Active filters can be used to limit the range of frequencies that may be passed to an amplifier. Filters can be designed to pass high frequencies, low frequencies, or a range of middle frequencies. Filters can be designed utilizing op-amps in an inverting amplifier configuration.
Symbols and Terms
High Pass Filter
- Cutoff Frequency: The frequency fc where the filter output voltage falls to 70.7% of its peak output. This is equivalent to 50% (-3dB) of the peak power output.
- Low Pass Filter: Attenuates signals with frequencies above Fc.
- High Pass Filter: Attenuates signals with frequencies below Fc.
- Band-Pass Filter: Attenuates signals with frequencies outside of a range of frequencies (passband).
- Q: The ratio of a Band-Pass Filter's center frequency to the bandwith of its passband. A higher "Q" indicates a narrow passband for a given center frequency.
- Roll-Off: The gradual reduction in signal amplitude beyond a Fc.
- Vi: The inverting input of the op-amp.
A high pass filter is as simple as adding a capacitor (Ci) in series with the input signal. The reactance of a capacitor is frequency dependent:
As the applied frequency increases, the reactance decreases and more signal is applied to the input of the op-amp. Likewise, the reactance increases as the frequency decreases. This causes lower frequency input signals to roll-off. Ci is calculated as:
For fc = 300 Hz and Ri = 10 kΩ, Ci = 1 / ( 2 * π * 300 * 10000 ) = 53 nF.
- Ci = 1 / ( 2 * π * fc * Ri )
Low Pass Filter
Adding a capacitor (Cf) in parallel with the feedback resistor produces a low pass filter. Since the reactance of the capacitor changes with frequency, the amount of feedback is affected by the frequency of the signal. As the frequency increases:
- The capacitor reactance decreases.
- The impedance of the feedback signal decreases, resulting in a lower voltage drop across Rf and Cf.
- Because RF, Cf, and R form a voltage divider, Vi increases.
- This means that less output voltage is required to balance the input current at higher frequencies.
Ci is calculated as:
For fc = 3 kHz and Ri = 10 kΩ, Ci = 1 / ( 2 * π * 3000 * 10000 ) = 5.3 nF.
- Cf = 1 / ( 2 * π * fc * Rf )
A simple band-pass filter is constructed by add Cf and Ci. The values of Ci and Cf are calculated as if the band-pass filter was separate high pass and low pass filters.
A steeper roll-off and a high "Q" can be achieved utilizing multiple feedback paths. This is simply achieved by rearranging the capacitors Ci and Cf. |
Based on Hands-On Radio from May-2003 QST