förstärkare och ad-da-omvandlareapachepersonal.miun.se/~bentho/dmt/download/f3.pdf · 2012. 1....

1

Copyright (c) Benny Thörnberg

Förstärkare och AD-DA-omvandlare

Input Signal

Output

SignalAmplifier at work

1:43


Outline

•What are amplifiers used for

•The unit decibel

•Operational Amplifiers

•The feedback loop

•The ideal operational amplifier

•The non inverting amplifier circuit

•The inverting amplifier circuit

•Common mode and Differential mode

•The difference amplifier

•The instrument amplifier

2:43

2


Outline•The summing amplifier

•The charge amplifier

•Integration and derivation

•Why both digital and analog signals

•Digital to Analog conversion

•Weighted resistors

•R-2R network

•Analog to Digital conversion

•A simple converter

•Successive approximation

•Flash converter

•Conversion error

•Sample and hold circuit

•Using a multiplexer

3:43


What are amplifiers used for

UIN UOUT

VF•

• The amplifier increases the magnitude of a signal by multiplying itwith a given constant FV

IN

OUT

U

U

VF =

UIN

UOUT

• This is a linear transformation of the signal

4:43

3


A general measurement system

Sensor Amplifier Filter AD-converter Signal processing

Depending on the application, this output signal is

connected to a display unit and/or to a host system for

further data or multi-signal processing.

What are amplifiers used for

5:43


The unit decibel

• This unit is used to express the relation between two parameter values

• For the amplifier as example, decibel is used to express the amplification, hence the relation between the input- and the output signal

)(log20 dBU

UF

IN

OUT

⋅=

6:43

4


The feed back loop

β

AV

Uin Uout

in

outV

U

UF =

( )outinVout UUAU ⋅−⋅= β

( ) inVVout UAAU ⋅=⋅+ β1

( )β⋅+=

V

V

in

out

A

A

U

U

1 ( )β⋅+=

V

VV

A

AF

1

7:43


The feed back loop

β

AVUin Uout

• Increase the amplification such that ∞→VA

ββ

1

1=

⋅+= ∞→

V

VAV

A

ALimF

V

• The amplification in this circuit is thus determined by external passive components and not by the amplifier itself

8:43

5


The ideal operational amplifier

• The ideal OP has an infinite high amplification

∞0=−i

0=+i

• There is no leakage currents on the input terminals

• The output impedance is zero, the output has unlimitedcapability to drive a load

9:43


The non inverting amplifier circuit

Determine the voltage amplification FV in this circuit!

The OP amplifier used in this circuit is ideal except from that it has an amplification limited to AV.

10:43

6



VA

utu

du =)1(

2

22

)2(R

fR

R

utuu

+⋅=

02

=−− ud

uin

u

2u

inu

du −=

2

2R

fR

R

utu

inu

vA

utu

+⋅−=

inu

Rf

R

R

VAut

u =+

+ )

2

21(

2

21

2

21

1

RR

RA

A

Rf

R

R

VA

inu

utu

F

f

V

VV

++

=

++

==

2

2)3(R

fR

R

utu

inu

du

+⋅−=

11:43



2

21RR

RA

A

inu

utu

F

f

V

VV

++

==

This expression looks familiar, don’t you think?

( )β⋅+=

V

VV

A

AF

1

β

AVUin Uou

t

12:43

7


The inverting amplifier circuit

• If you know that your OP can be approximated with an ideal OP,then you do not need to consider AV in your calculations.

• The OP input voltage can be assumed to be zero.

Virtual ground

• The inverting OP input has in this case zero potential – Virtual ground.

13:43


The inverting amplifier circuit

iii ==21

01

=⋅− Riin

u

1

)1(R

inu

i =

02

=⋅+ Riut

u

2

)2(R

utu

i −= 1

2R

R

inu

utu

FV −==

21

)21(R

utu

R

inu

o −=

)(

1

2log20 dBR

R

inu

utu

FV

⋅== and with 180 degrees phase shift

14:43

8


Common Mode and Differential Mode

2

DM

CM

A

SSV +=

2

DM

CM

B

SSV −=

Signal coming

from a sensor or

other equipment0

2BACM VVS

+=The common mode signal

BA

DMVVS −=The differential mode signal

BV

AV

15:43


The difference amplifier circuit

124321uu

utuRRRRR −=⇒====

1

41)

32(

1

)14

(3

2 R

Ru

RRR

RRRu

utu ⋅−

+

+⋅=

1

2

3

U1

R1

R2

R3

R4

1u

utu

2u

+

+

+Vi

i

i

+

+

-

-

R

kRu

kRRR

RkRkRu

utuRRRRkRR ⋅−

+

+⋅=⇒==∧⋅==

1)(

)(

22143

)12

( uukut

u −⋅=

16:43

9



Sensor

Difference amplifier

Output sensor signal

• The Difference amplifier is important in measurement systems because of its ability to sense a differential mode signal generated by a sensor output.

• Electromagnetic disturbance from the environment will generate a common mode signal equally on both wires and will thus (ideally)be completely suppressed.

17:43



• A real world differential amplifier (not ideal) will also respond to a common mode input signal FCM

• FDM is the amplification of a differential mode signal.

• A quality measure of the differential amplifier is its ability to suppresscommon mode signals and is given by the Common Mode Rejection Ratio, defined as )(log20 dB

F

FCMRR

CM

DM

⋅=

18:43

10


The instrumentation amplifier

1

2

3

U1

R

R

R

R

RA

RA

RF

U1

U2

UOUT

i

i

UB

UA

• An instrumentation amplifier is a difference amplifier with very high input impedance

19:43



1

2

3

U1

R

R

R

R

RA

RA

RF

U1

U2

UOUT

i

i

UB

UA

( )

+⋅−=−=

F

AABout

R

RUUUUU 2112

20:43

11



• This amplifier is used for the laboratory experiments in this course.

21:43



• The main benefit of an instrumentation amplifier is its higher input impedance than compared to a single OP-circuit. This higher input impedance comes from the fact that input signalsare connected directly to the input of the “close to ideal” OP.

• The whole instrumentation amplifier except the gain adjustment resistor can be integrated on chip. Amplification is then set externally by simply selecting value of RF.

22:43

12


Förstärkare som industriell komponent

Analog signalomvandlare är ett begrepp som inom området för automation vanligen motsvarar en justerbar förstärkare med integrerad strömförsörjning.

Ref. CC-U/STD från ABB

•Insignal•Ström +/- 0.9 till +/- 55mA•Spänning +/- 45 mV till +/- 11 V

•Utsignal Upp till +/- 55 mA eller +/- 11V

Grov justering av förstärkning

Fin justering av förstärkning

Justering av nollpunkt (offset)

23:43


Why both digital and analog signals

AD-converter DA-converterSignal processing

in computerAnalog signal

input from sensorAnalog signal

output to actuatorSignal Processing

24:43

13


Digital to Analog conversion

This converter requiresLOG2(no_of_descrete_levels) number of different resistorvalues

Weighted resistors

25:43


Digital to Analog conversion

This converter requires only two different resistor values.

R-2R network

26:43

14


Analog to Digital conversion

A simple counter based converter

•In worst case, 2n clock cycles are needed for an n-bit converter.

27:43



Successive approximation

28:43

15



Successive approximation• n clock cycles are needed

for an n-bit converter.

29:43



Flash converter• An n-bit converter requires 2n-1

number of comparators.

• An n-bit converter requires 2n

number of equal resistors.

• A decoder (combinatorial network)translates the 2n-1 comparator outputs to n binary coded outputs.

+ Fast!

-Expensive!- Power hungry

30:43

16



n

refULSB

21 =

Conversion error – Round to ceiling

1LSBLSB

UDA

UD

n

ref

utinn

ref

ut 122

+⋅

17


Nollfel

33:43


Skalfaktorfel

34:43

18


Linjäritetsfel

35:43


Differentiellt linjäritetsfel

36:43

19


Bortfall av koder

Differentiellt linjäritetsfel mindre än +/- 1/2LSB garanterar att inga

koder missas i överföringsfunktionen

37:43


Monotonitetsfel

38:43

20


Monotonitetsfel

39:43



Sample and Hold circuit

• We need a circuit that can freeze the analog signal duringthe time it takes for the AD-converter to perform the conversion.

• The sample and hold circuit operates synchronous with theconverter and are both controlled by the S/H signal.

40:43

21



Sample and Hold circuit

41:43



Using a multiplexer

42:43

22


Förstärkare och ADC som färdig enhet

Signalomvandlare eller Transmitter är begrepp som förutom strömförsörjning och förstärkare ibland även innefattar AD-omvandlare, mikroprocessor och kommunikation.

Ref. BUSC701 från BASI Instrument AB

Förstärkare Filter AD-omvandling Mikroprocessor

Kommunikation

SignalOmvandlare

Fältbuss/Field bus för kommunikation med ex PLC

Analog

Ingång/ar

43:43

förstärkare och ad-da-omvandlareapachepersonal.miun.se/~bentho/dmt/download/f3.pdf · 2012. 1....

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