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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.

*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)

*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

*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.

*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)

*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.

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

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