ANNUS, Paul paul.annus@elin.ttu.ee

1. ANNUS, Paul paul.annus@elin.ttu.ee Analog - to – Digitalconversionin measurement and data acquisition systems A / D muundaminemõõte- ja andmehõivesüsteemides www.analog.com/library/analogDialogue/archives/39-06/data_conversion_handbook.html http://focus.ti.com/lit/an/slod006b/slod006b.pdf

2. Signalprocessor Object Sensor Converter Mõõtmine on ?

3. A “bit” of history The earliest recorded binary DAC known is notelectronic at all, but hydraulic. Turkey, under the Ottoman Empire, had problems with itspublic water supply, and sophisticated systems were built to meter water. One of these dates to the 18th Century. An example of an actual dam usingthis metering system was the Mahmud II dam built in the early 19th century near Istambul. HS-810, 8-bit, 10-MSPS ADC Released by Computer Labs, Inc. in 1966 ADC-12U 12-Bit, 10-μs SAR ADC from Pastoriza Division of Analog Devices, 1969 1954 "DATRAC" 11-bit, 50-kSPS Vacuum Tube ADC Designed by Bernard M. Gordon at EPSCO

4. Kuidas muundame? • SAMPLING – diskreetimine ajas • KVANTIMINE – diskreetimine nivoos • KODEERIMINE 1) Sampling 2) Kvantimine 3) Kodeerimine Analoog Digitaalne Signaal Väljund ajas nivoos Fs=1/T 2n q 0 T 2T 3T

5. Ajast ja sagedusest NYQUISTI KRITEERIUM:DISKREETIMISSAGEDUS > 2* KÕRGEM KUI KÕRGEIM SAGEDUSSIGNAAL Gabor-Heisenberg uncertainty principle:

6. Mida rohkem on bitte seda väiksem on kvantimise viga.KVANTIMISE VIGA +-q/2 V

7. DAC – digitaalmaailmast analoogsignaaliks

8. ?

9. GAP/R's K2-W: a vacuum-tube op-amp (1953) 1941: First (vacuum tube) op-amp U.S. Patent 2,401,779 "Summing Amplifier" filed by Karl D. Swartzel Jr. of Bell labs in 1941. This design used three vacuum tubes to achieve a gain of 90 dB and operated on voltage rails of ±350 V. It had a single inverting input rather than differential inverting and non-inverting inputs, as are common in today's op-amps. Throughout World War II, Swartzel's design proved its value by being liberally used in the M9 artillery director designed at Bell Labs. This artillery director worked with the SCR584 radar system to achieve extraordinary hit rates (near 90%) that would not have been possible otherwise. 1947: First op-amp with an explicit non-inverting input 1963: First monolithic IC op-amp

10. Pre op-amp -> feedbackamplifier by Harold S. Black in 1927

11. Flash analoog-digital muundur n=3 bits, 23-1=7 komparaatorit ja 23 = 8 resistori

12. Flash analoog-digital muundur n=3 bits, 23-1=7 komparaatorit ja 23 = 8 resistori

13. Muundurite tüübid

14. SAR - Successive approximation ADC The basic algorithm used in the successive approximation (initially called feedbacksubtraction) ADC conversion process can be traced back to the 1500s relating to thesolution of a certain mathematical puzzle regarding the determination of an unknownweight by a minimal sequence of weighing operations. In this problem, asstated, the object is to determine the least number of weights which would serve to weighan integral number of pounds from 1 lb to 40 lb using a balance scale. One solution putforth by the mathematician Tartaglia in 1556, was to use the series of weights 1 lb, 2 lb,4 lb, 8 lb, 16 lb, and 32 lb. The proposed weighing algorithm is the same as used inmodern successive approximation ADCs. SAR algorithm dates back to the...1500's !

15. SAR - Successive approximation ADC

16. SAR - Successive approximation ADC

17. SAR - Successive approximation ADC An N-bit conversion takes N steps.

18. SAR 2 A simple 3-bit capacitor DAC based SAR. The switches are shown in thetrack, or sample mode where the analog input voltage, AIN, is constantly charging and discharging the parallel combination of all the capacitors. The hold mode is initiated byopening SIN, leaving the sampled analog input voltage on the capacitor array. Switch SCis then opened allowing the voltage at node A to move as the bit switches aremanipulated. If S1, S2, S3, and S4 are all connected to ground, a voltage equal to –AINappears at node A. Connecting S1 to VREF adds a voltage equal to VREF/2 to –AIN. Thecomparator then makes the MSB bit decision, and the SAR either leaves S1 connected toVREF or connects it to ground depending on the comparator output (which is high or lowdepending on whether the voltage at node A is negative or positive, respectively). Asimilar process is followed for the remaining two bits. At the end of the conversioninterval, S1, S2, S3, S4, and SIN are connected to AIN, SC is connected to ground, and theconverter is ready for another cycle.

19. Subranging ADC (Pipeline etc)

20. Subranging ADC (Pipeline etc)

21. Subranging ADC (Pipeline etc)

22. Subranging ADC (Pipeline etc)

23. Subranging ADC (Pipeline etc)

24. Võendamine, sampling, reconstruction, taastamine The sampling theorem Aliasing - rüsimine The Scientist and Engineer's Guide to Digital Signal Processing By Steven W. Smith http://www.dspguide.com Paul Annus paul.annus@elin.ttu.ee

25. Võendamine, sampling The sampling theorem Gábor Dénes (1900 – 1979) 1946 "Theory of communication" Edmund Taylor Whittaker(1873– 1956) 1915 "Expansions of the Interpolation-Theory", "Theorie der Kardinalfunktionen" Claude Elwood Shannon (1916 – 2001) 1949 "Communication in the presence of noise” If a function of time f(t) is limited to the band from 0 to W cycles per second it is completely determined by giving its ordinates at a series of discrete points spaced 1/2W seconds apart 1933 "On the transmission capacity of the 'ether' and of cables in electrical communications" Harry Theodor Nyqvist (1889 –1976) Владимир Александрович Котельников, (1908 – 2005) 1928 "Certain topics in telegraphtransmission theory”

26. Võendamine, sampling

27. Võendamine, sampling

28. Võendamine, sampling Jean Baptiste Joseph Fourier (1768 –1830) Mémoire sur la propagation de la chaleur dans les corps solides. (1807) Uuris soojusnähtusi ja kasutassiinussignaale temperatuuri jaotuste kirjeldamiseks. “...any continuous periodic signal could be represented as the sum of properly chosen sinusoidal waves.”

29. Võendamine, sampling X Dirac comb

30. Võendamine, sampling * Dirac comb

31. Võendamine, sampling, A->D

32. Võendamine, sampling, alias

33. Võendamine, sampling, filtrid

34. Võendamine, sampling, D ->A

35. Võendamine, sampling, filtrid

36. Võendamine, sampling, filtrid Bode plot

37. AD ja DA muundurite täpsusest www.analog.com/library/analogDialogue/archives/39-06/data_conversion_handbook.html Paul Annus paul.annus@elin.ttu.ee

38. AD (DA) muundur Fs=1/T 2n q 0 T 2T 3T

39. DC parameetrid, nulli viga ja võimendus

40. Integraalne lineaarsusvigaINL (inegral non linearity)

41. Differentsiaalne lieaarsusvigaDNL (differential non linearity)

42. Differentsiaalne lieaarsusviga 2DNL (differential non linearity)

43. Differentsiaalne lieaarsusviga 3DNL (differential non linearity) Subranging ADC

44. Differentsiaalne lieaarsusviga 4DNL (differential non linearity) Koodi muutusega kaasnev müra ja DNL

45. Ideaalse ADC AC parameetrid,kvantimisega kaasnev müra ajas

46. Ideaalse ADC AC parameetrid,kvantimisega kaasnev müra ajas 2

47. Ideaalse ADC AC parameetrid,kvantimisega kaasnev müra ajas 3

48. Koherentne muundamine

49. Sisendile taandatud müra

50. SINAD, ENOB Signal to noise and distortion ration – effective number of bits