Accurate amplificationAccurate amplification...Accurate amplificationAccurate amplification ET8016-2009 2 Right choice Orthogonalization Optimization Right choice Orthogonalization

ET8016-2009 1

Structured Electronic DesignStructured Electronic Design

Accurate amplificationAccurate amplification

ET8016-2009 2

Right choice

Orthogonalization

Optimization

Right choice

Orthogonalization

Optimization

ET8016-2009 3

• Clear definition of the function

• The criteria

NNSBC +

= log2

The criteriaThe criteria

ET8016-2009 4

bandwidth – noise – distortionbandwidth – distortion - noisenoise - bandwidth – distortionnoise – distortion - bandwidthdistortion - noise – bandwidthdistortion – bandwidth - noise


Design procedure?Design procedure?

Design?Specs verification

ET8016-2009 5

Structured design methodStructured design method

Orthogonality

Hierarchy

ET8016-2009 6

Specs Verification

HierarchyHierarchy

1MΩ

+

_ +

_

4.7MΩ 1MΩ

1nFvout

1MΩ

4.7MΩ

1MΩ

1nFvout

Q1Q2

Rs

Rt

Rl

ET8016-2009 7

What is an amplifier?What is an amplifier?

ET8016-2009 8

Information from source to load

• Signal power is enlarged

• Information stays unaltered

A,B,C,D indicate gainA,B,C,D constantA,B,C,D accurately known


A BC D

Accurate amplificationAccurate amplification

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛=⎟⎟

⎠

⎞⎜⎜⎝

⎛

out

out

in

in

iv

DCBA

iv

ET8016-2009 9

ClassificationClassification1. A,B,C,D indicate gain2. A,B,C,D constant3. A,B,C,D accurately known

1. A,B,C,D indicate gain2. A,B,C,D constant3. A,B,C,D accurately known

11

11

11

22

22

22

33

3333

33

33

33

33

33

ET8016-2009 10

Accurate elements Elements with gain

AccuracyGain

⎟⎟⎠

⎞⎜⎜⎝

⎛DCBA

⎟⎟⎠

⎞⎜⎜⎝

⎛DCBA

⎟⎟⎠

⎞⎜⎜⎝

⎛DCBA ( ) ( )

( ) ( )⎟⎟⎠⎞

⎜⎜⎝

⎛,....,,,,....,,,,....,,,,....,,,

cccc

cccc

VITDVITCVITBVITA

ωωωω

( ) ( )( ) ( )⎟⎟⎠

⎞⎜⎜⎝

⎛,....,,,,....,,,,....,,,,....,,,

dddd

dddd

VITDVITCVITBVITA

ωωωω

Classification of available componentsClassification of available components

( ) ( )( ) ( )⎟⎟⎠

⎞⎜⎜⎝

⎛,....,,,,....,,,,....,,,,....,,,

dddd

dddd

VITDVITCVITBVITA

ωωωω

ET8016-2009 11

The big question…The big question…

How can we combine the propertiesof the two orthogonal sets

in one system in a perfect way?

How can we combine the propertiesof the two orthogonal sets

in one system in a perfect way?



ET8016-2009 12

2R

1R

yU xU

2

1 2

Rx yR RU U+=

Accurate reduction

ET8016-2009 13

2R

1R

yU xU inU

1 2

2

R Ry inRU U+=

Accurate reduction

2

1 2

Rx yR RU U+=

Accurate amplification

ET8016-2009 14

2R

1R

inUNorrator

Nullator

1 2

2

R Ry inRU U+=

yU

Accurate amplification

ET8016-2009 15

• Nullor + passive components ⇒ accurate amplifier

• The perfect method

• Nullor = simplest model for active circuit

Negative feedbackNegative feedback

1 2

2

R Rout inRU U+=

2R

1R inUoutU

ET8016-2009 16

HierarchyHierarchy

Passive elements Active elementsSpecs verification

• Accurate reduction • Gain

• ONLY passive elements • ONLY active elements

Only!!Only!!

ET8016-2009 17

1) design of feedback network with nullor in the loop

2) design of the active circuit

Nullor: absolute design freedom

• No noise

• No distortion

• No bandwidth limitations

Amplifier design in two orthogonal stepsAmplifier design in two orthogonal steps

ET8016-2009 18

The general negative feedback systemThe general negative feedback system

sE cE

0tA

β

LEiEA

00

0

c

s

i

E

s E

c

Lt

EA

E

E

Eβ

=

=

=

=0L c

i s c

c i

t sE EE E βE

E

AE

A

E

= +

= +=

0tA : The direct transfer

ET8016-2009 19

sE cE

0tA

β

LEiEA

01

1tL

ts

AE AAE A

ββ β⎛ ⎞

= = + ⎜ ⎟−⎝ ⎠

The overall gain AtThe overall gain At

ET8016-2009 20

The loopgain LThe loopgain L

sE cE

0tA

β

LEiEA

L

01

1L

t ts

E AA AE A

ββ β⎛ ⎞

= = + ⎜ ⎟−⎝ ⎠0

11t

Lt

s

LL

AEAE β

⎛ ⎞= = + ⎜ ⎟−⎝ ⎠

ET8016-2009 21

0lim1

L tt tA AAβ→∞

∞= − =

The asymptotic gain At∞The asymptotic gain At∞

01

1tL

ts

LL

AEAE β

⎛ ⎞= = + ⎜ ⎟−⎝ ⎠sE cE

0tA

β

LEiEA

L

ET8016-2009 22

sE cE

0tA

β

LEiEA

L

The asymptotic gain modelThe asymptotic gain model

01

tt AAβ∞ = −

0

1 1tt

tLA A

L LA

∞

−= +

− −0

1 (!)tA β−

ET8016-2009 23

LLAA tt −

−= ∞ 1

Passive elements Active elementsNullorNullor

Hierarchy, OrthogonalityHierarchy, Orthogonality

sE cE

0tA

β

LEiEA

L 01

tt AAβ∞ = −

ET8016-2009 24

Amplifier design in two steps

1) design of with nullor in the loop

2) design of the nullor approximation

Nullor: absolute design freedom• No noise• No distortion• No bandwidth limitations

LLAA tt −

−= ∞ 1

∞tA

ET8016-2009 25

Nullor design

Hierarchical designHierarchical design

LLAA tt −

−= ∞ 1

∞tA

First passive elements Then active elementsSpecs verification

ET8016-2009 26

More detailed hierarchy..More detailed hierarchy..

Feedback network Nullor designSpecs verification

Specs 1 2 verificationC1 C2 C3 B

NNSBC +

= log2bandwidth – noise – distortionbandwidth – distortion - noisenoise - bandwidth – distortionnoise – distortion - bandwidthdistortion - noise – bandwidthdistortion – bandwidth - noise


ET8016-2009 27

Determination amplifier type:

• Specification input and output quantities

• Specification of the transfer

What may have influence and what not?

Step 1Step 1

What may have influence and what not?What may have influence and what not?

ET8016-2009 28

Specification input and output quantitiesSpecification input and output quantities

dQidt

=QvC

=C C

ET8016-2009 29

Specification of the transferSpecification of the transfer

V V V I I V I I

A B C D

ET8016-2009 30

Step 1: the right choiceStep 1: the right choice

• Feed back network determines transfer

• Source impedance no influence

• Load impedance no influence

• Best nullor implementation• No and no influence on L by source and load impedance

√

0tA

ET8016-2009 31

V V

VV

V I

VI

I V

IV

I I

II

v A v B i C iD

Best nullor implementationBest nullor implementation

ET8016-2009 32

Technological limitsTechnological limits

ET8016-2009 33

V V

VV

V I

VI

I V

IV

I I

II

Nullor implementation close to technologyNullor implementation close to technology

v Bv B v B v B

Zs

Zl

Zs

Zl

• Remember the best choice• Know the penalty for the others!• Remember the best choice• Know the penalty for the others!

ET8016-2009 34

The active part is a nullorThe active part is a nullor

Step 2, the feed back networkStep 2, the feed back network

V V V I I V I I

A B C D

ET8016-2009 35

Ideal feedback componentsIdeal feedback components

Transformer Gyrator

010

n

n

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

• No power dissipation• No noise production• No noise enlargement• No excess voltages or currents• Galvanic separation


01 0

R

R

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

ET8016-2009 36

Voltage amplifierVoltage amplifier

LRinv sR

n1• No power dissipation• No noise production• No noise enlargement• No excess voltages or currents• Galvanic separation


ET8016-2009 37

LR

invLR

invLR

inv

n1

Noise influenceNoise influence



ET8016-2009 38

Noise influenceNoise influence

LR

inv

n1

LR

inv

n1

LR

inv

n 11n

1

LR

inv

n1• No power dissipation• No noise production• No noise enlargement• No excess voltages or currents• Galvanic separation


ET8016-2009 39

Noise influence impedance networkNoise influence impedance network

LR

invLR

inv

n1

ET8016-2009 40

Trans-impedance amplifierTrans-impedance amplifier

1R

sI sR LR outV



ET8016-2009 41

Ideal versus reality: transformerIdeal versus reality: transformer

Not always feasible• Parasitic impedances• Limited frequency range• Non-linearity (saturation)• Technological problems

ET8016-2009 42

Ideal versus reality: gyratorIdeal versus reality: gyrator

i C

iC

• Needs controlled sources (active elements)• Practical implementation produces noise• Non-linearity• Bandwidth restrictions

ET8016-2009 43

“Poor mans” gyrator“Poor mans” gyrator

iv

Feature lost : No power dissipationFeature lost : No noise productionFeature lost : No noise enlargementFeature lost : No excess voltages or currents

☺ Galvanic separation

ET8016-2009 44

“Very poor mans” gyrator“Very poor mans” gyrator

Feature lost: No power dissipationFeature lost : No noise productionFeature lost : No noise enlargementFeature lost : No excess voltages or currentsFeature lost : Galvanic separationDirect connection between input and output node

iv

ET8016-2009 45

Why use the ideal transformers and gyrator?Why use the ideal transformers and gyrator?

Absolute minimum of:

• Power consumption

• Current swing

• Voltage swing

• Noise If already this it not enough…..

√ √

(The specifications)

(The specifications)

ET8016-2009 46

Z1

Z2

Z

v

iv

v

Z

Z1

Z2i

i v

i

Common feed back networksCommon feed back networks

ET8016-2009 47

ET8016-2009 48

LR

inv

SR

Common feed back networks : Reduced `flexibilityCommon feed back networks : Reduced `flexibility

NNSBC +

= log2

LR

inv

SR

LR

inv

n1

SR

LR

n1

SRinv

Non-inverting voltage amplifier

Inverting voltage amplifier Non-inverting voltage amplifier

ET8016-2009 49

Impedance networks: • Produce noise (R)• Enlarge contribution existing noise sources• Dissipate power (R)• Create excess voltage or current• Galvanic coupling

Impedance networks: • Produce noise (R)• Enlarge contribution existing noise sources• Dissipate power (R)• Create excess voltage or current• Galvanic coupling

Negative feedback networksNegative feedback networks

ET8016-2009 50

A,B,C,D < 1A,B,C,D constantA,B,C,D accurately known

A,B,C,D < 1A,B,C,D constantA,B,C,D accurately known

Information from source to load

• Signal power is enlarged

• Information stays unaltered

A BC D

Accurate AmplificationAccurate Amplification

ET8016-2009 51


AccuracyGain

⎟⎟⎠

⎞⎜⎜⎝

⎛DCBA

⎟⎟⎠

⎞⎜⎜⎝

⎛DCBA

⎟⎟⎠

⎞⎜⎜⎝

⎛DCBA ( ) ( )

( ) ( )⎟⎟⎠⎞

⎜⎜⎝

⎛,....,,,,....,,,,....,,,,....,,,

cccc

cccc

VITDVITCVITBVITA

ωωωω

( ) ( )( ) ( )⎟⎟⎠

⎞⎜⎜⎝

⎛,....,,,,....,,,,....,,,,....,,,

dddd

dddd

VITDVITCVITBVITA

ωωωω

Common classification of available componentsCommon classification of available components

( ) ( )( ) ( )⎟⎟⎠

⎞⎜⎜⎝

⎛,....,,,,....,,,,....,,,,....,,,

dddd

dddd

VITDVITCVITBVITA

ωωωω

ET8016-2009 52


AccuracyGain

⎟⎟⎠

⎞⎜⎜⎝

⎛DCBA

⎟⎟⎠

⎞⎜⎜⎝

⎛DCBA

⎟⎟⎠

⎞⎜⎜⎝

⎛DCBA ( ) ( )

( ) ( )⎟⎟⎠⎞

⎜⎜⎝

⎛,....,,,,....,,,,....,,,,....,,,

cccc

cccc

VITDVITCVITBVITA

ωωωω

( ) ( )( ) ( )⎟⎟⎠

⎞⎜⎜⎝

⎛,....,,,,....,,,,....,,,,....,,,

dddd

dddd

VITDVITCVITBVITA

ωωωω

Exactly according to the definitionExactly according to the definition

( ) ( )( ) ( )⎟⎟⎠

⎞⎜⎜⎝

⎛,....,,,,....,,,,....,,,,....,,,

dddd

dddd

VITDVITCVITBVITA

ωωωω

An amplifier is a non-dynamic circuit.Why would there be dynamic elements in the feedback network?

An amplifier is a non-dynamic circuit.Why would there be dynamic elements in the feedback network?

ET8016-2009 53

Impedance networks: • Produce noise (R)• Enlarge contribution existing noise sources• Dissipate power (R)• Create excess voltage or current• Galvanic coupling• Dynamic elements will cause specific problems later

Impedance networks: • Produce noise (R)• Enlarge contribution existing noise sources• Dissipate power (R)• Create excess voltage or current• Galvanic coupling• Dynamic elements will cause specific problems later

ET8016-2009 54

Nullor design

ConclusionConclusion

Known:

• Topology

• Best nullor implementation

• Voltage and current swing

• Power consumption

• Minimal noise level

• Penalties for “second-best” choices

Specs 1 2 verificationC1 C2 C3 B√√

ET8016-2009 55

Documents

Accurate amplificationAccurate amplification...Accurate amplificationAccurate amplification ET8016-2009 2 Right choice Orthogonalization Optimization Right choice Orthogonalization