A resistor-capacitor network can be arranged to create a low-pass filter in circuitry. It allows the designer to set an upper limit on the frequency allowed to pass through, attenuating signals greater than the desired frequency. Changes of a slower pace can be measured, while quick spikes and noise in higher frequencies are smoothed out.

In the image above, the high frequency of Vin causes the low-pass filter to attenuate the signal.

In the image above, the frequency of Vin was low enough that it passed through the filter without attenuation.

The cutoff frequency can be obtained by the following formula:

fc = frequency cutoff = 1/(2Π * R * C)

R = resistor value in ohms
C = capacitor value in farads

The voltage of Vout at any frequency can be obtained by the following formulas:

Vout = Vin * (Cr/√(R^2 * Cr^2)

Cr = 1/(2Π * f * C)

Vout = filtered voltage
Vin = unfiltered voltage
Cr = capacitive reactance of the capacitor
f = frequency of Vin
C = capacitor value in farads
R = resistor value in ohms

While making use of the RC low-pass filter, keep in mind that it is not a perfect system; it may slightly weaken certain signals that are desired, and it will not perfectly silence undesired signals. Frequencies deemed low enough to pass through the filter, but close to the cutoff point, or corner frequency, may still be subjected to attenuation. The frequencies that are closest to the cutoff point are affected the most. A similar effect can be observed in the frequencies ranging beyond the corner frequency. These frequencies that lie in the Stop Band will experience less attenuation the closer they are to the cutoff.

Image from http://www.electronics-tutorials.ws/filter/filter_2.html

Filtering out noise to obtain the desired frequency can be tricky business, even when the proper formulas are applied. Isolated environments, such as laboratory conditions, will often produce results closest to what the mathematics predicted. Issues often arise when products are applied to real-world scenarios, being subjected to unknown factors and unforeseen problems.

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