IDEC 혼성 모드 시스템 설계 및 실습

CMOS analog filter design

Changsik YooDepartment of Electronics and Computer Engineering

Hanyang University, Seoul, Koreacsyoo@hanyang.ac.kr

Winter Course of IT SoC Center (Dec. 13-17, 2004)

Introduction

3

Filters at mixed signal system

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

4

Analog filter

• General digital signal processing system

Band limiting

Noise suppression

• Wireless receiver

5

Specification of filter : Magnitude

6

Specification of filter : Phase

• Phase response is also important.– Equal phase for all frequencies is not desired.– Equal delay (group delay) for all frequencies is desired.

• For equal group delay, phase response should be linear function of frequency.

• For certain type of filters, the variation of group delay may be too large to be tolerated for target application.– Group delay equalization is required for some applications such as data

communication system.– All pass filter with group delay equalization

7

Types of filter

Butterworth : Maximally flat gain

Chebyshev :Equiripple in passband

Inverse Chebyshev :Equiripple in stopband

Elliptic (Cauer) :Equiripple in pass/stopband

Bessel :Maximally flat group delay

8

Group delay : Bessel filter

9

Group delay : Chebyshev filter

Passband ripple : 0.5dB Passband ripple : 2dB

10

Equalization of group delay with 2nd order all-pass filter

( ) ( )( ) 2

002

200

2

0 ωωωω

+++−

=sQssQsKsT

11

Classification of analog filters• Basic building block of analog filter : integrator• Analog filters are classified by the type of basic integrators.

– Active-RC / MOSFET-C / Gm-C / Gm-Opamp-C / Switched-capacitor

• According to the operating time domain, – Continuous-time : Active-RC / MOSFET-C / Gm-C / Gm-Opamp-C – Discrete-time : Switched-capacitor / Switched-current

Active-RC MOSFET-C Gm-C

12

Continuous-time filter• Gm-C, active-RC, MOSFET-C filter…• No pre- and post- processing required• Tuning circuits required to have desired frequency characteristics

1NN1N

2N

1

1MM1M

2M

1

asasasabsbsbsb

)s(Y)s(X)s(H

+−

+−

++++++++

=≡

-0.5 0 0.5-5

-4

-3

-2

-1

0

1

2

3

4

5

real f [MHz]

imag

inar

y f [

MH

z]

100 102 104 106 108-120

-100

-80

-60

-40

-20

0

f [Hz]

|H(f)

| [dB

]

13

Discrete-time filter• Switched-capacitor (SC) filter, switched-current (SI) filter• Pre- and post- processing required due to its sampling operation• Desirably accurate frequency characteristics

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

zDzNzH

+

+

++++

++++==

1

14

Comparison of analog filters

Active-RC MOSFET-C Gm-C SC

Unity-gain freq. of integrator 1/RC 1/ronC gm/C (C/C)

Linearity

High-freq. operation

Active circuit Op-amp Op-amp OTA Op-amp

Tools for freq. tuning Variable cap. or resistor MOSFET gm Not required

Variable voltage gain

15

Implementation of high-order filter (1)

Cascading of Biquad Blocks

Hi(z) HN/2(z)H1(z) .... ....X(z) Y(z)

H(z) = H1(z)...Hi(z)...HN/2(z)

( ) ( ) ∏∏== ++

++==

2N

1i 012

2

012

22N

1ii azaza

bzbzbzHzH

• Easy adjustment of frequency characteristics• Pole/zero pair matching• Biquad permutation issue• Gain distribution issue

16

Implementation of high-order filter (2)

RLC Prototype

C1

RS

X(s) Y(s)

RLC3

L2 L4

I2 I4

V1 V3

I0

( )( )( )( )( ) 2L434

3423

2312

1201

S10

sLRIVIsCIIVsLVVI

sCIIVRVXI

−=

−=

−=

−=−=

• Less sensitive to the variations of component values• Easy to obtain• Frequency transformation• Impedance transformation

17

Analog integrator

• Most basic building block |H(ω)|

ω0dB

ωunity

-6dB/oct

<H(ω)

ω0o

-90o

( ) ( )

( ) ( )( ) s

1KsVsVsH

dttvKtv

IN

OUT

inout

==⇒

= ∫

one poleone pole

( )

( )

( ) 90jH

KjH

j1KjH

°−=ω∠⇒ω

=ω⇒

ω=ω

18

Analog integrator : active-RC

Rvin vout

C

+

_A ( ) ( )

( ) s1

RC1

sVsVsH

IN

OUT ⋅−==

• Linearity guaranteed by negative feedback• Large variation of frequency characteristics • Resistive loading on op-amp• High-performance op-amp is required.

19

Analog integrator : MOSFET-C

RON

vin vout

C

+

_A ( ) ( )

( ) s1

CR1

sVsVsH

ONIN

OUT ⋅−==

• Linearity guaranteed by negative feedback but somewhat degraded due to the non-linear resistance of MOSFET

• Large variation of frequency characteristics• Resistive loading on op-amp• High-performance op-amp is required.

20

Analog integrator : Gm-C

vIN voutGm

iout = Gmvin

C

( ) ( )( ) s

1C

GsVsVsH m

IN

OUT ⋅==

• Low-power and high-frequency operation due to the open-loop architecture

• Poor linearity– Linearized transconductor is required.

21

Analog integrator : SC

+-

C2C1 φ2φ1vin vout

φ1φ2

( ) ( )( ) 1

1

2

1

IN

OUT

z1z

CC

zVzVzH −

−

−⋅==

• Accurate frequency characteristics• Linearity guaranteed by negative feedback• Large power dissipation for high frequency operation (fclk >> fsignal)• Anti-aliasing and smoothing filter required

IDEC 혼성 모드 시스템 설계 및 실습

Active-RC / MOSFET-C filter

23

Active-RC / MOSFET-C filter

• Active-RC / MOSFET-C integrator– With ideal operational amplifier ;

• Unity gain frequency of the integrator is determined by RC time constant.– The variation of R and C values does not track with each other and therefore RC

time constant can change as much as 50% due to PVT variations.– Tuning of frequency characteristics is required.

Either automatic or manual

sCRVV in

out −=RC

funity1

=

Rvin vout

C

+

_A

RON

vin vout

C

+

_A

24

Active filter synthesis from passive LC-ladder prototype

• Doubly terminated LC-ladder filter is most widely used as passive filter prototype.– Relatively immune to the variation of component values

LC-ladder

25

Synthesis of active filter from passive prototype

• Element substitution– R : R in active-RC filter– C : C– L : Gyrator

• Signal flow graph (SFG)– Same result as with element substitution– Useful for optimization (e.g. dynamic range optimization)– Will be explained in next slides.

26

Frequency and impedance scaling

• Component values of filter design handbook – For low-pass filter with cut-off frequency = 1rad/sec and source impedance = 1Ω

• For cut-off frequency = fcut-off [Hz] and source impedance = RS [Ω]– Component values should be scaled as ;

ISFS

LL ××→1

ISFSCC 11

××→ ISRR ×→

]rad/s[ 1[Hz]

2 offcutfFS −×= π

][ 1][

ΩΩ

= SRRS

27

Frequency translation

• Low pass → High pass( ωc : cut-off frequency of HP )

• Low pass → Band pass( ω0 : center frequency of BP, B : 3dB bandwidth of BP )

ss cω→

( )LsL

ssL

c

c

ωω

11

=→ ( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛=→

Cs

CssC cc ωω111

Bsss

20

2 ω+→

( )LBsBLsL

BsssL 2

0

20

2 1ω

ω+⎟

⎠⎞

⎜⎝⎛=

+→ ( )CBsB

CsCBs

ssC 20

20

2 1ω

ω+⎟

⎠⎞

⎜⎝⎛=

+→

28

How to obtain prototype low-pass specification

LP prototype

29

Element substitution• Key component for element substitution ; gyrator

gI1 I2

V1 V2

+

_

+

_⎥⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡−

=⎥⎦

⎤⎢⎣

⎡

2

1

2

1

00

VV

gg

II

2gsCZin = 2g

CL =

2gCL =

30

Signal flow graph (SFG)

• Graphical representation of KCL and KVL• Good design tool for analog filter synthesis• Some tips for analog filter synthesis

– Transfer function does not change as long as the loop gain is conserved.This property will be utilized for dynamic range optimization.

– Vertex variables (see the example on the next slide)Source voltageVoltage across shunt branchesCurrent through series branches

31

Design example with SFG : 5th order Chebyshev filter (1)

( )

S

SSS

SSS

GsCVGVGV

IVGVGsC

V

+−

=→

−−=

1

'2

1

211

1

1

SGsLVVV

2

31'2

−=

( )3

'4

'2

3 sCVVGV S −

=

SGsLVVV

4

53'4

−=

L

S

GsCVGV+

=5

'4

5

Snn RIV ⋅='

S

S

GsCG+1

K

SGsL2

1− 3sC

GS

SGsL4

1− L

S

GsCG+5

Vertex variables

32

Design example with SFG : 5th order Chebyshev filter (2)

S

S

GsCG+1

K

SGsL2

1− 3sC

GS

SGsL4

1− L

S

GsCG+5

33

Design example with SFG : 5th order Chebyshev filter (3)1'

max,2max,1 ==VV75.0max,3 =V

65.0'max,4 =V

5.0max, =outV S

S

GsCG+1

K

SGsL2

1−

3sCGS

SGsL4

1−

L

S

GsCG+5

3.15.065.0 ==α 15.165.075.0 ==β 33.175.01 ==γ

Voltage scaling forMaximum dynamic range

34

Operational amplifier (Op-amp) for active-RC filter

R

C

1

0

/1)(

psA

sA+

=

( )( ) 12

01

0

/1/11 pRCsRCApsA

VV

in

out

++++−=

( ) RCARCApppdm

001

1 111

≈++

≈

0101 )1(1 Ap

RCRCAppndm ≈

++≈

1/A0RC p1A0

A0

-90o

-180o

Gain

Phase

0.1*p1A0

1/RC should be in this region.

• The phase shift of an ideal integrator is –90o at the unity-gain frequency which is 1/RC for active-RC integrator.

• Required unity-gain BW of op-amp in active-RC filter > 10/RC

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Gm-C filter

36

Gm-C integrator

• Transconductance (Gm) amplifier

• Gm-C integrator

Low power, high SpeedPoor linearity

Gm+-

ioutvin+

vin-

( ) vvGvGi ininminmout−+ −⋅=⋅≡

Gm+-

ioutvin+

vin-

vout

C

KCL

( )( )

( )( ) ( ) sC

Gsvsv

svsvsv)s(H m

inin

out

in

out =−

=≡ −+

Open-loop characteristics

37

Gm amplifier basics

• Transconductance (Gm) amplifier

Single-ended Fully-differential

• Transconductance amplifier characteristics– Linearity– I/O impedances– Operating (dynamic) range– Frequency characteristics– Electrically programmable Gm value

Gm+-

ioutvin+

vin-

Gm

+-

ioutvin+

vin-

iout

+-

( ) vvGvGi ininminmout−+ −⋅=⋅≡

R , R outin ∞=∞=

38

Gm amplifier : basic differential pair (1)

( )( )2THxin2

2THxin1

Vvv2

i

Vvv2

i

−−β

=

−−β

=

−

+

M1 M2vin+ vin

-

i2i1

ISS

vx

SS21 Iii =+

2in

SSin21out v

2I2v

2iii ∆−

β∆

β=−≡

2inSS

2inSS

inm

VI4

V2I42V

IG∆−β

∆−β⋅

β=

∆∂∆∂

≡

0 ∆Vin=Vin+-Vin

-

+ISS

∆I=I1-I2

-ISS 0

Gm

∆Vin=Vin+-Vin

-

39

Gm amplifier : basic differential pair (2)

Varying β Varying ISS

0 ∆Vin

+ISS

∆I

-ISS

0 ∆Vin

∆I

2in

SSin21out v

2I2v

2iii ∆−

β∆

β=−≡

for large ISS, small β & ∆vin

SSm

inSSout

IG

vIi

β=∴

∆⋅β≈

40

Gm amplifier : differential pair with degeneration resistance (1)

M1 M2vin+ vin

-

i2i1

IBRC IB

MR

VC

iRC

1 2

BR2

BR1

Iii

Iii

C

C

=+

+=CR21 i2ii ⋅=−

( ) 2gs1gsinC

21out

in2gsCR1gsin

vvvR2iii

vvRivvC

−−∆=−≡∴

=+−− −+

( ) ( )( ) 0ii2

i2Vi2Vvv

21

2TH1TH2gs1gs

≈−β=

β+−β+=−for large β and small √i1- √i2

inC

out vR2i ∆⋅≅

( ) ( )THNGSMTHNGS

C VV2G VV

1R −β=⇒−β

≅When RC Implemented by MOSFET

41

Gm amplifier : differential pair with degeneration resistance (2)

Simple output stage Folded-cascode output stage

M1 M2

MGM

VINMVINP

IB IB

VCMFB

VBP2VBP2

VBN1

VBN2

VGM

42

Gm amplifier : differential pair w/ degeneration R and feedback

M1 M2vin+ vin

-

VC

M9

M3 M4

M5 M6

M7 M8

IB1 IB1

IB2 IB2

IB1-io IB1+io

io

VDD

VSS

• Negative feedback loops (M1-M5-M3 & M2-M6-M4) forces constant currents IB1 to flow through M1 and M2 vgs1 = vgs2

• Output currents available through current mirrors (M3-M7 & M4-M8)

43

Gm amplifier using MOS in linear

• Current in linear MOSFET

• Basic principle

• Example

( ) ⎥⎦⎤

⎢⎣⎡ −−β= 2

dsdsTHgsds v21vVvi

( ) ( ) −+ −∝−=−−− inin22 vvBACBCA

VC +_

vinp

+_

vinm

VC

i1 i2

( )

( ) ⎥⎦⎤

⎢⎣⎡ −−β=

⎥⎦⎤

⎢⎣⎡ −−β=

2CCTHinm2

2CCTHinp1

V21VVvi

V21VVvi

( )[ ]Cinminp

21outVvv

iii

−β=

−=

44

Gm-Opamp-C integrator

• Advantages– Op-amp input virtually short

Ease of designing GmSmall Ro allowedSmall parasitic cap. effect

– Large DC Gain

• Disadvantages– Reduced overall bandwidth– Increased power dissipation– Good CMFB required– Increased noise level

GM(s)+

VOUT-

+VIN-

OPA

45

1st order Gm-C filter

Vin(s)Gm1

+-

Gm2+-

Vout(s)

CA

CX

i1

i2

KCL

( ) ( )( ) 0

01

XA

2m

XA

1m

XA

X

in

outs

ksk

CCGs

CCGs

CCC

sVsVsH

ω++

⇐

⎟⎟⎠

⎞⎜⎜⎝

⎛+

+

⎟⎟⎠

⎞⎜⎜⎝

⎛+

+⎟⎟⎠

⎞⎜⎜⎝

⎛+

=≡

( )( )

A1

1X

XA02m

XA01m

Ck1

kC

CCGCCkG

−=

+⋅ω=+⋅=

46

2nd order Gm-C filter : biquad

KCL

Vout(s)Gm2+-

Gm4+-

Gm1+- Gm3

+-

Gm5+-

Vin(s)

CACBCX

AB

KCL

( ) ( )( )

( )

( )20

02

012

2

XBA

2m1m

XB

3m2

XBA

4m2m

XB

5m2

XB

X

in

out

sQ

s

ksksk

CCCGGs

CCGs

CCCGGs

CCGs

CCC

sVsVsH

ω+⎟⎠⎞

⎜⎝⎛ ω+

++⇐

++⎟⎟

⎠

⎞⎜⎜⎝

⎛+

+

++⎟⎟

⎠

⎞⎜⎜⎝

⎛+

+⎟⎟⎠

⎞⎜⎜⎝

⎛+

=≡

47

High-order Gm-C filter with biquads

• 16th order BPF for Japanese PDC– 2 x 8th-order BPF – Average of fo : 450.5kHz– σ of fo : ±1.5kHz– Tuning range of fo : 240~770kHz– 0.35-µm CMOS– Power : 4.8mA @ 2.5V – Active area : 2.5mm2

– Fujitsu ( IEEE ISSCC, 1999)

48

High-order Gm-C filter from LC ladder (1)

• 5th order Elliptic low-pass filter

Differentiator :impossible to implement

49

High-order Gm-C filter from LC ladder (2)

50

High-order Gm-C filter from LC ladder (3)

51

High-order Gm-C filter from LC ladder (4)

52

Effect of finite output resistance

Finite DC gain at BPF and HPFReduced phase (> -90o)

Q decreases

For φE<1o, GmROUT> 57.3 (35dB)

To Resolve,Cascode output stageCompensation technique

|H(ω)|

ω

<H(ω)

ω

ω0ω3dB

-90

0

|H(0)|

φE

0

OUT

OUTm

in

outRsC1

RGvv)s(H

⋅+⋅

=≡

⎥⎦

⎤⎢⎣

⎡⋅ωω

≅φOUTm

0E RG

arctan

OUTm RGQ2

QQ

⋅⋅

−∝∆

53

Effect of parasitic pole of Gm

Increased Phase (< -90o)

Q increases

For φE<1o, ωp> 57.3 ωo

To resolve,Careful designAdvanced processIntentional zero added

|H(ω)|

ω

<H(ω)

ω

ω0

-90

0

|H(0)|

φE

0

ωP

ω3dB

p

m

in

outs11

CG

vv)s(H

ω+⋅=≡

[ ]pE arctan ωω−≅φ

p

0EQ2

QQ

ωω

φ⋅⋅∝∆

54

Effect of parasitic zero of Gm

Decreased Phase (> -90o)

Q decreases

|H(ω)|

ω

<H(ω)

ω

ω0ω3dB

-90

0

|H(0)|

φE

0

ωZ

[ ]zm

inout s1

sCG

vv)s(H ω+⋅=≡ [ ]zE arctan ωω+≅φ

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Automatic tuning of continuous-time filters

56

Automatic tuning

• Frequency characteristics of continuous-time filter such as Gm-C and active-RC can vary as much as +/-50% due to process, voltage, and temperature variations.

• Some kind of automatic tuning scheme is required to get the desired frequency characteristics.

• Direct tuning– Directly measure the frequency characteristics of the filter and tune them till the

desired characteristics are obtained.– Tuning at power-up or during non-active period

• Master-slave tuning– Measure the frequency characteristics of tuning master which is built with the

same building blocks as the filter and tune the master till the desired characteristics are obtained. Then, the slave filter will have the desired characteristics as well if the master and slave filter match well.

57

Direct tuning (1)

( IEEE Tran. CAS-II, pp. 755-, 2003)

Gm-C biquad

Frequency and Q-factor are tuned by making

58

Direct tuning (2)

( IEEE Tran. CAS-II, pp. 755-, 2003)

59

Concept of master-slave tuning

• Tuning master – Voltage controlled oscillator (VCO) or voltage controlled filter (VCF)

implemented with the same integrators as in slave filter

• Frequency tuning loop– Cut-off frequency

• Phase tuning loop– Phase shift of integrator

60

VCO based tuning (1)

• Oscillation frequency is determined by time constant of the integrators (RC).– By tuning the oscillation frequency to fref, RC time

constant can be controlled.– Frequency tuning loop = PLL

61

VCO based tuning (2)

• Phase lead of integrator means the pole is in LHP.– Oscillation amplitude decreases exponentially.

• Phase lag of integrator means the pole is in RHP.– Oscillation amplitude increases exponentially.

• No phase error in integrator– Constant oscillation amplitude

• Phase tuning loop– Amplitude locked loop (ALL)

62

VCF based tuning (1)

• Second order biquad has low-pass and band-pass outputs.

63

VCF based tuning (2)

• Frequency tuning

– If ωref=ω0,

The phase difference between input and output is 90o.XOR gate is used to detect the phase difference.

• Phase tuning

– After frequency tuning is completed, ωref=ω0.

Phase error appears as the gain error, that is, error in Q value.

64

Single integrator based tuning (1)

• Basic element of analog filter is integrator.– Why don’t we use an integrator as a tuning master?

• Transfer function of integrator– Active-RC filter :

– Gm-C filter :

• Frequency tuning– Unity gain frequency of the master integrator is controlled, then the integrators

in slave filter is also tuned to correct unity gain frequencies.

• Phase tuning– Phase shift at the unity gain frequency is tuned to -90o.

( )RCj

jHω

ω 1=

( )Cj

gjH m

ωω =

65

Single integrator based tuning (2)

• Implementation in Gm-C filter– Frequency tuning loop :

gm is tuned till the gain at ωref is 1.Amplitudes of input and output are detected by the full wave rectifiers RECT1 and RECT2, respectively.

66

Single integrator based tuning (3)

• Implementation in Gm-C filter– Phase tuning loop :

Time constant of phase tuning loop is set to be much larger than frequency tuning loop so the frequency tuning completed first.Phase difference between input and output is detected by XOR gate and tuned to be 90o.

67

How to give tunability to active-RC filter

R

C• Frequency tunability can be given by ① Resistor array② Capacitor array③ Resistor and capacitor array④ MOSFET in series with passive resistor

• Phase tunability– Compensation of non-ideal phase shift of op-amp by RHP or LHP zero

① ②

④

IDEC 혼성 모드 시스템 설계 및 실습

Design exercise : Active-RC filter

69

Lab. 1 : Synthesis of active-RC filter from passive proto

RS C1 L2 C3 RL

1 1 2 1 1

• Design target– Cut-off frequency = 1.25MHz– Draw a block diagram of fully differential active-RC filter

• Optimize the dynamic range using signal flow graph• For SFG, choose VS, V1, V2’=RS*I2, and V3 as vertex variables.• Set RS=20kΩ.

70

Lab. 2 : Design of fully differential op-amp

• Design target– DC gain > 70dB– Phase margin > 45degree with 5pF load capacitance– VDD=2.5V– Unity gain frequency > 100MHz– CMFB for 1st and 2nd stages

71

Lab. 3 : Design of active-RC filter

• Design a fully differential active-RC filter using the results of lab. 1 and 2.

• See if the frequency characteristic is the same as the passive prototype (of course, except for the cut-off frequency).

• Apply a two-tone sinusoid of 1MHz and 1.25MHz and see the output spectrum.– By varying the input amplitude, you can find the in-band iIP3.

• Apply a two-tone sinusoid of 1.5MHz and 2.5MHz and see the output spectrum.– By varying the input amplitude, you can find the out-of-band iIP3.