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2nd Order Bandpass Filter

Schematic of a 2nd order Bandpass Filter

    Entering a value for the center frequency, bandwidth, and gain will find the optimum resistor and capacitor values for the bandpass filter shown. Unless otherwise specified, the capacitor’s tolerance is assumed to be 5%. If you wish to specify a different tolerance, enter it as a percentage (10% = 10).

    By default, the solver limits itself to resistor values greater than 1KΩ. You can change this behavior by entering a value for Min R. Note that the solver iterates through all RC value combinations to find the best value pair. This means that a change in Min R is unlikely to have an effect unless it value is changed in one decade increments (50 to 500 to 5K for instance). The value of Min R is ignored when calculated capacitor values become very small (<4.7pF).

    Even though solutions are provided for a number tolerance bands, the filter performs best when the resistors Ra are matched. For that reason, if you wish to implement the design with lower tolerance parts, best performance will be obtained when Ra is a 1% or lower tolerance. It is worth mentioning that the value of Ra is not critical and can be altered without affecting the filters center frequency or bandwidth.

    This particular implementation of a bandpass filter uses four op-amps. In this implementation, the open loop gain of the op-amp only needs to satisfy the gain * max frequency of the filter. This is not the case for all implementations. In addition, you can use a dual gang potentiometer to replace Rf and tune the center frequency of the filter while maintaining a constant Q (Q is the ratio of the center frequency to the bandwidth at the -3db points).

    For general information about filters, see the Filter Types article. The following equations are used to solve for the values.

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