Digital Electronics and Computer Interfacing

Digital Electronics and Computer Interfacing

Tim Mewes

5. Computer Interfacing – DAQ cards

Digital Electronics and Computer Interfacing 2

5.4 Digital to Analog conversion

5.4.1 Operational Amplifiers• Short: “Op-Amp”

• DC coupled amplifier withtwo inputs and one output

• Feedback network determines gain

Voltage Rule:The output attempts to do whatever is necessary to make the voltage difference between the inputs zero.

Current Rule:The inputs draw no current.

Golden rules (Horowitz & Hill):

VSupl. +

VSupl. -

Invertinginput

Non-invertinginput

Output


5.4.1 Operational Amplifiers

Summing amplifier

VSupl.+

VSupl. -

VOut

V1

V2

R1

R2 R3A

Current Rule non-inverting input ‘+’ draws no current thus it is at ground potential

Current Rule

032

2

1

1 R

V

R

V

R

V out

32

2

1

1

R

V

R

V

R

V out

)( 211

321 VV

R

RVRR out

)( 21321 VVVRRR out

Voltage Rule inverting input ‘-’ (and thus A) is at virtual ground potential


5.4.2 DAC using scaled resistors

VSupl.+

VSupl. -

VOut

V

8R

4R R

2R

R

0

1

2

3

LSB

MSB

4-Bit Digital to Analog converter

For n bits the largest resistor needs to be 2n-1 times as large as the smallest one!

Resistors need to be veryprecise!

Impractical for large numberof bits n



VSupl.+

VSupl. -

VOut

V=-8 V

8R

4R R

2R

R

0

1

2

3

LSB

MSBHow does it work?!

1

0

0

1

Voltage rule: Inverting input ‘-’ is at ground

Current rule:

08

R

V

R

V

R

V out

outVV )18

1(

VoltsVout 9)81(

10012=18+04+02+11=910




VSupl.+

VSupl. -

VOut

V=-8 V

8R

4R R

2R

R

0

1

2

3

LSB

MSBHow does it work?!

1

0

1

0


Current rule:

048

R

V

R

V

R

V out

outVV )4

1

8

1(

VoltsVout 3)21(

00112=08+04+12+11=310



5.4.2 R-2R ladder DAC

VSupl.+

VSupl. -

VOut

V

2R

2R R

2R

2R

3

2

1

0

MSB

LSB

4-Bit Digital to Analog converter2R

R

R

R

Only requires resistancevalues R and 2R

Resistors still need to be precise!

Can be used for arbitrarynumber of bits


1

0

1

0


VSupl.+

VSupl. -

VOut

V=-16 Volts

2R

2R R

2R

2R

3

2

1

0

MSB

LSB


R

R

R

How does it work?!


Current rule:

042

R

V

R

V

R

V out

outVV )4

1

2

1(

VoltsVout 1248)4

1

2

1(16

11002=18+14+02+01=1210

Why?!


1

0

1

0


VSupl.+

VSupl. -

VOut

V=-16 Volts

2R

2R R

2R

3

2

1

0

MSB

LSB

4-Bit Digital to Analog converter2R 2R

R

R

R

How does it work?!

042

R

V

R

V

R

V out

Why?!

R

2R

2R


1

0

1

0


VSupl.+

VSupl. -

VOut

V=-16 Volts

2R

2R R

3

2

1

0

MSB

LSB


R

How does it work?!

042

R

V

R

V

R

V out

Why?!

2R



V=-16 Volts2R


R

How does it work?!

042

R

V

R

V

R

V out

Why?!

2R

I

IGND

IVGND

R

V

RR

V

R

VI

tot 8

3

232

VGNDVGNDVGNDVGNDGND IIIIII2

3

2

1

R

V

R

VIIVGND 48

3

3

2

3

2



VSupl.+

VSupl. -

VOut

V=-16 Volts

2R

2R R

2R

2R

3

2

1

0

MSB

LSB


R

R

R

Summary

)16842

( 0123 VVVVVout

ibitondependingVolts

VoltsVi

0

16

VoltsVout 1028)16

0

8

1

4

0

2

1(16

1

1

0

0

10102=18+04+12+01=1010


5.4.3 Definitions

• Voltage resolution V: smallest voltage difference possible with DACdepends on the number n of bits used:

12minmax

n

VVV t

• Sampling rate fS

tfS

1

Digital Electronics and Computer Interfacing

Documents