For minimum DC offset, V+ = V−, the resistor values at both
inverting and non-inverting inputs should be equal, which
means
Scaled values:
R2 = R1 = 15.9 kΩ
R3 = R4 = 63.6 kΩ
C1 = C2 = 0.01 µF
(8)
An adjustment to the scaling may be made in order to have
realistic values for resistors and capacitors. The actual value
used for each component is shown in the circuit.
From Equation 1 and Equation 8, we obtain
(9)
2nd-Order High Pass Filter
A 2nd-order high pass filter can be built by simply interchang-
ing those frequency selective components (R1, R2, C1, C2) in
the Sallen-Key 2nd-order active low pass filter. As shown in
Figure 14, resistors become capacitors, and capacitors be-
come resistors. The resulted high pass filter has the same
corner frequency and the same maximum gain as the previ-
ous 2nd-order low pass filter if the same components are
chosen.
(10)
The values of C1 and C2 are normally close to or equal to
As a design example:
Require: ALP = 2, Q = 1, fc = 1 kHz
Start by selecting C1 and C2. Choose a standard value that is
close to
From Equations 6, 7, 9, 10,
R1= 1Ω
R2= 1Ω
R3= 4Ω
R4= 4Ω
The above resistor values are normalized values with ωn = 1
rad/s and C1 = C2 = Cn = 1F. To scale the normalized cutoff
frequency and resistances to the real values, two scaling fac-
tors are introduced, frequency scaling factor (kf) and
impedance scaling factor (km).
10006083
FIGURE 14. Sallen-Key 2nd-Order Active High-Pass Filter
State Variable Filter
A state variable filter requires three op amps. One convenient
way to build state variable filters is with a quad op amp, such
as the LMV324 (Figure 15).
This circuit can simultaneously represent a low-pass filter,
high-pass filter, and bandpass filter at three different outputs.
The equations for these functions are listed below. It is also
called "Bi-Quad" active filter as it can produce a transfer func-
tion which is quadratic in both numerator and denominator.
17
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