**RC and RL Low Pass Filter**

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

*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:

**fc**is called passband of the filter.

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})

_{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.

**fc**is called passband of the filter.

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 |