# Ohmforge Passive Filter Designer

> RC, RL and RLC low/high/band-pass filters: cutoff, Q, bandwidth, Bode plot, E-series parts. Analyses or designs passive filters: first-order RC and RL low- and high-pass, the two-stage RC ladder and series RLC low-pass, high-pass, band-pass and notch. Gives the cutoff or centre frequency, Q, bandwidth and exact −3 dB points (also with a load), Bode magnitude and phase from the transfer function, suggested standard parts – and checks the curve against Ohmforge's AC simulator.

Part of usefulweb.site (https://usefulweb.site/). Part of [Ohmforge](https://ohmforge.usefulweb.site/) (ownerApp: ohmforge). Results are deterministic calculations from the inputs and the listed assumptions; the API returns exactly what the web page shows.

## Use it
- Human interface: https://ohmforgefilterdesigner.usefulweb.site/ (interactive tool at https://ohmforgefilterdesigner.usefulweb.site/tool)
- JSON API: POST https://ohmforgefilterdesigner.usefulweb.site/api/v1/calculate with a JSON object of inputs (schema: https://ohmforgefilterdesigner.usefulweb.site/api/v1/tool)
- OpenAPI: https://ohmforgefilterdesigner.usefulweb.site/openapi.json
- MCP (Streamable HTTP): https://ohmforgefilterdesigner.usefulweb.site/mcp - tool `ohmforge_filter_designer`

## Inputs
- topology (select): Filter
- mode (select): Task
- r (text): R / R1 - Analyse: the resistor (first resistor of the RC ladder). Engineering notation: 1k, 4k7.
- l (text): L - Inductance for RL and RLC filters, e.g. 10m = 10 mH.
- c (text): C / C1 - Capacitance, e.g. 100n = 100 nF.
- r2 (text): R2 (RC ladder only)
- c2 (text): C2 (RC ladder only)
- frequency (number): Target frequency (design) - Cutoff (−3 dB) for first-order filters and the RC ladder, centre/resonant frequency f0 for RLC.
- q (number): Quality factor Q (design, RLC) - 0.7071 gives the flattest (Butterworth) low/high-pass; higher Q = narrower band-pass/notch.
- anchor (text): Part you choose (design) - Design keeps this value and computes the rest: the capacitor for RC, RC ladder and RLC filters, the resistor for RL filters.
- rload (text): Load resistance (optional) - Resistance across the output; changes the −3 dB points. Empty = unloaded.
- series (select): Standard resistor series - Resistors are rounded to this series; capacitors and inductors to E12.

## Method
- Each filter is a ladder of series and shunt impedances (R, jωL, 1/(jωC)). The transfer function H(jω) = Vout / Vin is the product of the sections' ABCD matrices; with a load RL, H = 1 / (A + B / RL). Magnitude is 20·log10|H|, phase is unwrapped.
- Formula values: fc = 1/(2πRC) or R/(2πL) for first order; f0 = 1/(2π√(LC)) and Q = √(L/C)/R for the series RLC filters (band-pass bandwidth f0/Q); f0 and Q of the two-stage RC ladder from its denominator 1 + s(R1C1 + R2C2 + R1C2) + s²R1C1R2C2.
- The −3 dB points are solved by bisection on |H| relative to the passband gain (DC for low-pass and notch, high-frequency gain for high-pass, the peak for band-pass), so they stay correct with a load or a resonant peak.
- Design keeps the part you choose and computes the rest (RC: R = 1/(2πfC); RL: L = R/(2πf); RLC: L = 1/((2πf0)²C), R = √(L/C)/Q; equal-value RC ladder: ωRC = 0.3742 for low-pass). Every computed part is tried at the series value below and above, and the combination closest to the target frequency (then Q) is suggested.
- Cross-check: the equivalent SPICE netlist is solved with Ohmforge's AC analysis over ±2 decades and the largest magnitude difference is reported.

## Limits
- Ideal components: no inductor winding resistance, no capacitor ESR, no source resistance. Real inductors limit the achievable Q, and component tolerances shift the corner (5 % parts move fc by about 5 %).