State-Variable Filter (KHN) Calculator
Design a 3-op-amp state-variable filter providing simultaneous low-pass, band-pass, and high-pass outputs. Tunable Q and f₀; classic Kerwin-Huelsman-Newcomb topology.
How to Use
- Enter center frequency f₀, Q, and integrator capacitor C.
- Tool computes R for the integrators and the Q-setting resistor.
- Three simultaneous outputs: LP, BP, HP. Sum them for a notch response.
Show Work
Formulas
History
William J. Kerwin, Lawrence P. Huelsman, and Robert W. Newcomb published the state-variable filter in a 1967 IEEE paper while at UC Berkeley. Their topology implements an analog state-space realization of a 2nd-order transfer function — three state variables (output of each integrator plus the summer output), each providing a different filter response.
The KHN filter became the defining topology of analog synthesizer VCFs (Voltage-Controlled Filters). Bob Moog\'s 1971 ladder-filter patent used a related but different topology (transistor ladder), but many competing synths from ARP, Oberheim, and Korg used state-variable designs. The Moog vs state-variable filter debate has animated synthesizer culture ever since.
Modern DSP VCF emulators (Korg Volca, Arturia, Roland digital) implement state-variable topology in code rather than op-amps, but the 1967 equations and signal-flow graph remain unchanged. The three-op-amp circuit is still the classic teaching example for state-space filter design.
About This Calculator
Enter center frequency f₀, Q, and integrator capacitor value C. The tool computes two matched integrator resistors R = 1/(2π·f₀·C) and the Q-setting feedback resistor R_q = R · (3Q-1). Use matched ±1% resistors and COG/NP0 caps for tight Q.
The three outputs appear simultaneously without reconfiguring: summing-amp output = HP, after 1st integrator = BP, after 2nd integrator = LP. Sum LP + HP to get a notch at f₀. For voltage-controlled tuning (VCF), replace integrator resistors with OTAs or LDR-opto-isolators. Everything runs client-side.
About the State-Variable Filter (KHN) Calculator
The State-Variable Filter (KHN) Calculator is a free tool for electronics and circuit design. It runs right in your web browser, so there is nothing to download. Design a 3-op-amp state-variable filter providing simultaneous low-pass, band-pass, and high-pass outputs. Tunable Q and f₀; classic Kerwin-Huelsman-Newcomb topology.
How it works
Type your numbers into the boxes. The answer shows up right away — you do not have to press a button. If you change a number, the answer changes too. So you can try different numbers and watch what happens, or check an answer you worked out yourself. Just make sure each box has the right kind of number in it.
Want the deeper story? The Knowledge Base explains the ideas behind the tools in more detail.
Frequently Asked Questions
KHN?
Kerwin-Huelsman-Newcomb — the three UC Berkeley engineers who published the original 1967 paper. Uses a summing op-amp feeding two integrators in sequence, with feedback from the BP and LP outputs.
Why three op-amps?
Each integrator provides one pole; the summer provides damping. Three op-amps let you get LP, BP, HP simultaneously without rebuilding the circuit — ideal for synthesizer filters with multi-mode output.
Q range?
1-100 easily. Above 100, component-tolerance sensitivity becomes a problem. Below 0.5, response is overdamped.
How do I use the State-Variable Filter (KHN) Calculator?
Just type your numbers. The answer shows up right away — there is no button to press. Change anything and it updates by itself.
Is it free? Does it work without internet?
Yes to both. It is free with no sign-up, and once the page has loaded it keeps working even with no internet.
Where does my data go?
Nowhere — every calculation runs on your own device. Nothing you enter is uploaded, logged, or stored.
Common Use Cases
Moog-Style Synth VCF
State-variable VCF with voltage-controlled R (via CMOS switch) and LP output for classic analog synthesizer sound.
Multi-Band EQ
Cascade SVFs at different f₀ with BP output for 5-10 band parametric equalizer.
Wide-Range Spectrum
Tunable SVF with LP + HP sum at the same f₀ creates a notch filter for harmonic-distortion analysis.
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