## Question:

### Introduction

In this project, we have designed an active band pass filter, using the components provided in the list. The op amp has been used as voltage follower.

The filters are 2nd order, and cascaded, so they resultant roll off of the band pass filter is 20dB/decade.

The coupling capacitors have been included in the circuit.

### Circuit Designing

#### General Circuit for Band pass filter

The general circuit for a band pass filter is:

High Pass Filter:

### Calculations

It’s given that,

The mid band gain,          G (dB) = 1.9 dB = 1.549

Low frequency cut-off, fL = 273 Hz

High frequency cut-off, fH = 6399 Hz

Mid band frequency,     fm = 1321.7 Hz

Thus,     Bandwidth, BW = fH – fL = 6126 Hz

Quality factor, Q = fm/BW = 0.216

Av = 20log(Vout/Vin) = 20log(0.707(1+R1/R2))

Now, for high pass filter,

R1/R2 = 0.245

Taking R1 as 10kΩ, R2 = 2.4 kΩ

Similarly, for high pass filter, taking R1 as 10kΩ, R2 = 2.4 kΩ

Now, fc = 1/2πRC

Thus, R3 for high pass filter: 1.6 kΩ

R3 for low pass filter: 38 kΩ

We have designed and simulated the circuit in PSpice Schematic.

After the first filter is designed, the low pass, high pass and buffer are cascaded to obtain the band pass filter as required.

The cascading increases the gain further in the circuit.

### Calculation of the transfer function

Transfer function of the band pass filter is given by:

H(s) = Vo/Vin = Hoβs/ (s2 + βs + ω2) = 5.88x106s/(s2 + 3.8x106 + 1.7x106)

Where, β = 2/CR3 = 3.8x106

### Bode Plot using standard component values

As all the components have standard values, expect 38 kΩ, it is replaced with 39 kΩ standard resistor.

### Laplace Transform of the Transfer Function

The transfer function expressed in s-domain is:

## Result and Conclusion

The circuit has been designed as per specification, and desired results have been obtained.

As the values of calculated components were almost equal to the standard values available, there is no significance difference in the result when calculated components were replaced with the standard components.

All the bode plots have been plotted using PSpice AC Sweep analysis.

Circuit has been designed and simulated in PSpice Schematic.

## References

Belle A. Shenoi (2006). Introduction to digital signal processing and filter design. John Wiley and Sons. p. 120.

Miroslav D. Lutovac, Dejan V. TošiÄ‡, Brian Lawrence Evans, Filter Design for Signal Processing Using MATLAB and Mathematica, Miroslav Lutovac, 2001.

A. Shenoi, Introduction to Digital Signal Processing and Filter Design, John Wiley & Sons, 2005.

L. D. Paarmann, Design and Analysis of Analog Filters: A Signal Processing Perspective, Springer, 2001.

J.S.Chitode, Digital Signal Processing, Technical Publications, 2009.

Leland B. Jackson, Digital Filters and Signal Processing, Springer, 1996.

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