1. Digital Electronics and Computer Interfacing Tim Mewes 5. Computer Interfacing – DAQ cards

2. Digital Electronics and Computer Interfacing2 5.4 Digital to Analog conversion 5.4.1 Operational Amplifiers Short: “Op-Amp” DC coupled amplifier with two 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): V Supl. + V Supl. - Inverting input Non- inverting input Output

3. Digital Electronics and Computer Interfacing3 5.4.1 Operational Amplifiers Summing amplifier V Supl.+ V Supl. - V Out V1V1 V2V2 R1R1 R2R2 R3R3 A Current Rule  non-inverting input ‘+’ draws no current thus it is at ground potential Current Rule Voltage Rule  inverting input ‘-’ (and thus A) is at virtual ground potential

4. Digital Electronics and Computer Interfacing4 5.4.2 DAC using scaled resistors V Supl.+ V Supl. - V Out 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 2 n-1 times as large as the smallest one! Resistors need to be very precise! Impractical for large number of bits n

5. Digital Electronics and Computer Interfacing5 5.4.2 DAC using scaled resistors V Supl.+ V Supl. - V Out V=-8 V 8R 4R R 2R R 0 1 2 3 LSB MSB How does it work?! 1 0 0 1 Voltage rule: Inverting input ‘-’ is at ground Current rule: 1001 2 =1  8+0  4+0  2+1  1=9 10 4-Bit Digital to Analog converter

6. Digital Electronics and Computer Interfacing6 5.4.2 DAC using scaled resistors V Supl.+ V Supl. - V Out V=-8 V 8R 4R R 2R R 0 1 2 3 LSB MSB How does it work?! 1 0 1 0 Voltage rule: Inverting input ‘-’ is at ground Current rule: 0011 2 =0  8+0  4+1  2+1  1=3 10 4-Bit Digital to Analog converter

7. Digital Electronics and Computer Interfacing7 5.4.2 R-2R ladder DAC V Supl.+ V Supl. - V Out V 2R R 3 2 1 0 MSB LSB 4-Bit Digital to Analog converter 2R R R R Only requires resistance values R and 2R Resistors still need to be precise! Can be used for arbitrary number of bits

8. Digital Electronics and Computer Interfacing8 1 0 1 0 5.4.2 R-2R ladder DAC V Supl.+ V Supl. - V Out V=-16 Volts 2R R 3 2 1 0 MSB LSB 4-Bit Digital to Analog converter 2R R R R How does it work?! Voltage rule: Inverting input ‘-’ is at ground Current rule: 1100 2 =1  8+1  4+0  2+0  1=12 10 Why?!

9. Digital Electronics and Computer Interfacing9 1 0 1 0 5.4.2 R-2R ladder DAC V Supl.+ V Supl. - V Out V=-16 Volts 2R R 3 2 1 0 MSB LSB 4-Bit Digital to Analog converter 2R R R R How does it work?! Why?! R2R

10. Digital Electronics and Computer Interfacing10 1 0 1 0 5.4.2 R-2R ladder DAC V Supl.+ V Supl. - V Out V=-16 Volts 2R R 3 2 1 0 MSB LSB 4-Bit Digital to Analog converter R How does it work?! Why?! 2R

11. Digital Electronics and Computer Interfacing11 5.4.2 R-2R ladder DAC V=-16 Volts 2R 4-Bit Digital to Analog converter R How does it work?! Why?! 2R I I GND I VGND

12. Digital Electronics and Computer Interfacing12 5.4.2 R-2R ladder DAC V Supl.+ V Supl. - V Out V=-16 Volts 2R R 3 2 1 0 MSB LSB 4-Bit Digital to Analog converter 2R R R R Summary 1 1 0 0 1010 2 =1  8+0  4+1  2+0  1=10 10

13. Digital Electronics and Computer Interfacing13 5.4.3 Definitions Voltage resolution  V: smallest voltage difference possible with DAC depends on the number n of bits used: tt Sampling rate f S