The Active Filter: Pass Only the Frequencies You Want
Sweep the frequency and find the line between pass and stop
The curve is how much passes at each frequency, the filter’s frequency response. Sweep the input frequency to move the operating point. Below the cutoff the response is flat and the signal passes through, but above the cutoff the response falls and the signal is cut more and more.
A capacitor’s impedance rides on frequency
A resistor has the same value regardless of frequency, but a capacitor is different. A capacitor’s impedance is inversely proportional to frequency: Zc = 1/(2πfC). At very low frequency, a slowly changing signal, the impedance is very large and it blocks as if nearly open; at very high frequency the impedance is small and it passes the signal as if nearly connected. So a capacitor behaves like a resistor whose value changes with frequency, and exactly this property is the heart of a filter that sorts by frequency.
RC sets where the cut happens: the cutoff
Pair one resistor with one capacitor and you get a first-order filter. At the frequency where the two impedances become equal, the cutoff frequency fc = 1/(2πRC), the response is 3 dB below the flat passband. Below the cutoff the capacitor’s impedance is large and the signal passes almost untouched; above the cutoff its impedance grows smaller and smaller, shunting the signal away, so the response falls -20 dB per decade. Where the cut happens is set by the product of R and C.
Active: the op-amp adds gain and a buffer
A resistor and capacitor alone make a filter, but such a passive filter is weak. It has no gain to boost the signal, and a resistance sits in its output, so attaching a next stage lets that load disturb the cutoff. Put the same RC around an op-amp and it becomes an active filter. The op-amp gives the passband a gain (often the resistor ratio -Rf/Rin, set separately from the cutoff), drives the output firmly with low output impedance so the next stage cannot shift it, and lets you stack several stages for a steeper cut. So an active filter cleanly carves the band you want out of a signal.
Back to the first screen
When the input frequency was low, the response was in the flat passband and the signal came through; raising the frequency, it passed the cutoff and the response fell and the signal was cut more and more. What drew that boundary was the way a capacitor’s impedance rides on frequency, and the cutoff fc = 1/(2πRC) where it equals the resistance. A passive RC alone can cut, but adding an op-amp puts gain on the passband and blocks interference from the next stage with low output impedance, cutting cleanly. This is the active filter. The op-amp, which set out from the ideal of infinite gain and passed through its real limits, is at last completed into a use that sorts by frequency.
What comes next
Up to here we have seen devices and circuits that handle signals. In the final group we change the stage and go to power electronics, which handles not signals but power itself. Stepping beyond diode rectification (B), we look at the basics of an SMPS that converts voltage efficiently by switching. There, where devices are only turned on and off to cut losses, the transistor becomes a switch rather than an amplifier.