Engineer Radio Electronic Communication cheat sheet

Free-space path loss: FSPL(dB) = 32.44 + 20log10(f in MHz) + 20log10(d in km); doubles (+6 dB) on each doubling of frequency or distance.

Friis transmission equation: Pr/Pt = Gt·Gr·(λ/4πd)²; valid in far field where d > 2D²/λ and d > λ.

Half-wave dipole: length ≈ 0.95·λ/2 in free space (end-effect shortening), feedpoint impedance ≈ 73 + j42 Ω, gain 2.15 dBi.

Quarter-wave monopole over a perfect ground plane has 5.15 dBi gain and ≈36 Ω feed impedance; it needs a ground plane or radials.

Antenna gain and effective aperture: Ae = G·λ²/4π; aperture efficiency of a parabolic dish is typically 0.5–0.65.

Fresnel zone radius at midpoint: r = 17.32·√(d1·d2/(f·D)) with r in m, distances in km, f in GHz; keep ≥60% of first zone clear for near free-space loss.

Ionospheric critical frequency foF2 relates to maximum usable frequency: MUF ≈ foF2 / cos(incidence angle); skywave needs f < MUF and above the lowest usable frequency.

Radio horizon distance (km) ≈ 3.57·√(h in m) for each terminal; two-antenna path ≈ 3.57·(√h1 + √h2), extended by k-factor refraction of ~4/3 Earth radius.

Characteristic impedance of a lossless line: Z0 = √(L/C); reflection coefficient Γ = (ZL − Z0)/(ZL + Z0); VSWR = (1+|Γ|)/(1−|Γ|).

Return loss (dB) = −20log10|Γ|; a VSWR of 2:1 corresponds to |Γ| = 0.333 and return loss ≈ 9.5 dB.

Quarter-wave transformer matches real impedances: Z0 = √(Zin·ZL), narrowband and λ/4 long at the design frequency.

L-section matching network Q is set by the impedance ratio: for a shunt-first L network, Q = √(Rhigh/Rlow − 1).

Insertion loss of cascaded two-ports adds in dB when stages are matched; Friis noise formula: Ftotal = F1 + (F2−1)/G1 + (F3−1)/(G1G2) + …

Resonant frequency of an LC tank: f = 1/(2π√(LC)); loaded Q = f0/BW(3 dB); filter order n gives ≈ 6(n+1) dB/octave roll-off for Butterworth.

Skin depth δ = √(ρ/(π·f·µ)); at HF copper δ ≈ 2.1 µm at 1 MHz, so silver plating and large surface area matter more than bulk conductor.

PIN diodes act as RF switches: low forward bias gives low RF resistance, reverse bias gives high isolation; switching speed is limited by carrier lifetime.

Carson's rule for FM bandwidth: BW ≈ 2(Δf + fm); modulation index β = Δf/fm; narrowband FM when β < ~0.3.

AM with modulation index m: total power Pt = Pc(1 + m²/2); envelope detection requires m ≤ 1 to avoid overmodulation.

FM demodulation gain improves output SNR by roughly 3β²(β+1) over baseband at high CNR; below threshold (~10 dB CNR) performance collapses.

Shannon capacity: C = B·log2(1 + S/N); the Shannon limit Eb/N0 = −1.59 dB for error-free transmission at vanishing rate.

BPSK and QPSK have identical Eb/N0 performance for BER 10⁻⁵ (≈9.6 dB); 16-QAM needs ≈4 dB more, 64-QAM ≈8 dB more than QPSK.

SSB occupies half the bandwidth of DSB/AM (≈3 kHz per voice channel) and needs a coherent BFO; suppressed carrier means no envelope detection.

OFDM subcarrier spacing Δf = 1/Tsymbol; a cyclic prefix of length ≥ channel delay spread removes ISI at a bandwidth cost of TCP/(T+TCP).

Spread spectrum: processing gain (dB) = 10log10(chip rate / data rate); DSSS recovers with correlation, FHSS hops across channels per a hop sequence.

Superheterodyne receiver: image frequency fimage = fLO + (fLO − frf) = frf + 2·fIF for high-side injection; image rejection depends on the RF preselector.

Choose IF to place images outside the RF filter passband; common IFs are 455 kHz (AM), 10.7 MHz (FM broadcast), 21.4 MHz and 45 MHz (land mobile).

Reciprocal mixing: local oscillator phase noise mixes with strong adjacent signals; improve with lower phase-noise LO and higher first-IF selectivity.

Direct-conversion (zero-IF) receivers suffer DC offset and 1/f noise; IQ imbalance creates image at −f that cannot be removed by IF filtering.

Transmitter chain: oscillator → buffer → mixer/upconverter → driver → PA → harmonic filter; the harmonic filter must pass the fundamental and reject 2nd/3rd harmonics ≥ 40 dB typically.

PA classes: Class A conducts 360°, max efficiency 50%; Class B 180°, 78.5%; Class AB between; Class C <180° for high efficiency with severe distortion.

Sensitivity: minimum detectable signal = −174 dBm/Hz + NF + 10log10(B) + required SNR; a 12.5 kHz channel with 6 dB NF and 10 dB SNR gives ≈ −121 dBm.

AGC maintains constant output over input range; capture ratio, blocking, and intermodulation-free dynamic range describe receiver robustness.

Nyquist sampling: fs ≥ 2·fmax; aliasing folds frequencies above fs/2 back into the baseband, so an anti-alias filter is required before the ADC.

Quantization SNR for a full-scale sine in an N-bit ADC: SNR ≈ 6.02N + 1.76 dB; ENOB = (SINAD − 1.76)/6.02.

Matched filter maximizes output SNR at the sampling instant; output peak SNR = 2E/N0, and it is the time-reversed transmit pulse.

Raised-cosine pulse shaping: occupied bandwidth = (1+α)·Rs/2 for symbol rate Rs; α = 0 gives sinc (zero excess BW), α = 0.35 is typical.

Convolutional code rate r = k/n; constraint length K; Viterbi decoding is ML for hard/soft decisions; coding gain ≈10log10(r·dfree) for hard decisions.

FFT of N points resolves bins spaced fs/N; windowing (Hann, Blackman-Harris) trades main-lobe width for sidelobe suppression in spectral measurements.

Constellation EVM relates to SNR: EVM(%) ≈ 100/√(SNR linear); a 1% EVM equals roughly 40 dB SNR.

DSP decimation by M filters then keeps every Mth sample; interpolation by L inserts zeros then low-pass filters to raise the sample rate by L.

Far-field boundary r > λ/2π; beyond it E/H = 377 Ω and fields fall as 1/r, while near-field E and H fall as 1/r² or 1/r³.

Shielding effectiveness SE(dB) = 20log10(Eincident/Etransmitted) = absorption loss A + reflection loss R + multiple-reflection correction B.

Absorption loss A(dB) ≈ 8.686·(t/δ); reflection loss for a plane wave is highest at low frequency for electric fields and high for magnetic fields.

Common-mode currents on cables are the dominant cause of radiated emissions; a ferrite clamp adds series impedance that rises with frequency.

Intermodulation products at 2f1 − f2 and 2f2 − f1 (third order) are the most troublesome; odd-order products fall in-band and cannot be filtered.

CISPR 16 defines quasi-peak and average detectors; conducted emissions are measured 150 kHz–30 MHz with a LISN, radiated 30 MHz–1 GHz at 3 or 10 m.

Ground loops inject 50/60 Hz and harmonics; break them with single-point grounding, isolation, or balanced differential inputs.

Desensitization (blocking) occurs when a strong off-channel signal drives the receiver front end into compression; measure with two-tone and blocking tests.

Spectrum analyzer: displayed average noise level ≈ −174 dBm/Hz + NF + 10log10(RBW); halving RBW lowers the noise floor 3 dB and doubles sweep time.

For pulsed or modulated signals, RBW must be ≥ the signal's modulation bandwidth to read true peak power; too narrow an RBW under-reads pulsed power.

Occupied bandwidth per ITU-R SM.328 is the bandwidth containing 99% of mean power; necessary bandwidth is defined by the emission designator.

Frequency measurement uncertainty should be ≤1/10 of the frequency tolerance; use a GPS-disciplined reference and count over a gate time long enough for the required resolution.

Field strength E(dBµV/m) = measured level (dBm) + antenna factor (dB/m) + 107 for a 50 Ω system; account for cable loss.

Antenna factor AF(dB/m) = 20log10(f in MHz) − G(dBi) − 29.79 for a 50 Ω system in free space.

Adjacent-channel power ratio (ACPR) is measured in a defined offset bandwidth; it is a key figure for transmitter spectral regrowth.

EIRP = Pt + Gt − Lcable; ERP = EIRP − 2.15 dB (dipole reference); verify with field-strength measurement at a known distance.

ITU Radio Regulations divide the world into three Regions (1: Europe/Africa, 2: Americas, 3: Asia-Pacific); allocations may differ by region and by footnote.

Radio services are primary or secondary; secondary stations must not cause harmful interference to primary stations and cannot claim protection from them.

Emission designator (ITU-R SM.1138): bandwidth + class of emission + nature of modulating signal, e.g. 16K0F3E = 16 kHz, FM, telephony.

Licensing regimes: individual licence, class licence (blanket), and licence-exempt; licence-exempt devices must accept interference and operate at low power.

Frequency tolerance, spurious emission limits (e.g. −36 dBm below 1 GHz, −30 dBm above in many regimes) and out-of-band limits are set nationally per ITU recommendations.

Call sign and station identification rules require periodic identification; amateur and land-mobile services define identification intervals and formats.

Harmful interference definition: any emission that endangers, obstructs, or seriously degrades a radiocommunication service operating per regulations.

Coordination zones and protection distances are calculated from transmitter EIRP, antenna height, and propagation models agreed in bilateral agreements.

Cellular reuse: cluster size N = i² + ij + j²; co-channel reuse ratio D/R = √(3N); capacity rises as N falls but co-channel interference rises.

SINR-based capacity: C = B·log2(1 + S/(I+N)); sectorization (120° sectors) cuts co-channel interference by roughly 3× in a 3-sector site.

Handover types: hard (break-before-make) in FDMA/TDMA, soft (make-before-break) in CDMA; hysteresis and dwell time prevent ping-pong.

Trunking: Erlang B formula gives blocking probability for offered load A = λ·H; Erlang C applies when calls queue rather than block.

OSI layers for radio networks: physical (RF/modulation), data link (MAC, ARQ), network (IP/routing), transport (TCP/UDP), application.

TETRA, P25, and DMR are digital PMR standards; TETRA uses 25 kHz TDMA with 4 slots, P25 Phase 2 uses 2-slot TDMA in 12.5 kHz.

Mesh and ad-hoc networks use multi-hop routing; throughput falls with hop count and hidden-terminal collisions require CSMA/CA or RTS/CTS.

Link budget: Prx = Ptx + Gtx + Grx − Lpath − Lcable + margins; add fade margin for availability target (e.g. 20–30 dB for 99.9% in fading).