The classical "state-variable" (two-integrator) filter (see
the figure, a) is famous for its insensitivity to device parameter tolerances,
as well as its ability to provide three simultaneous separate outputs: high
pass, bandpass, and low pass. These advantages often offset the fact that a
quad operational amplifier is needed to implement the circuit.
A modification of the classical scheme that applies the input voltage via
amplifier UD rather than UA provides a bandpass output
with a fixed peak gain that doesn't depend on the Q of the filter.1
It was found by employing that configuration, a fourth notch-filter output can
be obtained if R11 = R6 (see
the figure, b) .
If R1 = R6 = R2, the gains of both the notch
and bandpass outputs are unity, regardless of the Q factor, as determined by
R3. R1, R2, R4, R5, and
R6 are preferably of a monolithic resistor network. The resonant
(or cut-off) frequency is given by ω= 1/Ro × CZo. Depending on the capacitor values and the frequency ω, the resistors Ro may also share the same monolithic network
for maximum space economy. As with the classical configuration, the resonant
frequency ω can be electronically controlled by switching resistors
Ro, or by employing analog multipliers in series with the integrators.
1Bernie Hutchins, "Filter's Gain Is Independent Of Q,"
EDN, Nov. 24, 1982.
