IC Lab

CMOS ANANLOG INTEGRATED FILTERS

2001. 7. 5.

JOONGHO CHOI

Department of Electrical Engineering

University of Seoul

jchoi@ee.uos.ac.kr

IC Lab

OUTLINE

l Introduction to Analog Integrated Filters

l Introduction to Transconductance (Gm)-C Filters

ü Transconductance Circuits

ü High-Order Gm-C Filters

ü Design Issues for Gm-C Filters

ü Design Examples

l Introduction to Switched-Capacitor (SC) Filters

ü Switched-Capacitor Integrators

ü High-Order SC Filters

ü Design Issues for SC Filters

ü Design Examples

l Simulation Exercises

IC Lab

Introduction

IC Lab

Mixed-Signal Systems

AnalogMedia

Pre-Amp Rx-Filter

ADC

DAC

Tx-FilterDriver

DSP&

MCU

DigitalData

A

A

AnalogMedia

Pre-Amp Rx-Filter

ADC

DAC

Tx-FilterDriver

DSP&

MCU

DigitalData

D

D

AFE1

AFE2

Performance Requirements

AFE1 < AFE2

Performance Requirements

AFE1 < AFE2

IC Lab

A n a l o g I n t e g r a t e d F i l t e r s

l Analog Filters vs Digital Filters

:-) Speed, Power Dissipation, Si l icon Area

:-( Dynamic Range, Programmabil ity, Control labi l i ty

l Continuous-Time Filters

è Gm-C Fi lter, MOSFET-C Filter, Active R-C Filter, …

è No Pre- & Post- Processing Required

è Tuning Circuits Required

l Discrete-Time Filters

è Switched-Capacitor (SC) Fi lter, Switched-Current Filter

è Pre- & Post- Processing Required

è Desirably Accurate

IC Lab

F i l t e r F r e q u e n c y R e s p o n s e

l Magnitude Characteristics

l Phase Characteristics

l Operating Types

è Lowpass, Highpass, Bandpass, Bandreject, Allpass

è Frequency Transformation from LPF Prototype

l Response Types

è Butterworth, Chebyshev (I,II), Ell iptic, Equiripple

|H(f)|

f

AS

AP

fS1

fS2

fP1

fP2

IC Lab

H i g h - O r d e r F i l t e r I m p l e m e n t a t i o n 1

l Easy Adjustment of Frequency Characteristics

l Pole/Zero Pair Matching

l Biquad Permutation

l Gain Distribution

Hi(z) H

N/2(z)H

1(z) .... ....X(z) Y(z)

H(z) = H1(z)...H

i(z)...H

N/2(z)

( ) ( ) ∏∏== ++

++==

2N

1i 012

2

012

22N

1i

i azazabzbzb

zHzH

Cascading of Biquad Blocks

IC Lab

H i g h - O r d e r F i l t e r I m p l e m e n t a t i o n 2

l Implemented with Many Integrators

l Less Sensitive to Variations of Components

l Easy to Obtain

l Frequency Transformation

l Impedance Transformation

RLC Prototype

C1

RS

X(s) Y(s)

RLC

3

L2

L4

I2

I4

V1

V3

I0

( )( )

( )( )

( ) 2L4343423

2312

1201

S10

sLRIVI

sCIIV

sLVVI

sCIIV

RVXI

−=

−=

−=

−=

−=

IC Lab

C o n t i n u o u s - T i m e F i l t e r R e s p o n s e

100

102

104

106

108

-120

-100

-80

-60

-40

-20

0

f [Hz]

|H(f

)| [

dB

]

1NN1N

2N

1

1MM1M

2M

1

asasasa

bsbsbsb)s(Y)s(X

)s(H+

−+

−

++++

++++=≡

L

L

-0.5 0 0.5-5

-4

-3

-2

-1

0

1

2

3

4

5

real f [MHz]

ima

gin

ary

f [

MH

z]

IC Lab

D i s c r e t e - T i m e F i l t e r R e s p o n s e

0 0.2π 0.4π 0.6π 0.8π π-120

-100

-80

-60

-40

-20

0

ω

|H(ω

)| [d

B]

-1 -0.5 0 0.5 1

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

real ω

imag

inar

y ω

( ) ( )( )1MM

1N-2

N1

1MMM-

2M

1

azazazabzbzbzb

zDzN

zH+

+

++++++++

==L

L1

IC Lab

Continuous-Time Filter(Gm-C Filter)

IC Lab

G m A m p l i f i e r B a s i c s

l Transconductance (Gm) Amplif ier

Single-Ended Fully-Differential

l Transconductance Amplifier Characteristics

è Linearity

è I/O Impedances

è Operat ing (Dynamic) Range

è Frequency Characterist ics

è Electr ical ly Programmable Gm Value

Gm+

-

ioutvin+

vin-

Gm+

-

ioutvin+

vin

-

iout

+

-

( ) vvGvGi ininminmout −+ −⋅=⋅≡ R , R outin ∞=∞=

IC Lab

G m A m p C i r c u i t E x a m p l e s

l Simple Differential Pair Example

for large ISS, small β & v i n

M1

M2

vin

+ vin

-

i2

i1

ISS

vx

io=i

1-i

2

vin=v

in+-v

in-

Gm

+ISS

-ISS

( )

( )2THxin2

2

THxin1

Vvv2

i

Vvv2

i

−−β

=

−−β

=

−

+

SS21 Iii =+

2

inSS

in21out v2I2

v2

iii −β

β=−≡

SSm IG β≅∴

inSSout vIi ⋅β≈

IC Lab

l Differential Pair w/ Degenerate Resistor Example

for large β and small √i1- √i2

M1

M2

vin

+ vin

-

i2

i1

IB

RC I

B

MR

VC

iRC

1 2

( ){ }2gs1gsinC

21out

in2gsCR1gsin

vvvR2

iii

vvRivvC

−−∆=−≡∴

=+−− −+

BR2

BR1

Iii

Iii

C

C

=+

+=CR21

i2ii ⋅=−

( ) ( ) ( ) 0ii2i2Vi2Vvv 212TH1TH2gs1gs ≈−β=β+−β+=−

Cin

out

in

outm R

2v

iv

iG ≅

∆=

∆∂∂

≡∴

IC Lab

l Differential Pair w/ Degenerate Resistor & Feedback Example

Negative feedback loops (M1-M 5-M 3 & M2-M6-M 4) forces constant

currents IB1 to f low through M1 and M2 è vgs1 = vgs2

M1

M2

vin

+ vin

-

VC

M9

M3

M4

M5

M6

M7

M8

IB1

IB1

IB2

IB2

IB1

-io

IB1

+io

io

VDD

VSS

IC Lab

T C A m p u s i n g M O S i n S a t u r a t i o n

l Current in Saturation MOSFET

l Basic Principle

l Composite Transistor

( )2THgsds Vv2i −β

=

( ) ( ) ( )−+ −⋅=−⋅+=− inin22 vvkBABABA

Mn

Mp

VGSeq

+

-

ID

( )2THeqGSeqeqD VV2I −β

=

( )2PNPN

eq

THPTHNTHeq

SGPGSNGSeq

2221

VVV

VVV

β+β

ββ≡β

+≡

+≡

M1

M2

v1

v2

M3

M4

i1

VFV

+-

+-

VFV

i2

[ ] ( )21THeqFVeqout vvVV2i −⋅−β=

IC Lab

T C A m p u s i n g M O S i n L i n e a r

l Current in Saturation MOSFET

l Basic Principle

l Example

( )

−−β= 2dsdsTHgsds v2

1vVvi

( ) ( ) −+ −∝−=−−− inin22 vvBACBCA

VA

i1

ip

VSS

M2

M1

M3

M4

VB

MA

MB

i2

i4

i3

im

VA1

VB1

VB2

VA2

Vin2

Vin1

IBIAS

IBIAS

( ) ( ) ( ) ( )32414231mpout iiiiiiiiiii −−−=+−+=−=

( )( ) ( )

−−−−−β=

=−

2

2B1B2B1BTH2BB

B41

VV21

VVVVV2

i2ii

( )( ) ( )

−−−−−β=

=−

2

2A1A2A1ATH2AA

A32

VV21

VVVVV2

i2ii

IC Lab

G m - C I n t e g r a t o r

Gm

+

-

ioutv

in+

vin

-v

out

C

KCL

CG

sCG

vv

)s(H

munity

m

in

out

=ω

=≡

|H(ω)|

ω0dB

ωunity

-6dB/dec

IC Lab

1 s t - O r d e r G m- C F i l t e r

Vin(s)

Gm1

+

-

Gm2+

-

Vout

(s)

CA

CX

i1

i2

KCL

( ) ( )( ) 0

01

XA

2m

XA

1m

XA

X

in

out

sksk

CCG

s

CCG

sCC

C

sVsV

sHω+

+⇐

+

+

+

+

+

=≡

( )( )

A

1

1X

XA02m

XA01m

Ck1

kC

CCG

CCkG

−=

+⋅ω=

+⋅=

IC Lab

2 n d - O r d e r G m- C F i l t e r ( B i q u a d )

KCL

Vout

(s)Gm2

+

-

Gm4

+

-

Gm1

+

-G

m3

+

-

Gm5+

-

Vin(s)

CA

CBC

X

AB

KCL

( ) ( )( )

( )

( )20

02

012

2

XBA

2m1m

XB

3m2

XBA

4m2m

XB

5m2

XB

X

in

out

sQ

s

ksksk

CCCGG

sCC

Gs

CCCGG

sCC

Gs

CCC

sVsV

sHω+

ω+

++⇐

++

+

+

++

+

+

+

=≡

IC Lab

l Characteristic Function

l Filtering Operations

ü Lowpass k2 = k1 = 0

ü Highpass k1 = k0 = 0

ü Bandpass k2 = k0 = 0

20

02 sQ

s rdenominato ω+

ω+=

( )XBA2m1m

0 CCCGG+

=ω

A

XB2

3m

2m1m

CCC

GGG

Q+

=

( )XBA4m2m

0

XB

5m1

XB

X2 CCC

GGk

CCG

k CC

Ck

+=

+=

+=

IC Lab

H i g h - O r d e r G m - C F i l t e r w / B i q u a d s

l H1(s)

G m1 =G m2 =17.06µ, Gm3 =0.80µG m4 =4.18µ, Gm5 =0µCA =C B =5p, C X=0.319p

l H2(s)

G m1 =G m2 =16.19µ, Gm3 =1.52µG m4 =0.21µ, Gm5 =0µCA =C B =5p, C X=0.319p

l H3(s)

G m1 =G m2 =14.89µ, Gm3 =0.67µG m4 =0µ, Gm5 =1.89µCA =C B =5p, C X=0p

6th-order Elliptic BPF

ü Passband : 480kHz~520kHz

ü Passband Ripple : < 0.05dB

ü Stopband Attenuation : > 80dB

104

105

106

107

-100

-80

-60

-40

-20

0

IC Lab

H i g h - O r d e r G m - C F i l t e r f r o m R L C

C1

RS

X(s) Y(s)

RLC3

L2

L4

I2

I4

V1

V3

I0

+ -

+ -

+ -

X(s) Y(s)

τ1

τ2

AS

+ -

+ -

τ3

τ4

V1

V2

V3

V4

V0

( )( )

( )( )

( ) 2L4343423

2312

1201

S10

sLRIVI

sCIIV

sLVVI

sCIIV

RVXI

−=

−=

−=

−=

−= ( )( )( )( )( ) 434

3423

2312

1201

1S0

sYVV

sVVV

sVVV

sVVV

VXAV

τ−=

τ−=

τ−=

τ−=

−=

Frequency Transformation & Impedance Transformation Required

IC Lab

N o n - I d e a l i t i e s

l Finite Output Resistance

ü Finite DC Gain : BPF, HPF

ü Reduced Phase (>-90o): Q decreases

ü Cascode Output Stage & Compensat ion Technique

l Finite Parasitic Pole Frequency

ü Increased Phase (

IC Lab

L i n e a r i t y P r o b l e m s

l Nonlinearity

l Harmonic Distortion

l Inter Modulation Distortion

ü IMD2 è ω1+ω2, ω1-ω2ü IMD3 è ω1+2ω2, 2ω1 +ω2, 2ω1-ω2, ω1-2ω2,

( ) ( ) ( )[ ] ( )[ ] L+++≡ 3in32in2in1out tVatVatVatI

( ) ( )tsinAtV 0in ω=

( ) ( ) ( ) ( ) L+ω+ω+ω= t3sinIt2sinItsinItI 030201out

( ) ( ) ( )[ ] 2121in , tsintsinAtV ω≈ωω+ω=

+++≡

2

1

2

4

2

3

2

2

I

IIIlog10]dB[ THD

L

IC Lab

D y n a m i c R a n g e P e r f o r m a n c e

l IIP3 : Input-Referred Third-Order Intercept Point

l IP1dB : Input-Referred 1-dB Compression Point

l SFDR : Spurious-Free Dynamic Range

VIN

[dBm]

VOUT

[dBm]

IIP3Fundamental

NO

SFDR

IMD3

1dB

IP1dB

IC Lab

G m V a r i a t i o n s

l Values of Gm might change due to

process variation, temperature, aging, … .

l Trimming after chip fabrication possible, but one-time event.

5 6 7 8 9 10 11

-60

-50

-40

-30

-20

-10

Freq. [MHz]

[dB]

Notch Filter

TT :SS :FF :

l freq. change

l Q change

l freq. change

l Q change

IC Lab

O n - C h i p T u n i n g E x a m p l e f o r B i q u a d

20

02 sQ

s

)s(D)s(H

ω+

ω+

=

LPFphase

comparator

VCO

amplitudecomparator

LPF

Qreference

ckt.

VIN

VOUT

filte

r H

(s ;

ωO

,Q)

ωREF

VREF

ωO

VO

Vω o

VQ

PLL

MLL

ω0

Q

IC Lab

R e c e n t A d v a n c e E x a m p l e 1

55 Mbps Equal izer for Magnetic Storage Read Channels

l 4-pole & 1-zero

l Equalization

l for Peak-Detect Scheme

l 2.0-µm CMOS Technology

l SNR > 57 dB, THD < 1%

l Power = 40 m W

l UCLA (& IEEE JSSC, 1994)

2.0 mm

1.8 mm

IC Lab

Recent Advance Example 27-th Order Equiripple Gm-C Filter

l 0.4-µm CMOS Technology

l fcutoff = 50 MHz

l THD < 1 %, Power = 100 mW (3 V)

l Hitachi (& IEEE ISSCC, 1997)

IC Lab

Recent Advance Example 3Raised-Cosine Matched Filter for 480 MHz QPSK Demodulator for DBS

Analog Devices (& IEEE ISSCC, 1997)

IC Lab

Recent Advance Example 416th-order BPF for J-PDC

l 2 x 8th-order BPF

l Average of fo : 450.5kHz

l σ of fo : ±1.5kHz

l Tuning Range of fo : 240~770kHz

l 0.35-µm CMOS

l Power : 4.8mA @ 2.5V

l Active Area : 2.5mm2

l Fujitsu

(& IEEE ISSCC, 1999)

IC Lab

Recent Advance Example 5

7th-order Equiripple Group Delay LPF

l 1 + 3 x Biquads

l f3dB : 450.5kHz

l f3dB Accuracy: ±10%

l Group Delay Acc. : ±5%

l 0.25-µm CMOS

l Power Supply : 2.5V

l Chip Area : 3mm2

l Texas Instruments

(& IEEE ISSCC, 1999)