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Designing of Band Reject Filter

Written By: 

A. M. Bhatt

 

There are 2 cut off frequencies for band reject filter.

1.       upper cut off frequency (f1) - the frequency below which all the frequencies are passed

2.       lower cut off frequency (f2) - all the frequencies above this frequency are passed

Similar to band pass filter but the difference is f1 < f2. That means upper cut off frequency is lesser than lower cut off frequency. Two types of band reject filters are

1.       Wide band reject filter - suppresses wide range of frequencies.

Overview of Wide Band Reject Filter

Fig. 1: Overview of Wide Band Reject Filter

2. Narrow band pass filter - suppresses single frequency or few frequencies near centre frequency.

Wide Band Reject filter

It’s actually combination of LPF and HPF as shown in figure

Here F1 > F2. So we have to design HPF with F1 and LPF with F2. Suppose we want to suppress the band of frequencies between 10 KHz to 20 KHz. so F1 = 20000 Hz and F1 = 10000 Hz.

 

Designing HPF section

Step 1: assume the required value of capacitor. it should be less than 0.1 micro Farad. This is required for better frequency stability. Suppose we assume value C as 1 nF (nano farad)

Screenshot of Calculations Required to Find Resistance and Pass Band Gain for HPF Section

Fig. 2: Screenshot of calculations required to find resistance and pass band gain for HPF Section

Designing LPF section

Step 4: assume the required value of capacitor. Suppose we assume value C as 10 nF

Screenshot of Calculations Required to Find Resistance and Pass Band Gain for LPF Section

Fig. 3: Screenshot of calculations required to find resistance and pass band gain for LPF Section

Final design with component values are as shown. Op-amp is active component and it requires +ve and -ve biasing voltages. one can test the circuit by applying input through signal generator and observing output on DSO or oscilloscope as well as bode plotter as shown in figure.

Circuit Diagram of LM741 OPAMP IC based Band Reject Filter

Fig. 4: Circuit Diagram of LM741 OPAMP IC based Band Reject Filter

Note: - the schematic design is prepared in NI's multisim 11 software. Software is available as free for 1 month trial period from NI's website. 

Narrow Bank Reject Filter (Notch Filter)

Step 1: select notch frequency that is the frequency to be rejected. Mostly such filters are used to remove power line frequency that is 50 Hz. So take Fn = 50 Hz

Step 2: assume capacitor value C as 1 micro F (because frequency is too low the capacitor value should be large)

Screenshot of Calculations Required to Find Resistance for Notch Filter

Fig. 5: Screenshot of calculations required to find resistance for Notch Filter

 

Step 5: to construct T network with C  - R/2 - C, we need R/2 value. So connect two resistors in parallel of same value R

Step 6: to construct T network with R - 2C - R, we need 2C value. So connect two capacitors in parallel of same value C

Final design is as shown below.

Circuit Diagram of LM741 OPAMP IC Based Notch Filter

Fig. 6: Circuit Diagram of LM741 OPAMP IC based Notch Filter

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