Methodology & References
Every formula and simulation on rftools.io traces back to a textbook, IEEE paper, ITU-R recommendation, or open-source reference library. This page lists the citations for the tools and calculators where methodology matters most.
Editorial standard
- RF, antenna, and microwave formulas are validated against Pozar — Microwave Engineering (4th ed.), Razavi — RF Microelectronics, and the relevant IEEE / ITU-R recommendations.
- Where an open-source reference implementation exists (scikit-rf, ITU-Rpy, openEMS, DEAP), our results are benchmarked against it — see the “Powered by” badges on individual tool pages.
- Physical constants use 2019 SI exact values: c = 299,792,458 m/s, k = 1.380649 × 10⁻²³ J/K, e = 1.602176634 × 10⁻¹⁹ C.
- Hard-coded magic numbers are avoided — every formula is auditable in the calculator’s open-source TypeScript / Python source.
Cited libraries we align with
- scikit-rf — open-source RF/microwave toolkit, IEEE MTT-S Microwave Magazine paper, 7,200+ weekly PyPI downloads.
- ITU-Rpy — reference implementation of ITU-R propagation models (P.453, P.530, P.618, P.676, P.838, P.839, P.840, P.837, P.1144), validated against ITU’s own test vectors.
- openEMS — open-source FDTD EM simulator used by the FDTD transmission line tool.
- DEAP — evolutionary algorithm framework powering the NSGA-II magnetics optimizer.
Simulation tools with full methodology
Broadband Impedance Matching Synthesizer
Powered by scikit-rf
- Microwave Engineering, 4th ed. — David M. Pozar (2011), Chapter 5 — Impedance Matching and Tuning
- Network Analysis and Feedback Amplifier Design — Hendrik Bode (1945) — Bode-Fano bandwidth limit
- HF Filter Design and Computer Simulation — Randall W. Rhea (1994)
Wire Antenna Simulator (NEC-2)
Powered by NEC-2 (PyNEC)DEAP
- Numerical Electromagnetics Code (NEC) — Method of Moments — G. J. Burke and A. J. Poggio, Naval Ocean Systems Center TD 116 (1981)
- Antenna Theory: Analysis and Design, 4th ed. — Constantine A. Balanis (2016)
- Three-Element Yagi Models: Standards of Comparison — L. B. Cebik, W4RNL
- A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II — K. Deb, A. Pratap, S. Agarwal and T. Meyarivan, IEEE Trans. Evolutionary Computation 6(2), 2002
- Frequency-Domain Characterization of Power Distribution Networks — István Novak and Jason R. Miller, Artech House (2007)
- Power Integrity Modeling and Design for Semiconductors and Systems — Madhavan Swaminathan and A. Ege Engin, Prentice Hall (2007)
Satellite & Terrestrial Link Budget
Aligned with ITU-Rpy
- ITU-R P.618-13 — Propagation data and prediction methods required for the design of Earth-space telecommunication systems
- ITU-R P.676-12 — Attenuation by atmospheric gases (Annex 2, slant paths)
- ITU-R P.840-8 — Attenuation due to clouds and fog
- ITU-R P.838-3 — Specific attenuation model for rain for use in prediction methods
- ITU-R P.530-17 — Propagation data and prediction methods required for the design of terrestrial line-of-sight systems
- ITU-R P.837-7, P.839-4, P.836-6, P.1510-1, P.1511-1 — Rain rate, rain height, water vapour, surface temperature and topography digital maps
RF Cascade Budget Analyzer
Matches scikit-rf cascade
- Noise Figures of Radio Receivers — Harald T. Friis, Proc. IRE 32(7), pp. 419–422 (1944)
- Microwave Engineering, 4th ed. — David M. Pozar (2011), Chapter 10 — Noise and Nonlinear Distortion
- RF Microelectronics, 2nd ed. — Behzad Razavi (2011), Chapter 2 — Cascaded Noise and Intercept Points
- IEEE Std 182-1989 — IEEE Standard for Measurement of Amplifier Noise Figure
Calculators with full methodology
- Transmission Line Design Handbook — Brian C. Wadell, Artech House (1991), Chapter 3 — Microstrip
- Microwave Engineering, 4th ed. — David M. Pozar (2011), Chapter 3.8 — Microstrip and effective permittivity
- A Note on a Simple Transmission Formula — Harald T. Friis, Proc. IRE 34(5), pp. 254–256 (1946)
- ITU-R P.525-4 — Calculation of free-space attenuation
- ITU-R P.618-13 — Rain and atmospheric attenuation for Earth-space links
- Microwave Engineering, 4th ed. — David M. Pozar (2011), Chapter 14 — Wireless Communication Systems
- Microwave Engineering, 4th ed. — David M. Pozar (2011), Chapter 2.3 — Reflection coefficient and VSWR
- Fundamentals of RF and Microwave Transistor Amplifiers — Inder J. Bahl (2009), Chapter 2 — S-parameters and VSWR
- Microwave Engineering, 4th ed. — David M. Pozar (2011), Chapter 1 — dBm and power units
- RF Circuit Design Theory and Applications — Reinhold Ludwig & Pavel Bretchko (2000), Chapter 2 — Power and gain definitions
- Noise Figures of Radio Receivers — Harald T. Friis, Proc. IRE 32(7), pp. 419–422 (1944)
- Microwave Engineering, 4th ed. — David M. Pozar (2011), Chapter 10
- RF Microelectronics, 2nd ed. — Behzad Razavi (2011), Chapter 2
- IEEE Std 182-1989 — IEEE Standard for Measurement of Amplifier Noise Figure
- Microwave Engineering, 4th ed. — David M. Pozar (2011), Chapter 1.6 — Skin depth and surface resistance
- Classical Electrodynamics, 3rd ed. — John D. Jackson (1999), Chapter 5 — Skin effect in conductors
- Microwave Engineering, 4th ed. — David M. Pozar (2011), Chapter 1.3 — Wavelength and wave velocity
- ITU Radio Regulations — International Telecommunication Union (2020), Article 2 — Frequency and wavelength definitions
- Microwave Engineering, 4th ed. — David M. Pozar (2011), Chapter 3.4 — Coaxial line
- Transmission Line Design Handbook — Brian C. Wadell, Artech House (1991), Chapter 3
- Microwave Engineering, 4th ed. — David M. Pozar (2011), Chapter 3.4 — Coaxial line loss
- Times Microwave LMR Coaxial Cable Datasheet — Times Microwave Systems (2020), Application Note AN-107
- ETSI EN 300 220-1 V3.1.1 — Short Range Devices (SRD) — ISM band coexistence (2017)
- FCC Part 15 — Unlicensed ISM Devices — Federal Communications Commission (47 CFR Part 15)
- Microwave Engineering, 4th ed. — David M. Pozar (2011), Chapter 7.5 — Resistive attenuators
- Matthaei, Young & Jones — Microwave Filters, Impedance-Matching Networks — Artech House (1980), Appendix B
- Transmission Line Calculator — Phillip H. Smith, Electronics 12(1), pp. 29–31 (1939)
- Microwave Engineering, 4th ed. — David M. Pozar (2011), Chapter 2.4 — The Smith Chart
- Electronic Applications of the Smith Chart, 2nd ed. — Phillip H. Smith (1995)
- Antenna Theory: Analysis and Design, 4th ed. — Constantine A. Balanis (2016), Chapter 4 — Dipole antenna radiation resistance and gain
- Antenna Theory and Design, 3rd ed. — Warren L. Stutzman & Gary A. Thiele (2012), Chapter 3 — Wire antenna analysis
- Antenna Theory: Analysis and Design, 4th ed. — Constantine A. Balanis (2016), Chapter 14 — Microstrip patch antenna transmission-line model
- Microstrip Antenna Design Handbook — R. Garg, P. Bhartia, I. Bahl & A. Ittipiboon, Artech House (2001), Chapter 3 — Patch dimensions
- ITU-R BS.705-1 — HF transmitting antennas — characteristics and diagrams (EIRP definitions)
- Antenna Theory: Analysis and Design, 4th ed. — Constantine A. Balanis (2016), Chapter 2 — EIRP, ERP, and radiation intensity
- Microwave Engineering, 4th ed. — David M. Pozar (2011), Chapter 6.1 — Quality factor and resonator loss
- RF Circuit Design Theory and Applications — Reinhold Ludwig & Pavel Bretchko (2000), Chapter 4 — Q factor definitions
- Microwave Engineering, 4th ed. — David M. Pozar (2011), Chapter 3.3 — Rectangular waveguide modes and cutoff
- Time-Harmonic Electromagnetic Fields — Roger F. Harrington (2001), Chapter 8 — Waveguide theory
- Antenna Theory: Analysis and Design, 4th ed. — Constantine A. Balanis (2016), Chapter 2 — Directivity, gain, and half-power beamwidth
- Antenna Theory and Design, 3rd ed. — Warren L. Stutzman & Gary A. Thiele (2012), Chapter 2 — Aperture antenna beamwidth
- ITU-R P.525-4 — Calculation of free-space attenuation
- A Note on a Simple Transmission Formula — Harald T. Friis, Proc. IRE 34(5), pp. 254–256 (1946)
- Microwave Engineering, 4th ed. — David M. Pozar (2011), Chapter 14.1
- Introduction to Radar Systems, 3rd ed. — Merrill I. Skolnik (2001), Chapter 1 — The Nature of Radar
- Principles of Modern Radar: Basic Principles — Mark A. Richards, James A. Scheer, William A. Holm (2010)
- Radar Handbook, 3rd ed. — Merrill I. Skolnik, editor (2008)
- RF Power Amplifiers for Wireless Communications, 2nd ed. — Steve C. Cripps (2006), Chapter 2 — Efficiency definitions
- Microwave Engineering, 4th ed. — David M. Pozar (2011), Chapter 12 — Power amplifier gain and PAE
- RF Microelectronics, 2nd ed. — Behzad Razavi (2011), Chapter 6 — Nonlinearity and intermodulation
- Nonlinear Microwave and RF Circuits, 2nd ed. — Stephen A. Maas (2003), Chapter 3 — Intermodulation and IP3
- RF Circuit Design — Peter Vizmuller (1995), Chapter 3 — IIP3 and OIP3
- A Simple Model of Feedback Oscillator Noise Spectrum — D. B. Leeson, Proc. IEEE 54(2), pp. 329–330 (1966)
- Oscillator Design and Computer Simulation — Randall W. Rhea, SciTech Publishing (1995), Chapter 3 — Phase noise and jitter conversion
- A Simple Model of Feedback Oscillator Noise Spectrum — D. B. Leeson, Proc. IEEE 54(2), pp. 329–330 (1966)
- Microwave Oscillator Design — Alexander Chenakin, Artech House (2012), Chapter 6 — Vibration-induced phase noise
- Microwave Engineering, 4th ed. — David M. Pozar (2011), Chapter 5.3 — Return loss and mismatch error
- Applying Error Correction to Network Analyzer Measurements — Keysight Application Note AN 1287-3 (2002)
- Antenna Theory: Analysis and Design, 4th ed. — Constantine A. Balanis (2016), Chapter 10 — Yagi-Uda array design
- Antenna Theory and Design, 3rd ed. — Warren L. Stutzman & Gary A. Thiele (2012), Chapter 5 — Yagi-Uda element spacing and gain
- Antenna Theory: Analysis and Design, 4th ed. — Constantine A. Balanis (2016), Chapter 13 — Aperture antennas and horn gain
- Antenna Theory and Design, 3rd ed. — Warren L. Stutzman & Gary A. Thiele (2012), Chapter 8 — Horn antenna beamwidth
- Antenna Theory: Analysis and Design, 4th ed. — Constantine A. Balanis (2016), Chapter 15 — Reflector antennas and parabolic dish gain
- Antenna Theory and Design, 3rd ed. — Warren L. Stutzman & Gary A. Thiele (2012), Chapter 9 — Parabolic reflector efficiency and directivity
- Antenna Theory: Analysis and Design, 4th ed. — Constantine A. Balanis (2016), Chapter 5 — Small and large loop antennas
- Antenna Theory and Design, 3rd ed. — Warren L. Stutzman & Gary A. Thiele (2012), Chapter 4 — Loop antenna radiation resistance
- ITU-R P.526-15 — Propagation by diffraction — Fresnel zone clearance
- Microwave Engineering, 4th ed. — David M. Pozar (2011), Chapter 14 — Fresnel zones and path clearance
- ITU-R P.525-4 — Calculation of free-space attenuation — power flux density
- ICNIRP Guidelines 2020 — International Commission on Non-Ionizing Radiation Protection, Health Physics 118(5), pp. 483–524 (2020)
- Microwave Engineering, 4th ed. — David M. Pozar (2011), Chapter 8.5 — Baluns and power dividers
- Matthaei, Young & Jones — Microwave Filters, Impedance-Matching Networks — Artech House (1980), Chapter 4 — Coupled resonators and transformers
- ITU-R P.525-4 — Calculation of free-space attenuation
- A Note on a Simple Transmission Formula — Harald T. Friis, Proc. IRE 34(5), pp. 254–256 (1946)
- Nonlinear Microwave and RF Circuits, 2nd ed. — Stephen A. Maas (2003), Chapter 5 — Mixer spurious products
- RF Circuit Design — Peter Vizmuller (1995), Chapter 4 — Mixer spur analysis
- Microwave Engineering, 4th ed. — David M. Pozar (2011), Chapter 2 — Reactance and susceptance
- The ARRL Handbook for Radio Communications — ARRL (2023), Chapter 4 — Reactance formulae
- Introduction to Radar Systems, 3rd ed. — Merrill I. Skolnik (2001), Chapter 3 — Doppler effect in radar
- Microwave Engineering, 4th ed. — David M. Pozar (2011), Chapter 14 — Doppler frequency shift
- Coplanar Waveguide Circuits, Components and Systems, ch. 2 — R. N. Simons, Wiley 2001
- Transmission Line Design Handbook, §3.3 (coplanar lines) — B. C. Wadell, Artech House 1991
- Handbook of Mathematical Functions, ch. 17 (elliptic integrals) — Abramowitz & Stegun, NBS 1964
All 241 calculators also include a formula.reference field citing their primary textbook source; the list above highlights the hero set with full methodology blocks.
Corrections
If you spot a formula error, a missing citation, or a case where our result diverges from a published reference, please submit a correction via the request page or email hello@rftools.io. Corrections are reviewed and deployed with a note in the tool’s methodology block.