Section Index Owatonna Steele County Amateur Radio 20-Jul-2007

Active Filters

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

• 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. High Pass Filter
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:
• Xc = 1 / ( 2 * π * fc ).
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:
• Ci = 1 / ( 2 * π * fc * Ri )
For fc = 300 Hz and Ri = 10 kΩ, Ci = 1 / ( 2 * π * 300 * 10000 ) = 53 nF. 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:

• Cf = 1 / ( 2 * π * fc * Rf )
For fc = 3 kHz and Ri = 10 kΩ, Ci = 1 / ( 2 * π * 3000 * 10000 ) = 5.3 nF.

Band-Pass Filter

 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

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