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Active Low Pass & Band Pass Filters AIM

This document describes designing and testing active low pass and band pass filters. It provides the equipment needed, including op-amps, resistors, and capacitors. The theory section explains how low pass filters allow frequencies below a cutoff to pass, while attenuating higher frequencies. Band pass filters are formed by cascading high pass and low pass sections, and have upper and lower cutoffs. The design section sizes the components for first-order low pass and band pass filters with specific cutoff frequencies. The circuits are constructed and their voltage gains are measured over a range of frequencies to obtain the output characteristics for each filter type.

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105 views7 pages

Active Low Pass & Band Pass Filters AIM

This document describes designing and testing active low pass and band pass filters. It provides the equipment needed, including op-amps, resistors, and capacitors. The theory section explains how low pass filters allow frequencies below a cutoff to pass, while attenuating higher frequencies. Band pass filters are formed by cascading high pass and low pass sections, and have upper and lower cutoffs. The design section sizes the components for first-order low pass and band pass filters with specific cutoff frequencies. The circuits are constructed and their voltage gains are measured over a range of frequencies to obtain the output characteristics for each filter type.

Uploaded by

Aditi
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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ACTIVE LOW PASS & BAND PASS FILTERS

AIM

To design a first order low pass & band pass filter and obtain its characteristics

EQUIPMENT / COMPONENTS REQUIRED

Sl.No Components Range Quantity


1. DCRPS 0-30V 2
2. IC 741 - 1
3. Resister 10 k Ω 6
15.9 k Ω 1
20 k Ω POT 2
4. Capacitor 0.01µf 1
0.05µf 1
5. CRO - 1
6. Connecting wires - As
required

THEORY :

Low Pass Filter

Active filters may be of different order and types. A first order filter consists of a single RC network,
connected to the +ve input terminals of a non-inverting op-amp amplifier. Resistors Rf & Ri
determines the gain of the filter, in the pass band.

In the frequency response, it has maximum gain, A0 at f = 0 Hz. At fH , the gain falls to 0.707 (ie., -
3dB down) the maximum gain (A0). The frequency range from 0 to fH is called the pass band. For f >
fH, the gain decreases at constant rate of -20dB / decade. That is, when the frequency is increased ten
times, the gain decreases by 20 dB (= 20 log 10). Hence, gain rolls off at rate of 20 dB / decade or 60
dB / octave, after frequency f. The frequency range f > fH, is called stop band.

Band Pass Filter

There are 2 types of band pass filters, which are classified as per the figure of merit (or) quality
factor (Q).

9 Narrow band pass filter ( Q > 10)

9 Wide band pass filter (Q < 10)


The following relationships are important.

Q = f0 / BW = f0 / (fh – fl)

f0 = √(fh fl)

where, f = upper cut off frequency

fl = lower cut off frequency

f0 = central frequency

The important parameters in a band pass filter (BPF) are upper & lower cut-off frequencies
( fh & fl ) , band width (BW), the central frequency (f0), Gain A0 and selectivity, Q.

A wide band pass filter can be formed, by cascading a high pass filter (HPF) & low pass filter (LPF)
sections. If the HPF & LPF are of the first order, BPF will have a roll off rate of -20 dB / decade. To
obtain BPF of -40 dB / decade fall off rate, second order LPF & HPF sections are to be cascaded.

DESIGN

Low Pass Filter

Cut off frequency fc = 10 kHz

fc = 1/2 π RC

Let C = 0.001 µF

R = 1 / (2π fc C) = 1 / (2π x 104 x 0.001 x 10-6 )

R = 15.9 k Ω

Let Band pass gain = 2 db

A0 = 1 + (Rf / R1 )

ie., Rf / R1 = 2 – 1 = 1

Rf = R1 = 10 k Ω

Band Pass Filter

High Pass Section

Lower cut off frequency fL = 200 Hz

fL = 1 / (2π R C)

Let C = 0.05µF

R = 1 / (2π x 200 x 0.05 x 10-6) = 15.915 k Ω


For gain = 2,

AfL = 1 + (Rf / R1 ) = 2

ie., Rf = R1 = 10 k Ω

Low Pass Section:

Upper cut off frequency fU = 2 kHz

fU = 1 / (2π R’ C)

Let C = 0.05µF

R’ = 1 / (2π x 2 x 103 x 0.05 x 10-6 ) = 15.915 k Ω

For gain = 2, Af1 = 1 + (Rf / R1 ) = 2

ie., Rf = R1 = 10 k Ω
LOW PASS FILTER

CIRCUIT DIAGRAM

Ri Rf

+12 V

2 7

IC 741 6 VO

R 3 4
Vi
- 12V

C=

MODEL GRAPH

A0
A0
3 dB
0.707A
0

Pass Stop Band


Band

fC
BAND PASS FILTER

CIRCUIT DIAGRAM
10 kΩ 10 kΩ

10 kΩ 10 kΩ
+12 V

+12 V 2 7

2 7 IC 741 6

IC 741 6 3 4
0.05 µF - 12V
3 4 15.9 kΩ
Vi
- 12V
0.01 µF
10 kΩ

15.9 kΩ

MODEL GRAPH
Gain

Afr
0.707 Afr
Pass

Frequency
Stop Stop
TABULATION

Low Pass Filter

Sl.No. Frequency (Hz) Output Voltage (volts) Voltage Gain (dB) = 20 log (V0 / Vin)

Band Pass Filter

Sl.No. Frequency (Hz) Output Voltage (volts) Voltage Gain (dB) = 20 log (V0 / Vin)
PROCEDURE

Low Pass Filter

¾ Connections are made as per the circuit diagram

¾ Input is given to circuit

¾ Frequency & gain values are noted down and output characteristics are plotted

Band Pass Filter

¾ Connections are made as per the circuit diagram

¾ Input is given to circuit

¾ Frequency & gain values are noted down and output characteristics are plotted

RESULT :

The low pass & band pass filters are designed, constructed and their outputs are verified.

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