CHAPTER 3: Active Filter

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Chapter Outcomes

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Describe the frequency response of basic filters

Describe the three basic filter response characteristics

Analyze low-, high- and band-pass filters

Design active filter

Introduction

PASSIVE FILTER ACTIVE FILTER•RC, RL and RLC circuits •Active components + passive components

•Transistors or op-amps + RC/RL/RLC

•Provides frequency selectivity

•Provides voltage gain

•Advantage: simple •Advantage: Loading effect is minimal

-o/p independent of the load

driven

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Filters are circuits that are capable of passing signals with certain selected frequencies while rejecting signals with other frequencies

2 types of filter

Introduction

Types of active filter:Low-Pass FilterHigh-Pass FilterBandpass Filtero Cascaded Low-Pass and High-Pass Filtero Multiple-Feedback Band-Pass Filtero State-Variable Filtero Biquad Filter

Bandstop Filter o Multiple-Feedback Band-Stop Filtero State-Variable Band-Stop Filter

The op-amp active filter provides controllable cutoff frequencies and controllable gain

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Frequency Response Pass Band: The range of

frequency seen in the filter output. Has the same meaning as the bandwidth (BW) of the filter

Stop Band: The range of frequency blocked by the filter. These frequency are not see in the filter output

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AV (dB)

f (Hz)

f (Hz)

AV (dB)

3dB

Ideal

Practical

AV (dB)

AV (dB)

f (Hz)

f (Hz)

3dB

Ideal

Practical

Pass Band

Stop Band

TransitionRegion

Transition region: The frequency between the pass band and the stop band

Cut off Frequency : The highest or lowest frequency that is allowed to pass or determines the pass band. The cutoff frequency of real filter is the -3 dB frequency of that filter

Decibel (dB) This is a relative power unit. At audio frequencies a change

of one decibel (abbreviated dB) is just detectable as a change in loudness under ideal conditions.

For a given power ratio the decibel change is calculated as:

dB = 10 log P2/P1

If we used voltage or current ratios instead then it becomes:

dB = 10 log (V22 / R)/(V1

2 / R) = 20 log V2/V1 = 20 log AV

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Basic Diagram of An Filter

Inverting or non-inverting?? Which part is the filter?

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_

+Vin

R1

R2

Vo

+V

-V

RC Circuit

Gain

Frequency

1

2

1V

RA

R

Cut-Off Frequency

In electronics, cut-off frequency (fc) is the frequency

at which the gain on a frequency-response plot is 3 dB less than at mid-band gain

The cutoff frequency often called 3-dB frequencies

Also called the knee frequency, due to a frequency response curve's physical appearance.

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AV(dB)

-3.012dB

fc=1Hz

Slope =20dB/decade

f=1Hz, Av(dB)=-3dB

f=10Hz, Av(dB)=-20dB

f=100Hz, Av(dB)=-40dB

3dB At -3dB, the output power is half of the output power

at pass band

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V@passband

V@passband

V@passband

20 log A -20 log 2

20 log A -10log 2

20 log A 3.012

2

@outP

out passband

VP

R

2 2@

@ 3 2 2out passband outP outRMS

out dB

P V VP

R R

@ 32outP

o dB outRMS

VV V

@@ 3

2 2V passbandoutP

V dB

in

AVA

V

Filter Response Characteristics

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The Butterworth characteristic response is very flat. The roll-off rate -20dB per decade. This is the most widely used.

The Chebyshev characteristic response provides a roll-off rate greater than -20dB but has ripples in the passband and a non-linear phase response.

The Bessel characteristic response exhibits the most linear phase response making it ideal for filtering pulse waveforms with distortion.

The damping factor of an active filter determines the type of response characteristic

The output signal is fed back into the filter circuit with negative feedback determined by the

combination of R1 and R2

The negative feedback ultimately determines the type of filter response is produced. The equation below defines the damping factor

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DF = 2 – R1/R2

List of the roll-off rates, damping factors, and feedback resistors for up to six order Butterworth filters

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Back

1. Low Pass Filter

Low-pass filter passes low frequencies well, but attenuates (or reduces) frequencies higher than the cutoff frequency

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a) 1st Order

R1

R2

_

+Vin

+V

-V

RA CA Vo

AV (dB)

AV(max)

AV(max) - 3

fc 10fc100fc

AV(max) - 20

AV(max) - 40

-20dB/dec

f (Hz)

The capacitor CA in

conjunction with the resistor

RA provides the filtering

action, while the op-amp with its associated resistor

R1 and R2 function as non-

inverting amplifier and provides the needed gain

BW

Analysis

It is low pass filter ifNo s at numerator

V+ = VC

It is 1st order system ifThe highest order is s1

Only one pair RC at +input of op-amp

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Vo = 1+ V+

R1

R2

_

+Vin

+V

-V

RA CA Vo V+ = Vi

1sCA

1sCA

+RA

R1

R2

Vo = 1+

R1

R2

Vi

V+ = Vi1

sRACA+1

1

V+ = VcA

AV = = 1+

R1

R2Vi

1Vo

sRACA+1

sRACA+1

Analysis

At 0 < f < fc, low pass filter will pass

the frequencies because XCA=∞, thus,

V+=VCA =Vi

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AV (dB)

AV(max)

AV(max) - 3

fc 10fc100fc

AV(max) - 20

AV(max) - 40

-20dB/dec

f (Hz)

AV(max) = 1+ R1

R2

At f = fc, the gain is

0.707AV(max) or in dB AVdB(max)-

3. The magnitude of the

capacitive reactance, XCA

equals the resistance of the

resistor, RA

At f > fc, low pass filter will

attenuate the frequencies at roll-off of -20dB/decade

because XCA is reducing to 0.

When XCA=0,

V+=VCA=0

AV = 0

1 2fcCA

= RA

fc =1

2RACA

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b) 2nd Order (Sallen-Key)

One of the most common configurations for 2nd order filter

There are two pairs of RC that provide roll-off of -40dB/dec

The capacitor CA provides feedback for shaping the

response near the edge of the pass band (-3dB not -6dB)

Vo

R1

R2

_

+Vin

+V

-V

RA

CA

RB CB

1

2

1

22

11

1 11

A B A Bo

in

B B A B A A

A B A B A B A B

R

R R R C CV

V RR C R C R C

Rs s

R R C C R R C C

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R1=10k, R2=17.2k , RA=RB=3.18k, CA=CB=0.01F

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AV (dB)

AV(max)

AV(max) - 3

fc 10fc100fc

AV(max) - 40

AV(max) - 80

-40dB/dec

f (Hz)BW

AV(max) = 1+ R1

R2

1 2 RARBCACB

fc = fAfB

1 2RACA

1 2RBCB

=

=

Higher Order Low Pass Filter

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R1

R2

_

+Vin

+V

-V

RA

CA

RB CB

R3

R4

_

++V

-V

RC CC Vo

R1

R2

_

+Vin

+V

-V

RA

CA

RB CB

Vo

R3

R4

_

++V

-V

RC

CC

RD CD

Table for Butterworth response

3rd order system

4th order system

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• By adding more RC networks the roll-off can be made steeper