The Butterworth Sallen-Key (SK)
high-pass (HP) filter is a 2nd-order active filter. Vref provides a DC offset to accommodate
for single-supply applications.
filter is usually preferred when small Q factor is desired, noise rejection is prioritized,
and when a non-inverting gain of the filter stage is required. The Butterworth topology
provides a maximally flat gain in the pass band.
- Select an op amp with sufficient input
common-mode range and output voltage swing.
- Add Vref to bias the input
signal to meet the input common-mode range and output voltage swing.
- Select the capacitor values first since
standard capacitor values are more coarsely subdivided than the resistor values. Use
high-precision, low-drift capacitor values to avoid errors in fc.
- To minimize the amount of slew-induced
distortion, select an op amp with sufficient slew rate (SR).
- For HP filters, the maximum frequency is
set by the gain bandwidth (GBW) of the op amp. Therefore, be sure to select an op amp with
The first step is to find component
values for the normalized cutoff frequency of 1 radian/second. In the second step the cutoff
frequency is scaled to the desired cutoff frequency with scaled component values.
The transfer function for the second-order
Sallen-Key high-pass filter is given by:
- Set normalized values of C1 and
C2 (C1n and C2n) and calculate normalized values of
R1 and R2 (R1n and R2n) by setting
wc to 1 radian/sec (or fc = 1 / (2 × π) Hz). For the second-order Butterworth
filter, (see the Butterworth Filter Table in the Active Low-Pass Filter Design Application
- Scale the component values and cutoff
frequency. The resistor values are very small and capacitors values are unrealistic, hence
these have to be scaled. The cutoff frequency is scaled from 1 radian/sec to
w0. If m is assumed to be the scaling factor, increase the resistors by
m times, then the capacitor values have to decrease by 1/m times to keep
the same cutoff frequency of 1 radian/sec. If the cutoff frequency is scaled to be
w0, then the capacitor values have to be decreased by 1 / w0. The
component values for the design goals are calculated in steps 3 and 4.
- Set C1 and C2 to
10nF, then calculate m.
- Select R1 and R2
based on m.
- Calculate the minimum required GBW and SR
The TLV9062 device has a GBW of 10MHz
and SR of 6.5V/µs, so it meets these requirements.
AC Simulation Results
Transient Simulation Results
The following image shows the filter output
in response to a ± 2.5-V, 10-kHz input signal (gain is 1V / V).
The following image
shows the filter output in response to a ± 2.5-V, 10-Hz input signal (gain is 0.014V /
- See Analog
Engineer's Circuit Cookbooks for TI's comprehensive circuit library.
- SPICE Simulation File - SBOMB38.
- TI Precision
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