Chapter 12

1. Chapter 12 Interfacing Analog and Digital Circuits

2. Analog Signals • Signals that vary continuously throughout a defined range. • Representative of many physical quantities, such as temperature and velocity. • Usually a voltage or current level.

3. Digital Signals • Signals that take on specific values only. • Required for operation with digital logic. • A representative of physical quantities by a series of binary numbers.

4. Advantages of Analog Representation • Varies continuously, like the property being measured. • Represents continuous values.

5. Advantages of Digital Representation • Values are limited to specific discrete segments. • Not subject to the same distortions as an analog signal. • Can be easily copied and stored.

6. Advantages of Digital Representation

7. Analog Voltage Sampling • A sample is an instantaneous measurement of an analog voltage. • Sampling frequency is the number of samples taken per unit time.

8. Accuracy of Digital Representation • Depends on sampling frequency and quantization. • Quantization is the number of bits used to represent an analog voltage as a digital number. • Resolution is the analog step size.

9. Accuracy of Digital Representation

10. Accuracy of Digital Representation

11. Accuracy of Digital Representation

12. Accuracy of Digital Representation

13. Resolution of a Digital Representation • The difference in analog voltage corresponding to two adjacent digital codes. • Directly proportional to the reciprocal of 2n, where n is the number of bits used in the digital code.

14. Analog-to-Digital Conversion • Uses a circuit that converts an analog signal at its input to a digital code. • Called an A-to-D converter, A/D converter, or ADC.

15. Unipolar ADC • Converts positive input voltages. • Generates a 2n-bit binary code for any given input voltage.

16. Unipolar ADC Code Equation • Va = analog input voltage to be sampled. • FS = Full scale range of input voltage. • n = number of bits in the output code.

17. Unipolar ADC Code Equation

18. Unipolar ADC Output Codes

19. Bipolar ADC (Offset Binary Coding) • Used to represent positive and negative input voltages. • Output code an unsigned binary number. • Numbers below 0 V are negative. • Numbers above 0 V are positive.

20. Bipolar ADC (Offset Binary Coding)

21. Bipolar ADC Code Equation

22. Bipolar ADC Output Codes

23. Bipolar ADC (2’s Complement Coding) • Uses a 2’s complement number system. • Most significant bit (MSB) is the sign bit. • MSB = ‘1’ sign negative. • MSB = ‘0’ sign negative.

24. 2’s Complement Output Codes

25. 2’s Complement Output Codes

26. Digital-to-Analog Conversion • Uses a circuit that converts a digital code at its input to an analog voltage or current. • Called a D-to-A converter, D/A converter, or DAC.

27. Unipolar DAC • One input code corresponds to a single digital code. • DAC has 2n discrete output voltage values.

28. Unipolar DAC

29. Unipolar DAC Equation

30. Bipolar DAC (Offset Binary Coding) • Input code for 0 V is halfway through the range of digital input codes. • Output voltage equation:

31. Bipolar DAC (Offset Binary Coding)

32. Bipolar DAC (2’s Complement) • Accepts digital codes in 2’s complement format. • Code = a 2’s complement signed number.

33. Bipolar DAC (2’s Complement)

34. DAC General Operation • Uses digital inputs to control proportionally weighted currents. • Currents are binary weighted – the MSB has the largest, the second LSB has ½ the current, and so on. • Currents feed an op-amp that converts current to voltage.

35. DAC General Operation

36. DAC Output Voltage • If Va is the output, Iref a fixed reference current, and RF the op-amp feedback resistor, then for n bits:

37. DAC Characteristics • The maximum output is always one least significant bit less than full scale. • An n-bit converter has 2n input codes, ranging from 0 to 2n – 1.

38. Weighted Resistor D/A Converter • Uses a parallel network of binary-weighted resistors to feed the op-amp. • Seldom used since a wide range of resistor values is required for a large number of bits. • Difficult to achieve accuracy for a high number of bits.

39. Weighted Resistor D/A Converter

40. R-2R Ladder DAC • Produces an analog current that is the sum of binary-weighted currents. • Uses only two values of resistors. • Easily modified to add additional bits – each new bit requires 2 resistors, values R and 2R.

41. R-2R Ladder DAC

42. R-2R DAC Equation • b3, b2, b1, and b0 are binary values either ‘1’ or ‘0’.

43. MC1408 Integrated Circuit DAC • Popular, inexpensive 8-bit multiplying DAC. • Also designated DAC0808. • Output is proportional to the reference voltage.

44. Operation of the MC1408 • Requires an external op-amp to increase the output voltage and current. • Can be wired to produce a bipolar output voltage, that is, voltages that have both positive and negative values.

45. Operation of the MC1408

46. MC1408 Equations

47. DAC Performance Specifications – 1 • Monotonicity means that the magnitude of the output voltage increases every time the input digital code increases. • Absolute accuracy is the measure of the DAC output voltage with respect to its expected value.

48. DAC Performance Specifications – 2

49. DAC Performance Specifications – 3

50. DAC Performance Specifications – 4 • Relative accuracy is the deviation of the actual from the ideal output voltage as a fraction of the full-scale voltage. • Settling time is the time required for the outputs to switch and settle within ½ LSB when the input switches form all 0s to all 1s.