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# RL High-Pass Filters

Like an RC element, an RL element is also a frequency-dependent voltage divider. In this case, however, the inductive reactance *X*_{L} increases with the frequency *f*. Consequently, the element's output voltage *U*_{L} also increases with the frequency. In other words, an RL element allows high frequencies to pass while progressively blocking low frequencies. An RL element is accordingly termed a *high-pass filter*. The diagram below illustrates the relationships between the various voltages.

The output voltage *U*_{L} can be calculated as in the case of the purely ohmic voltage dividers employed in DC circuits according to the following formula:

The ratio between the output and input voltages is defined as follows:

*Z* is the total impedance of the element.

Plotting the ratio for specific values of *R* and *L* as a function of the frequency provides, as in the case of the RC element, the RL element's *amplitude response*, as exemplified in the illustration below. At low frequencies, the low inductive reactance results in practically no voltage drop across the coil, whereas at high frequencies, the coil has a high impedance leading to a correspondingly large drop in supply voltage across the coil. The amplitude response here is therefore entirely the inverse of that for an RC element, which as we have seen acts as a low-pass filter.

Also when represented in dB (see following illustration), RL amplitude response looks like a mirror image of RC amplitude response.

RL high-pass filters have a cut-off frequency too, defined in this case by the following formula:

The phase displacement j between the voltages of an RL element is described by the following equation:

The diagram below shows the associated phase response. At high frequencies, both voltages are nearly in phase; at low frequencies, the phase shift on RL elements approaches +90°. The phase shift at the cut-off frequency is +45°.

The following interactive animation shows the amplitude response of an RL element at different values of *R* and *L*, as well as the position of the cut-off frequency (red vertical line). On the right-hand edge of the display you can select a variety of component parameters to observe their effect on the amplitude response.