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PASSIVE AND ACTIVE FILTERS

Passing and Rejecting Signals Based on Their Frequency

by James Antonakos

Start ý A Filter by Any Other Name ý Whatýs the Frequency, Kenneth? ý A Closer Look ý Itýs Just a Phase ý Whatýs Load Got to Do with It? ý Activate That Filter! ý Filters to the Rescue ý Sources and PDF

WHATýS THE FREQUENCY, KENNETH?

In the case of the low-pass and high-pass filters, you refer to the corner frequency of the filter as the frequency where the input signal begins getting passed or rejected. For the passive filters (see Figures 1a and b), the corner frequency depends on the value of resistor and capacitor used in the filter. For example, if R = 1 kilohm and C = 0.1 ýF, the corner frequency is 1591 Hz.

Figures 1a and býPassive low-pass and high-pass filtersý frequencies are determined by R and C.

Letýs think about this frequency, 1591 Hz. You canýt hook a frequency counter up to the filter and measure the corner frequency. Instead, the corner frequency tells you something about the gain of the filter. In fact, the passive low-pass and high-pass filters both have a gain of 0.707 when the input signal has a frequency equal to the corner frequency (see Figures 2a and b).

Figures 2a and býGain versus frequency for the passive low-pass and high-pass filters can be seen here. Note that each filter has a gain of 0.707 at the corner.

The low-pass filter has a gain of 1.0 below its corner. This indicates that the output signal has the same amplitude as the input signal at frequencies below the corner. As frequency increases, the output begins to roll off, lowering to 0.707 of its maximum value at the corner and going even lower at frequencies above the corner.

The opposite is true for the high-pass filter. At frequencies below the corner, there is little output amplitude. Only when the input frequency is at or above the corner does the output become large (0.707 or more of its maximum).

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