What are the essential RF design formulas?

From RF Design Wiki · By the RF Design Wiki editorial team · Published October 21, 2026 · Last reviewed October 21, 2026 · How we research

This page collects the most-used RF design equations in one place, each linked to the article that explains it. Formulas use linear quantities unless marked dB; Z₀ is the reference impedance, k is Boltzmann’s constant, T₀ = 290 K.

Which formulas cover power, noise and linearity?

dBm = 10·log10(P/1 mW); dBµV = dBm + 107 (50 Ω). More
Thermal noise: N = kTB → −174 dBm/Hz + 10·log10(B). More
Friis noise: F = F₁ + (F₂ − 1)/G₁ + …; T_e = T₀(F − 1). More
Sensitivity: −174 + NF + 10·log10(B) + SNR. More
IIP3 = P_in + ΔP/2; 1/IIP3 = 1/IIP3₁ + G₁/IIP3₂ + …; SFDR = ⅔(IIP3 − N). More

^[1]^[2]

Which formulas cover lines and matching?

λ = c/(f√ε_eff); δ = 1/√(πfμσ). More
Γ = (Z_L − Z₀)/(Z_L + Z₀); VSWR = (1 + |Γ|)/(1 − |Γ|); RL = −20·log10|Γ|. More
Z_in = Z₀(Z_L + jZ₀tan βℓ)/(Z₀ + jZ_Ltan βℓ); quarter-wave Z₁ = √(Z₀Z_L). More
Coax Z₀ = (60/√ε_r)ln(D/d). More
L-network Q = √(R_high/R_low − 1), X_s = QR_low, X_p = R_high/Q. More
Stability: K > 1 and |Δ| < 1, or μ > 1. More

^[1]

Which formulas cover antennas, links and oscillators?

Friis: P_r = P_tG_tG_r(λ/4πd)². FSPL(dB) = 32.45 + 20·log10(f_MHz) + 20·log10(d_km). More
A_e = Gλ²/(4π); far field R = 2D²/λ. More
Fresnel r₁ = 17.32√(d₁d₂/(f_GHzd)) m. More
Radar: P_r = P_tG²λ²σ/((4π)³R⁴); ΔR = c/(2B). More
PLL: f_out = N·f_ref/R; multiplication adds 20·log10(N) to phase noise. More
Jitter: σ_t = √(2∫ℒ df)/(2πf₀); ADC SNR_jitter = −20·log10(2πf_inσ_t). More
ADC: SNR = 6.02N + 1.76 dB. More

^[3]^[4]^[5]

Frequently asked questions

Are these formulas exact?

Most are exact under stated assumptions; microstrip and some others are approximations.

Why 290 K?

It is the standard reference temperature for noise figure.

Can I use these for design sign-off?

Use them for estimates; verify with simulation and measurement.

References

Online sources accessed October 21, 2026; printed works cited by edition. See all sources.

“Microwave Engineering, 4th ed.”. D. M. Pozar, Wiley. 2012.
“RF Microelectronics, 2nd ed.”. B. Razavi, Prentice Hall. 2012.
“A Note on a Simple Transmission Formula”. H. T. Friis, Proceedings of the IRE, vol. 34, no. 5, pp. 254-256. May 1946.
“Antenna Theory: Analysis and Design, 4th ed.”. C. A. Balanis, Wiley. 2016.
“Introduction to Radar Systems, 3rd ed.”. M. I. Skolnik, McGraw-Hill. 2001.

Categories: Reference

Articles on RF Design Wiki

Start here	Main page What is RF design Learning path Design workflow
Fundamentals	Decibels and dBm RF power Wavelength and frequency Thermal noise Noise figure Noise temperature SNR and Eb/N0 Skin effect Q factor Nonlinearity and harmonics Intermodulation and IP3 P1dB compression Dynamic range and SFDR
Transmission lines	Transmission line theory Characteristic impedance Γ, VSWR and return loss Input impedance of a line Quarter-wave transformer Microstrip Stripline Coplanar waveguide Coaxial cable Waveguides RF connectors
Matching and S-parameters	Impedance matching Maximum power transfer Smith chart L-network matching Pi and T networks Stub matching Bode–Fano limit S-parameters Touchstone files Z, Y, ABCD parameters De-embedding Mixed-mode S-parameters
Filters and passives	RF filter basics Filter approximations LC filter design Microstrip filters Cavity and dielectric filters SAW and BAW filters Diplexers and duplexers Wilkinson divider Couplers and hybrids Baluns Circulators and isolators RF attenuators Passive components
Amplifiers	Gain definitions Amplifier stability LNA design Power amplifier basics PA classes Efficiency and PAE Doherty amplifier Linearization and DPD Load-pull Transistor technologies Transistor biasing ACPR and EVM
Mixers and frequency generation	RF mixers Mixer specifications Image frequency I/Q modulators Oscillator basics Crystal oscillators VCO design Phase noise Jitter from phase noise PLL basics PLL loop filter Fractional-N synthesis Direct digital synthesis Multipliers and dividers
Antennas and propagation	Antenna fundamentals Gain and directivity Dipole antenna Monopole antenna Patch antenna Arrays and beamforming Small antenna limits Polarization Friis equation Free-space path loss Link budget Multipath and fading Atmospheric and rain loss Path loss models Fresnel zones
Receivers and systems	Receiver architectures Superheterodyne Direct conversion Low-IF receiver Software-defined radio Receiver sensitivity Blocking and selectivity Transmitter architectures Modulation ADCs for RF Radar basics
PCB layout and materials	RF PCB layout RF PCB materials Grounding and vias Controlled-impedance stackup Decoupling RF shielding Thermal design
EMC and EMI	EMC and EMI basics FCC Part 15 CISPR standards Immunity and ESD EMI filters and ferrites Precompliance testing RF exposure limits
Test and measurement	Vector network analyzer VNA calibration Spectrum analyzer Noise figure measurement Phase noise measurement RF power measurement Signal generators TDR Antenna measurement Oscilloscopes for RF
Simulation	Simulation overview Harmonic balance EM simulation EM solver methods SPICE for RF
Standards and bands	Frequency bands Radar band letters ISM bands 5G NR bands Wi-Fi and Bluetooth RF GNSS frequencies Amateur radio bands Spectrum regulation
Reference	Formula cheat sheet Textbooks and references Glossary FAQ All sources
About	About Editorial policy