Ref:080222HKN EE3110 Active Filter (Part 1) 1

Lecture 4 Active Filter (Part I)

• Introduction of passive and active filter• Categories of filter

– Low pass, high pass, band-pass, band stop (notch)

• Butterworth/chebyshev/Bessel response• Poles and multiple stages• Transfer Function• Bode Plot

Ref:080222HKN EE3110 Active Filter (Part 1) 2

Book references

• Microelectronic Circuits Analysis and Design, By Muhammad H. Rashid (PWS Publishing Company)

• Microelectronic Circuit Design, By Richard C. Jaeger and Travis N. Blalock (Mc Graw Hill)

• Introduction to Filter Theory, By David E. Johnson (Prentice Hall)

Ref:080222HKN EE3110 Active Filter (Part 1) 3

Passive Filters• made up of passive components - resistors, capacitors and in

ductors• no amplifying elements (- transistors, op-amps, etc) • no signal gain • 1st order - design is simple (just use standard equations to fi

nd resonant frequency of the circuit) • 2nd order - complex equations • require no power supplies • not restricted by the bandwidth limitations of the op-amps • can be used at very high frequencies • can handle larger current or voltage levels than active device

s • buffer amplifiers might be required

Ref:080222HKN EE3110 Active Filter (Part 1) 4

Passive elements : Inductor BIG PROBLEM!

• high accuracy (1% or 2%), small physical size, or large inductance values are required ??

• standard values of inductors are not very closely spaced

• difficult to find an off-the-shelf inductor within 10 percent of any arbitrary value

• adjustable inductors are used

• tuning such inductors to the required values is time-consuming and expensive for larger quantities of filters

• inductors are often prohibitively expensive

Ref:080222HKN EE3110 Active Filter (Part 1) 5

Active Filter• no inductors • made up of op-amps, resistors and capacitors • provides virtually any arbitrary gain • generally easier to design • high input impedance prevents excessive loading of the

driving source • low output impedance prevents the filter from being

affected by the load • at high frequencies is limited by the gain-bandwidth of the

op-amps • easy to adjust over a wide frequency range without altering

the desired response

Ref:080222HKN EE3110 Active Filter (Part 1) 6

Categories of Filters

-3dB {

f2

f

A v(dB)

-3dB {

f1

f

A v(dB)

Low-pass response High-pass response

Low Pass Filters:

pass all frequencies from dc up to the upper cutoff frequency.

High Pass Filters:

pass all frequencies that are above its lower cutoff frequency

Ref:080222HKN EE3110 Active Filter (Part 1) 7

Categories of Filters

-3dB {

f2

f

A v(dB)

f1

-3dB {

ff2f1

A v(dB)

Band Pass Response Band Stop Response

Band Pass Filters:

pass only the frequencies that fall between its values of the lower and upper cutoff frequencies.

Band Stop (Notch) Filters:

eliminate all signals within the stop band while passing all frequencies outside this band.

Ref:080222HKN EE3110 Active Filter (Part 1) 8

Filter Response CharacteristicsAv

ButterworthBesselChebyshev

f

Ref:080222HKN EE3110 Active Filter (Part 1) 9

Bessel Characteristic

• Flat response in the passband.

• Role-off rate less than 20dB/decade/pole.

• Phase response is linear. • Used for filtering pulse w

aveforms without distorting the shape of the waveform.

Av

f

Ref:080222HKN EE3110 Active Filter (Part 1) 10

Butterworth Characteristic

• Very flat amplitude, Av(dB) ,

response in the passband.

• Role-off rate is 20dB/decade/pole.

• Phase response is not linear.

• Used when all frequencies in the passband must have the same gain.

• Often referred to as a maximally flat response.

Av

f

Ref:080222HKN EE3110 Active Filter (Part 1) 11

Chebyshev Characteristic• Overshoot or ripples in th

e passband.

• Role-off rate greater than 20dB/decade/pole.

• Phase response is not linear - worse than Butterworth.

• Used when a rapid roll-off is required.

Av

f

Ref:080222HKN EE3110 Active Filter (Part 1) 12

Pole

• A pole is nothing more than an RC circuit –

• n-pole filter contains n-RC circuit.

Ref:080222HKN EE3110 Active Filter (Part 1) 13

Single-Pole Low/High-Pass Filter

v out

-

+

+V

-V

R 1

R f1

R f2

C 1

v in

vout

-

+

+V

-V

R1

Rf1

Rf2

C1

vin

Low Pass Filter High Pass Filter

Ref:080222HKN EE3110 Active Filter (Part 1) 14

Two-Pole (Sallen-Key) Filters

-

+

+V

-V

R 1

R f1

R f2

C 1

v in

v out

C 2

R 2

-

+

+V

-V

R1

Rf1

Rf2

C2

vin

vout

R2

C1

Low Pass Filter High Pass Filter

Ref:080222HKN EE3110 Active Filter (Part 1) 15

Three-Pole Low-Pass Filter

-

+

+V

-V

R1

Rf1

Rf2

C1

vin

C2

R2

-

+

+V

-V

R3

Rf3

Rf4

C3 vout

Stage 1 Stage 2

Ref:080222HKN EE3110 Active Filter (Part 1) 16

Two-Stage Band-Pass Filter

R2 R1

vin

C1

C2

Rf1

Rf2

C4 C3

R3

R4

+V

-V

vout

Rf3

Rf4

+

-

+

-

+V

-V

Stage 1Two-pole low-pass

Stage 2Two-pole high-pass

BW

f1 f2

f

Av

Stage 2response

Stage 1response

fo

BW = f2 – f1

Q = f0 / BW

Ref:080222HKN EE3110 Active Filter (Part 1) 17

Multiple-Feedback Band-Pass Filter

R1

R2

C1

C2

vin

Rf

+V

-V

-

+vout

Ref:080222HKN EE3110 Active Filter (Part 1) 18

Band-Stop (Notch) FilterThe notch filter is designed to block all frequencies that fall within its bandwidth. The circuit is made up of a high pass filter, a low-pass filter and a summing amplifier. The summing amplifier will have an output that is equal to the sum of the filter output voltages.

f1

f2

v in v out

Low passfilter

High passfilter

Summingamplifier

-3dB{

f

f2f1

Av(dB)

low-pass high-pass

Block diagram Frequency response

Ref:080222HKN EE3110 Active Filter (Part 1) 19

Notch filter

Ref:080222HKN EE3110 Active Filter (Part 1) 20

Transfer function H(j)

TransferFunction

)( jHVoVi

)(

)()(

jV

jVjH

i

o

)Im()Re( HjHH

22 )Im()Re( HHH

)Re(

)Im(tan 1

H

HH 0)Re( H

)Re(

)Im(tan180 1

H

HH o 0)Re( H

Ref:080222HKN EE3110 Active Filter (Part 1) 21

Frequency transfer function of filter H(j)

HL

HL

o

o

o

o

ffffjH

fffjH

ffjH

ffjH

ffjH

ffjH

and 0)(

1)(

Filter Pass-Band (III)

1)(

0)(

Filter Pass-High (II)

0)(

1)(

Filter Pass-Low (I)

response phase specific a has

allfor 1)(

Filter shift)-phase(or Pass-All (V)

and 1)(

0)(

Filter (Notch) Stop-Band (IV)

fjH

ffffjH

fffjH

HL

HL

Ref:080222HKN EE3110 Active Filter (Part 1) 22

Passive single pole low pass filterR

C VoVi

iC

Co V

RX

XV

iio VCRj

VR

Cj

CjV

1

11

1

0

1

1)(

jjH

RCo

1where

or

0

0)(

s

sH

js where

0

1tan)(

Ref:080222HKN EE3110 Active Filter (Part 1) 23

CRjjH

11

)(

ioV

CRjV

11

0 Vo = Vi max. value

∞ Vo = 0 min. value

Vo = ??

RC1

ioV

jV

11

iioVVV

2

1

11

122

frequency) off-(cut 1

RCoc

c

ov

maxov

2maxo

v

c

)( jH

2

1

1

Ref:080222HKN EE3110 Active Filter (Part 1) 24

Decibel (dB)

By Definition:

1

2

10log10

P

PdB

(1) Power Gain in dB :

in

o

p P

PdBA

10log10)(

in

in

P

PdB

10log100

in

in

P

PdB 2

1

log10310

in

in

P

PdB

2log103

10

Pin Pout

(2) Voltage Gain in dB: (P=V2/R)

vin vout

in

o

v v

vdBA

10log20)(

in

in

v

vdB

10log200

in

in

v

vdB 2

1

log20610

in

in

v

vdB

2log206

10

Ref:080222HKN EE3110 Active Filter (Part 1) 25

Cascaded SystemAv1 Av2 Av3

x10 x10x10vin vout

20dB 20dB 20dB

321 vvvvAAAA

310101010 v

A

32110

log20)(vvvv

AAAdBA

310210110

log20log20log20)(vvvv

AAAdBA

dBAdBAdBAdBAvvvv 321

)(

dBdBdBdBAv

202020)(

dBdBAv

60)( dB2010log20

10

dB6010log20 3

10

Ref:080222HKN EE3110 Active Filter (Part 1) 26

Bode Plot (single pole)

o

jCRj

jH

1

11

1)(

2

1

1)(

o

jH

2

101011log20)(log20)(

o

dBjHjH

o

dBjH

10log20)(

For >>o

R

C VoVi

Single pole low-pass filter

Ref:080222HKN EE3110 Active Filter (Part 1) 27

dBjH )(

(log)x

x

2 x10

6d

B2

0d

B slope-6dB/octave

-20dB/decade

o

jH

10log20)(

For octave apart,1

2

o dBjH 6)(

For decade apart,1

10

o dBjH 20)(

Ref:080222HKN EE3110 Active Filter (Part 1) 28

Bode plot (Two-pole)

R1 R2

C1 C2vi vo

21 oo

2

2

2

1

10111log20)(

oo

jH