FiltersBackground:

. Filters may be classified as either digital or analog.

. Digital filtersDigital filters are implemented using a digital computer

or special purpose digital hardware.

. Analog filtersAnalog filters may be classified as either passive or active and are usually implemented with R, L, and C components and operational amplifiers.

FiltersBackground:

. An active filteractive filter is one that, along with R, L, and C components, also contains an energy source, such as that derived from an operational amplifier.

. A passive filterpassive filter is one that contains only R, L, and C components. It is not necessary that all three be present. L is often omitted (on purpose) from passive filter design because of the size and cost of inductors – and they also carry along an R that must be included in the design.

Passive Analog Filters

Background: Four types of filters Four types of filters - “Ideal”- “Ideal”

lowpasslowpass highpasshighpass

bandpassbandpass bandstopbandstop

Background: Realistic Filters:Realistic Filters:

lowpasslowpass highpasshighpass

bandpassbandpass bandstopbandstop

Passive Analog Filters

Passive Analog FiltersLow Pass Filter Consider the circuit below.

R

CVI VO

+

_

+

_

1( ) 1

1( ) 1OV jw jwCV jw jwRCRi jwC

Low pass filter circuit

Passive Analog FiltersLow Pass Filter

0 dB

1

0

1/RC

1/RC

Bode

Linear Plot

.-3 dB

x0.707

Passes low frequenciesAttenuates high frequencies

Passive Analog Filters

High Pass Filter Consider the circuit below.

CRVi VO

+

_

+_

( )1( ) 1

OV jw jwRCRV jw jwRCRi jwC

High Pass Filter

Passive Analog Filters

High Pass Filter

0 dB

.

. -3 dB

0

1/RC

1/RC

1/RC

10.707

Bode

Linear

Passes high frequencies

Attenuates low frequencies

x

Passive Analog Filters

Bandpass Pass Filter Consider the circuit shown below:

C L

RViVO

+

_

+

_

When studying series resonant circuit we showed that;

2

( )1( )

O

i

R sV s LRV s s sL LC

Passive Analog Filters

Bandpass Pass FilterWe can make a bandpass from the previous equation and selectthe poles where we like. In a typical case we have the following shapes.

0

0 dB-3 dB

lo

hi

.

. .

.10.707

Bode

Linear

lo

hi

A Bandpass Filter

RLC Band stop FilterConsider the circuit below:

RL

C

+

_

VO

+

_Vi

The transfer function for VO/Vi can be expressed as follows:

)(sGv

LCs

LRs

LCs

sGv 1

1

)(2

2