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.
Application Notes (Continued)
For minimum dc offset, V+ = V−, the resistor values at both
inverting and non-inverting inputs should be equal, which
means
4.4.3 2nd-order High Pass Filter
A 2nd-order high pass filter can be built by simply inter-
changing those frequency selective components (R1, R
,
2
C1, C2) in the Sallen-Key 2nd-order active low pass filter. As
shown in Figure 14, resistors become capacitors, and ca-
pacitors become resistors. The resulted high pass filter has
the same corner frequency and the same maximum gain as
the previous 2nd-order low pass filter if the same compo-
nents are chosen.
(8)
From Equation (1) and Equation (8), we obtain
(9)
(10)
The values of C1 and C2 are normally close to or equal to
As a design example:
Require: ALP = 2, Q = 1, fc = 1KHz
Start by selecting C1 and C2. Choose a standard value that
is close to
10006083
FIGURE 14. Sallen-Key 2nd-Order Active High-Pass
Filter
From Equations (6), (7), (9), (10),
R1= 1Ω
R2= 1Ω
R3= 4Ω
R4= 4Ω
4.4.4 State Variable Filter
A state variable filter requires three op amps. One conve-
nient way to build state variable filters is with a quad op amp,
such as the LMV324 (Figure 15).
The above resistor values are normalized values with ωn =
1rad/s and C1 = C2 = Cn = 1F. To scale the normalized cut-off
frequency and resistances to the real values, two scaling
factors are introduced, frequency scaling factor (kf) and im-
pedance scaling factor (km).
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
function which is quadratic in both numerator and
denominator.
Scaled values:
R2 = R1 = 15.9 kΩ
R3 = R4 = 63.6 kΩ
C1 = C2 = 0.01 µF
17
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