AMD vtu notes.
- 1.ANALOG AND MIXED MODE VLSI VI SEM ENC DATA CONVERTER FUNDAMENTALSIntroductionWhy data Conversion? Most real-world signals are analog in nature. Real-world signals-Continuous time, Continuous amplitude However Digital signal processing allows us to efficiently manipulate information. Digital abstraction-discrete time, discrete amplitude To take advantage of DSP we must be able to move from analog to digital and back as neededWhat is data Converter? A device that converts a signal from analog to digital domain and vice versa.What type of systems require data converters? Any system that requires real inputs from outside world that need to be processed digitally or any system that wants to convert digital data to analog signal that can be interpreted in the outside world need a converter.How does a data converter fit in to signal chain? Data converters typically accept analog signals from sensorsonce these signals have been conditioned, and pass off digitaldata to a processor. They can also accept digital data from these devices and passthem off for signal conditioning and analog system output.1
2. Applications- wide range. Performance requirements such as resolution and bandwidthare set by intended applications. Portable devices-push the limits of technology by requiringfaster speed and lower power. Communications: Wireless transceivers, Modems Computing and control: Imagers,displays, Multimedia Measurement & Instrumentation: Test equipment, Industrial andscientific Instrumentation, Sensors & actuators. Consumer Electronics: Video/Audio, Control (Automotive,Appliances, etc). Embedded data Conversion2 3. Types of Data ConvertersTwo types:1. Analog to digital Converter(ADC)2. Digital to analog Converter(DAC)Analog to digital converter consists of two basic functions. Sampling: convert a continuous time input signal to a discrete time representation. Quantization: convert a continuous amplitude input signal to a discrete amplitude representation. Input signal must be bandlimited to no more than FS to prevent aliasing. 3 4. Uniform Sampling and QuantizationUniform Sampling and Quantization-Sample signal Uniformly in time-Quantize signal Uniformly in amplitudeIssues:How fast to sample?How much noise added to quantization?How can we reconstruct signal back to analog form?Discrete time signals-Discrete time signals are simply a sequence of numbers with a set ofcorresponding discrete time indexes.-Intermediate signal values are not defined.-Mathematically convenient but non-physical:use the term sampleddata signals.4 5. -Representing signals in discretetime domain determines anincrease in ambiguity in frequency domain; undesired frequencytranslation /interaction(aliasing)Sampling theoryFig. shown below illustrates the sampled signal in time and frequencydomain.5 6. 6 7. Types of SamplingNyquist rate Sampling: Sampling at twice the signal frequencyDown samplingUp sampling7 8. Over Sampling8 9. Down Sampling fs -1LSB)i.e. one or more of the possible 2 n binary codes arenever output.DNL specifies the deviation of any adjacent code in the transferfunction of DAC or ADC from an ideal code width of 1 LSB. 13 14. -DNL is determined by subtracting the locations of successive codetransition points after compensating for gain and offset errors.-positive DNL implies that the code is longer than the ideal codewidth.- negative DNL implies that the code is Shorter than the idealcode width- DNL is measured in the increasing code direction of the transfercurve.- The transition of code N is compared to that of code N+1.- For DAC, DNL error of -1LSB implies that the output did notincrease for increasing input code.-14 15. - For DAC, DNL error of greater than -1LSB implies that thedevice is non-monotonic.- For an ADC,DNL error of greater than -1LSB implies that atleast one code is missing, meaning that there is no analogvoltage which will generate a particular code.- Manufactures includeNo missing Codesspec.Gain and Offset error- Gain error has a non ideal slope.- Ideally, in the graphs above, as the analog input increases at acertain rate, the output codes would also increase at the samerate.- If the output codes increase at a different rate than the analoginput does, then it results in gain error.Gain error can be defined as the difference between the level thatproduces the greatest code and the smallest code, versus the ideallevels that produce these codesIn an ideal situation, data converter would begin to notice deviationsfrom true zero voltage.However, because of offset error, a small constant analog voltage isalways present before the conversion begins to function linearly.15 16. 16 17. Dynamic Characteristics1. SNR (Signal-to-Noise Ratio)- RMS value representing the ratio of the amplitude of thedesired signal to noise power below one half of the frequency.- Measure of strength of a signal to background noise.- Contributes to the overall dynamic performance of the device athigher frequencies and affects the linearity at thosefrequencies.- In audio world, a low SNR means the device has lots of hissand static high rating.- Key measure of Data converter.2. Total Hormonic Distortion- The ratio of sum of the powers of all hormonic frequencies abovethe fundamental frequency to the power of the funadamentalfrequency.(dB)-expression of distortion effect of signal harmonics on the originalsignal.3.ENOB(Effective Number of bits)-The number of bits achieved in a real system, discounting bitsthat are affected by noise.-Another way of specifying SNR.4. SFDR(Spurious dynamic range)-Distance in dB between the fundamental input and the worst spur.-headroom available in FFT plot.-difference between the signal amplitude and the first and largestharmonic spur.-measure of signal quality.-higher values are desirable.17 18. Data Converters Building blocks Sample and Hold Circuits Operational Amplifiers,OTAs Comparators Filters Current sources Reference Circuits Logic Circuits 18 19. Data Converters blocks-DACDigital n-bit word 19 20. For an n-bit word, the MSB has a weight of2 (n-1) = 2 n / 2 where n is the total number of bits in the word, LSB has a weight of 1. The Least and Most Significant Bits(LSB & MSB) are just whattheir name implies.Digital coding techniques20 21. Thermometer code Thermometer-code differs from a binary code in that a thermometer-code has 2N - 1 digital inputs to represent 2N different digital values, Typically, in a thermometer-code the number of 1s represent the decimal value.Features Low DNL errors Guarnteed monotonocity Reduced glitch area Increased complexity(binary code needs only N digital inputs to represent 2N different digital values.) 21 22. The transfer function of DAC is a series of discrete points asshown in fig. 1 LSB corresponds to the height of a step between successiveanalog outputs, A DAC can be thought of as a digitally controlled potentiometerwhose output is a fraction of the full scale analog voltagedetermined by the digital input data. Resolution: The number of bits in the digital input word. Each of the possible digital input word has its own uniqueanalog output voltage.An N-bit digital word is mapped in to an equivalent analog voltage byscaling a reference.22 23. Analog output of unipolar DAC is Vref need special care for design.VLSB is the voltage change when one LSB changes.Data Converters DAC spec-NonlinearityThe maximum analog voltage that can be generated is known asfull-scale voltage, VFS(does not equal to Vref, because theresolution is finite) and is defined as the difference between Vrefand VLSB or the analog output for the largest digital word(1111) and the analog output for the smallest digitalword(000..0). 23 24. Consider 3 bit DAC.Vref: 5VVout = F Vref F-fraction determined by n-bit wordF=D/2NVout(max) = 7/8 Vref.Max. analog voltage generated-full scale voltage VFSI LSB = Vref/2NFor 3-bit DAC 1 LSB= 5/8 V = 0.625VMSB causes the output to change by Vref.Ex- Find the resolution of DAC if the output voltage is desired tochange in 1mV, Vref is 5V.Solution : DAC must resolve1mV/5V = 0.0002 =.02%Accuracy required = 1/2N =0.0002N=Log (5V/1mV)= 12.29 = 13 bitsComparison of 3,8 16 bit DAC with Vref=5vResolution Comb 1LSB% accuracyVfs 3 8 0.625V 12.54.375V 825619.5mV 0.3914.985V1665,536 76.29uV 0.00153 4.9999V Increasing the resolution by 1 bit increases the accuracy by afactor of 2. Precision required to map the analog voltage at high resolutionis very difficult to achieve, Vout approaches that of Vref as N increases. 24 25. DAC-NonlinearityDifferential Nonlinearity: Ideal increments as per the ideal curve= 0.625V=1LSB Nonideal components cause the analog increments to differfrom ideal values.The difference between actual and ideal-differential nonlinearity is DNLn = Actual increment height of transition n Idealincrement height N-number corresponding to digital input transition.Differential Nonlinearity:Examplen=3, Vref=5V1LSB=1/8 of Vout/VrefDNL 1=DNL 2=DNL 7=0DNL 3=1.5 LSB-1 LSB =0.5 LSB=0.3125VDNL 4=0.5 LSB-1 LSB =-0.5 LSBDNL 5=0.25 LSB-1 LSB =-0.75 LSBDNL 6=1.75 LSB-1 LSB =0.75 LSB 25 26. Differential Nonlinearity:ExamplePlot DNL in LSB versus input digital code.DNL for the converter is 0.75LSB since the overall error of DAC isdefined by its worst-case DNL.Generally, DAC will have 1/2 LSB of DNL ,if it is to be n-bitaccurate.Differential Nonlinearity:Example5-bit DAC with .75LSBs of DNL has resolution of 4-bit DAC.If the DNL for DAC is less than -1LSBs, then DAC is said to benonmonotonic.DAC-should exhibit monotonicity if it is to function witout error.The DNL specification measures how well a DAC can generateuniform analog LSB multiples at its output. 26 27. Integral Nonlinearity: Another important Static characteristic of DAC. Difference between the data converter output values and areference straight line drawn through the first and last outputvalues. INL defines the linearity of overall transfer curve as INL n = Output value for input code n ou