Band Pass Filter

Question: Describe about Band Pass Filter? Answer: 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: Low Pass Filter: Buffer: Calculations Its 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 10k, R2 = 2.4 k Similarly, for high pass filter, taking R1 as 10k, R2 = 2.4 k Now, fc = 1/2RC Thus, R3 for high pass filter: 1.6 k R3 for low pass filter: 38 k Circuit Design in PSpice 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. Image of the breadboard filter Calculation of the transfer function Transfer function of the band pass filter is given by: H(s) = Vo/Vin = Hos/ (s2 + s + 2) = 5.88x106s/(s2 + 3.8x106 + 1.7x106) Where, = 2/CR3 = 3.8x106 Bode Plot using calculated component values Bode Plot using standard component values As all the components have standard values, expect 38 k, it is replaced with 39 k standard resistor. Bode plot obtained from measurements Bode plot for comparison in same figure Laplace Transform of the Transfer Function The transfer function expressed in s-domain is: Measured Values 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. ToiĆ¡, 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.