LOW PASS FILTER (RC & RL)

Hello friends, welcome to ELECTRICAL ENCYCLOPEDIA. In this article we will study about the Low Pass Filter.

WHAT IS LOW PASS FILTER?

As the name suggests, low pass filter allows only low frequencies to pass through it. The maximum frequency which is allowed to pass through it is called cutoff frequency, fc 

TYPES OF LOW PASS FILTER

There are mainly two types of low pass filter :

1. Low-Pass RC Filter.

2. Low-Pass RL Filter.

LOW-PASS RC FILTER

As we know that low pass filter allows only low frequencies upto cut-off frequency, fc. The range of frequency upto fc is called passband of the filter. 
A simple low pass RC filter is shown in the figure below:

Fig-1 :low pass RC circuit

The output voltage is taken across the capacitor. The reactance offered by capacitor C decreases with the increase in frequency, therefore when the frequency is low then reactance offered by capacitor is more and hence a voltage develops across the capacitor. But when the frequency is high then the reactance offered by capacitor C is less and hence no voltage appears across the capacitor.

* Cutoff Frequency  fc = 1/ 2*π*C*R

* Output Voltage, Vo = V_i* {(-j)*Xc / (R-jX_c)

* At the cutoff frequency , output signal voltage is reduced to 70.7% of the input voltage i.e, output voltage ,Vo = 70.7% * Vi 

* The output is -3 dB at cutoff frequency.

* The phase angle between output voltage Vo and input voltage Vi is -45 at cutoff frequency.

* R = X_c , at cutoff frequency

Frequency Response of Low Pass RC Filter 

This figure shows the frequency response curve of such filter. It shows that how the Output Voltage ,Vo varies with the signal frequency .

Fig-2 :Frequency Response of Low pass RC circuit

LOW-PASS RL FILTER

As we know that low pass filter allows only low frequencies upto cut-off frequency, fc. The range of frequency upto fc is called passband of the filter. 

A simple low pass RL filter is shown in the figure below:

Fig-3 :low pass RL circuit

The output voltage is taken across the resistance. The reactance offered by inductor L increases with the increase in frequency, therefore when the frequency is low then reactance offered by inductor is low. Hence, low frequencies upto fc can pass through coil without much opposition

* Cutoff Frequency, fc = L/ 2*π*R

* Output Voltage, Vo = V_i* {R / (R+jX_L) 

* At the cutoff frequency , output signal voltage is reduced to 70.7% of the input voltage i.e, output voltage ,Vo = 70.7% * V_i = 0.707* V_i

* The output is -3 dB at cutoff frequency.

* The phase angle between output voltage Vo and input voltage Vi is +45 at cutoff frequency.

* R = X_L , at cutoff frequency

Frequency Response of Low Pass RL Filter 

This figure shows the frequency response curve of low pass RL filter. It shows that how the Output Voltage ,Vo varies with the signal frequency .

Fig- 4 :Frequency Response of low pass RL filter

         

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