State variable biquad
State variable biquad with computed response and explicit circuit realisation.
Development preview. Check the assumptions below before relying on a result. Calculations run in your browser.
How it calculates
State equations: HP = G Vin − BP/Q − LP; BP = (ω0/s) HP; LP = (ω0/s) BP
Integrator scale: ω0 = 1/(Rint C)
Common denominator: D(s) = s² + (ω0/Q)s + ω0²
Assumptions
- The original five-amplifier schematic implements all polarities explicitly: input inverter, inverting summer, first inverting integrator, band-pass inverter, and second inverting integrator. Identically named nets are wired together. Damping and input resistors assume a summing-stage feedback resistor equal to the entered scale. LP and HP asymptotic gains are G; the unnormalised BP peak is GQ.
Worked example
These are the calculator's default inputs. Change any input above to recalculate.
Inputs
- Natural frequency
- 1000 Hz
- Q
- 0.707107
- Input gain
- 1
- Both integrator capacitors
- 1e-8 F
- Summing resistor scale
- 10000 Ω
Results
- Both integrator resistors
- 15915.5 Ω
- Damping input resistor
- 7071.07 Ω
- Signal input resistor
- 10000 Ω
- Band-pass feedback coefficient
- 1.41421
- Band-pass peak gain
- 0.707107