#cutoff-frequency

First-order RC and RL passive-filter design as an API, computed locally and deterministically. The lowpass and highpass endpoints take a resistor and capacitor (RC) or a resistor and inductor (RL) and return the −3 dB cutoff frequency (fc = 1/(2πRC) for RC, R/(2πL) for RL), the time constant (τ = RC or L/R) and the angular cutoff; pass a frequency as well and they add the magnitude response as a linear gain and in decibels and the phase shift in degrees — a 1 kΩ / 1 µF low-pass has fc ≈ 159.15 Hz, and right at the cutoff the gain is −3.01 dB with −45° phase for a low-pass or +45° for a high-pass. The component endpoint solves the missing one of fc, R and C from the other two (fc = 1/(2πRC)), so you can size a resistor or capacitor for a target cutoff. All quantities are SI: ohms, farads, henries and hertz. Everything is computed locally and deterministically, so it is instant and private. Ideal for electronics, audio, embedded, signal-processing and EE-education app developers, filter-design and circuit-sizing tools, and maker software. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is first-order single-pole filter design; for full RLC impedance and resonance use an impedance API and for stored capacitor energy a capacitor API.

api.oanor.com/rcfilter-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