electronica iii clase 05

Electrónica III Clase 05

Síxifo Falcones, Ph.D.

Agenda:

• Filtros de 2do Orden

• Filtros Sallen-Key

– Filtro Pasa Bajos

– Filtro Pasa Altos

Filtros de 2do Orden

There are two main topologies for a second-order filter, the Sallen-Key and the Multiple Feedback (MFB) topology.

Sallen-Key Multiple Feedback

Source: Rod Elliott (ESP)

Low-Pass Filter

2222

0

1 nn

AjG

21

tann

nArcjG

2

00

0

1

)(

ss

AsG

A0: Band pass gain

ω0: Critical frequency

ωn: Normalized frequency

α: Damping coefficient

0

n

Damping (Amortiguamiento)

Effects of the Damping Coefficient

Effects of the Damping Coefficient

• A0 may be different

• F-3db does not equal f0

• Transient response varies widely

• f0 is constant

Butterworth Low-Pass Filters The Butterworth low-pass filter provides maximum passband flatness. Therefore, a Butterworth low-pass is often used as anti-aliasing filter in data converter applications where precise signal levels are required across the entire passband.

Source: National Semiconductor

Chebyshev Low-Pass Filters The Chebyshev low-pass filters provide an even higher gain rolloff above f0. However, the passband gain is not monotone, but contains ripples of constant magnitude instead. For a given filter order, the higher the passband ripples, the higher the filter’s rolloff.


Bessel Low-Pass Filters The Bessel low-pass filters have a linear phase response over a wide frequency range, which results in a constant group delay in that frequency range. Bessel low-pass filters, therefore, provide an optimum square-wave transmission behavior. However, the passband gain of a Bessel low-pass filter is not flat and the transition from passband to stopband is not sharp.


General Sallen-Key Low-Pass Filter

2

2121210211

0

11)(

sCCRRsCRARRC

AsG

3

40 1

R

RA

Unity-Gain Sallen-Key Low-Pass Filter 1/3

To simplify the circuit design, it is common to choose unity-gain (A0 = 1), and R1 = R2 = R.

21

02

1

CCRf

2

12C

C

2

21

2

121

1)(

sCCRsRCsG

10 A


Source: Jacob, Textbook

Example 7-3 from Textbook

• Design a filter using the Sallen-Key unity gain low pass active filter to meet the following specifications:

– Rolloff rate: 40 dB/dec

– Critical frequency: 2 kHz

– Pass band as flat as possible

– Gain of 5 at DC

Equal-Component Sallen-Key Low-Pass Filter

222

0

0

31)(

sCRsARC

AsG

A special case of the general Sallen-Key topology is the application of equal resistor values and equal capacitor values: R1 = R2 = R and C1 = C2 = C.

RCf

2

10

03 A

Equal Component



• Design a filter using the Sallen-Key equal component low pass active filter to meet the following specifications:

– Rolloff rate: 40 dB/dec

– Critical frequency: 2 kHz

– Pass band as flat as possible

– Gain of 5 at DC

Frequency Correction Factor

03 fkf lpdB


Ejercicio:

• The task is to design a second order equal component Chebyshev low pass active filter with a frequency f-3dB = 3 kHz and a 3dB passband ripple.

High-Pass 2nd Order Active Filter


High-Pass Filter (cont.)

2

0 0

( )

1

AG s

s s

A∞: Band pass gain

ω0: Critical frequency

ωn: Normalized frequency

α: Damping coefficient

0

n

2222

2

1 nn

nAjG

21

tann

nArcjG

The general Sallen-Key topology

2 1 2 1 2

2

1 2 1 2 1 2 1 2

( )1 1 1 1

1

AG s

R C C R C A

R R C C s R R C C s

3

41R

RA

Unity-Gain Sallen-Key High-Pass Filter

2

21

2

21

21 1111

1)(

sCCRsCRC

CCsG

1A

21

02

1

CCRf

1

2

2

1

C

C

C

C

Equal-Component Sallen-Key High-Pass Filter

CCC

RRR

21

21

3 A

2 2 2

( )3 1 1 1

1

AG s

A

RC s R C s

RCf

2

10

Frequency Correction Factor

03 fkf hpdB

lp

hpk

k1


• For an equal component high pass active filter whose components are listed below, calculate the -3dB frequency, filter type and pass band gain. – R = 10kΩ – C = 0.1μF – R4 = 5.8kΩ – R3 = 10kΩ

• Gain-Bandwith product for a 741 is 1MHz.

electronica iii clase 05

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