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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.
Source: National Semiconductor
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.
Source: National Semiconductor
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
Unity-Gain Sallen-Key Low-Pass Filter 2/3
Source: Jacob, Textbook
Unity-Gain Sallen-Key Low-Pass Filter 3/3
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
Source: Jacob, Textbook
Equal Component
Source: Jacob, Textbook
Example 7-5 from Textbook
• 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
Source: Jacob, Textbook
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
Source: National Semiconductor
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
Example 7-9 from Textbook
• 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.