9lpf.ppt [호환 모드]bandi.chungbuk.ac.kr/~ysk/rf9lpf.pdf · 2009-07-28 · 2nd-order...
TRANSCRIPT
OutlineFilter 소개
Selecting Filter Functions
Filter Realization techniques
G C FiltGm-C Filters
OTA Models and Building Blocks
Ladder DesignLadder Design
Gm-C Filter Design Procedure
Examples
2전자정보대학 김영석
Types of FiltersLPF(Low Pass Filter)
HPF(High Pass Filter)
BPF(Band Pass Filter)
BSF(Band Stop Filter)BSF(Band Stop Filter)
3전자정보대학 김영석
Filter TerminologyTransfer Function
asasa
(s)V
(s)VT(s)
01M
1MM
M
i
o
+⋅⋅⋅++
=
−
)p(s)p)(sp(s
)z(s)z)(sz(sa
bsbs
asasa
N21
M21M
01N
1NN
01MM
−⋅⋅⋅−−−⋅⋅⋅−−
=
+⋅⋅⋅+++++
= −−
−
)p(s)p)(sp(s N21
N=Filter Order, For Stability M<=N
Poles: p1, p2, …
Zeros: z1, z2, …
Passband Edge(Ripple Bandwidth)Passband Edge(Ripple Bandwidth), fp [Hz]
Passband Ripple, Amax (dB)
St b d Ed f (H )Stopband Edge, fs (Hz)
Minimum Required Stopband Attenuation, Amin (dB)
4전자정보대학 김영석
Operating Frequency RangeFilter invention in 1915 by Wagner and Campbell
Vacuum Tube => Active Filter in 1930
Filter using OPAMP and ICs in 1960
Switched-Capacitor Filter in 1972 by FriedSwitched Capacitor Filter in 1972 by Fried
OTA Filter lately
5전자정보대학 김영석
Filters in Superheterodyne and Direct Conversion RxSuperheterodyne Receiver
Duplexer and Image Filter selects System Band
IF Filter selects the Wanted Channel
Direct Conversion ReceiverDirect Conversion Receiver
Duplexer selects System Band
Channel Selection must be provided to reduce ADC Dynamic RangeRange
6전자정보대학 김영석
Typical Noise SpecificationsInput/Output Impedance of All Blocks = 50 Ohm
dBdBNFdBLNFLL
NFLA
NFNFNFp
E 6.3115105)()(1165651
5
65
5
65 ==+=+=•=
−+=
−+= −
Input/Output Impedance of IF Filters = 500 Ohm
NFNF
dBA
NFNFNFp
ED
p
11
1.1453.2568.985.1510
16.3110110/5
10/12
44
5
==+=−
+=−
+=
dBNFNFNF
dBdBNFdBLNFLL
NFLA
NFNFNF
C
DDD
p
DC
7967842358113.102101
3.1021.201.146)()(11
10/2
3313
33
3
==+=−
+=−
+=
==+=+=•=−
+=−
+= −
dBdBNFdBLNFLL
NFLA
NFNFNFNF
dBA
NFNF
BBBB
Atot
Bv
79.879.62)()(11
79.678.42.358.1)10(
10
11111
220/15222
=+=+=•=−
+=−
+==
==+=+=+=
−LAp 11
outin PPLNF /CircuitsLossy of Figure Noise
==
7
Ref: RF Microelectronics, Razavi
전자정보대학 김영석
Typical Linearity Specifications
IF Filter lowers the interferers by 30dB while attenuating the desired channel by 5dB
VAAAAA
xxx
rmsEIP 1.22 70
)10( 11
y
32
220/30
2
25,1
2
25,1
22
33
221
=∴=≈+=
•+•+•=−αα
αααdesired channel by 5dB
dBA
mVdBmAAAAA
AAAA
rmsDIPIPIPIPDIP
rmsEIPIPIPIPEIP
11
3985 1 11
7.0
,324,3
25,3
24,1
24,3
2,3
,3226,3
26,3
25,3
2,3
==∴≈+=α
dBmAdBmA
dBmA
AIP
BIP
CIP
6.106.12
11
,3
,3
,3
−=
−=
=
8
Ref: RF Microelectronics, Razavi
전자정보대학 김영석
Selecting Filter FunctionsButterworth(Maximally Flat)
Flat in the Passband/Stopband(Ideal Brick Filter와 유사)
But, Insufficient Attenuation
Chebychev FiltersChebychev Filters
Passband Ripple, Flat in the stopband
Good Attenuation
I Ch b h FiltInverse Chebychev Filters
Flat in the Passband, Ripple in the Stopband(zero 삽입)
Stopband Attenuation 우수우수
9전자정보대학 김영석
Selecting Filter FunctionsElliptic Filters(Cauer)
Ripple in the Passband/Stopband
Very Good Attenuation
But, Strong Group Delay VariationBut, Strong Group Delay Variation
Bessel Filters
C t t G D lConstant Group Delay
Insufficient Attenuation
예제: ws/wp=1.5, Amin=50dB, Amax=0.5dB
Butterworth: n=17
Chebyshev: n=8Chebyshev: n=8
Elliptic: n=5
10전자정보대학 김영석
Integrated Analog FiltersSwitched-Capacitor(SC) Filters
Resistors replaced by switched Capacitors
Sampled time
R C FiltR-C Filters
Standard active filter, R, C and OPamps with feedback
Resistors often implemented with MOSTs: so-called MOSFET-CResistors often implemented with MOSTs: so called MOSFET C filters
Gm-C Filters
Resistors replaced by transconductors
12전자정보대학 김영석
SC Filter CharacteristicsGood
Very high precision without tuning
Realize functions with no CT(Continuous-Time) equivalent
S ll d l di i ti f f<20kHSmall area and low power dissipation for f<20kHz
Parasitic insensitive
Integrates with digital CMOSIntegrates with digital CMOS
Bad
Sample-data effects (noise, aliasing etc.)
Needs clock circuits and anti-aliasing filters
Fully-balanced-differential structures for high dynamic range
I ffi i t f b d idthInefficient use of bandwidth
Not suited for high-frequency applications
13전자정보대학 김영석
R-C Filter CharacteristicsGood
Moderate-to-high precision with tuning
Classical R-C-active structures
S ll d l di i ti f f<100kHSmall area and low power dissipation for f<100kHz
Feedback reduces sensitivity to parasitics
Can realize all biquadsCan realize all biquads
Integrates with digital CMOS
No sample-data effects
Bad
On-chip tuning and corresponding circuitry
F ll b l d diff ti l t t f li itFully-balanced-differential structures for linearity
OPamps and feedback limit use of bandwidth
Not suited for high-frequency applicationsNot suited for high frequency applications
14전자정보대학 김영석
Gm-C Filter CharacteristicsGood
Moderate precision with tuning
Based on simple open-loop OTAs
S ll d l di i ti f f<10MHSmall area and low power dissipation for f<10MHz
Can realize most biquads
Integrates with digital CMOS and bipolarIntegrates with digital CMOS and bipolar
No sample-data effects
Efficient use of bandwidth
Bad
On-chip tuning and corresponding circuitry
F ll b l d diff ti l t t f hi h d iFully-balanced-differential structures for high dynamic range
Difficult to desensitize to parasitics – no feedback
OTAs are voltage-controlled current sourcesOTAs are voltage controlled current sources
15전자정보대학 김영석
Gm-C FiltersBasic buliding block: integrator from transconductor and capacitor
Applications
Disk drive read-channel filters
TelecommunicationTelecommunication
Wireless communication
PLLs
Anti-aliasing
17전자정보대학 김영석
OTA(Operational Transconductance Amplifier)
Basic CMOS transconductance stage: single-ended and differentialBasic CMOS transconductance stage: single ended and differential output
d di lF
22
1
1
B
im
o
imo
IWCg
VgI
VgI
μ=
•=
•=
:aldifferenti For
:ended-singleFor
18
221 oxnm L
Cg μ=
전자정보대학 김영석
OTA Model
Small-signal model for a transconductor and its symbolsSmall signal model for a transconductor and its symbols
MrpFpFuS 5250C10C200gExample For
Ω
kHzr
dBrgMrpFpFuS
o
om
o
128C21
6010005,25.0C,1.0C ,200g
o
oim
frequency 3dB-
gain frequency low
≈=
==•=
Ω====
π
19
MHz128 frequency gain unity =
전자정보대학 김영석
OTA Building Blocks: ResistorsResistors (a) grounded, (b) floating, (c) negative and differential
mi
iimoi gI
VRVgII 1 , ==•==:grounded For
i
mmoi
mi
gIV
R
gI-VVR)-V(VgIII
g
1
1 , 2121
−==
==•===
:negative For
:floating For
mi gI
20전자정보대학 김영석
OTA Building Blocks: IntegratorsGm-C integrators (a) voltage-mode, (b) small-signal model, (c) current-mode
m
gsCg
-VVV
=−+ (Ideal) 11
2
omo
m
oo
m
rggg
gCCsg
==
++=
gain DC Finite
(Real) )(
o
o
CCg+
= frequency 3dB-
21전자정보대학 김영석
OTA Building Blocks: Lossy gm-C Integrator(1st order LPF)
m
m
m
ggCCCsg
gsCg
-VVV
++++=
+=−+
2)2( 1
2
1
11
2
(Real)
(Ideal)
om
om
m
omio
CCCgg
ggg
ggCCCs
+=
+=
++++
22
2
2)2(
2
2
1
2
frequency 3dB-
gain DC Finite
io CCC ++ 2
22전자정보대학 김영석
OTA Building Blocks: Differential Integrator
[ ]
[ ]sC
VgsC
I(a) V imoo
11
11111 == ++
[ ]C)s(
)V(gC)s(
I(b) V imoo 212
21
111 == ++
(Ideal) 2
1
m
m
i
o
ii
oo
gsCg
VV
-VV-VV
+==−+
−+
23전자정보대학 김영석
Eliminating the effect of nonnegligible bottom capacitance
Bottom capacitance(Cg) has 10 ~ 30 % of total CStructure (d) => Maintain the circuit’s symmetry and balance
24전자정보대학 김영석
OTA Building Blocks: Summers
(Ideal) 40
43
0
32
0
21
0
1 Vgg
Vgg
Vgg
Vgg
Vm
m
m
m
m
m
m
mo +−+=
26전자정보대학 김영석
OTA Building Blocks: Grounded Inductor(Gyrator)
sCVVgIVgI ===
12121
1
2112221
where
,
mmmm
mm
ggCLsL
ggCs
IVZ
sCVVgIVgI
==⎟⎟⎠
⎞⎜⎜⎝
⎛==∴
===
27전자정보대학 김영석
OTA Building Blocks: Floating Inductor
2
21212
21
21
/)(/)(mm
mm
gCL
sLVVsCVVgVgIIVgVgsCV
=∴
−=−===−=
mg
28전자정보대학 김영석
1st-Order Filters
m
m
mm
gsCgasC
VV
VgCVasVgVVsaC
0)1()(
2
1
1
2
2221112
++
=
=+−+−−
(ideal)
oieff
omeff
meff
CCCCggsC
gasC
2
2
2
1
++=++
+=
where
(real)
LPF: a=0, HPF: gm1=0
30전자정보대학 김영석
2nd-Order Filters(Biquad)
(BPF)122 mgsCV=
(LPF)
(BPF)
4322212
43
1
4322212
1
mmm
mmo
mmm
gggsCCCsgg
VV
gggsCCCsV
++=
++
33전자정보대학 김영석
Higher-Order FiltersCascade Design
Lower sensitivities to component tolerances
Simplicity and flexibility of the design compared to complete higher-order filterg
Cascaded stages do not load each other,
Ladder Design
LC ladders have lower sensitivities to component tolerances
|||| 12 outin ZZ >>
LC ladders have lower sensitivities to component tolerances over active filters
Higher bandwidth
38전자정보대학 김영석
Ladder DesignSource Transformation and Element Replacement
OTA1 for Source Transformation
OTA2 for R1
OTA3, 4, 6, 7 for L
OTA5 for R2OTA5 for R2
39전자정보대학 김영석
Filter Design Procedure1. Determine the transfer function from filter specifications
2. Determine the component values of LC ladder
3. Element replacement using OTA
4 Ci it d i f OTA4. Circuit design of OTA
5. Layout of LPF
40전자정보대학 김영석
Example1Find an Elliptic transfer function
(Amax=0.5dB, Amin=65dB, wp=1000rad/s, ws=2krad/s)
Sol.
11
22
222 (w)] Rε/[|T(jw)| n+= :Filter Elliptic
1log1011log10log20/1log20
log20log201log10
222max
min
22min
]ε[)](Rε[α)(wRεα
)(wRε)] (wRε[α
n
sn
snsn
+=+==>=+
+≈+=Graph
14741log202
min dB./εα/ww ps
=+=
5nGraphUsing
56773100978470364954120280392610 22 )()( ++=>
==>
Table
5n GraphUsing
03402119255056773100978470
5250580540364954120280
392610392610
22 .s.s).(s.
.s.s).(s.
.s.T(s)
+++
•++
+•
+=
41
Ref: Design of Analog Filters, Schaumann
전자정보대학 김영석
Example2Find the lossless twoport from the transfer function
Sol.
kHzfkRRw.)w.(
)w.(|H(jw)|
pLs 60,4.241761023
236222
2222
===+−−
=
Sol.
|H(jw)|orH(s)Find1
5.08912.0|)1(|182602.3
max2 dBjH
kHzkHzfz==>=
=×=α
ZinFind3
|
Compute 2.|H(jw)| or H(s)Find 1.
230960.0|)(|1|)( 2226
622
)w.(wwjwHjw
−+=−=ρ
parameters-y or z Determine 4.
ZinFind 3.
1725301524850722172530152485072
23
2
.s.s.s.s.s.R(s)Z sin +++
++=
43
Ref: Design of Analog Filters, Schaumann
전자정보대학 김영석
Example3Find the LC ladder from the LPF spec.
Sol.
ΩRRdBdB,α.α
kk,ff
Ls
sp
1002710
160100minmax
====
==
Sol.
dB
ff ps
32.26
6.1/
min ===
=
α 1.5,ws 4,ntable the From
.L.C
., C.L.C
'
'
''
'
840680546721
436280883100799620
4
3
22
1
==
===
nFf
.Cp
' 73.122
1100799620
1
4
==π
스케일링
mHLnFC
nFmH, Cf
.L
'
'
'
p
'
p
1338.062.24
94.61405.02
1100883100
4
3
22
==
==×=π
4
44
Ref: 애널로그 IC 필터의 설계, 박송배
전자정보대학 김영석
Example4Design a gm-C LPF from LC ladder
Sol.
kΩ.RRdBdB, α.α
MHzMHz, ff sp
422290
2817
21
minmax==
====
Sol.
SkRg sm 7.4164.2/1/1
=>
=Ω==
OTAs2SourceVoltage1.
μ
=>
>
6 13pFC1Input3OTA 1 Rs 2.
ladder passive in loss 6dB overcome to parallel in cells gm 2
OTAs2Source Voltage 1.
pFCpFCpFCpFpFC
CCCCCCCs
i
rceVoltageSouoRoigyratoroi
2501093.4 13.62.1
)2()()( '1
'1
'11
===∴=+=
+++++==
where
6.13pFC1Input 3.
pF.CpF .C)CC(C pF.μS)(μH.gLC
pFCpFC
'L
'Lgyratoroi
'L
mL
oi
027022724175815
25.0,1.0
22
=∴+=++==•=•=
=>
6 13 FC3O t t5
Gyrator Inductor Floating 15.58uH 4.
pFCpFpFCCCCCCC
LRoigyratoroi
43.5 13.67.0 )()(
'1
'3
'33
=∴=+=++++=
= 6.13pFC3 Output 5.
46전자정보대학 김영석
OutlineSimple OTA and Models
CMFB
3rd Order Elliptic Filter Using Simple OTA
I i Li itImproving Linearity
OTAs using Triode MOSFETs
OTAs using Active MOSFETsOTAs using Active MOSFETs
LPF 설계 예
Wide Bandwidth LPF for IEEE802.11g
49전자정보대학 김영석
Simple OTA Model
uSg 220
fFI
CIV
fF.CMHzrC
f
MΩ.rdBrgAuSg
iiii
ooo
dB
oomv
m
801
922 8.52
121 48262
220
3
===>=
==>==
==>==•==
− π
fπfVfC i
ii
ii 22π
53전자정보대학 김영석
Improving linearity
−=id VVV 21
−=
⎟⎠⎞
⎜⎝⎛−=−=
THGS
idid
SSo
id
VVΔVΔV
/VV
ΔVI
III
where
2
12
21
21
≤⎟⎠⎞
⎜⎝⎛<<
ido
idid
V I
ΔVVei ΔV
/V
linear isand
If
,2.,.,2
12
=
==
oxnD
)id(
ido
ΔVL
WCμI
VΔV 340mV 200mV, Example For
21 2
max
↓=>↑⇒↑⇒↓⇒ m)id(D gVΔVL
WI But Const max
58전자정보대학 김영석
Using Source Degeneration Resistor
(max)
:Improved is Linearity•= SDid RIV
2/
(max)
SD RI by lower is Voltage Mode Common Input (b) •
SDid
59전자정보대학 김영석
OTA Using Triode Transistors(1) Using a Fixed-Bias Triode Transistor
Q3, Q7 Current MirrorQ1, Q5, Q3 Negative Feedback to set V1C Constant
60
, , g
전자정보대학 김영석
OTA Using Triode Transistors(2) Using a Fixed-Bias Triode Transistor with P-Channel Input
Simple
61전자정보대학 김영석
OTA Using Triode Transistors(3) Using Varying Bias Triode Transistor
Fi d VDS 증가 ID감소 R h증가
( )[ ]2/2DSDSTHGSoxnD VVVV
LWCμI −−=
Fixed : VDS 증가=>ID감소=>Rch증가Varying: V1증가=>VGS3증가=>위의 Rch증가분 상쇄V2증가=>VGS4증가=>위의 Rch증가분 상쇄
62전자정보대학 김영석
OTA Using Triode Transistors(4) Using Constant Drain-Source Voltages
Negative Feedback에 의해 VD1, VD2 고정=> Q1, Q2 채널 저항 일정하게 유지
63전자정보대학 김영석
11)(
1 )(2m
Rb
gRa
=
=
( )[ ]2/
)(
2
332 omm
VVVVWCμI
rggRb
=
=> 일정하게 채널저항일정하게 VDS1을 작게하여 R을
( )[ ]2/DSDSTHGSoxnD VVVVL
CμI −−=
64전자정보대학 김영석
OTA Using Active Transistors(1) Source-Connected Differential Pair
Constant=+=−−+−+=+
)(2 )2/()2/(21
SSCM
SSiCMSSiCMGSGSVV
VvVVvVVV
66전자정보대학 김영석
OTA Using Active Transistors(2) Simulated Source-Connected Differential Pair
0( ) R
311
10
(c) R
g(b) R(a) R
m
=
=
4343 rgg(c) R
mm
=
67전자정보대학 김영석
OTA Using Active Transistors: Inverter-Based
( )( )( )
( )( )( )( )
eqGSeqGSeqteqGSeqGSeqo
eqteqGSeq
eqteqGSeq
VVVVVKiiiVVKiVVKi
−−−−−
−−
−−
−−+=−=−=−=
212121
222
211
2( )( )( )( )ineqtCeq
inCCeqtCCeqvVVK
vVVVVVK−
−
−=−+−−=
1
21214
22
68전자정보대학 김영석
OTA Using Active Transistors:Differential-Pair with Floating Voltage Sources (1)
++−++=+ )( 1121 GSGSGSGS VVVVVVVV( )
Constant =+=
+++++
2
)( 1121
tnx
tnxGStnxGSGSGSVV
VVVVVVVV
69전자정보대학 김영석
OTA Using Active Transistors:Differential-Pair with Floating Voltage Sources (2)
The Floating Voltage Sources are simulatedThe Floating Voltage Sources are simulated using two Source Followers
70전자정보대학 김영석
OTA Using Active Transistors:Differential-Pair with Floating Voltage Sources (3)
• The Floating Voltage Sources drive the transistor gatesInstead of the transistor sources
71전자정보대학 김영석
LPF 설계(예)
무선 LAN(IEEE 802.11g)용 LPF
LNA BPF
Down Mixer
LPF VGA ADCANT
Power Amp Drive AmpVCO PLL
p
DACLPF
Up Mixer
72전자정보대학 김영석
Wide Bandwidth LPF SPEC
Parameter Test Condition Spec
Ripple Bandwidth(fp) 1dB 5MHzRipple Bandwidth(fp) 1dB 5MHz
Passband Ripple(Amax) 1dB
Stopband Edge(fs) 25MHz
Stopband Attenuation(Amin) 40dB
IIP3 5dBm
Voltage Gain With Load -6dB
Rin 100Kohm
Rout 2Kohm
NF 25dB
Input/Output DC Bias 3.3V supply 1.65V
73전자정보대학 김영석
Design Procedure
SPEC: gain=-6dB, amax=1dB, amin=40dB, fp=10MHz, fc=25MHz
5th Order Elliptic LPF RLC Ladder
+gm
+
gm
+ ++
+
gm gm gm gm
++
++
+
gmgm gm gm gm
gm-C LPF (OTA)
-+
-
gm1
-
+-
gm2
-
+-
-
+-
-+
-
-
+-
gm3
gm4
gm5
gm6
-
+-
-+
-
-
+-
-+
-
-
+-
gm11
gm7
gm8
gm9
gm10
74전자정보대학 김영석
Wide bandwidth LPF - OTA Design
Pseudo Differential OTA
M32 M11
M29 M26M25
M4 M5
M7 M8
M22 M23M21 M24
Vref
Out+M1 M3
M6
In+
Out+M2
In-
Out-
M22 M23M21 M24Out-
M9
M31 M10
M28M30M27
OTA core block CMFB block
75전자정보대학 김영석
Pseudo-Differential OTA(Simulated Source-Connected Differential Pair)
1(a) R =
221
111
omm
m
rgg(b) R
g(a) R
=221 omm
76전자정보대학 김영석
Wide Bandwidth LPF - Simulation
- 2 . 1
Frequency Response
10MHz
- 2 0 . 0 35dB
10MHz
- 4 0 . 0 25MHz25MHz
- 6 0 . 0
- 8 0 . 0
- 9 0 . 5
78
F r e q u e n c y
1 0 . 0 K H z 1 . 0 0 M H z 1 0 0 . 0 M H z1 . 0 0 K H z 7 . 7 4 G H zV D B ( R L b : 2 )
9 0 . 5
전자정보대학 김영석