#microwave

Transmission-line RF maths as an API, computed locally and deterministically for a lossless line. The input-impedance endpoint transforms a complex load impedance along a line, Zin = Z0·(ZL + jZ0·tanβl)/(Z0 + jZL·tanβl), from the characteristic impedance, the load resistance and reactance and the electrical length in degrees — a quarter-wave (90°) line inverts the load to Z0²/ZL while a half-wave (180°) line repeats it, which is the basis of impedance matching. The quarter-wave endpoint computes the characteristic impedance Z0 = √(Z1·Z2) of a quarter-wave transformer that matches two real impedances, exact at one frequency. The electrical-length endpoint converts a physical line length to its electrical length in wavelengths, degrees and radians at a frequency, using the on-line wavelength λ = vf·c/f with a velocity factor for the dielectric. Impedances are in ohms (the load split into resistance and reactance), electrical length in degrees, physical length in metres and frequency in hertz. Everything is computed locally and deterministically, so it is instant and private. Ideal for RF, antenna-matching, PCB, radar and microwave app developers, stub-matching and transformer-design tools, and electromagnetics education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is line impedance transformation; for SWR and return loss use a VSWR API and for microstrip trace geometry a PCB API.

api.oanor.com/transmissionline-api

Rectangular-waveguide microwave maths as an API, computed locally and deterministically. The cutoff endpoint computes the cutoff frequency fc = (c/2)·√((m/a)²+(n/b)²) and cutoff wavelength of any TEmn or TMmn mode of a rectangular waveguide of inner width a and height b — below the cutoff a mode is evanescent and cannot propagate, and for the usual a > b the dominant mode is TE10 with fc = c/(2a). The guide-wavelength endpoint computes, at an operating frequency, the free-space wavelength, the guide wavelength λg = λ0/√(1−(fc/f)²) which is longer than free space, and the phase velocity (greater than c) and group velocity (the energy speed, below c). The modes endpoint lists every mode that propagates at a given frequency, sorted by cutoff, and identifies the dominant mode — so single-mode operation needs the frequency between the first and second cutoffs. Dimensions are in millimetres and frequencies in gigahertz, with c = 299,792,458 m/s. Everything is computed locally and deterministically, so it is instant and private. Ideal for RF, microwave, radar, satellite and antenna-feed app developers, waveguide-band and component-design tools, and electromagnetics education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is metallic rectangular waveguide; for optical-fibre guiding use a fibre API and for SWR a VSWR API.

api.oanor.com/waveguide-api