9lpf.ppt [호환 모드]bandi.chungbuk.ac.kr/~ysk/rf9lpf.pdf · 2009-07-28 · 2nd-order...

LPF 설계LPF 설계

충북대학교 전자정보대학 김영석

2 1 92010.9

1

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)


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)


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


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


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


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


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


Selecting Filter Functions

11

Ref: Design of Analog Filters, Schaumann


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


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


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


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


Filter Realization Techniques


Gm-C FiltersBasic buliding block: integrator from transconductor and capacitor

Applications

Disk drive read-channel filters

TelecommunicationTelecommunication

Wireless communication

PLLs

Anti-aliasing


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=


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 =


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


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-


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


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

+==−+

−+


Eliminating the effect of nonnegligible bottom capacitance

Bottom capacitance(Cg) has 10 ~ 30 % of total CStructure (d) => Maintain the circuit’s symmetry and balance


OTA Building Blocks: Amplifiers

(Ideal) 2

1

1

2

m

m

gg

VV

=21 mg


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 +−+=


OTA Building Blocks: Grounded Inductor(Gyrator)

sCVVgIVgI ===

12121

1

2112221

where

,

mmmm

mm

ggCLsL

ggCs

IVZ

sCVVgIVgI

==⎟⎟⎠

⎞⎜⎜⎝

⎛==∴

===


OTA Building Blocks: Floating Inductor

2

21212

21

21

/)(/)(mm

mm

gCL

sLVVsCVVgVgIIVgVgsCV

=∴

−=−===−=

mg


OTA Building Blocks

Differential Grounded Inductor

29

Differential Floating Inductor


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


1st-Order Filters


2nd-Order Filters(Biquad)

(BPF)122 mgsCV=

(LPF)

(BPF)

4322212

43

1

4322212

1

mmm

mmo

mmm

gggsCCCsgg

VV

gggsCCCsV

++=

++


Gm-C Biquad with Arbitrary Zeros

/

)( 22

22

Qwss

sT z++=

βα

34

/ 200

2 wQsws ++


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


Ladder DesignSource Transformation and Element Replacement

OTA1 for Source Transformation

OTA2 for R1

OTA3, 4, 6, 7 for L

OTA5 for R2OTA5 for R2


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


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



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



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


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.


LPF 설계 예제LPF 설계 예제

충북대학교 전자정보대학 김영석

2 1 92010.9

48

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


Simple OTA


Simple OTA I-V (gm)


Input Linearity of Simple OTA

W=3u, 6u, 9u, 12u


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


CMFB of Simple OTA

Cgvvv mooo =

−= −+

−+

kHzC

gf

sCvvvm

t

iii

3502

==

−+

π


CMFB continued


3rd Elliptic LPF


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


Using Source Degeneration Resistor

(max)

:Improved is Linearity•= SDid RIV

2/

(max)

SD RI by lower is Voltage Mode Common Input (b) •

SDid


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


OTA Using Triode Transistors(2) Using a Fixed-Bias Triode Transistor with P-Channel Input

Simple


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


OTA Using Triode Transistors(4) Using Constant Drain-Source Voltages

Negative Feedback에 의해 VD1, VD2 고정=> Q1, Q2 채널 저항 일정하게 유지


11)(

1 )(2m

Rb

gRa

=

=

( )[ ]2/

)(

2

332 omm

VVVVWCμI

rggRb

=

=> 일정하게 채널저항일정하게 VDS1을 작게하여 R을

( )[ ]2/DSDSTHGSoxnD VVVVL

CμI −−=


OTA Using Active Transistors: VGS1+VGS2=Constant


OTA Using Active Transistors(1) Source-Connected Differential Pair

Constant=+=−−+−+=+

)(2 )2/()2/(21

SSCM

SSiCMSSiCMGSGSVV

VvVVvVVV


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

=


OTA Using Active Transistors: Inverter-Based

( )( )( )

( )( )( )( )

eqGSeqGSeqteqGSeqGSeqo

eqteqGSeq

eqteqGSeq

VVVVVKiiiVVKiVVKi

−−−−−

−−

−−

−−+=−=−=−=

212121

222

211

2( )( )( )( )ineqtCeq

inCCeqtCCeqvVVK

vVVVVVK−

−

−=−+−−=

1

21214

22


OTA Using Active Transistors:Differential-Pair with Floating Voltage Sources (1)

++−++=+ )( 1121 GSGSGSGS VVVVVVVV( )

Constant =+=

+++++

2

)( 1121

tnx

tnxGStnxGSGSGSVV

VVVVVVVV



The Floating Voltage Sources are simulatedThe Floating Voltage Sources are simulated using two Source Followers



• The Floating Voltage Sources drive the transistor gatesInstead of the transistor sources


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


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


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


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


Pseudo-Differential OTA(Simulated Source-Connected Differential Pair)

1(a) R =

221

111

omm

m

rgg(b) R

g(a) R

=221 omm


Pseudo-Differential OTA gm


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


Layout

LPF[21 29]LPF[21-29],

OTA[7-18]


Test set up - Low Pass Filter


9lpf.ppt [호환 모드]bandi.chungbuk.ac.kr/~ysk/rf9lpf.pdf · 2009-07-28 · 2nd-order...

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