Analogue filter designer

How it calculates

Butterworth poles: pk = exp[j(π/2 + (2k+1)π/(2n))]

Chebyshev poles: pk = −sinh(μ)sin θk + j cosh(μ)cos θk; μ = asinh(1/ε)/n

Bessel polynomial: θn(s) = Σ[(2n−k)!/(2^(n−k)(n−k)!k!)] s^k

Frequency transforms: LP: s/ωc; HP: ωc/s; BP: (s²+ω0²)/(B s); BS: B s/(s²+ω0²)

Assumptions

• Butterworth/Bessel corner is −3 dB. Chebyshev corner is the ripple edge, with even-order DC gain below unity. Linkwitz–Riley uses two identical half-order Butterworth sections and has −6 dB at the corner. Band transforms double the prototype order.
• LP Sallen–Key labels: input → R1 → node N → R2 → non-inverting input; C1 from non-inverting input to ground; C2 from N to output. Unity design uses R1=R2 and C2=4Q² C1. Equal-component design uses K=3−1/Q. HP uses the dual network described by FIL-02.
• MFB labels follow FIL-02: C1 is feedback from output to the inverting node; C2 goes from the intermediate node to ground. LP unity magnitude synthesis uses R1=R2=R3 and C2=9Q² C1. Gain normalisers are realised as buffered passive dividers, unity/inverting amplifiers or non-inverting amplifiers; their rounded resistor ratios are included in the response.
• Rounded response is recomputed from rounded R/C/gain-setting resistor values. It does not include component tolerance. BP, BS and all-pass use the wired five-amplifier state-variable core shown below, followed by a two-amplifier signed output mixer. Mixer branches are labelled MIXHP, MIXBP and MIXLP; negative BP weight uses BN. Unused branches are omitted. Each mixer has feedback RMIX and a unity output inverter. A first-order all-pass uses matched inverting resistors with its non-inverting input driven by a buffered RC low-pass. Time response integrates the ideal section cascade. The GBW rule 100 f0 max(1,Q²) is conservative screening, not a stability guarantee.

Worked example

These are the calculator's default inputs. Change any input above to recalculate.

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