6 amplification circuits

6 Amplification Circuits

6.1 Requirements for Amplification

6.2 Structure of Amplifiers

6.3 Real Behaviour of Amplifiers

6.4.2 Zero Point Errors

6.4.3 Noise

Input Resistances, Output Resistance, Offset-Voltage,

Offset-Current, Bias-Current Drift, Transfer Behaviour, Output Voltage Swing,

Gain-Bandwidth-Product, Slew Rate , Common Mode Rejection

Difference Amplifier, Operation Amplifier

6.4 Correction of the Real Behavior

6.4.1 Frequency Behavior

P. 6-1

Prof. Dr.-Ing. O. Kanoun

Chair for Measurement and Sensor Technology

6.5 Instrumentation Amplifier

6.6 Applications of Inverting AmplifiersMultiplication, Division, Charge Amplifier,

Schmitt-Trigger, Control Circuits

6.7 Active Filters

defined transfer behaviour:

Linearity

Amplification independent on aging, fluctuations, environment influence and voltage supply

high input sensitivity

no influence on the measurand: High input resistance

for voltage amplifier very high

for current amplifier very low

stable output: Low output resistance

long life time

low noise

low energy consumption

6.1 Requirements to Amplification

P. 6-2




Important:

Ouput circuit is galvanically independent

on the input circuit

positiver Eingangsruhestrom

Eingangswiderstand

negativer Eingangsruhestrom

Ue

Ua

Positive Input Bias Current

Output Resistance

Input ResistanceNegative Input Bias Current

Un

Ua

Ua

+ Uv

- Uv

Ud

Ua

+ Uv

- Uv

Saturation

Saturation

Equivalent Circuit and Transfer Characteristic

npd UUU

0V open loop voltage gain

Amplification

da UVU 0

CMCMda UVUVU 0

Total Amplification

with 740 1010 CMV

V

Real 104 < V0 < 107

Ideal

CMV common mode amplification

npCM UUU VUd 0

CMCMa UVU

Ideal 0

2

np

CM

UUUwith

(Differenzverstrkung)

(Gleichtaktverstrkung)

P. 6-4




Principle of the Difference Amplifier

Ube1= Ube2 Ic1= Ic2 UA1= UA2

Ube1> Ube2 Ic1>> Ic2 UA1>> UA2

P. 6-5




Simple Amplifier

Difference Amplifier Output stage

P. 6-6




Integrated Standard Operation Amplifier xx741 (Principle)

Current Mirror

Difference Amplifier

Second Amplification Stage Output Stage

P. 6-7




P. 6-8




Integrated Standard Operation Amplifier xx741 (Principle)

Small Signal Equivalent Circuit of an Op-Amps(1)

Difference Input Resistance

Common Mode Input ResistancesInput Bias Currents

Offset Voltage

Output Resistances

P. 6-9




uCM VCM

rCMrCM

P. 6-10


Data Sheets


Data Sheet OPA 365 [Texas Instruments]

Rail-To-Rail-inputs

Input voltages are amplified until the level of the supply voltage distortion-free

2.2V, 50MHz, Low-Noise, Single-Supply Rail-to-Rail

P. 6-11



uCM VCM

rCMrCM

)i(i

ur

NP

DE

2

1 ) (ideal 100T ... 1G ErDifferential Input Resistance

(Differenzeingangswiderstand)

) (ideal 1T ... 1M CMr)i(i

ur

NP

CMCM

2

1Common Mode Input Resistance

(Gleichtakteingangswiderstand)

const.uA

AA

D

i

ur

0) (ideal 100 ... 2Ar

Output Resistance

(Ausgangswiderstand )


P. 6-12



uCM VCM

P. 6-13

Input Bias Current (Eingangsruhestrme):

(typ. 1 nA...500 nA)

IP = Ib+IO mit Ib Bias Current

IN = Ib- IO IO Offset Current (typ. 20 fA...20 nA) RCMP

+

-

Ri

kue

=

UO

=

In

Ip

ue

ua

RCMN

ud

(Bipolar)A 1 (FET);fA 50 bb II


Common Mode Input Resistances RGlP RGlN(Gleichtakteingangswiderstnde)

Differential Input Voltage (Differenz-Eingangsspannung):

Ud (typ. 3V.... 30 V)


Common Mode Input Voltage

(Gleichtakteingangsspannung):

UCM (typ. 13V... 16V )

Input voltage relative to ground

Output Voltage Swing (Ausgangsspannungshub):

UAmax (typ. 27 V.... 32 V)

Maximal value of the output voltage without

amplitude limitation

P. 6-14



Rail-to-Rail

output voltage swing next the voltage supply VCC

+VCC

-VCC

maximal output voltage


Input-Offset Voltage U0 (Offset-Spannung):

(typ. 0,5 V... 5 mV)

Voltage between difference inputs, so that

the output voltage 0V is reached

VUUU da 0)( 0 RCMP

+

-

Ri

kue

=

UO

=

In

Ip

ue

ua

RCMN

ud

P. 6-15



Offset Voltage Drift (Offsetspannungsdrift):

(typ. 0,01 V/C ... 15 V/C)

tt

UU

U VV

OOO0

UUU

Input Current Drift (Eingangsstromdrift):

(typ. 10 fA/C ... 1 A/C)

..,

p,i

constUconstU

n

pN

i


[OPA 365, TI]

Different behaviour compared to A 741 (see Page 13)

P. 6-16




Transfer Function

Corresponds to the complex amplification

Hzf 101

MHzf 52 DecadedB /20

21

0

11)(

)()(

jj

V

U

UG

D

A

P. 6-17



agegea xkxkxxkx ''

'

'

'

'

1

1

1

1

kfrxk

x

kk

xkk

kx

e

g

e

g

e

g

a

Smaller amplification, but just dependent on kg if k is sufficently high

Selection of stabile circuit elements

independence on changes of amplifier properties

Band width (Frequenzbereich) becomes higher.

Input resistance of voltage Amplifiers and by Current Amplifiers

Output resistance by voltage output and and by current output

Advantages:

kxe xa

kgxg

-


Feedback (Closed Loop)

P. 6-18



gkk

k'

'

1

gkk'1

'k

gg kkf '' 1


Professur fr Mess- und Sensortechnik P. 6-19




Feedback (Closed Loop)

Amplification

Amplification of the

system with feed

back

Amplification

Gain-Bandwidth-Product (Verstrkungs-Bandbreite-Produkt ): GBW

(typ. 0.8 MHz..3 MHz)

In the sector in which the amplification is sinking with 20 dB/Dekade, the product of

frequency and corresponding amplification is constant.

00GBW gfV

P. 6-20




Slew Rate (Maximale Anstiegssteilheit):

SWR (typ. 0.5 V/s...50 V/s)

SWR is the maximum possible change of

the output voltage pro Time Unit

max

SWR

t

uA

P. 6-21




dBV

VCMR

CM

12080lg20

Common Mode Rejection Ratio

(Gleichtaktunterdrckung ): CMRR

(typ. 80dB...120dB)

Proportion of the open voltage gain to

the common mode gain

Supply Voltage Rejection (Betriebsspannungsunterdrckung ): SVR

(typ. -60dB..-100dB)

Proportion of the offset voltage change related to the changes of the voltage supply

Signal-Noise-Ratio: SNR

P. 6-22




Families of Op-Amps

P. 6-23




Ideal Amplifier

is a useful Model for amplification circuits

any Ia, Ua are possible

very high difference amplification

Common mode amplification

low output resistance

no cut-off frequency

V

0aR

0GlV

Ie 0

High input resistance

eR

0eU

+

-

eU

aU

eI

P. 6-24




Frequency Behaviour

Open Loop Amplification

e

a

U

Ulg20

gf

Tf

DecadedB /20

gf

fj

kk

1

'0'


P. 6-25



cut-off frequency

ideal behaviour

real behaviour

Smaller gain band width product Slew-Rate reduction

Frequency Behaviour

Correction

P. 6-26



Frequency Behaviour


P. 6-27

f1

|j| > 180 Oscillation

321

'0'

111f

fj

f

fj

f

fj

kk

Real amplifier

Many amplification stagesFrequency Behaviour


Closed loop

lower amplification more band width

Tg

gg

ffv

fvfv

100100

101011

For every amplification level, a different compensation is necessary

A transimpedance amplifier is a special amplifier with very high band width and

a variable amplification

P. 6-28



Frequency Behaviour


ReP

+

-

Ri

kue

=

UO

=

In

Ip

ue

ua

ReN

ud

How can we treat offset voltages and input bias currents?

Application of the superposition principle

Example: u/u amplifier

Zero Point Error

P. 6-29




Superposition Principle

The reaction on every source of errror is considererd alone:...... additionally available voltage sources are short-circuited

...... additionally available current sources are broken

The results are added to each other

+

-

Ri

kue

=

UO

=

In

Ip

ue

=Uq

Rq

R1

R2

IR

ug

ua

P. 6-30



Zero Point Error


+-

Ri

kue

=

UO

=

In

Ip

ue

=Uq

Rq

R1

R2

IR

ug

ua

Influence of Off-Set Voltage

OOa UR

RRUU

2

21)(0 gO UU

0,0 npq IIU

Input Mesh:

uk

P. 6-31



Zero Point Error


P. 6-32

Influence of Ip

pqpa IRR

RRIU

2

21)(

0,0,0 nOq IUU

Input Mesh: Ip flows over Rq

Influence of In

nna IRIU 1)(

0,0,0 pOq IUU

In flows to the node between R1 und R2 2RIIU Rng

Input Mesh: 0gU Rn II

+

-

Ri

kue

=

UO

=

In

Ip

ue

=Uq

Rq

R1

R2

IR

ug

ua

+

-

Ri

kue

=

UO

==

InIn

IpIp

ue

==Uq

Rq

R1

R2

IR

ug

ua

Influence of Input Bias Current

Zero Point Error


P. 6-33

npqOqnpOqa I

RR

RRIRUU

R

RRIIUUU

21

21

2

21),,,(

Superposition principle

+

-

Ri

kue

=

UO

=

In

Ip

ue

=Uq

Rq

R1

R2

IR

ug

ua

+

-

Ri

kue

=

UO

==

InIn

IpIp

ue

==Uq

Rq

R1

R2

IR

ug

ua

Compensation for Rq=R1R2

OqOqnpqOqa IRUUR

RRIIRUU

R

RRU

2

21

2

21

Zero Point Error


Noninverting Amplifier

qDn RR

eG

GTa U

R

RRU

P. 6-34



Zero Point Error


Input bias currents flowing through the resistances at the input are acting like an off-set voltage

If the resistances are equal to each other, no difference voltage is amplified

Rq

UE

Inverting Amplifier

Gq

qG

DpRR

RRR

ngpDp

q

Gnpa IRIR

R

RIIU

1),(

O

E

GOa U

R

RUU

1)(

The Offset voltage is not amplified!

nGna IRIU )(

DpR

Iq Rq

Ie

Ip over RDp has a similar influence to UO

Ognpa IRIIU ),(

P. 6-35



Zero Point Error


Reduction of the Signal-to-

Noise- Ratio

P. 6-36



Noise


... Is a precision amplifier

with difference input and

an output related to the ground

But a high input impedance is not easy to realise!

3

4

R

RV

3

43

21

2

R

RR

RR

RV

4

3

2

1

R

R

R

R

3

4

R

RV

ua

-

+

R3

R1

i1

u1

R4

R2u2

Subtraction

6.5 Instrumentation Amplifier (1)

P. 6-37



Impedance converter for amplification of difference voltages

121

2 UUR

RUa

Amplification changes only by changing two resistances!

For example for Bridges


P. 6-38



Impedance Converter

121

221 UUR

RUa

2211'

1 URRIV R

1

211

R

UUIR

212

'

2 RIUV R

'

1

'

2 VVUa

211 2RRIU Ra


P. 6-39



Multiplication

221221214

1uuuuuu

e. g. Thermal Transducer

u1u2

uaX k

21 uukua

6.6 Applications of Inverting Amplifier

P. 6-40



Division

-

+

Rg

R1

ig

i1

uau1

ug

X ku2

2uuku ag

2

1

12 u

u

Rk

R

uk

uu

gg

a

1

11

2

R

ui

R

uku

R

ui

g

a

g

g

g 11

uR

Ru

g

g


P. 6-41



Realisation of arithmetic operations by closed loop

(Generalization)

ea iku'

-

+

ei

gi

au

Gk

aGg uki

I U

'k

eg ii

aGg uki

e

G

ea ik

iku1'

Gkk

1'

The amplification in the forward direction should be always the

inverse operation to the element in the feedback

Forward Amplification Feedback Amplification

divide Multiply

square root square

integrate differenciate

logarithmize exponentiate


P. 6-42

43

Charge Amplifier for Piezoelectric Sensors




Electric polarized Crystals,

e.g. SiO2 (Quarz

F Force

Q Charge

k Transfer Faktor

++++- - - -

FkQ

ApF

[N]

[As]

F

F0

t

Uq

Uq0

ttq = RqCq

~1 sOutput voltage should be integrated!

Charge Amplifier

dt

tduC

dt

tdQti A

)()()(

Problem: Input bias currents will be also integrated!

)(1

)( tQC

tu A

d ttitQ )()(Charge

P. 6-44




Regulator Circuits (1)

P-Regulator Simple Amplifier

I-Regulator Integration

PI-Regulator

-

+

Reie

uaue

Rg Cg

dtuCR

uR

Ru e

ge

e

e

g

a 1

P. 6-45




Regulator Circuits (2)

PID- Regulator

-

+

Reie

uaue

Rg

Ce

dtuCRdt

duCRu

C

C

R

Ru e

ge

eege

g

e

e

g

a

1

Cg

P. 6-46




47

0

0

)(

)(

))((

))((

)(

)())(()(

dtetx

dtetx

tX

tX

pX

pXtgpG

pt

e

pt

a

e

a

e

a

)()()( pXpGpX ea

)()()( tgtXtX ea

Transfer Function

)(tg : pulse response

)(th : Step response )()( tht

tg

Time Domain

Frequency Domain

Frequency Response (Fourier-Transformed)

))(()()( tgFourierdtetgjF tj

dtep

pG

jp

pGth

j

j

tp

)(

2

1)()( 1


48

F(P) 1/F(P)xe(t) xa(t) xe(t)= xa(t) * g(t)

sensor dynamic

correction

)(*)()()(0

tgtxdtxtx a

t

ae tt

)(/1)( 1 PFLtg

aaae xxx

ktx

2

00

121)(

Transfer Function:

: Attenuation ratio

0: Angular frequency

of non attenuated oszillation

System of Second Order

System of First Order

aae xxk

tx t1

)(

t: Time constant

Realisation of Defined Transfer Functions (1)


Example: Dynamic Correction of Linear Systems

49


-

+

ie

ue ua

Ze

Zgvirtual ground

Short Circuit Kernel Impedance Short Circuit Kernel Impedance

Zk

I2

U1

Short Circuit Kernel Impedance

e

e

g

a uZ

Zu


50


Short Circuit Kernel ImpedanceCircuit

s=p


52


PID-Regulator

Low pass filter

CRp

CR

2

1 1

11

tCR

eR

RU 2

1

1

2 1

p

CRp

CRp

CR

112222

11

t

CRCRt

CRCRCRU

22112211

12

1)(

11

Transfer Function

Transfer Function

Transfer Function

Transfer Function


53



54

Low pass

High pass

Band pass

Notch

6.7 Active Filters

Pass Band

Attenuation Band

Filter: Circuit with a frequency dependent frequency response

Passive Filter: R, L, C - Filter

Active Filter: Op-Amps, No Inductivities

sperr

55

Ripple in the pass band

Ripple in the attenuation band

Properties of real filters

Cut-off frequency: decay of the modulus by )3(2

1dB

6.7 Active Filters

n

i

i

i pc

ApG

1

0

1

)(

Transfer Function of a Filter of order n

ic real Filter-Coefficientsn Order of the filter

R

CUe Ua RCp

pG

1

1)(

One negative Pol

n negative pols

Low pass- Filter 1st order

P. 6-56



6.7 Active Filters

57

Low pass filter High pass filter

Active filter

6.7 Active Filters

58

Gau (1): flat amplitude characteristic

Bessel (2): Optimal Transfer of square pulses for f < fggroup delay time indipendent on , low ripple.

Butterworth (3): Amplitude characteristic optimized for f < fg, constant.

Tschebyscheff (4): Filter with riple e = 0,5 dB

gr

g

gr tT

2

ttgr

Group delay time

Normed group delay time

Properties of different filter types

6.7 Active Filters

59

Amplitude characteristic of active Filter of 4th Order

6.7 Active Filters

1 RC with critical damping

2 Bessel

3 Butterworth

4 Tschebyscheff with 3 dB ripples

4. Ordnung

10. Ordnung

Butterworth

maximal constant frequency response

P. 6-60



6.7 Active Filters

Bessel

Group delay time independent on frequency

in the pass Band

P. 6-61



6.7 Active Filters

1 RC with critical damping

2 Bessel

3 Butterworth

4 Tschebyscheff with 3 dB ripples

62

Active Filter 2nd Order

2

21

0

1)(

SaSa

ASG

gg

jpS

Multiple feedback

2

3221

2

1

32321

12

1

)(

SRRCCSR

RRRRC

RRSG

gg

1

20

R

RA Comparison of Coefficients

1

323211

R

RRRRCa g

3221

2

2 RRCCa g

6.7 Active Filters

63

1

20

R

RA

1

323211

R

RRRRCa g

3221

2

2 RRCCa g

0

21

A

RR

21

0221

2

2

2

121

24

14

CCf

AaCCCaCaR

g

221

22

23

4 RCCf

aR

g

2

1

02

1

2 14

a

Aa

C

C

Capacitance values are given

2

21

0

1)(

SaSa

ASG

6.7 Active Filters

Active Filter 2nd Order

64

Low pass

Z1 = R1Z2 = open

Z3 = 1/s C1Z4 = R2Z5 = 1/s C2

High pass

Z1 = 1/s C1Z2 = open

Z3 = R1Z4 = 1/s C2Z5 = R2

Band pass

Z1 = R1Z2 = open

Z3 = 1/s C1Z4 = 1/s C2Z5 = R3 // C3

6.7 Active Filters

Sallen-Key-Filter

- For analoge filters 2nd Order

- Low pass filter, high pass filter and band pass filter are possible with the same

structure

- Notch und Cauer-Filter are not possible

Low pass High pass Band pass

General

6.7 Active Filters

Amplification is hold on a

specific value2

21

0

1)(

SaSa

ASG

0A

212111 1 CRRRCA g

3221

2

2 RRCCa g

Positive Feed Back Low Pass Amplifier 2nd Order

Transfer function

P. 6-66



6.7 Active Filters

67

0A

11 RCa g

22 RCa g

Fr R1=R2=R3=R und C1=C2=C

Critic

Damping

Bessel-

Filter

Butterworth-

Filter

Tschebyscheff-Filter

with 1 dB ripple

1,0 1,268 1,856 1,955

Special case:

defines the filter typ

)1(3 R

6.7 Active Filters

Positive Feed Back Low Pass Amplifier 2nd Order

Positive Feedback High Pass Filter

P. 6-68



6.7 Active Filters

69

Band Pass Filter with a Simple Positive Feed Back

Resonance frequency

(Extreme low damping)

Performance of rejection

RCfr

2

1

kf

fQ r

3

1

Amplification at frk

kAr

3

6.7 Active Filters

70

Aktives Doppel-T-Sperrfilter, Notch-Filter

Resonance frequency

(unfinite barrier effect)

Performance of rejection

RCfr

2

1

)2(2

1

kf

fQ r

Amplification kA 0

6.7 Active Filters

6 amplification circuits

Documents

sensor technology6

current amplifier

structure of amplifiers6

sensor technology36

output voltage swing

low stable output

charge amplifier

transfer behaviour