ee 508 lecture 4 - class.ece.iastate.educlass.ece.iastate.edu/ee508/lectures/ee 508 lect 25 fall...

EE 508EE 508 Lecture 25Lecture 25

Integrator Design

Parasitic Capacitances on Floating NodesParasitic Capacitances on Floating Nodes

P1

P2

Parasitic capacitances ideally have no affect on filter when on a non-floating node but directly affect transfer function when they appear on a

floating node

Parasitic capacitances are invariably large, nonlinear, and highly process dependent in integrated filters. Thus, it is difficult to build

accurate integrated filters if floating nodes are present

Generally avoid floating nodes, if possible, in integrated filters

Review from last time

VOUT

VIN

R3 R1 R2

C1

C2

C1

C2

R2R1

VIN

VOUTK

R3

Sallen-Key Type (Dependent Sources)

Infinite Gain Amplifiers

Integrator Based Structures

Which type of Biquad

is really used?Integrator-based structures with no floating

nodes dominantly used in integrated filters

Some high-frequency or programmable

integrated filters with floating nodes are used


Filter Design/Synthesis ConsiderationsFilter Design/Synthesis Considerations

( ) 1 2 mT s T T T= ii

I1(s)

Integrator

I2(s)

Integrator

I3(s)

Integrator

I4(s)

Integrator

Ik(s)

IntegratorVIN

VOUTIk-1(s)

Integrator

a2a1

+

Cascaded Biquads

Leapfrog

Multiple-loop Feedback – One type shown

Observation: All filters are comprised of summers, biquads

and integrators

And biquads

usually made with summers and integrators

Integrated filter design generally focused on design of integrators, summers, and amplifiers (Op Amps)

Will now focus on the design of integrators, summers, and op amps


Basic Filter Building BlocksBasic Filter Building Blocks (particularly for integrated filters)(particularly for integrated filters)

• Integrators

• Summers

• Operational Amplifiers

Integrator Characteristics of Interest

0Is

( ) 0II s = s

( ) 0II jω = ω

( )I∠ 0jω = -90

Unity Gain Frequency = 1

Properties of an ideal integrator:

Gain decreases with 1/ω

Phase is a constant -90o

( )0I Ij = 1

How important is it that an integrator have all 3 of these properties?

Integrator Characteristics of Interest

− 0Is

0Is+

( ) =20

2 20 0

- IT s

s + αI s + I

0 0ω = Iα1Q =

0Is

( ) 0II s = s

( ) 0II jω = ω ( )I∠ 0jω = -90

How important is it that an integrator have all 3 of these properties?

Consider a filter example:

In many (most) applications it is critical that an integrator be very nearly ideal(in the frequency range of interest)

( )0I Ij = 1

Band edges proportional to I0Phase critical to make Q expression valid

Some integrator structuresSome integrator structures

VOUT

CVIN

R ( )I s = −1

RCs

Are there other integrator structures?

Inverting Active RC Integrator

I

I=

OUT m IN

OUT OUT

= - g V1V

sC

( )I s = − mgsC 0I = mg

C

Termed an OTA-C or a gm-C integrator

Some integrator structuresSome integrator structuresAre there other integrator structures?

I

I= −

OUT m IN

OUT OUT

= g V1V

sC

( )I s = − mgsC

Termed a TA-C integrator

VOUT

CVIN RMOS

VC

( )I s = −MOS

1sCR

Termed MOSFET-C integrator

Some integrator structuresSome integrator structuresAre there other integrator structures?

INI−

=

2 1

2 1OUT

1V = VsC

V - VIR

( ) OUT

IN

II sI

= = −1

sRC

Termed active RC current-mode integrator

• Output current is independent of ZL

• Thus output impedance is ∞

so provides current output

Some integrator structuresSome integrator structures

( )I s = −1

sRC

VOUT

CVIN

R

VOUT

CVIN RMOS

VC( )I s = −

1sRC

( )I s = −MOS

1sR C

( )I s = − mgsC

( )I s = − mgsC

There are many different ways to build an inverting integrator

There are other useful integrator structures (some will be introduced later)

Integrator FunctionalityIntegrator Functionality

VOUT

CVIN

R( )I s = −

1sRC

1OUT INk

k

1V VCR s

n

k== − ∑

OUTdiffVINdiffV

OUTdiff INdiff1V V

CRs= −

CVIN

R VOUTRA

RA

( )I s =1

sRC

VIN

VOUTR

C

RF

FOUT IN

F

RRV V

1+CR s= −

Summing Integrator

Fully Differential Integrator

Noninverting Integrator

Lossy

Integrator

Basic Active RC Inverting Integrator

Many different types of functionality from basic inverting integratorSame modifications exist for other integrator architectures

Integrator-Based Filter Design

− 0Is

0Is+XIN

α

XO1

XO2

VOUT

CVIN RMOS

VC

Any of these different types of integrators can be used to build

integrator-based filters

Example –

OTA-C Tow Thomas Biquad

− 0Is

0Is+XIN

α

XO1

XO2

1OUT 2 m2V sC =g V+ −1 1 m1 OUT m3 IN m4 1V sC = -g V g V g V

( )+OUT m3 m2

2IN 1 2 m4 2 m1 m2

V g g=V s C C sg C +g g

⎛ ⎞⎜ ⎟⎝ ⎠

⎛ ⎞⎛ ⎞+⎜ ⎟⎜ ⎟

⎝ ⎠⎝ ⎠

2m3 m

2mOUT

2IN 2 m4 m m

2m

g gg CV =

V g g gs s +g C C

Assume gm1

=gm2

=gm

, C1

=C2

=C

20

200Q

⎛ ⎞⎜ ⎟⎝ ⎠

⎛ ⎞+⎜ ⎟

⎝ ⎠

m3

mOUT

2IN

g ωgV =

V ωs s +ω

0mgω =

Cm

m4

gQ = g

express as

where

0Is

0Is + α

0Is

−

0Is + α

−

0kIs

1

OkOUT

IXs

n

k=

±= ∑

0kk

Is+α 1

OkOUT

k

IXs+α

n

k=

±= ∑

0Is

IN+X

IN-X

OUT+X

OUT-X

( )OUT OUT IN IN+ + + +0IX X X X

s− = −

0IsINdiffX OUTdiffX

OUTdiff INdiff0IX Xs

=

Basic Integrator Functionality

Basic Integrator FunctionalityBasic Integrator Functionality

0Is

OUTIN 0Is

− OUTIN

Noninverting Inverting

•

An inverting/noninverting integrator pair define a family of integrators•

All integrator functional types can usually be obtained from the

inverting/noninverting integrator pair

•

Suffices to focus primarily on the design of the inverting/noninverting integrator pair since properties of class primarily determined by properties of integrator pair

Example Example ––

Basic OpBasic Op--Amp Feedback IntegratorAmp Feedback Integrator

VOUT

CVIN

R

CVIN

R VOUTRA

RA

Inverting Integrator of Family Noninverting Integrator

VOUT

CVIN1

R1

VINn

Rn

Summing Inverting Integrator

1OUT INk

k

1V VCR s

n

k== − ∑

OUT IN1V V

CRs= − OUT IN

1V VCRs

=



VOUT

CVIN

R

Inverting Integrator of Family VOUT

CVIN1

R1

VINn

Rn


1OUT INk

k

1V VCR s

n

k== − ∑

OUT IN1V V

CRs= −

Lossy


1

1

nINk

kOUT

n

R VR

V1+CR s

n

k

−

== −∑

VOUT

CVIN1

R1

VINnRn

RF

1

FIN k

kO U T

F

R VR

V1 + C R s

n

k == −∑



VOUT

CVIN

R

Inverting Integrator of Family

OUT IN1V V

CRs= −

Lossy


VOUT

CVIN1

R1

VINnRn

RF

1

FIN k

kO U T

F

R VR

V1 + C R s

n

k == −∑

VIN

VOUTR

C

RF

Lossy

Inverting Integrator

FO U T IN

F

RRV V

1 + C R s= −



VOUT

CVIN

R


OUT IN1V V

CRs= −

Balanced Differential Inverting Integrator

C

R

C

R

IN+V

IN-V

OUT+V

OUT-V

INdiffV OUTdiffV Axis of Symmetry

OUT IN1V V

CRs+ += −

OUT IN1V V

CRs− −= −

OUTdiff INdiff1V V

CRs= −



VOUT

CVIN

R


OUT IN1V V

CRs= −

Fully Differential Inverting Integrator

OUTdiff INdiff1V V

CRs= −OUTdiffVINdiffV

Integrator TypesIntegrator Types

0Is

VOUTVIN

Voltage Mode

oOUT IN

IV Vs

=

0Is

IOUTIIN

Current Mode

oOUT IN

II Is

=

0Is

VOUTIIN

Transresistance Mode

oOUT IN

IV Is

=

0Is

IOUTVIN

Transconductance Mode

oOUT IN

II Vs

=

Will consider first the Voltage Mode type of integrators

Voltage Mode IntegratorsVoltage Mode Integrators

•

Active RC (Feedback-based)

•

MOSFET-C (Feedback-based)

•

OTA-C•

TA-C

•

Switched Capacitor•

Switched Resistor

Sometimes termed “current mode”

Will discuss later

Active RC Active RC Voltage Mode IntegratorVoltage Mode Integrator

OUT IN1V V

CRs= −

•

Limited to low frequencies because of Op Amp limitations•

No good resistors for monolithic implementationsArea for passive resistors is too large at low frequencies

Some recent work by Haibo

Fei

shows promise for some audio frequency applications•

Capacitor area too large at low frequencies for monolithic implementatins•

Active devices are highly temperature dependent, proc. dependent, and nonlinear•

No practical tuning or trimming scheme for integrated applications with passive resistors

MOSFETMOSFET--C C Voltage Mode IntegratorVoltage Mode Integrator

•

Limited to low frequencies because of Op Amp limitations•

Area for RMOS

is manageable !•

Active devices are highly temperature dependent, process dependent•

Potential for tuning with VC•

Highly Nonlinear (can be partially compensated with cross-coupled input

VOUT

CVIN RMOS

VC

MOSOUT IN

1V VCR s

= −

A Solution without a Problem

MOSFETMOSFET--C C Voltage Mode IntegratorVoltage Mode Integrator

•

Improved Linearity •

Some challenges for implementing VC

VOUT

CVIN RMOS

VC

MOSOUT IN

1V VC R s

= −

Still A Solution without a Problem

MOSOUT IN

1V VC R s

= −

OTAOTA--C C Voltage Mode IntegratorVoltage Mode Integrator

•

Requires only two components•

Inverting and Noninverting structures of same complexity•

Good high-frequency performance•

Small area•

Linearity is limited (no feedback in integrator)•

Susceptible to process and temperature variations•

Tuning control can be readily added

Widely used in high frequency applications

NoninvertingInverting

VOUTVIN

C

gm

= mOUT IN

gV VsC

= − mOUT IN

gV VsC


Programmable Integrator

= mOUT IN

gV VsC

( )=m ABCg f I

= mOUT IN

gV VsC


Lossy

Integrator

( )( ) ( )

OUT m FIN F

V s g R = V s 1+s R C

But RF

is typically too large for integrated applications

= mOUT IN

gV VsC

VOUT

VIN

C

gm

RF

ee 508 lecture 4 - class.ece.iastate.educlass.ece.iastate.edu/ee508/lectures/ee 508 lect 25 fall...

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