PROJECT INDEX: PRJ 046.

BY

F17/1768/2006.KINYUA JAMLICK MURIMI.

SUPERVISOR: MR. DHARMADHIKHARYEXAMINER: MR. OMBURA

DATE: 23RD MAY 2011.

FOURTH ORDER ACTIVE BAND PASS FILTER USED IN GRAPHIC EQUALIZER.

Study of active filters, design and implement a fourth order active band pass filter to be used

in graphic equalizer.

OBJECTIVE.

Filters are essential components in many electrical systems that have to do with selective use of

frequency. Analog filters fall in one of the two categories:

The most common filter types are the Butter worth, Chebyshev and Bessel.

INTRODUCTION

• Passive filters• Active filters.

Categories of filters

Filters are categorized by the manner in which the output voltage varies with the frequency of the input. These are:

Ø High pass Ø Low passØ Band passØ Band stop/Band reject Ø All pass filters

Forms of active Filters.

The active filter takes the following forms.

Ø Infinite gain Multiple feedback(IGMF).Ø Biquadratic (Biquad) filters.Ø Voltage controlled voltage source (VCVS)

In the filter design, active filters are used over the passive filters since active filters have the following advantages:

The filter design.

ØActive filters can have gain greater than one.ØHigher order filters can easily be cascaded.ØFilters are smaller in size as longs as no inductors are used which makes it very useful as an integrated circuit.

The cascade filter design.The filter is designed by cascading a second order

low pass filter with a second order high passfilter.

The cutoff point of low pass filter is the fh and thatof the high pass is the fl

The centre frequency is the geometric mean of thetwo frequencies.

The band width is the difference between the twofrequencies. Bw=fh – fl.

fc=

Block diagram of LPF and HPF cascaded

Block diagram of an active filter

The high pass filter response determines the low cut off frequency of the band pass.

The high pass filter response

The low pass filter.

Cascading the two filter responses that is HPF and LPF results in a band pass filter.

The band pass filter response.

Filter Calculations

Band width B w = fc/Q =fh – fl

Center Frequency , fc = √(flfh)Quality Factor = Q = fc/Bw

f = 1 / 2∏RCFc = √(40k x 100) = 2kHzFh – Fl = 40khz – 100Hz = 39.9kHz

In the design the biquad filter is used since it has advantages over the other forms. These includes:

Advantage of biquad:1.Its gain and cut off frequency are easily

adjusted. 2.It has a good stability, important in the

cascading several stages.3.It is capable of attaining Q’s of 100 or more,

which is beyond the capability of other circuits.

The Biquad Filter

The quality factor

This can simply be defined as the ratio of the centre frequency fc, to the band width Bw.

Q = fc/Bw

The value of the Q is an indication of the selectivity of the band pass filter. The higher the value of Q, The narrower the bandwidth and the better the selectivity for a given value of fc. Band pass filters are sometimes classified as narrow band or wide band .

Simulated results.

The objective of the project was achieved since the results obtained from the test did not differ

appreciably with the simulated results. Thus the simulation give a response that agrees with the

theory.

The small deviations were due to:

Conclusion.

§ Non ideal nature of the Op-Amp.

THANK YOU.