ee 508 lecture 4 - iowa state universityclass.ece.iastate.edu/ee508/lectures/ee 508 lect 25 fall...

EE 508

Lecture 25

Integrator Design

Parasitic Capacitances on Floating Nodes

CP1

CP2

Z1

Z2

Zk

CP

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

Floating Node

Not Floationg Node

Review from last time

VOUT

VIN

R3 R1 R2

C1

C2

C1

C2

R2

R1

VIN

VOUT-K

C1

C2

R2

R1

VIN

VOUTK

R3

R0

R1 RQ

RA

RAR2

C1 C2

VOUT

VIN

Sallen-Key Type (Dependent Sources)

Infinite Gain Amplifiers

Integrator Based Structures

Which type of Biquad is really used? Floating NodeNot Floationg Node


Filter Design/Synthesis Considerations

T1(s)

Biquad

T2(s)

Biquad

Tk(s)

Biquad

VOUTVIN Tm(s)

Biquad

1 2 mT s T T T

I1(s)

Integrator

I2(s)

Integrator

I3(s)

Integrator

I4(s)

Integrator

Ik(s)

Integrator

VIN

VOUTIk-1(s)

Integrator

a2a1

T1(s)

Biquad

T2(s)

Biquad

Tk(s)

Biquad

αF

XOUTXIN

α1α2 αk

α0

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 Blocks (particularly for integrated filters)

• Integrators

• Summers

• Operational Amplifiers

Integrator Characteristics of Interest

0I

s

XOUTXIN

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

0I

s

0I

sXIN

α

XO1

XO2

20

2 20 0

- IT s

s + αI s + I

0 0ω = I

1Q =

0I

s

XOUTXIN 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 I0

Phase critical to make Q expression valid

Some integrator structures

VOUT

C

VINR

I s 1

RCs

Are there other integrator structures?

Inverting Active RC Integrator

VOUT

VIN

C

gm

IOUT I

I

OUT m IN

OUT OUT

= - g V

1V

sC

I s mg

sC0I mg

C

Termed an OTA-C or a gm-C integrator

0I1

RC



C

VOUT

VINgm

IOUT

VBB

I

I

OUT m IN

OUT OUT

= g V

1V

sC

I s mg

sC

Termed a TA-C integrator

VOUT

C

VINRMOS

VC

gmV1C

VOUT

V1

VIN

IOUT

I s MOS

1

sCR

Termed MOSFET-C integrator

0I mg

C

0IFET

1

R C



INI

2 1

2 1OUT

1V = V

sC

V - VI

R

OUT

IN

II s

I

1

sRC

Termed active RC current-mode integrator

IIN

IOUT

R

C

ZL

V1

V2

• Output current is independent of ZL

• Thus output impedance is ∞ so provides current output

0I1

RC


I s 1

sRC

IIN

IOUT

R

C

ZL

V1

V2

C

VOUT

VINgm

IOUT

VBB

VOUT

C

VINR

VOUT

C

VINRMOS

VC

VOUT

VIN

C

gm

IOUT

I s 1

sRC

I s MOS

1

sR C

I s mg

sC

I s mg

sC

There are many different ways to build an inverting integrator

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

Integrator Functionality

VOUT

C

VINR

I s 1

sRC

VOUT

C

VIN1R1

VINn

Rn

1OUT INk

k

1V V

CR s

n

k

C

C

R

R

OUTdiffVINdiffV +

-+-

Axis of

Symmetry

OUTdiff INdiff

1V V

CRs

C

VINR VOUTRA

RA

I s 1

sRC

VIN

VOUTR

C

RF

F

OUT INF

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 integrator

Same modifications exist for other integrator architectures

Integrator-Based Filter Design

0I

s

0I

sXIN

α

XO1

XO2

IIN

IOUT

R

C

ZL

V1

V2

VOUT

VIN

C

gm

IOUT

C

VOUT

VINgm

IOUT

VBB

VOUT

C

VINRMOS

VC

VOUT

C

VINR

I1(s)

Integrator

I2(s)

Integrator

I3(s)

Integrator

I4(s)

Integrator

Ik(s)

Integrator

VIN

VOUTIk-1(s)

Integrator

a2a1

Any of these different types of integrators can be used to build integrator-based filters

T1(s)

Biquad

T2(s)

Biquad

Tk(s)

Biquad

VOUTVIN Tm(s)

Biquad

T0(s)First-

Order

Are new integrators still being invented?

Example – OTA-C Tow Thomas Biquad

VOUT

VIN

C

gm

IOUT

0I

s

0I

sXIN

α

XO1

XO2

1OUT 2 m2V sC =g V

C1

gm1

VOUT

C2

gm2

gm3

gm4

VIN

V1

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

2

m3 m2

mOUT

2IN 2 m4 m m

2

m

g g

g CV=

V g g gs s +

g C C

Assume gm1=gm2=gm, C1=C2=C

2

0

200

Q

m3

mOUT

2IN

gω

gV=

V ωs s +ω

0 mg

ω = C

m

m4

gQ =

g

express as

where

0I

s

XOUTXIN

0I

s + α

XOUTXIN

0I

s

XOUTXIN

0I

s + α

XOUTXIN

XOUT

XIN1

XINk0kI

s

XINn

1

OkOUT

IX

s

n

k

XOUT

XIN1

XINk0k

k

I

s+

XINn

1

OkOUT

k

IX

s+α

n

k

Noninverting Inverting

Lossy Noninverting Lossy Inverting

Summing (Multiple-Input) Inverting/Noninverting

Summing (Multiple-Input) Lossy Inverting/Noninverting

0I

s

Balanced Differential

IN+X

IN-X

OUT+X

OUT-X

OUT OUT IN IN+ + + +0IX X X X

s

0I

s

Fully Differential

INdiffX OUTdiffX

+ +

- -

- -

+ ++ +- - OUTdiff INdiff

0IX Xs

Basic Integrator Functionality

Basic Integrator Functionality

0I

s

XOUTXIN 0I

s

XOUTXIN


• 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 – Basic Op-Amp Feedback Integrator

VOUT

C

VINR

C

VINR VOUTRA

RA

Inverting Integrator of Family Noninverting Integrator

VOUT

C

VIN1R1

VINn

Rn

Summing Inverting Integrator

1OUT INk

k

1V V

CR s

n

k

OUT IN1

V VCRs

OUT IN

1V V

CRs


VOUT

C

VINR

Inverting Integrator of Family VOUT

C

VIN1R1

VINn

Rn

Summing Inverting Integrator

1OUT INk

k

1V V

CR s

n

k

OUT IN1

V VCRs

VOUT

C

VIN1R1

VINn

Rn

Rn-1VINn-1

Lossy Summing Inverting Integrator

1

1

nINk

kOUT

n

RV

RV

1+CR s

n

k

VOUT

C

VIN1R1

VINn

RnRF

1

FINk

kOUT

F

RV

RV

1+CR s

n

k


VOUT

C

VINR

Inverting Integrator of Family

OUT IN1

V VCRs

Lossy Summing Inverting Integrator

VOUT

C

VIN1R1

VINn

RnRF

1

FINk

kOUT

F

RV

RV

1+CR s

n

k

VIN

VOUTR

C

RF

Lossy Inverting Integrator

F

OUT INF

RRV V

1+CR s


VOUT

C

VINR


OUT IN1

V VCRs

Balanced Differential Inverting Integrator

C

R

C

R

IN+V

IN-V

OUT+V

OUT-V

+

-

+

-

INdiffV OUTdiffVAxis of

Symmetry

OUT IN

1V V

CRs

OUT IN

1V V

CRs

OUTdiff INdiff

1V V

CRs


VOUT

C

VINR


OUT IN1

V VCRs

Fully Differential Inverting Integrator

OUTdiff INdiff

1V V

CRs

C

C

R

R

OUTdiffVINdiffV +

-+-

Axis of

Symmetry

Integrator Types

0I

s

VOUTVIN

Voltage Mode

oOUT IN

IV V

s

0I

s

IOUTIIN

Current Mode

oOUT IN

II I

s

0I

s

VOUTIIN

Transresistance Mode

oOUT IN

IV I

s

0I

s

IOUTVIN

Transconductance Mode

oOUT IN

II V

s

Will consider first the Voltage Mode type of integrators

Voltage 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 Voltage Mode Integrator

VOUT

C

VINR

OUT IN1

V VCRs

• Limited to low frequencies because of Op Amp limitations

• No good resistors for monolithic implementations Area 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

MOSFET-C Voltage 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

C

VINRMOS

VC

MOS

OUT IN1

V VCR s

A Solution without a Problem

MOSFET-C Voltage Mode Integrator

• Improved Linearity

• Some challenges for implementing VC

VOUT

C

VINRMOS

VC

MOS

OUT IN1

V VC R s

Still A Solution without a Problem

MOS

OUT IN1

V VC R s

VOUT

C

VIN RMOS

VC

VC

OTA-C Voltage 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


V O U T

V IN

C

gm

m

O U T IN

gV V

sC

VOUTVIN

C

gm

m

O U T IN

gV V

sC


Programmable Integrator

VOUTVIN

C

gm

IABC

m

O U T IN

gV V

sC

m A B Cg f I

VOUTVIN

C

gm

m

O U T IN

gV V

sC


Lossy Integrator

OUT m F

IN F

V s g R =

V s 1+s R C

But RF is typically too large for integrated applications

VOUTVIN

C

gm

m

O U T IN

gV V

sC

VOUT

VIN

C

gm

RF

End of Lecture 25

ee 508 lecture 4 - iowa state universityclass.ece.iastate.edu/ee508/lectures/ee 508 lect 25 fall...

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