DESIGN OF A LOW-PASS

BUTTERWORTH FILTER

NEEMA AGGARWAL, HADAR COHEN, JOE MERCEDES, CAROLINE YU

PROF. H. AHMAD SPRING 2014 ECE 194A

INTRODUCTION

Purpose: design a low-pass Butterworth linear filter

Specifications: maximum passband attenuation Amax=1dB minimum stopband attenuation Amin= 20dB passband edge frequency fc= 25kHz stopband edge frequency fs=50kHz variable dc gain Ko in the range 5< Ko < 10

Process: Determine the order and transfer function Select an appropriate topology Design and construct circuit Obtain measurements and check results using MATLAB

INTRODUCTION- BUTTERWORTH FILTER

All-pole lowpass filter with no ripples in the passband

Butterworth filter has a slower frequency response roll off as compared to a Chebyshev

Comparison of Butterworth and Chebyshev Filters Ideal Low-Pass Filter

TRANSFER FUNCTION

SIMULATION DIAGRAM

A cascade topology was chosen with:

Two 2nd-order Sallen-Key filters

One 1st-order lowpass filter

One inverting amplifier to provide gain

SALLEN-KEY #1

741

SALLEN-KEY #2

741

FIRST ORDER LOW-PASS

741

INVERTER

741

UNIT STEP RESPONSE

Found at long duty cycle

Peaked at amplitude of 10 at .4 seconds

IMPULSE RESPONSE

Found at short duty cycle

Peaked at amplitude of 7 at .2 seconds

FREQUENCY RESPONSE

Frequency Range: 18Hz to 100Hz

INPUT AMPLITUDE RESTRICTIONS

The effective input voltage range is approximately from

400mV to 1V.

Outside of this range the filter degenerates and the

voltage gain deviates from the designed specifications.

CONCLUSIONThe implementation of this Lowpass

Butterworth Filter followed the design

specifications with a degree of unavoidable

error due to:

Tolerances of electrical components (resistors, capacitors, and operational

amplifiers)

The precision and accuracy of the equipment used (oscilloscope, power

source, and function generator)

In future implementations of this filter, it may

prove fruitful to examine different realizations,

such as direct form, parallel, and feedback

configurations.