For a RC Low Pass filter, what is the approximate amplitude (as a decimal proportion of input amplitude) at 1/4 the cutoff frequency?

Explanation:

RC low Pass Filter is an electronic circuit that comprises of a resistor and capacitor and it functions to permit low-frequency signals depending on the design and reject the high-frequency signals above a given frequency known as the cutoff frequency.

From the diagram attached below:

= the input signal  

= the output signal

Since;  is used across the capacitor C,

By using the potential divider equation we have:

From above; = capacitive reactance ;

and The total impedance Z is illustrated as

Thus;

Recall that;

Here; f denotes the frequency of the input signal

Since the cutoff frequency is related to the frequency at which the capacitive reactance and resistance are said to be the same, then:

The Cutoff frequency can be expressed as:

Also;

the frequency of input signal

Hence;

Finally;

From

Z 4.12R

As such, the output will be:

So, if we regard to be the input amplitude, then i.e the output amplitude will also be =

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