The Active Filter: Pass Only the Frequencies You Want
Sweep the frequency and find the border between pass and stop
The curve is the filter's frequency response, which shows how much of the signal gets through at each frequency. The horizontal axis is logarithmic, and the vertical axis is in decibels. As you sweep the input frequency and move the operating point, the response is flat below the cutoff marked on the horizontal axis and the signal passes unchanged, but beyond the cutoff the response slopes down and the signal is cut more and more. The indicator shows in decibels how much the signal is reduced at that frequency.
A capacitor’s impedance depends 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). For very low frequencies, that is, slowly changing signals, the impedance is very large and blocks almost as if the circuit were cut; for very high frequencies the impedance becomes small and lets the signal through almost as if it were connected. In this way a capacitor behaves like a resistor whose value changes with frequency, and this property is the basis of filters that sort out frequencies.
RC sets where the cut happens: the cutoff
Pair one resistor with one capacitor and you get a 1st-order filter. The frequency at which the two impedances have equal magnitude is the cutoff frequency fc = 1/(2πRC), and at this frequency the response is -3 dB below the flat passband. Below the cutoff, the capacitor's impedance is large and the signal passes almost unchanged; above the cutoff, the impedance keeps shrinking and diverts the signal into a side path, so the response falls by -20 dB for every 10 times the frequency. The product of R and C decides where to cut, and the larger the product, the lower the cutoff.
Active: the op-amp adds gain and a buffer
Resistors and capacitors alone can make a filter, but such a passive filter has weaknesses. With no gain it cannot enlarge the signal, and because a resistor sits on the output side, attaching a following stage loads it and disturbs the cutoff. Place the same resistor and capacitor around an op-amp and you get an active filter. A common form puts a capacitor in parallel with the feedback resistor of an inverting amplifier; as frequency rises, the capacitor shorts around the feedback resistor and the gain drops. The op-amp gives the passband a gain (often set by the resistor ratio -Rf/Rin, chosen separately from the cutoff) and drives the output firmly with its low output impedance so the following stage cannot disturb it. Stacking several stages also builds a steeper cutoff, so an active filter cleanly carves the desired band out of a signal.
Back to the first screen
When the input frequency was low, the response sat in the flat passband and the signal came out unchanged; as you raised the frequency, the response fell past the cutoff and the signal was cut more and more. What drew that border was the capacitor's impedance changing with 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 following stage with its low output impedance, so the cut is clean. This is the active filter. The op-amp, which started from the ideal of infinite gain and passed through its real limits, has become a useful circuit that picks out frequencies.
What comes next
So far you have looked at devices and circuits that handle signals. The last group changes the stage and moves to power electronics, which handles power itself rather than signals. Going one step beyond diode rectification (B), it covers the basics of the SMPS, which converts voltage efficiently by switching. There, devices are only switched fully on and off to cut losses, and the transistor serves not as an amplifier but as a switch.