1. Understanding ADC Specifications September 2005

2. 2 Definition of Terms 000 Analogue Input Voltage 001 010 011 100 101 110 111 Digital Output Code FS1/2 FS3/4 FS1/4 FS0 code width Transition point is where the output code changes from one code to an adjacent code with respect to an analogue input voltage V REF = Full-Scale (FS) + 1LSB Voltage Ideal code Width = 1LSB 1 LSB = V REF / 2 n ie: V REF = 4.096V, for a 12-bit ADC LSB size = 4.096/2 12 = 1mV Transition Points Ideal transfer function for a 3-bit A/D

3. 3 ADC Specifications: Resolution  For an ADC, Resolution is simply a measure of how many segments the input analogue range can be divided into.  Resolution IS NOT THE SAME AS ACCURACY!  You could have a 16-bit ADC that is less accurate than an 8-bit ADC  Why? Monotonicity, A/D converter noise, etc

4. 4 ADC Specs: Quantisation Error 000 Analogue Input Voltage 001 010 011 100 101 110 111 Digital Output Code FS1/2 FS3/4 FS1/4 FS0 The difference between the actual input voltage and the digital code representation of the input voltage. Even in the case of a perfect ADC, quantisation error will be ± 1/2 LSB. Increasing bits reduces the error

5. 5 Sampling and Quantisation 4-bit (16 level) ADC sampling a sinewave input, time domain Input Sinewave ADC Output Quantisation Error TIME OUTPUT DIGITAL WORD 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111 2345678910111213

6. 6 ADC Specs: Offset Error 000 Analog Input Voltage 001 010 011 100 101 110 111 Digital Output Code FS1/2 FS3/4 FS1/4 FS0 Offset Error Offset Error is the difference between the first transition point and the ideal first transition point. (Measured in LSBs) Digital Code Out = A + Vin where A is the analogue offset error Offset Errors can be corrected in Firmware Correction for offset error can be made by adding (or subtracting) the correction from each code. Ideal transfer function Actual transfer function

7. 7 ADC Specs: Gain Error (full scale error) 000 Actual full scale range 001 010 011 100 101 110 111 Digital Output Code Full scale range is the difference between the first and last code transition points. The ideal full scale range minus the actual full scale range equals Gain Error. (Measured in LSBs) Digital Code = B V IN where B is the gain error Gain Errors can be corrected in firmware Corrections for gain error can be made by multiplying each code by the ratio of ideal to actual full scale range. Ideal transfer function Actual transfer function Ideal full scale range

8. 8 ADC Specs: A/D Converter with Offset and Gain Error 000 001 010 011 100 101 110 111 Digital Output Code With most ADCs, you will have to deal with both Gain and offset Errors! Digital Code = A + B V IN where A is the Offset Error and B is the Gain Error Ideal transfer function Actual transfer function FS1/2 FS3/4 FS1/4 FS0

9. 9 ADC Specs: Differential Nonlinearity (DNL) 000 001 010 011 100 101 110 111 Digital Output Code DNL is a measure of variations in code widths from the ideal code width. A DNL of ±½ LSB implies that: ½ LSB < all code widths < 1½LSB A missing code means DNL = -1 LSB Ideal transfer function Actual transfer function Narrow code, <1 LSB Wide code, >1 LSB

10. 10 DNL Plot for 12bit ADC 0 4095 This DNL plot shows the variation of code widths for each code for a 12 bit ADC

11. 11 ADC Specs: Missing Codes 000 001 010 011 100 101 110 111 Digital Output Code If the DNL spec goes beyond - 1LSB, then missing codes will appear. The term ‘No Missing Codes’ means that no digital output codes are skipped as the analog input is swept from zero to full scale. Most ADCs today will include the specification ‘No missing codes’ 1/2 FS3/4 FS1/4 FS0 Analogue Input Voltage The 100 Code is ‘Missing’

12. 12 ADC Specs: Monotinicity 000 001 010 011 100 101 110 111 Digital Output Code If the output code of an ADC is guaranteed to output increasing codes as long as the input signal is increasing, it is called Monotonic If at some point in the transfer function the digital output code decreases as the analog input increases, then it is non- monotonic. Almost all ADCs on the market today are guaranteed monotonic 1/2 FS3/4 FS1/4 FS0 Analog Input Voltage Non-monotonicity

13. 13 ADC Specs: Integral Nonlinearity (INL) 000 001 010 011 100 101 110 111 Ideal transfer function Actual transfer function INL < 0 INL is the maximum deviation between an actual code transition point and its corresponding ideal transition point. Measured in LSBs, and calculated after offset and gain error have been compensated for. This is a measure of the transfer function’s deviation from linearity. A positive INL indicates transition(s) occurring later than ideal. Negative INL means transition(s) earlier than ideal INL < 0 Digital Output Code

14. 14 ADC Specs: Integral Nonlinearity (INL) 000 001 010 011 100 101 110 111 Ideal transfer function Actual transfer function INL > 0 Digital Output Code This diagram shows an INL error greater than zero whereas the previous diagram showed INL errors of less than zero. As you may have guessed, INL and DNL are very closely related; if you have one you also always have the other

15. 15 INL Plot for a (poor, non Silabs) 12bit ADC 0 4095 This INL plot shows the variation of code transition points for each code for a 12 bit ADC

16. 16 But First, a quick look at FFTs…… AC Specs

17. 17 Fast Fourier Transforms (FFT) 10203040 50 -120 -100 -80 -60 -40 -20 0 Input Signal Amplitude (dB) Frequency (Hz) 4096 points, f in = 10.2kHz, -0.5dB Number of points taken Input Signal Frequency Input Signal Headroom 1/2 of Sampling Rate

18. 18 Fast Fourier Transforms (FFT) Fundamental or Primary Frequency (The input signal) Harmonic or Secondary Frequencies (Distortion caused by the part Average Noise Floor

19. 19 ADC Specs: Total Harmonic Distortion (THD)  A frequency domain spec evaluated using an input sinewave and FFT analysis  Calculated as the ratio of the RMS sum of the number of harmonics (usually the first 5) to the RMS value of the input. It is always specified at a particular frequency and is measured in dB.  In layman’s terms, it is a measure of the amount of signal energy distributed in harmonics vs amount in primary  It is caused by A/D converter nonlinearities, which generate harmonics of the input signal which to appear in the output  Typical values are -78dB to -85dB.

20. 20 THD Plot 1010 2020 3030 4040 5050 - 120 - 100 -80 -60 -40 -20 0 Amplitude (dB) Frequency (Hz) 1010 2020 3030 4040 5050 - 120 - 100 -80 -60 -40 -20 0 Amplitude (dB) Frequency (Hz) Good THD Bad THD THD(-dB) = 20LOG  (V 2 ) 2 + (V 3 ) 2 + … + (V n ) 2 V 1 V 1 (Fundamental) V2V2 V4V4 V3V3 V5V5

21. 21 ADC Specs: Signal to Noise Ratio (SNR)  SNR is a frequency domain spec measured using a sinewave input and FFT analysis  It is the ratio of RMS signal amplitude to the RMS output noise for a specific input frequency and amplitude,excluding harmonic noise  In laymans terms, it’s a measure of how much noise is present with respect to the actual signal  It is expressed in dB  Ideal SNR is equal to (6.02n + 1.76 dB) where “n” is the number of bits  For 12-bit A/D, ideal SNR = 74dB

22. 22 ADC Specs: Signal to Noise and Distortion Ratio (SINAD)  SINAD is a frequency domain spec measured using a sinewave input and FFT analysis  It is the ratio of RMS signal amplitude to the RMS sum of the noise and distortion products for a specific input frequency and amplitude  In laymans terms, it’s a measure of noise generated by the part itself  It is expressed in dB

23. 23 Effective Number of Bits vs Noise-Free Bits  Assuming that system noise is Gaussian, histogram will approximate a Normal Distribution

24. 24 Noise-Free Resolution  “Effective Noise” is the specification that is used for dynamic signals  “Noise-Free Resolution” is the specification that is used for DC signals involving a display

25. 25 Example F350 calculation  Out of 1024 samples:  Min code = -33  Max code = 32  Average code = -0.5  Variance = 123  1 sigma = sqrt Variance = sqrt (123) = 11 LSBs  RMS Noise = +/- 11 LSBs  Effective Bits = Log 2 (2 23 /1 sigma) = 19.5 bits  Noise-Free bits = Log2(2^23/6.6*sigma) = 17 bits  2^17 is 131,072, which equates to 5 ½ digits on the scale display

26. 26 ADC Specs: Effective Number of Bits (ENOB)  ENOB is a measurement of the resolution of the ADC and is directly related to Signal to Noise+Distortion (SINAD)  ENOB = [SINAD - 1.76]/6.02  For ideal SNR (74dB) and no distortion, ENOB = [74-1.76]/6.02 = 12 bits!

27. 27 ADC Specs: Spurious Free Dynamic Range (SFDR)  SFDR is a frequency domain measurement that is evaluated using a sine wave input and FFT analysis  The SFDR is always given at a particular frequency  SFDR is the difference of Fundamental minus highest spur in dB.  In laymans terms, it’s a measure of the size of the biggest spike compared to the next biggest spike. In a perfect world, there would be only one big spike  The larger the number the better. SFDR specs range from 80 - 90 dB.

28. 28 SFDR Plot Spurious Free Dynamic Range (SFDR) is the difference between primary and next highest spur SFDR

29. 29 ADC Specifications: Sample Time and Conversion Time  Every A/D conversion is made up of a sample or tracking period and a conversion period  The terms ‘track and hold’ and ‘sample and hold’ are sometimes interchanged, although most serial ADCs are ‘track and hold’ devices  The period of time when the input signal is sampled or tracked is the Sample Time.  Can be measured in time or number of clock cycles  Conversion Time is the time required to convert the sampled input signal to a digital word.  Can also be measured in time or number of clock cycles

30. 30 ADC Specifications: Throughput Rate  Throughput rate is the number of times you can do a sample + conversion in a period of time  Usually specified in ksps or Msps  Example: A fictitious SAR ADC with sample time of 2 clock cycles and 13 clocks required for a 12 bit word. (Fclk=1Mhz) 15 clocks * 1uS = 15us CS time = 600ns Period = 15us + 600ns = 15.6us f t = 1/15.6uS = 64 ksps

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