Analog to digital and digital to analog converters

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Sophia Short
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1 Analog to digital and digital to analog converters A/D converter D/A converter ADC DAC ad da Number bases Decimal, base, numbers - 9 Binary, base, numbers and Oktal, base 8, numbers - 7 Hexadecimal, base 6, numbers 9 and A - F

2 The structure of a decimal number Integer number 346= Number with decimals 5.857= Conversion between bases Decimal to hexadecimal = 46 = = 9 6 = 6 9 = 9 6 ( 346 ) = ( 9A) 6 = A 6

3 Conversion between bases cont. Decimal to octal 346 = = = = ( 346 ) = ( 445) 8 Conversion between bases cont. Decimal to binary = = = = = = = 8 8 = 9 9 = 4 4 = = = ( 346 ) = ( ) 3

4 Conversion between bases cont. Hexadecimal to binary ( 3AD ) 6 = ( ) One hexadecimal digit = four binary bits Word length 8 bits = byte (char) 6 bits = word (short, short integer, some times integer) 3 bits = long word or double word (long, long integer, some times integer) 64 bits = long long word 4

5 Floating point numbers IEEE S Exponent, E Mantissa, M N = S E 7 ( ) (.M) < E < 55 Sign bit Smallest number 6,8 38 Largest number ( ) 3.4 Integer values Fixed point Fractional numbers 5

6 Negative numbers Sign bit value Two complement ( ) value = value + value Two complement ( ) = ( ) invert all bits ( ) add one to LSB 6 + ( 38) ( 6) = ( 38) + ( 6) = ( ) ( ) = ( ) + ( ) = + = ( ) 6

7 General A/D- and D/A-quantities n bits gives n N= different values Resolution or N max = = = N n max n nipolar and bipolar converters n/ - Out - max (- -(n-) ) max In - n/ 7

8 Conversion error, SQNR nipolar SQNR = unipolar = max log = max n maximal level log maximal log error level = log max = max log = max N n + ( ) = ( n+ ) log( ) = 6. ( n+ ) 6 ( n+ ) SQNR Conversion error, SQNR bipolar = = log maximal Bipolar maximal amplitude max log = max n error level log = log max = n ( ) = n log( ) = 6. n 6 n max log = max N Number of bits SQNR [db]

9 Logarithmic converter compander A-law, A=87.56 A- and µ-law companding µ-law, µ= Operational amplifiers 9

10 Comparator + in - out ref in < ref out negative in > ref out positive Comparator cont. in < in out negative in > in out positive

11 Inverting amplifier in out out in R R R R I I = = = Summing amplifier in, 3 in, 3 out 3 out in, in, 3 R R R R R R R I I I = = + = +

12 Non-inverting amplifier out R + R = R R = + R in Buffer out = in

13 Buffer cont. in source load out Buffer cont. in + out 3

14 Integrating amplifier out in = t R C D/A-converters Resistance ladder converter MX 4

15 Current summing D/A One bit = max out, LSB = max Current summing D/A Two bits = max out, LSB = 4 max = max out, bit = max 5

16 Current summing D/A Four bits R-R ladder D/A One bit I ref = R ref + R = R ref I f I ref = = R max max = I f R f = = 6

17 R-R ladder D/A Two bits R-R ladder D/A Four bits 7

18 D/A-converted signal Smoothing filter Amplitude Time Amplitude Smoothed DAC signal Time A/D converters Flash converter Decoding net 8

19 A/D converters Flash converter cont. Interval ref 4 ref ref 4 Bits from comparators Binary word ref 3 ref 4 3 ref ref 4 p-counting ADC 9

20 p-counting ADC cont. p-counting ADC cont. Limitations Large variation in conversion time The conversion time depends on the level of the input voltage npredictable conversion time

21 p-counting ADC cont ADC using succesive approximation

22 ADC using succesive approximation cont. max Voltage in Time Single-slope integrating ADC S C out ( ) ref = R C ref t = t R C - ref R - Integrator + + Analog input in Clock Comparator - Control logic Stop conversion Start/stop count Counter Digital output n bits

23 Single-slope integrating ADC cont. ref t R C Dual-slope integrating ADC 3

24 Dual-slope integrating ADC cont. Voltage Variable slope Fixed slope Phase in = t R C ref in RC ref RC Phase = Phase ref t R C Time Phase Phase Fixed interval t ref Variable interval t x Aliasing H Aliased signals True signals f s / f s f 4

25 Sampling cont. Sampling theorem: For faithful reproduction of the sampled signal the sampling frequency has to be more than twice the highest signal frequency Sampling cont. 5

26 Oversampling Sample & Hold 6

27 Sample & Hold cont Sampled signal with hold circuits Amplitude Time Sample & Hold cont Sampled signal with track and hold circuit Amplitude Time 7

28 Sigma-delta modulator Sigma-delta modulators and noise Noise shaping 8

29 ADC with multiplexed inputs Analog inputs ADC with multiplexed inputs cont. Maximal sampling frequency with single channel f s, max Maximal sampling frequency with N channels f s, max N 9

30 Angle decoders Incremental decoders Angle decoders cont. Absolute decoders 3

31 Angle decoders cont. Absolute decoders Decimal Bit Bit Bit Angle decoders cont. Absolute decoders cont. Bit Bit Bit Decimal 3 Correct/False Correct False 6 False 4 Correct 3

32 Angle decoders cont. Absolute decoders cont. Gray coding Decimal Bit Bit Bit Voltage to frequency converters 3

33 Converter specifications Voltage span Resolution Accuracy Conversion time (ADC) Settling time (DAC) Offset error Amplification (scale factor) error Linearity error Converter specifications cont. Offset error n - Out -n max (- -n ) max In 33

34 Converter specifications cont. Amplification (scale factor) error n - Out -n max (- -n ) max In Converter specifications cont. Linearity error n - Out -n max (- -n ) max In 34

35 Skew in parallel communication Bit Bit Bit Skew Bit 3 35

Analog-to-Digital Converter (ADC) And Digital-to-Analog Converter (DAC)

1 Analog-to-Digital Converter (ADC) And Digital-to-Analog Converter (DAC) 2 1. DAC In an electronic circuit, a combination of high voltage (+5V) and low voltage (0V) is usually used to represent a binary