Based with permission on lectures by John Getty Laboratory Electronics II (PHSX262) Spring 2011 Lecture 9 Page 1

Transcription

1 Today 3// Lecture 9 Analog Digital Conversion Sampled Data Acquisition Systems Discrete Sampling and Nyquist Digital to Analog Conversion Analog to Digital Conversion Homework Study for Exam next week (in class 3/9/) Covers everything up through Lecture 8 and Lab 7 Reading A/D converters (pages 6-64). Lab Do DAC pre-lab before lab meeting. Graded at start of lab!!! Sequential logic lab book due 3/5 at 0am. Laboratory Electronics II (PHSX6) Spring 0 Lecture 9 Page

2 Analog Digital Analog Why convert from analog to digital Digital transmission and storage of analog signals Compression, Reliability, Error Correction Digital signal processing Powerful algorithm, adaptable, ease of implementation Why convert from digital to analog We live (see, hear, and feel) in an analog world Replay stored, transmitted, or processed data Music, messages, movies Relay information from computers to humans Digital control of analog systems Convert virtual worlds to reality Laboratory Electronics II (PHSX6) Spring 0 Lecture 9 Page

3 Key Elements of a Sampled Signal Processing System * *ref: Analog Devices; Application Note AN-8 Laboratory Electronics II (PHSX6) Spring 0 Lecture 9 Page 3

4 In many systems the signal is Converts the analog signal converted Key back Elements into analog of a Sampled into a digital Data representation: System (sometimes The final after part short of the or process long A DSP is a term storage includes in additional memory): conditioning Sample microprocessor and Hold * is in the analog domain. Interface to sampled analog optimized circuitry system: for that Latch holds the digital data Precision buffer/gain ensures manipulating the amplifiers ADC digitized sees a until the Some D/A can D/As finish can produce the inband glitches This also that allows must be preserve the stable, integrity analog unchanging signals: of analog conversion. signal. Sometimes signal Perform auto-scale the time operations input the DSP removed processor at this to move stage. required to accurately on to Anti-alias filter perform is such a the LPF, as conversion. typically digital other Analog tasks. filtering can be used with steep roll-off (allows to ensure filtering for undersampling Often >f there and are FFTs. no The D/A to reverses compensate the for the signal components sample advanced is also /. process discrete used on nature the input of the D/A, used for side of improving the system. overall system topic in system A/D) control. fidelity. Some systems are made to A/D can Vector be any processors. of a wide faithfully reproduce (CD range of Field devices. programmable More players) or improve (noise on this gate later. arrays (FPGA). cancelling headphones) on *ref: Analog Devices; Application Note AN-8 the original analog input. Laboratory Electronics II (PHSX6) Spring 0 Lecture 9 Page 4

5 Discrete Sampling of 0 Hz Signal at 5Hz fsignal 0Hz 5Hz fsample Sample interval = 00mS Sample Rate = 5Hz Milliseconds Laboratory Electronics II (PHSX6) Spring 0 Lecture 9 Page 5

6 Discrete Sampling of 0Hz signal at 0Hz fsignal 0Hz 0Hz fsample Sample interval = 00mS Sample Rate = 0Hz Milliseconds Laboratory Electronics II (PHSX6) Spring 0 Lecture 9 Page 6

7 Discrete Sampling at 0Hz fsignal 0Hz fsample 0Hz Milliseconds Sample interval = 50mS Sample Rate = 0Hz Laboratory Electronics II (PHSX6) Spring 0 Lecture 9 Page 7

8 Nyquist Sampling Theorem The sampling theorem states that for a limited bandwidth (band-limited) signal with maximum frequency f max, the equally spaced sampling frequency f sample must be GREATER THAN twice the maximum frequency of the signal, f max, in order to uniquely reconstruct the signal without aliasing. fsample f max => f max is called the Nyquist sampling rate. Half of the sampling rate of an A/D is sometimes called its Nyquist frequency, and is the max frequency that a A/D can record. Laboratory Electronics II (PHSX6) Spring 0 Lecture 9 Page 8

9 Discrete Sampling at f s =f max f F 0Hz f 0Hz S Sample interval = 50mS Sample Rate = 0Hz Milliseconds f s =f max is not sufficient, Nyquist sampling requires f s f max Laboratory Electronics II (PHSX6) Spring 0 Lecture 9 Page 9

10 Aliasing Original Signal fsig Hz Seconds Sample Freq. fsamp 0Hz Sample Period TSamp 50mS Sample_Rate_.XLS Laboratory Electronics II (PHSX6) Spring 0 Lecture 9 Page 0

11 Aliasing in the Frequency Domain The frequency of aliased signals is the difference between and sum of the sampling frequency f S and signal being sampled, f F. These aliased signals repeat around each integer multiple of the sampling frequency. f F f A L f 8 S f F f f and f f f 4 S S f F fs f F F fs.5 A f AL H f S S f AH f F Nyquist Frequency If you low pass filtered at f s, the you know only f<f s are real. Laboratory Electronics II (PHSX6) Spring 0 Lecture 9 Page Hz

12 Digital to Analog Converter (DAC) Terminology Number of Bits: A DAC with n bits provides n discrete output steps or counts. For example an 8 bit DAC has 56 possible output values. Output Range: Difference between the maximum and minimum output values. Resolution: Also known as the step size, represents the minimum change in output voltage. Typically equal to output range / ( n -) Dynamic Range: Output Range divided by Resolution or Noise Voltage. Would be ( n -) if the noise was less than step size of DAC. Laboratory Electronics II (PHSX6) Spring 0 Lecture 9 Page

13 In-Class Exercise Assume a 0 bit DAC is set up to output a voltage from -V dc to +V dc. Determine the resolution. The 0 bits produce a total of 0 = 04 steps. The range is +V dc -(-V dc ) = +4V dc. Therefore the resolution is 4Vdc/03 = V. 3.5mV/step! Laboratory Electronics II (PHSX6) Spring 0 Lecture 9 Page 3

14 One Approach to DAC: R-R Ladder Circuit Vout kohm kohm kohm kohm kohm kohm kohm kohm Key = D Key = C Key = B Key = A V ref 5V V out A B C D V What is V max? V max =V ref *5/6=4.69V V min =0 Laboratory Electronics II (PHSX6) Spring 0 Lecture 9 Page 4

15 nd Approach to DAC: Scaled Summing Junction DAC 50kohm 3 Vout V 0kohm 0kohm 40kohm 80kohm Key = D Key = C Key = B Key = A This approach is the one we will implement in lab. V out A50k B50k C50k D50k V 80k 40k 0k 0k A B C D V What is Range? V max =0, V min =-0V*5/6=-4.69V Range=4.69V Laboratory Electronics II (PHSX6) Spring 0 Lecture 9 Page 5

16 Analog to Digital Converter (ADC) Terminology Number of Bits: An ADC with n bits divides the input range into n discrete steps. For example, an 8 bit ADC can produce a total of 56 different output codes. Full Scale Input Range Difference between the minimum and maximum input voltage that can be measured. Resolution: Quantization, also known as the step size, is the change in input voltage represented by each count at the output. Often referred to as LSB (least significant bit) Dynamic Range: Input Range divided by resolution or noise. Typically equals n -, if noise is less than LSB. Laboratory Electronics II (PHSX6) Spring 0 Lecture 9 Page 6

17 ADC Accuracy QUANTIZATION ERROR Inherent accuracy (±/LSB, least significant bit) INTEGRAL NON-LINEARITY (INL) is a measure of the deviation of each individual code from a line drawn from zero scale or negative full scale ( LSB below the first code transition) through positive full scale ( LSB above the last code transition). The deviation of any given code from this straight line is measured from the center of that code value. DIFFERENTIAL NON-LINEARITY (DNL) is the measure of the maximum deviation from the ideal step size of LSB. DNL is commonly measured at the rated clock frequency with a ramp input. MISSING CODES are output codes that are skipped or never appear at the ADC outputs. These codes cannot be reached by any input value. OFFSET ERROR is the difference between the ideal and actual LSB transition point. FULL SCALE ERROR is how far the last code transition is from the ideal.5 LSB below positive V_ref (V_ref is n times step size) GAIN ERROR is number of LSB gained from conversion from lowest to highest output. It is a measure of the deviation of the ADC from linear (gain = ) conversion. See figure 9.44 in H&H page 65 Laboratory Electronics II (PHSX6) Spring 0 Lecture 9 Page 7

18 Ideal ADC: Quantization Error Quantization Error LSB QUANTIZATION ERROR LSB FULL SCALE ERROR Quantization error is the inherent deviation of the output from a straight line. -Note last transition is.5 LSB from V ref (used to measure full scale error) Laboratory Electronics II (PHSX6) Spring 0 Lecture 9 Page 8

19 Sampled System Errors - INL INL Error Integral Non-Linearity is the deviation of the output from a straight line. Can be measured at each code or stated as maximum for all codes. Laboratory Electronics II (PHSX6) Spring 0 Lecture 9 Page 9

20 Sampled System Errors - DNL DNL Error DNL= LSB (step is correct, but INL of 00 is.0lsb) Differential Non-Linearity is the maximum difference between the expected stepsize ( LSB) and that steps actually produced by the DAC. Laboratory Electronics II (PHSX6) Spring 0 Lecture 9 Page 0

21 Sampled System Errors - Offset Offset Error Offset Error is measured at 000. Laboratory Electronics II (PHSX6) Spring 0 Lecture 9 Page

22 Sampled System Errors - Gain Gain Error Gain Error is measured at. The offset error must be known to compute slope. (y=mx+b) Gain Error is given in LSB over full scale. Laboratory Electronics II (PHSX6) Spring 0 Lecture 9 Page

23 Sampled System Errors - Gain Gain Error LSB offset Gain Error is measured at. The offset error must be known to compute this value. (y=mx+b) Laboratory Electronics II (PHSX6) Spring 0 Lecture 9 Page 3

24 References. Paul Horowitz and Winfield Hill (989). The Art of Electronics, nd Ed., Cambridge. Analog Devices, Fundamentals of Sampled Data Systems, accessed MAR Efunda, Engineering Fundamentals web site; accessed MAR National Semiconductor: accessed MAR Laboratory Electronics II (PHSX6) Spring 0 Lecture 9 Page 4