State variable filter

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A state variable filter is a type of active filter which can produce simultaneous lowpass, highpass and bandpass outputs from a single input.

[edit] Circuit

Image:State-variable-filter.png

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:

Rf1 = Rf2

C1 = C2

R1 = R2

Then:

F_0 = \frac{1}{2\pi R_{f1}C_1}

Q = (1 + \frac{R_4}{R_q})(\frac{1}{2+\frac{R_1}{R_g}})

The pass-band gain for the LP and HP outputs is given by:

A_{HP} = A_{LP} = \frac{R_1}{R_G}

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.

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