First-order Continuous-time Implementation
The simple first-order electronic high-pass filter shown in Figure 1 is implemented by placing an input voltage across the series combination of a capacitor and a resistor and using the voltage across the resistor as an output. The product of the resistance and capacitance (R×C) is the time constant (τ); it is inversely proportional to the cutoff frequency fc, that is,
where fc is in hertz, τ is in seconds, R is in ohms, and C is in farads.
Figure 2 shows an active electronic implementation of a first-order high-pass filter using an operational amplifier. In this case, the filter has a passband gain of -R2/R1 and has a corner frequency of
Because this filter is active, it may have non-unity passband gain. That is, high-frequency signals are inverted and amplified by R2/R1.
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