, 128 symbols; 8th = parity), extended ASCII/ISO-8859, EBCDIC (8-bit, IBM), Unicode/UTF-8 (universal). Line codes (baseband shaping): NRZ, RZ, Manchester (self-clocking, no DC — Ethernet), AMI/HDB3/B8ZS (telephony, DC-balanced), 4B/5B; choose for clock recovery, DC content, bandwidth, error detection.
- Standards/interfaces: RS-232 (Unit-6 §6.16), RS-485 (multidrop), USB, Ethernet; protocols layered (OSI/TCP-IP): framing, flow control (stop-and-wait/sliding-window), error control (ARQ §8.7).
UGC NET focus
baud × log₂M = bps numericals; ASCII = 7 bits/128 symbols; Manchester self-clocking + no-DC; async start/stop overhead; simplex/half/full definitions; line-code property matching.
§ 8.13Mobile (Cellular) Communication
- Cellular principle: divide coverage into cells (idealized hexagons), reuse frequencies in non-adjacent cells → enormous capacity from limited spectrum; small cells = more reuse + lower power but more handoffs.
- Frequency reuse in clusters of N cells:
Reuse geometry $$ N = i^{2} + ij + j^{2}\ (=3,4,7,12\ldots); \qquad \frac{D}{R} = \sqrt{3N}\ \ (\text{co-channel reuse ratio}) $$larger N → less co-channel interference but fewer channels/cell.
- Core mechanisms: handoff/handover (hard — break-before-make GSM; soft — make-before-break CDMA), roaming, power control, sectorization (120°/3-sector antennas), cell splitting/microcells for capacity.
- Architecture: MS → BTS/Node-B/gNB → BSC/RNC → MSC/core → PSTN/Internet; HLR/VLR for mobility; authentication (SIM).
- Generations (recognition table): 1G analog FM/FDMA (AMPS) → 2G digital GSM (TDMA+FDMA, 200 kHz, SMS) / IS-95 CDMA → 3G WCDMA/UMTS (data, ~2 Mbps) → 4G LTE (OFDMA, all-IP, 100 Mbps+) → 5G NR (mmWave, massive MIMO, network slicing, <1 ms latency, eMBB/URLLC/mMTC). Propagation: path loss (Hata/Okumura), multipath fading (Rayleigh/Rician), Doppler, shadowing → diversity, equalization, MIMO.
UGC NET focus
N = i²+ij+j² allowed cluster sizes; D/R = √(3N); soft (CDMA) vs hard (GSM) handoff; generation↔access mapping (2G TDMA, 3G CDMA, 4G OFDMA); frequency-reuse rationale; hexagon model.
§ 8.14Satellite Communication
- Orbits: GEO at 35,786 km (≈ 36,000 km), period 24 h, appears fixed → 3 satellites cover the globe; ~250 ms one-way / 500 ms round-trip delay (the GEO drawback). MEO (GPS ~20,200 km), LEO (500–2000 km — low latency, large constellations: Starlink/Iridium, but moving → tracking/handover).
- Transponder: receive uplink → LNA → frequency-translate (down) → power amp (TWTA/SSPA) → transmit downlink. Uplink > downlink frequency (e.g., C-band 6/4 GHz, Ku 14/12 GHz, Ka 30/20 GHz) — downlink lower for less rain loss and easier ground power. Bands collide with terrestrial → rain fade worse at Ku/Ka.
- Link budget: dominated by free-space path loss (Friis §7.14 — ~200 dB at GEO); figure of merit G/T (gain-to-noise-temperature) of the earth station; EIRP = P_t G_t; carrier-to-noise C/N = EIRP − FSL + G/T − k − B. High-gain dishes (1.22λ/D narrow beams), station-keeping, sun-outage.
- Access: FDMA/TDMA/CDMA + DAMA (demand-assigned); applications: DTH broadcast, VSAT networks, GPS/GNSS, remote sensing, backhaul, disaster/maritime comms.
UGC NET focus
GEO 35,786 km / 24 h / ~250 ms; 3 satellites for global cover; uplink > downlink + band pairs (6/4, 14/12); transponder block; G/T and EIRP terms; LEO low-latency trade-off; rain fade at high bands.
§ 8.15Optical Sources: LED & Semiconductor Lasers
Both are forward-biased direct-gap junctions (Unit-1 §1.16); emission wavelength \( \lambda(\mu m) = 1.24/E_g(\text{eV}) \). Fiber windows: 850 nm (GaAlAs), 1310 nm (zero dispersion), 1550 nm (minimum loss) — InGaAsP.
| Property | LED | Laser diode (LD) |
|---|---|---|
| Emission | spontaneous | stimulated (needs population inversion + optical cavity) |
| Threshold | none (linear) | lases above I_th |
| Spectral width | wide (~30–50 nm) → more dispersion | narrow (< nm; DFB ~MHz) → long-haul |
| Coherence/directionality | incoherent, broad | coherent, narrow beam → couples to single-mode fiber |
| Modulation speed | ≲ hundreds of MHz | GHz–tens of GHz |
| Power/cost/linearity/T-stability | low/cheap/linear/robust | high/costly/needs cooling+bias control |
| Use | short-haul, multimode, LANs | long-haul single-mode, WDM, high-speed |
- Laser conditions: population inversion (forward-bias injection) + optical feedback (cleaved-facet Fabry–Pérot cavity or DFB/DBR grating) + gain > loss at threshold; output ∝ (I − I_th) above threshold.
- Structures: homojunction → double heterostructure (carrier + optical confinement, low I_th) → quantum-well (lowest threshold, tunable λ — §1.13); VCSELs (surface-emitting, cheap arrays, datacom).
- Source figures: launched power, spectral width (→ chromatic dispersion §8.17), E/O bandwidth, linearity (analog), reliability/lifetime.
UGC NET focus
spontaneous (LED) vs stimulated (laser) + the three lasing requirements; threshold current and linear vs thresholded output; LED wide spectrum → dispersion penalty; 1310 (zero-D) and 1550 (min-loss) windows; λ = 1.24/E_g.
§ 8.16Optical Detectors: PIN & APD
Reverse-biased photodiodes: a photon with \( h\nu \ge E_g \) creates an EHP in the depletion region; the field sweeps carriers → photocurrent. Cutoff wavelength \( \lambda_c = 1.24/E_g \); Si to ~1.1 µm, InGaAs for 1.3/1.55 µm, Ge.
Responsivity & quantum efficiency
$$ \eta = \frac{\text{collected EHPs}}{\text{incident photons}}; \qquad R = \frac{I_p}{P_{opt}} = \frac{\eta q}{h\nu} = \frac{\eta\lambda(\mu m)}{1.24}\ \text{A/W} $$
| PIN photodiode | Avalanche photodiode (APD) | |
|---|---|---|
| Mechanism | wide i-region → large absorption, low C, fast | high reverse field → impact-ionization gain M (10–100) |
| Internal gain | 1 (no multiplication) | M > 1 → better sensitivity in noise-limited links |
| Bias | low (few V) | high (tens–hundreds V), T-sensitive M |
| Noise | shot + thermal | + excess noise F(M) = M^x (avalanche statistics) |
| Use | most receivers, short/medium haul | long-haul, low received power |
- PIN's wide intrinsic layer = high η + low junction capacitance (fast) — the same i-region idea as the microwave PIN (§7.16), here as an absorber.
- Receiver sensitivity limited by shot + thermal + (APD) excess noise; there's an optimum M trading gain vs F(M). Front end: transimpedance amplifier (§4.12).
UGC NET focus
R = ηλ/1.24 A/W numericals; PIN gain = 1 vs APD multiplication M; APD excess noise F = Mˣ trade-off; InGaAs for 1.55 µm / Si limit 1.1 µm; cutoff λ_c = 1.24/E_g; why the i-region (low C, high absorption).
§ 8.17Optical Fibers: Attenuation, Dispersion, Bandwidth & WDM
Guidance
- Core (n₁) + cladding (n₂ < n₁) → guidance by total internal reflection (§7.9).
Acceptance & modes $$ NA = \sqrt{n_1^2 - n_2^2} = n_0\sin\theta_a;\quad \Delta = \frac{n_1 - n_2}{n_1};\quad V = \frac{2\pi a}{\lambda}NA\ \ (\text{single-mode if } V < 2.405) $$
- Multimode (large core ~50 µm: step or graded-index) → modal dispersion, short reach, LED-driven; single-mode (~9 µm core, V < 2.405) → no modal dispersion, long-haul, laser-driven.
Attenuation
Loss
$$ \alpha\,(\text{dB/km}) = \frac{10}{L}\log_{10}\frac{P_{in}}{P_{out}} $$
- Mechanisms: Rayleigh scattering (∝ 1/λ⁴ — dominates short λ), material/OH⁻ absorption peaks (~1383 nm), bending/microbending losses. Minima → ~0.2 dB/km at 1550 nm, ~0.35 at 1310; sets repeater spacing (EDFAs amplify at 1550).
Dispersion — the bandwidth limiter
- Modal (multimode only — different ray paths); cured by graded index or single mode.
- Chromatic = material + waveguide dispersion: different λ's travel at different speeds; \( \Delta\tau = D\,L\,\Delta\lambda \) (D in ps/nm·km). Zero at ~1310 nm in standard fiber; dispersion-shifted fiber moves zero to 1550 nm.
- Polarization-mode dispersion (PMD) limits ultra-high-rate links. Pulse spreading → ISI → bandwidth–distance product (MHz·km / GHz·km) — the fiber's figure of merit; dispersion compensation (DCF, gratings) for long-haul.
WDM
- Wavelength-division multiplexing = FDM in the optical domain: many λ-channels on one fiber via multiplexers/AWGs. CWDM (20 nm spacing, no cooling) vs DWDM (0.8/0.4 nm, ITU grid around 1550 nm, EDFA-amplified, 40–160 channels → Tbps). Multiplies capacity without new fiber; OADMs drop/add channels.
- Fiber advantages recap: huge bandwidth, ultra-low loss, immunity to EMI, security, light/thin, no crosstalk — vs fragility, splicing skill, cost of terminal optics.
UGC NET focus
NA = √(n₁²−n₂²) and V < 2.405 single-mode condition; α dB/km from P_in/P_out; 0.2 dB/km @1550 and zero-dispersion @1310; modal vs chromatic dispersion; Δτ = D·L·Δλ; Rayleigh ∝ 1/λ⁴; DWDM = optical FDM.
§ 8.18Fundamentals of IoT for Communication
- IoT = networks of sensor/actuator-equipped "things" with unique addressing, sensing/processing/communicating to the Internet for monitoring and control. Core blocks: sensing → (edge) processing → connectivity → cloud/analytics → application/actuation.
- Layered architecture: Perception (sensors/actuators, RFID, MEMS) → Network/Transport (connectivity + gateways) → Processing/Middleware (edge/fog/cloud, data management) → Application (smart home/city/health/industry); security and management span all layers.
- Connectivity by range/power (recognition table):
- Short-range: BLE, Zigbee/Thread & 6LoWPAN (IEEE 802.15.4 mesh), Z-Wave, NFC, Wi-Fi (HaLow 802.11ah).
- LPWAN (long-range, low-power, low-rate): LoRaWAN (unlicensed, km-range), NB-IoT & LTE-M (licensed cellular, deep indoor), Sigfox.
- Cellular/5G mMTC for massive machine-type communication; satellite IoT for remote.
- Protocols: MQTT (lightweight publish/subscribe over TCP — broker-based, ideal for constrained links), CoAP (RESTful over UDP), AMQP, HTTP/WebSocket; IPv6 (vast address space for billions of devices, 6LoWPAN header compression). Data formats JSON/CBOR.
- Edge/fog computing: process near the source → lower latency, bandwidth and cloud load; key for real-time control and privacy.
- Constraints & challenges: energy (battery/energy-harvesting, duty cycling), limited compute/memory, scalability, interoperability/standards, and security/privacy (lightweight crypto, authentication, OTA updates — the dominant concern). Enabling trends: low-power MCUs (8051-class to ARM Cortex-M), MEMS sensors, cheap connectivity, cloud analytics/AI.
- Applications: smart home/metering, industrial IoT (Industry 4.0, predictive maintenance), smart cities, agriculture, healthcare/wearables, environmental monitoring — and lab/process instrumentation telemetry.
UGC NET focus
Layered architecture (perception/network/processing/application); MQTT pub-sub vs CoAP/UDP; LPWAN (LoRa/NB-IoT) = long-range low-power; 802.15.4 → Zigbee/6LoWPAN; IPv6 necessity; edge computing benefit; protocol↔use matching.
§ 8.19Unit-8 Formula Sheet
| Topic | Formula | Notes |
|---|---|---|
| AM index | m = (V_max − V_min)/(V_max + V_min) | BW = 2f_m |
| AM power | P_t = P_c(1 + m²/2); η ≤ 33.3% | each SB = m²P_c/4 |
| SSB / DSB-SC | SSB BW = f_m; DSB-SC BW = 2f_m | need coherent detection |
| FM index | β = Δf/f_m | carrier null at β = 2.405 |
| Carson's rule | BW = 2(Δf + f_m) = 2f_m(β+1) | WBFM 75/15 kHz → 180 kHz |
| Image frequency | f_im = f_s + 2f_IF | IF 455 kHz (AM), 10.7 MHz (FM) |
| Thermal noise | P_n = kTB; v_n² = 4kTRB | −174 dBm/Hz |
| Shot noise | i_n² = 2qI_DC·B | white |
| Noise figure | F = (S/N)_in/(S/N)_out; T_e = (F−1)290 | — |
| Friis cascade | F = F₁ + (F₂−1)/G₁ + … | use ratios; stage 1 dominates |
| Entropy | H = −Σp_i log₂p_i | max = log₂M (equiprobable) |
| Channel capacity | C = B log₂(1 + S/N) | Shannon limit E_b/N₀ ≥ −1.6 dB |
| Error coding | d_min ≥ 2t + 1; 2^r ≥ k + r + 1 | Hamming syndrome locates error |
| PCM | R_b = nf_s; SQNR = 6.02n + 1.76 dB | telephony 64 kbps |
| Delta mod | Δ/T_s ≥ 2πf_m A_m (no slope overload) | granular noise if Δ large |
| Companding | µ = 255 (NA); A = 87.6 (Europe/India) | non-uniform quantization |
| Digital M-ary | R_b = R_s log₂M; BW ÷ log₂M | BPSK best BER; QPSK = BPSK at ½ BW |
| BER | BPSK Q(√(2E_b/N₀)); ASK/FSK Q(√(E_b/N₀)) | BPSK 3 dB better |
| TDM rates | E1 = 2.048 Mbps; T1 = 1.544 Mbps | R_b = Nnf_s |
| CDMA | G_p = R_chip/R_bit | reuse = 1, near–far |
| Modem | R_b = baud × log₂M | ASCII 7-bit |
| Cellular reuse | N = i² + ij + j²; D/R = √(3N) | hexagon clusters 3,4,7,12 |
| Satellite | GEO 35,786 km; ~250 ms; uplink > downlink | C/4, Ku 14/12, Ka 30/20 GHz |
| Optical λ | λ(µm) = 1.24/E_g | windows 850/1310/1550 nm |
| Responsivity | R = ηλ/1.24 A/W | PIN gain 1, APD gain M |
| Fiber NA | NA = √(n₁²−n₂²); V < 2.405 single-mode | α = (10/L)log(P_in/P_out) |
| Dispersion | Δτ = D·L·Δλ | zero @1310, min loss 0.2 dB/km @1550 |
§ 8.20Quick Revision Notes — Unit 8 in 25 Points
Rapid-fire recap (last-day revision)
- AM: m = (V_max−V_min)/(V_max+V_min), BW = 2f_m, P_t = P_c(1+m²/2), η_max = 33.3% at m = 1; SSB halves BW and saves power but needs coherent detection.
- Envelope detector window 1/f_c ≪ RC ≪ 1/f_m; too-large RC → diagonal clipping.
- FM: Δf set by message amplitude (independent of f_m), β = Δf/f_m; Carson BW = 2(Δf+f_m); carrier vanishes at β = 2.405; constant envelope → constant power.
- Armstrong = crystal NBFM + multipliers; FM needs a limiter; pre-/de-emphasis 75 µs; FM trades bandwidth for noise immunity (capture effect).
- Superhet: f_LO = f_s + f_IF, image f_im = f_s + 2f_IF (reject before the mixer); IFs 455 kHz / 10.7 MHz; sensitivity↔NF, selectivity↔IF filter, fidelity↔BW.
- Thermal noise P_n = kTB (−174 dBm/Hz), v² = 4kTRB; shot 2qIB; flicker 1/f at low frequencies; noise powers add.
- F = SNR_in/SNR_out, T_e = (F−1)290; Friis cascade F = F₁ + (F₂−1)/G₁ + … (ratios!) — first stage dominates → LNA first; attenuator F = L.
- Entropy H = −Σp log₂p, maximum log₂M for equiprobable; Huffman = optimal prefix-free (merge least-probable); efficiency H/L̄.
- Shannon–Hartley C = B log₂(1+S/N); 3 kHz @30 dB ≈ 30 kbps; absolute limit E_b/N₀ ≥ −1.6 dB.
- Error control: d_min ≥ 2t+1 (correct), ≥ s+1 (detect); Hamming (7,4) syndrome gives the error position; CRC = polynomial-division remainder; RS for bursts; interleaving spreads bursts.
- PCM: sample→quantize→encode; R_b = nf_s, SQNR = 6n+1.76 dB; telephony 64 kbps; companding µ=255 / A=87.6.
- Delta mod: 1-bit; small Δ → slope overload (Δ/T_s ≥ 2πf_mA_m), large Δ → granular noise; ADM fixes both.
- Digital BER order: BPSK best (Q(√(2E_b/N₀))), ASK/FSK 3 dB worse; M-ary packs log₂M bits/symbol → narrower BW, higher SNR.
- QPSK = BPSK BER at half the bandwidth (2 bits/symbol); QAM keys amplitude+phase (16/64/256), needs linear PA + high SNR; Gray coding minimizes bit errors.
- FDM = frequency slices (analog, guard bands, intermod); TDM = time slots (digital, guard times, sync); E1 = 2.048, T1 = 1.544 Mbps.
- Access axes: FDMA frequency / TDMA time / CDMA code (G_p = R_chip/R_bit, reuse 1, near–far); OFDMA = orthogonal subcarriers + cyclic prefix (4G/5G); FDD vs TDD duplex.
- Modem: bps = baud × log₂M; ASCII 7-bit/128; Manchester self-clocking & DC-free; async = start/stop bits; simplex/half/full.
- Cellular: hexagonal reuse, N = i²+ij+j² (3,4,7,12), D/R = √(3N); soft handoff (CDMA) vs hard (GSM); generations 1G FDMA→2G TDMA/CDMA→3G WCDMA→4G OFDMA→5G mmWave/MIMO.
- Satellite: GEO 35,786 km, 24 h, ~250 ms delay, 3 cover the globe; uplink > downlink (6/4, 14/12, 30/20 GHz); G/T and EIRP; LEO low-latency constellations.
- Optical sources: LED spontaneous (wide spectrum, no threshold, LANs) vs laser stimulated (needs inversion + cavity, narrow, threshold I_th, long-haul); λ = 1.24/E_g; windows 850/1310/1550.
- Detectors: R = ηλ/1.24 A/W; PIN (wide i-layer, gain 1, fast) vs APD (multiplication M, excess noise F = Mˣ, high bias); InGaAs for 1.55 µm, Si to 1.1 µm.
- Fiber: NA = √(n₁²−n₂²), single-mode V < 2.405; α from 10/L·log(P_in/P_out); min loss 0.2 dB/km @1550, zero dispersion @1310; Rayleigh ∝ 1/λ⁴.
- Dispersion: modal (multimode), chromatic Δτ = D·L·Δλ, PMD; pulse spreading → ISI → bandwidth–distance product.
- WDM = optical FDM; CWDM (20 nm, uncooled) vs DWDM (0.8/0.4 nm, EDFA, Tbps); fiber = huge BW, low loss, EMI-immune, secure.
- IoT: perception→network→processing→application; short-range BLE/Zigbee(802.15.4)/6LoWPAN vs LPWAN LoRa/NB-IoT; MQTT pub-sub (TCP) / CoAP (UDP); IPv6, edge computing, and security as the dominant challenge.