Figure 1.
Circuit Diagram for a First-Order Butterworth High-Pass Filter
The circuit
shown in Figure 1 is a first-order Butterworth high-pass filter. A
high-pass filter is a circuit that blocks signals with frequencies lower
than a cut-off frequency fc.
The circuit in Figure 1 uses an op-amp configured as a non-inverting
amplifier, with an RC circuit at the non-inverting input to do the
filtering of the low-frequency signals. The cut-off frequency fc of this
circuit is determined by R and C, i.e., fc = 1/{2π(RC)}.
The pass-band
gain Gp of this filter is given by: Gp = 1 + (RF/R1). Thus, if the
frequency f of the input signal is higher than fc, Vo ≈ Gp x Vin.
If f = fc, Vo ≈ 0.707 Gp x Vin. If f < fc, Vo < Gp x Vin.
Figure 2.
Circuit Diagram for a Second-Order Butterworth High-Pass Filter
As the
frequency of the input signal goes lower than fc, the gain of the
first-order Butterworth high-pass filter in Figure 1 decreases at a rate
of -20 dB/decade. If one desires a better high-pass frequency
response than this, the second-order Butterworth high-pass filter in
Figure 2 can be used. This circuit exhibits a -40 dB/decade
roll-off at f<fc, wherein fc = 1/{2π x sqrt(R2R3C2C3)}. Also, for this
circuit, the magnitude of Vo/Vin = (1+RF/R1)/(sqrt(1+(fc/f)4)).
See Also:
Butterworth Low-Pass Filters;
Op-Amp-based High-Pass Filter;
Operational Amplifiers
