Outline
Filter Design – Passive & Active
Design
•
•
•
•
•
•
Howard Luong
EEE, HKUST
eeluong@ee.ust.hk
2358-8514
Functionality
Figures of Merit
Passive Filter Design
Active Inductors (Gyrators)
Passive-To-Active Filter Transformation
Active Filter Design
Passive & Active Filter, Howard Luong
Functionality
Filter Response
• To provide filtering to desired signals while
attenuating undesired signals.
• Image rejection and channel selection
• Needs to have reasonably flat pass band and
high roll off or attenuation
• Needs to have a wide dynamic range, that is
low noise and high linearity
Passive & Active Filter, Howard Luong
2
3
Q
f
 selectivity
BW
O
Passive & Active Filter, Howard Luong
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Passive Filter
 Makes Use of LC Resonant Networks
 With Ideal Inductors:
– High Q
– Very Low Noise
– Extremely High Linearity
– Wide Dynamic Range
– No Power Consumption
Passive Filter Design and
Synthesis
Passive & Active Filter, Howard Luong
Quality Factor Q - Capacitors
Passive Filters
In Practice, Performance is Heavily Dependent on
On-Chip Inductors
With Low-Q Inductors, All Parameters are
Significantly Degraded
High Loss and thus High NF
Performance Sensitive to Process Variation =>
Automatic Tuning is Critical
C
RPC
RSC
Z C  RSC 
7
Q
energy stored
energy lost
C
1
1
 QC 
 RPC C ;
j C
RSC C
RPC  RSC (1  QC 2 ) ~
Passive & Active Filter, Howard Luong
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1
(C ) 2 RS
Passive & Active Filter, Howard Luong
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Quality Factor Q - Inductors
Passive First-Order Filters
vo
vo
L
L
vi
RPL
R
vi
C
R
L
RSL
L
Z L  RSL  jL  QL 
RPL
RSL
(L)
 RSL (1  QL 2 ) ~
RSL

RPL
L
2

c = 1/RC
Passive & Active Filter, Howard Luong
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c = L/R
Passive & Active Filter, Howard Luong
Resonator
10
Quality Factor Q - Resonator
C
L
L
C
ZP
ZS
RSL
RSC
parallel
series
f res 
ZP
f
Passive & Active Filter, Howard Luong
RPC
RPL
L
C
ZS

f
1
C
2 LC
Req  RPL RPC  Qeq 
11
Req
L
Req
L
Passive & Active Filter, Howard Luong
 ReqC
12
Passive Filter Design – Filter Type
Passive Filter Design –Frequency
Normalization and Scaling
• Trade-off between attenuation and filter order for other
performance in terms of passband flatness and group delay
• Butterworth:
– Maximally flat frequency response
– Medium-Q with less attenuation for a given order
• Chebyshev:
– High-Q with high attenuation for a given order
– Passband response is not as flat
• Bessel:
– Constant group delay or linear phase response
– Similar attenuation compared to Butterworth but less
attenuation compared to Chebyshev
Passive & Active Filter, Howard Luong
• Through Frequency Normalization, All Filters Can
Be Generated Through A Low-Pass Filter Prototype
Normalized to Cut-Off Frequency of 1rad/s and
Load Impedance of 1
• Through Transformation, Actual Normalized Filters
(LPF, HPF, BPF) Can Be Derived
• Through Scaling, Filters with Actual Frequency
Characteristic Can Be Obtained
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Passive & Active Filter, Howard Luong
Passive Filter Design
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•
14
Passive Low-Pass Filter Prototypes
Start with Frequency and Impedance
Normalization to Design a Low-Pass Prototype
with c = 1 rad/s and RL =1 
Scale Component Values Using Formulas:
RL = 1
1 rad/s

filter prototype
Cf 
Cn
2f c RLf
Lf 
Ln RLf
2f c
Rsf  Rsn RLf
Passive & Active Filter, Howard Luong
RL = RLf
c

final filter
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Passive & Active Filter, Howard Luong
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Passive Low-Pass Filter Design
Passive Low-Pass Filter Design
1. Define or specify the response in terms of
– Desirable attenuation at frequencies of interest
– Maximum allowable ripple in the pass band
– Ratio of the source resistance RS and the load
resistance RL
2. Normalize the frequencies of interest in terms of
the cut-off frequency fc to determine the ratios f/fc
Passive & Active Filter, Howard Luong
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Passive & Active Filter, Howard Luong
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Chebyshev LPF Prototype
(0.1dB Ripple)
Butterworth LPF Prototype
Adb ( )  10 log[1  (
3. Determine Appropriate Filter Type and Minimum
Order to Meet Required Specification Using either
Attenuation Equations or Curves
4. Determine Normalized Values of Components for
Low-Pass Prototype By Table Look-Up or By
Filter Tools (Matlab)
5. Scale all Component Values to the Desired
Frequency and Impedance Appropriately
 2n
) ]
c
Passive & Active Filter, Howard Luong
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Passive & Active Filter, Howard Luong
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Example of Passive Low-Pass Filter
25 dB
No ripple  Butterworth
f
 3  n3
f
R
 0.5
R
C 1.181F  C 1.88nF
L  0.779H  L 12.4H
C  3.261F  C  5.19nF
Example of Passive Low-Pass Filter
0.5
0.779 H
Normalized
1
C
MHz MHz
RS  50
RL  100
No Ripple
1.181 F
3.261 F
S
50
L
1n
1f
2n
2f
3n
3f
Passive & Active Filter, Howard Luong
12.4 H
100
Scaled
1.88 nF
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5.19 nF
Passive & Active Filter, Howard Luong
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Passive High-Pass Filter Design
Passive High-Pass Filter Design
1. Define or specify the response in terms of
– Desirable attenuation at frequencies of interest
– Maximum allowable ripple in the pass band
– Ratio of the source resistance RS and the load
resistance RL
2. Normalize the frequencies of interest in terms of
the cut-off frequency fc to determine the ratios fc/f
3. Determine Appropriate Filter Type and Minimum
Order to Meet Required Specification Using either
Attenuation Equations or Curves or Matlab
3. Determine Normalized Values of Components for
Low-Pass Prototype By Table Look-Up or By
Filter Tools (Matlab)
4. Replace Each Reactive Component with Its Dual
and with Reciprocal Value. More Specifically,
Passive & Active Filter, Howard Luong
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Cn
1/Cn
Ln
1/Ln
5. Scale all Component Values to the Desired
Frequency and Impedance Appropriately
Passive & Active Filter, Howard Luong
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Example of Passive High-Pass Filter
25 dB
Example of Passive High-Pass Filter
0.5
Normalized LPF:
0.779 H
No ripple  Butterworth
MHz
fc
R
 3  n  3; S  0.5
f
RL
MHz
C1n 1.181F
RS  50
L2 n  0.779 H
RL  100
LPF-To-HPF
Transformation
C3n  3.261F
No Ripple
Passive & Active Filter, Howard Luong
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L1 f 
L1n RLf
C2 f 
C2 n
1

 2.0nF
2f c RLf 2 *1M * 0.779 *100

2f c
Ln RLf
2f c

50
1
1.181 F
3.261 F
0.5
1/0.779 F
1/3.261 H
1
1/1.181 H
Passive & Active Filter, Howard Luong
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Passive Band-Pass Filter Design
Example of Passive High-Pass Filter
Lf 
Normalized
LPF
100
 13.5H
2 *1M *1.181
•
For Bandpass Filters, Ratio of Bandwidth of
Interest BW and -3dB Bandwidth BWC Becomes
More Important than Ratio of Frequencies
100
 4 .9  H
2 *1M * 3.261
2.0 nF
Scaled
100
13.5 H
4.9 H
Passive & Active Filter, Howard Luong
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Passive & Active Filter, Howard Luong
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Passive Band-Pass Filter Design
Passive Band-Pass Filter Design
1. Define or specify the response in terms of
– Desirable attenuation at frequencies of interest
– Maximum allowable ripple in the pass band
– Ratio of source resistance RS and load resistance RL
2. Normalize Bandwidth of Interest in terms of the -3dB
Bandwidth BWc to determine the ratios BW/BWc
3. Determine Appropriate Filter Type and Minimum
Order to Meet Required Specification Using either
Attenuation Equations or Curves or Matlab
3. Determine Normalized Values of Components for
Low-Pass Prototype By Table Look-Up or By
Filter Tools (Matlab)
4. Replace Each Inductor and Capacitor with Series
and Parallel Resonant Tanks, Respectively
Cn
Cn
Ln
Ln
Ln
Cn
5. Scale all Component Values as Follows:
Passive & Active Filter, Howard Luong
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•
For Parallel Resonant Components:
For Series Resonant Components:
BWC = 7 MHz
C
p

C
pf
2 ( BW ) R
c L
R ( BW )
c
 L
L
pf
2
2f L
o p
Ripple < 0.1 dB
> 36 dBc
 fo 
f1 f 4 
C sf 
( BW c )
2f o 2 C S R L
BW = 28 MHz
R L LS
2 ( BW c )
RS  50; RL  100
Lsf 
Passive & Active Filter, Howard Luong
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Example of Passive Band-Pass Filter
Passive Band-Pass Filter Design
•
Passive & Active Filter, Howard Luong
f 2 f3
fo = 75 MHz
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Passive & Active Filter, Howard Luong
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Example of Passive Band-Pass Filter –
Normalized LPF Prototype
Example of Passive Band-Pass Filter –
Normalized BPF Transformation
 0.1  dB Chebyshev
BW
R
 4  n  3; S  0.5  LPF prototype
BWC
RL
0.5
0.5
0.838 H
0.838 F
3.159 H
1
0.838 H
1.853 H
1.853 F
3.159 F
1
3.159 F
1.853 F
Passive & Active Filter, Howard Luong
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Example of Passive Band-Pass Filter - Scaling
1.853
C1 p  2 (100
 421 pF
)( 7*106 )
Passive & Active Filter, Howard Luong
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Example of Passive Band-Pass Filter –
Final Design Parameters
6
*( 7*10 )
L1 p  2 (100
 10.69nH
75*106 )(1.853)
50
1.91 H
2.34 pF
6.26 nH
C2 s  2 ( 75*107*610
 2.34 pF
)( 0.838)100
6
*( 0.838)
L2 s  100
 1.91H
2 ( 7*106 )
10.69 nH
421 pF
718.5 pF
100
3.159
C3 p  2 (100
 718.5 pF
)( 7*106 )
6
*( 7*10 )
L3 p  2 (100
 6.26nH
75*106 )( 3.159 )
Passive & Active Filter, Howard Luong
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Passive & Active Filter, Howard Luong
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Passive Filter – High Frequencies
•
May Be Cascaded and Combined with
Interstage LNA to Compromise Performance
Passive Filter – High Frequencies
•
May Use Negative-Gm Compensation
Technique to Achieve High and Tunable Q
 Improve
Gain and NF
Sacrifice Linearity and Power
Geq
GP
-Gm
C
LP
LP
C
LNA
Geq = GP – Gm < GP
Cascaded Filter
Passive & Active Filter, Howard Luong
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Single-Ended Negative Gm
Implementation
38
Differential-Ended Negative Gm
Implementation
-Gm
-Gm
vo
M2
Passive & Active Filter, Howard Luong
M1
g g
 Gm   m1 m 2
g m1  g m 2

Passive & Active Filter, Howard Luong
vo+
M2
vo M1
 Gm   g m
g m1
2
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Passive & Active Filter, Howard Luong
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Passive Filters - Summary

Good linearity
 Low noise
 Low power
High Loss => NF degradation
Component values are too large to be integrated
except high frequency (~ GHz)
Filter characteristic highly sensitive to component
values and accuracy
=> Solution: Active Filters
Passive & Active Filter, Howard Luong
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Active Inductors (Gyrators)
•
C2
Active Inductors (Gyrators)
 Useful
Use Gm Cells Connected in Feedback to
Emulate Inductors
Gm1
to Generate High Inductance
Poor Performance due to Gm Cells:
LG
C2
-Gm2
Active Filter Design Using Active
Inductors (Gyrators)
Noise
Linearity
Power Consumption
C1
LG 
Passive & Active Filter, Howard Luong
C1
Gm1Gm2
43
Passive & Active Filter, Howard Luong
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Active Low-Pass Filter
•
Passive-To-Active Filter
Transformation
Transform from Passive Low-Pass Filter
vo
R
+
vi
vi
C
vo 
vo
1
-
1
1 vi  vo
1
dt 
 ic dt 

 (vi  vo )dt
C
C
R
RC
Passive & Active Filter, Howard Luong
With change of variable
iL*
2
vi
-
1
1
*
*
vo   (iS  iL )dt   (iS  iL )dt  1  R*C
1
C
i L  iL R * 
*
vi
L *
*
 vo dt  2  * ; i  iR
2
R
47
vo
1
1
vo
-
2
2 
1
Passive & Active Filter, Howard Luong
Replace each integrator by its corresponding
active lossless resonator
1
+
C
•
+
L
vo
1
+
is
is*
+
vo
Active LPF-To-BPF Transformation
+
Active Lossless Resonator
46
-
 1 2
Passive & Active Filter, Howard Luong
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Active Lossy Resonator
Active Lossy Resonator
L
R*
 1  CR ;  2  * ;  
R
R
vo
s 2
 2
 band  pass
vi s  1 2  s 2  1
*
= R*/R


L
C
R
vi
 v1 -
v2
1
2
vo
v1
s 2 1 2

 high  pass
vi s 2 1 2  s 2  1
+
vi
+
vo
v2
1
 2
 low  pass
vi s  1 2  s 2  1
-
Passive & Active Filter, Howard Luong
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Passive & Active Filter, Howard Luong
Generic Active Biquadratic Filter
50
High-Order Ladder Filter
= R*/R
K1

v1
K2
1
v3
-
v2
2
+
vi
+


-
K3
vo
= R*/RL
vo K1s 2 1 2  K 2 s 2  K 3

vi
s 2 1 2  s 2  1
Passive & Active Filter, Howard Luong
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= R*/RS
Passive & Active Filter, Howard Luong
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Active Filter – Design Procedure
1.
2.
3.
4.
5.
Determine from the specifications the filter type
and the filter order required
Do a table look-up to find out the associated
passive low-pass prototype
Transform the passive low-pass prototype to the
passive filter type desired
Perform a passive-to-active transformation
Replace each reactive component by its
associated integrator
Passive & Active Filter, Howard Luong
2.
3.
4.
Determine from specifications filter type and
filter order required
Use Some Tools to Obtain Poles and Zeros
Required
From Poles and Zeros, Construct Transfer
Function
Implement Transfer Function Using Cascade of
Bi-Quadratic Filters
Passive & Active Filter, Howard Luong
1.
2.
3.
4.
Determine from specifications filter type and
filter order required
Do a table look-up to find out associated passive
low-pass prototype
Perform a passive-to-active transformation to
obtain active low-pass implementation
Transform directly the active low-pass to
corresponding active band-pass by replacing
each integrator with a corresponding resonator
53
Active Filter – Alternative Procedure
1.
Active Filter – Band-Pass Filter
Passive & Active Filter, Howard Luong
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Active Filters – Summary
Filter Specification
Attenuation Curves or
Equations
Filter Tools (Matlab)
Filter Type and Order
Filter Tools (Matlab)
Table Look-Up
LPF Component Values
55
Zeros and Poles
Passive-To-Active
Construct Biquads
Ladder Filter
Biquad Filter
Passive & Active Filter, Howard Luong
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Active Bandpass Filters – Summary
+
1
-
Passive-To-Active LPF
Passive LPF to Passive BPF
+
+
+
-
integrator

v
vi
o
1
+
-
+
vi
1
-

-
2
resonator
Active Ladder BPF

1

2
Key components include integrators and
lossless or lossy resonators
• Key components can be realized in either
continuous-time (Gm-C) or discrete-time
(switched-capacitor) domain
• Trade-off between operation frequency and
accuracy
•
resonator
LPF Component Values
integrator
Active Filter Design
v
o
resonator
Passive & Active Filter, Howard Luong
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Passive & Active Filter, Howard Luong
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Switched-Capacitor Filters
Continuous-Time Filters
• Switched-Capacitor Filters
• Continuous-Time Filters (Gm-C, RC)
 Insensitive to Process Variation => Accurate
=> No Need for Tuning
 Good Linearity and Low Distortion
Low-Frequency Operation (< 10 MHz) due to
High Required Sampling Frequency
Noise Folding due to Sampling
High-Performance Amplifier => Relatively
High Power Consumption
 Relatively High Frequency (> 100 MHz)
Sensitive to Process Variation => Inaccurate
=> Need Tuning Circuitry
Large Noise Contribution
Highly Non-Linear
High Power Consumption
Passive & Active Filter, Howard Luong
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Passive & Active Filter, Howard Luong
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References
References
• C. Bowick, RF Circuit Design, Sams, 1994
• R. Gregorian, and G. Temes, Analog MOS Integrated
Circuits for Signal Processing, New York, Wiley, 1986
• Y. P. Tsividis, and J. O. Voorman, Integrated ContinuousTime Filters: Principles, Design, and Applications, New
York, IEEE Press, 1993
• D. Johns, and K. Martin, Analog Integrated Circuit
Design, New York, Wiley, 1997
• P. Gray, et al, Analysis and Design of Analog Integrated
Circuits, New York, Wiley, 4th ed., 2001.
• B. Razavi, Design of Analog CMOS Integrated Circuits,
McGraw Hill, 2001
• M. Ismail and T. Fiez, Analog VLSI Signal and
Information Processing, Mc-Graw-Hill, 1994
• T. Choi and H. C. Luong, "A High-Q and Wide-DynamicRange 70-MHz CMOS Bandpass Filter for Wireless
Receivers," IEEE Transactions on Circuit and Systems II
(TCAS II), pp. 433-40, May 2001
• V. S. L. Cheung, H. C. Luong, and W. H. Ki, “A 1-V
Switched-Opamp Switched-Capacitor Pseudo-2-Path
Filter,” IEEE Journal of Solid-State Circuits (JSSC), Vol.
36, No. 1, pp. 14-22, January 2001
• V. S. L. Cheung and H. C. Luong, Design of Low-Voltage
CMOS Switched-Opamp Switched-Capacitor Systems,
Kluwer Academic Publishers, July 2003
Passive & Active Filter, Howard Luong
Passive & Active Filter, Howard Luong
61
References
• V. S. L. Cheung, H. C. Luong, and W. H. Ki, “A
1-V Switched-Opamp Switched-Capacitor
Pseudo-2-Path Filter,” IEEE Journal of SolidState Circuits (JSSC), Vol. 36, No. 1, pp. 14-22,
January 2001
Passive & Active Filter, Howard Luong
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