# Passive RC Filter

Entering a value for corner frequency, f (-3dB), will find the optimum values for R and C. If you specify the values for R and C, the corner frequency is found. If you enter a resistor or capacitor value (R or C) along with the corner frequency, the other value will be found.

Unless otherwise specified, the capacitor 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). This option might be useful if the filter is followed by an unbuffered load.

This solver works for either lowpass or highpass RC first order filters. For general information about filters, see the Filter Types article. To find the amplitude and phase at a particular frequency, use the highpass and lowpass amplitude and phase calculators.  The following equation is used to solve for the values.

The following figure depicts the response of a RC lowpass filter. Although this plot is for a specific corner frequency, all RC lowpass filters will have this shape. The only thing that changes is the horizontal (frequency) axis labels.

This plot assumes a 1V input and has a linear vertical axis and the typical log scale axis for frequency. The plot shown below is the same with the exception that it is a log-log plot where both axis are log scale.

The following figure depicts a log-log plot of a high pass filter. Notice that it has a similar, although mirror imaged, shape as the lowpass filter.  The corner frequency is found in the same way.  Not that the phase in this case is positive rather than negative.

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