The Simple Low Pass Filter can be designed by using a capacitor and a resistor is series.

The Low Pass Filter as the name suggests the circuit allows only the frequency of the till the cut off frequency of the circuit and other all frequencies above the cut off frequency are rejected.

In this type of filter arrangement the input signal is applied to the series combination i.e. the resistor and capacitor are connected in series but the output signal is taken across the capacitor only.

The formula above is for calculating the reactance of the capacitor with respect to frequency of the signal i.e. given to it. Where Xc is the reactance of the capacitor and the Term F represents the frequency of the signal given as input to the capacitor and C is the capacitance of the capacitor.

The reactance provided by the capacitor changes in accordance with the frequency of the signal. As shown in the capacitors reactance formula the reactance of the capacitor increases when the frequency of the signal is low due to which the low frequency signal is seen at the across the capacitor i.e. at the output. While the capacitor provides very low reactance to the high frequency signals due to which the high frequency signals pass through the capacitor to the ground.so it won’t appear across the capacitor i.e. from where the output is taken.

The above figure Shows the ideal output of the Low pass filter. The Output shown above is not possible to achieve

The practical output of the low pass filter is shown. From this we can see that the frequencies below the cut-off frequency fc the frequency are allowed to pass and the band allowed to pass is known as pass band while the others are attenuated the band which is attenuated is known as stop band.

It’s a first order Low pass filter due to which the attenuation is at 20 db per decade i.e attenuation is 20 dB per 10 hz.

Second Order Low Pass Filter

So now we have studied about the single-pole arrangement i.e. a Low pass filter designed using single capacitor and single that gives us a roll-off slope of -20dB/decade attenuation of frequencies above the cut-off point.

However, sometimes in filter circuits this -20dB/decade angle of the slope may not be enough to remove an unwanted signal then two stages of filtering can be used as shown.

In the second order circuit that uses two passive first-order low pass filters connected together to form a Second-order filter network. Therefore we can see that a first-order low pass filter can be converted into a second-order type by simply adding an additional RC network to it and the more RC stages we add the higher becomes the order of the filter.

The Order of the filter increases as the number of First order low pass filters are connected together in series. The Order of the filter is dependent on the number of the filter connected in series. If Two first order are connected together than the Order of the filter is second and has the Roll-off of the attenuation of -40db/decade. If Three first order are connected together than the Order of the filter is Third and has the Roll-off of the attenuation of -80db/decade.