LOW PASS FILTER

By: Ayesha Saeed

INTRODUCTION

Most of the signals we deal with in real life get corrupteed in some way or another by some unwanted signals.

For the purpose of signal processing and analysis, it is imperative to get rid of these interferences, or at least reduce their effects.

This is achieved through applying Signal Filtering techniques.

A Filter  is an electronic circuit that removes / attenuates, from a signal, some unwanted component or feature.

Filter ApplicationEliminate background noise Radio tuning to a specific frequencyDirect particular frequencies to different speakersModify digital imagesRemove specific frequencies in data analysis

FILTER CHARACTERISTICS:

To understand the basics of filtering, it is first necessary to learn some important terms used to define filter characteristics.

Cut-Off Frequency (fc): Also referred to as the corner frequency, this is the frequency or frequencies that define the limits of the filter range.

Stop Band: The range of frequencies that is filtered out.Pass Band: The range of frequencies which is let through and recorded.Transition Band: Region that Separates the pass band and stop band.

LOW-PASS FILTER:

A low-pass filter is an electronic filter that passes low-frequency signals and attenuates (reduces the amplitude of) signals with frequencies higher than the cutoff frequency. The actual amount of attenuation for each frequency varies from filter to filter.

It is sometimes called a high-cut filter, or treble cut filter when used in audio applications.

There are two basic kinds of circuits capable of accomplishing this objective, and many variations of each one:

The inductive low-pass filter The capacitive low-pass filter

THE INDUCTIVE LOW-PASS FILTER

The inductor's impedance increases with increasing frequency. This high impedance in series tends to block high-frequency signals from getting to the load.

 

THE RESPONSE OF AN INDUCTIVE LOW-PASS FILTER FALLS OFF WITH INCREASING FREQUENCY.

THE CAPACITIVE LOW-PASS FILTER

The capacitor's impedance decreases with increasing frequency. This low impedance in parallel with the load resistance tends to short out high-frequency signals, dropping most of the voltage across series resistor R1.

THE RESPONSE OF A CAPACITIVE LOW-PASS FILTER FALLS OFF WITH INCREASING FREQUENCY.

All low-pass filters are rated at a certain cutoff frequency. The cutoff frequency for a low-pass filter is that frequency at which the output (load) voltage equals 70.7% of the input (source) voltage. This cutoff percentage of 70.7 is not really arbitrary, all though it may seem so at first glance. In a simple capacitive/resistive low-pass filter, it is the frequency at which capacitive reactance in ohms equals resistance in ohms. In a simple capacitive low-pass filter (one resistor, one capacitor), the cutoff frequency is given as:

 A simple filter will be two elements - a capacitor or inductor and a resistor. A capacitor will tend to "trap" low frequencies.

In the case of a low pass filter made of a capacitor and resistor, the output voltage will be measured across the capacitor.

Inductors are the opposite, so the output would be across the resistor.

There are a great many different types of filter circuits, with different responses to changing frequency. The frequency response of a filter is generally represented using a Bode plot.

• First-order filter• Second-order filter• Third and Higher order filters

First-order filter: A first-order filter, will reduce the signal strength by

half (about −6 dB) every time the frequency doubles. The magnitude Bode plot for a first-order filter looks like a horizontal line below the cutoff frequency, and a diagonal line above the cutoff frequency.

SECOND-ORDER FILTER

A second-order filter does a better job of attenuating higher frequencies. The Bode plot for this type of filter resembles that of a first-order filter, except that it falls off more quickly.

For example, a second-order filter will reduce the signal strength to one fourth its original level every time the frequency doubles.

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