A state variable filter is a type of active filter. It consists of one or more integrators, connected in some feedback configuration. Any LTI system can be described as a state-space model, with n state variables for an nth-order system. A state variable filter realizes the state-space model directly. The instantaneous output voltage of one of the integrators corresponds to one of the state-space model's state variables. The example given below can produce simultaneous lowpass, highpass and bandpass outputs from a single input. This is a second-order (biquad) filter. Other filter orders are possible, with more or fewer integrators.
Circuit
The signal input is marked Vin; the LP, HP and BP outputs give the lowpass, highpass and bandpass filtered signals respectively. For simplicity, we set: <math>R_{f1} = R_{f2}</math> <math>C_1 = C_2</math> <math>R_1=R_2</math> Then: <math>F_0 = \frac{1}{2\pi R_{f1}C_1}</math> <math>Q = (1 + \frac{R_4}{R_q})(\frac{1}{2+\frac{R_1}{R_g}})</math> The pass-band gain for the LP and HP outputs is given by: <math>A_{HP} = A_{LP} = \frac{R_1}{R_G}</math> It can be seen that the frequency of operation and the Q factor can be varied independently. This and the ability to switch between different filter responses make the state-variable filter widely used in analogue synthesizers. Values for a resonance frequency of 1 kHz are Rf1=Rf2=10k, C1=C2=15nF and R1=R2=10k
See also
References
- Texas Instruments' UAF42 Universal Active Filter datasheet
- Analog Devices Interactive Design Tools
