ANALOG FILTERSANALOG FILTERSELEC 202 Circuit Analysis II

DefinitionDefinitionA frequency-selective device or circuit

designed to pass signals with desired frequencies and reject or attenuate signals with unwanted frequencies

Limit the frequency spectrum of a signal to some specified band of frequencies

Applications in communications and control systems

Types of FiltersTypes of FiltersLowpass – passes low frequencies and

stop high frequenciesHighpass – passes high frequencies and

rejects low frequencies Bandpass – passes frequencies within a

certain band and blocks frequencies outside the band

Bandstop – passes frequencies outside a certain band and blocks frequencies within the band

Lowpass Filter Highpass Filter

Bandpass Filter Bandstop Filter

Passive vs. Active FiltersPassive vs. Active FiltersA passive filter consists of only passive

elements (e.g., R, L, and C).

An active filter consists of active elements (e.g., transistors and op amps) in addition to passive elements.

Cutoff FrequencyCutoff FrequencyThe frequency at which the frequency

response drops in magnitude to 70.71% (or 3dB) of its maximum value.

Or, the frequency at which the output power of the filter is half of the maximum input power half-power frequency

Also called corner frequency or roll-off frequency

Obtained by setting the magnitude of to

)( jH 2/1

Lowpass FilterDesigned to pass only frequencies from dc up tothe cutoff frequency.

RCjjH

1

1)(0)H(

21

11)()(

222

CRjHjM

ccc

RCc1

Highpass FilterDesigned to pass all frequencies above its cutofffrequency.

RCjRCjjH

1)(

1)H(

21

1)()(

222

CRRCjHjMc

ccc

RCc1

ExampleWhat type of passive filter does the followingcircuit represent? Also, calculate its cutofffrequency.

FCHLkR 2,2,2

ExampleFor the circuit shown, identify the type offilter it represent by obtaining and calculate its corner frequency.

)(/)( jVjV io

mHLRR 2,10021

Bandpass FilterDesigned to pass all frequencies within a certainBand of frequencies.

)/1()(CLjR

RjH

0)H( 0)1H(

frequency center o

sfrequencie power-half , 21

bandwidth passband dB-3 - 21

Bandpass Filter)/1()(

CLjRRjH

11

)()(2

2

CLR

RjHjM

oo

oo

LCo1

21

1)()(

22

CLR

RjHjM

LCLR

LR 1

222

1

LCL

RL

R 122

2

2

Bandstop FilterDesigned to stop all frequencies within a certainband of frequencies.

)/1()/1()(CLjR

CLjjH

1)H( 1)1H(

frequency rejection o

sfrequencie power-half , 21

bandwidth rejection dB-3 - 21

Bandstop Filter

11

)()(2

2

CLR

RjHjM

oo

oo

LCo1

21

1)()(

22

CLR

RjHjM

LCLR

LR 1

222

1

LCL

RL

R 122

2

2

)/1()/1()(CLjR

CLjjH

Narrowband vs. WidebandRule of thumb: If the 3-dB bandwidth of a bandpass filter

is more than twice the center frequency, the filter is said to be wideband.

Examples of narrowband filters: Resonator, Comb filters, notch filters, inverse comb filters