# Passive RL Filter

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

Unless otherwise specified, the inductor 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 50Ω. You can change this behavior by entering a value for Min R. Note that the solver iterates through all RL 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 inductor values become very small (<10nH).

This solver works for either lowpass or highpass RL 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 RL lowpass filter. Although this plot is for a specific corner frequency, all RL 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.