EE 505 Lecture 7. Spectral Performance of Data Converters - Time Quantization - Amplitude Quantization Clock Jitter Statistical Circuit Modeling
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1 EE 505 Lecture 7 Spectral Performance of Data Converters - Time Quantization - Amplitude Quantization Clock Jitter Statistical Circuit Modeling
2 . Review from last lecture. MatLab comparison: 512 Samples with Standard Sweep Spectre Results MatLab Results
3 . Review from last lecture. MatLab comparison: 512 Samples with Strobe Period Sweep Spectre Results MatLab Results
4 . Review from last lecture. Comparison of 4 windows
5 . Review from last lecture. Comparison of 4 windows
6 . Review from last lecture. Preliminary Observations about Windows Provide separation of spectral components Energy can be accumulated around spectral components Simple to apply Some windows work much better than others But windows do not provide dramatic improvement and can significantly degrade performance if sampling hypothesis are met
7 . Review from last lecture. Post-processing Method of circumventing the coherent sampling problem Can also be used for addressing spectral purity problem for test signal generation x kt S N 1 k 0 Post-Processor Χ k N 1 k 0 Non-coherent Easily implemented in MATLAB Will be considered in the laboratory Removes fundamental from samples and replaces with coherent fundamental before taking DFT
8 Spectral Characterization of Data Converters Distortion Analysis Time Quantization Effects of DACs of ADCs Amplitude Quantization Effects of DACs of ADCs Clock Jitter
9 Quantization Effects (time and amplitude depicted) 16,384 pts res = 4bits N P =25 20 msec
10 Quantization Effects (time and amplitude depicted) 16,384 pts res = 4bits N P =25 20 msec
11 Quantization Effects (time and amplitude depicted) 16,384 pts res = 4bits
12 Quantization Effects (time and amplitude depicted) Simulation environment: N P =23 f SIG =50Hz V REF : -1V, 1V Res: will be varied N=2 n will be varied
13 Spectral Characterization of Data Converters Distortion Analysis Time Quantization Effects of DACs of ADCs Amplitude Quantization Effects of DACs of ADCs Clock Jitter
14 Quantization Effects Res = 4 bits
15 Quantization Effects Res = 4 bits Axis of Symmetry
16 Quantization Effects Res = 4 bits
17 Quantization Effects Res = 4 bits
18 Quantization Effects Res = 4 bits
19 Quantization Effects Res = 4 bits Expect quantization noise effects to be uniformly distributed!!
20 Quantization Effects Res = 4 bits Expect quantization noise effects to be uniformly distributed!!
21 Quantization Effects Res = 4 bits Expect quantization noise effects to be uniformly distributed!!
22 Quantization Effects Res = 4 bits Note presence of odd-ordered harmonic terms!!
23 Res = 4 bits Why are there spectral components present in the quantization noise? Recall the uncorrelated assumption was good only for about 4 bits or more!
24 Quantization Effects Res = 10 bits Quantization noise is much more uniform
25 Quantization Effects Res = 10 bits
26 Quantization Effects Res = 10 bits Harmonic Components not Visible
27 . Review from last lecture. Quantization Effects Res = 10 bits Compared to the previous slide, it appears that the quantization noise has gone down why does this occur?
28 Quantization Effects Res = 10 bits Compared to the previous slide, it appears that the quantization noise has gone down even more why does this occur?
29 Quantization Effects Res = 10 bits Compared to the previous slides, it appears that the quantization noise has gone down even more why does this occur?
30 Quantization Effects Res = 10 bits
31 Quantization Effects Res = 10 bits Very small third harmonic component but does not extend above other noise terms
32 . Review from last lecture. Spectral Characterization Amplitude Quantization Does not introduce spectral components for n large Nearly uniformly distributed Decreases with increasing N
33 Spectral Characterization of Data Converters Distortion Analysis Time Quantization Effects of DACs of ADCs Amplitude Quantization Effects of DACs of ADCs Clock Jitter
34 Spectral Characteristics of DACs and ADCs
35 Spectral Characteristics of DAC t Periodic Input Signal Sampling Clock T SIG t Sampled Input Signal (showing time points where samples taken)
36 Spectral Characteristics of DAC T SIG Quantization Levels T PERIOD Quantized Sampled Input Signal (with zero-order sample and hold)
37 Spectral Characteristics of DAC T DFT WINDOW T PERIOD T SIG T CLOCK Sampling Clock T DFT CLOCK DFT Clock
38 Spectral Characteristics of DAC T DFT WINDOW T PERIOD T SIG T CLOCK Sampling Clock T DFT CLOCK DFT Clock
39 Spectral Characteristics of DAC Sampling Clock DFT Clock
40 Spectral Characteristics of DAC Sampled Quantized Signal (zoomed) DFT Clock Sampling Clock
41 Spectral Characteristics of DAC Consider the following example f SIG =50 Hz f CL =500 Hz (DAC clock) f DFTCL =71.24K Hz n DFT =15 (coherent sampling) N P1 =23 (number of signal periods in DFT window) N P =1 n res =8 bits Xin(t) =.95sin(2πf SIG t) (-.4455dB) Matlab File: afft_quantization_dac_jan2017.m
42 DFT Simulation from Matlab n sam =
43 DFT Simulation from Matlab Expanded View n sam = Width of this region is f CL Analogous to the overall DFT window when directly sampled but modestly asymmetric
44 DFT Simulation from Matlab Expanded View n sam =
45 DFT Simulation from Matlab Expanded View n sam =
46 DAC Comparisons with Quantization Fundamental, second harmonic, and third harmonic N θ Nsam n A 1 A 2 A 3 32K K
47 Spectral Characteristics of DAC Consider the following example f SIG =50 Hz f CL =500 Hz (DAC clock) f DFTCL =71.24K Hz n DFT =18 (coherent sampling) N P1 =23 (number of signal periods in DFT window) N P =1 n res =8 bits Xin(t) =.95sin(2πf SIG t) (-.4455dB) Matlab File: afft_quantization_dac.m
48 DFT Simulation from Matlab n sam =
49 DFT Simulation from Matlab Expanded View n sam =
50 DFT Simulation from Matlab Expanded View n sam =
51 DFT Simulation from Matlab Expanded View n sam =
52 Spectral Characteristics of DAC Consider the following example f SIG =50 Hz f CL =500 Hz (DAC clock) f DFTCL =71.24K Hz n DFT =18 (coherent sampling) N P1 =23 (number of signal periods in DFT window) N P =1 n res =14bits Xin(t) =.95sin(2πf SIG t) (-.4455dB) Matlab File: afft_quantization_dac.m
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56 Spectral Characteristics of DAC Consider the following example f SIG =50 Hz f CL =500 Hz (DAC clock) f DFTCL =71.24K Hz n DFT =18 (coherent sampling) N P1 =23 (number of signal periods in DFT window) N P =1 n res =16bits Xin(t) =.95sin(2πf SIG t) (-.4455dB) Matlab File: afft_quantization_dac.m
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60 Spectral Characteristics of DAC Consider the following example f SIG =50 Hz f CL =497.8 Hz (DAC clock) f DFTCL = K Hz n DFT =16 (not coherent sampling) N P1 =23 (number of signal periods in DFT window) N P =1 n res =16bits Xin(t) =.95sin(2πf SIG t) (-.4455dB) Matlab File: afft_quantization_dac.m
61 DFT Simulation from Matlab
62 DFT Simulation from Matlab
63 DFT Simulation from Matlab
64 Skip to Next Separator
65 The spectral characteristics of DACs as affected by DAC clock rate, by DAC resolution, and by the length of the DFT window will be considered
66 Notation: T CL : Clock Period (=1/f CL ) T SIG : Signal Period (=1/f SIG ) T DFT : DFT period (=1/f DFT ) N SIG1 : Number of Signal Periods to establish periodicity with sampling clock N CL1 : Number of Clock Periods to establish periodicity with sampling clock N SIG : Number of Signal Periods in DFT window N CL : Number of Clock Periods in DFT window N P : Number of Periods in DFT window N SAM : Number of DFT samples in each clock period n: Length of DFT window in binary bits N: Length of DFT window n Q Number of binary bits of quantization
67 Graphical Interpretation of Signals for DAC Spectral Characterization T PERIOD T DFT Window T SIG T CLK T DFT Signal Clock Time Quantized Signal DFT CL In this example, N SIG1 =3, N CL1 =8, N P =2, N SIG =6, N CL =16
68 Consider the Following Examples Frequencies Number of Samples fsig fclk ffft NSIG1 NCLK1 NP NSIG NCL nfft N NSAM nq 1 a b c d e f a b c d e a b c d e f g a b c d e e
69 Quantization Effects N Q =6, 12 and 24 DFT = 1024
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73 Magnitude of Fundamental nd Harmonic in db Res 12 No. points 1024 fsig = No.DFT Periods 5.00 No Sig Periods fcl/fsig Nsamp = 6.83 Rectangular Window Pyyt = Columns 1 through Columns 8 through Columns 15 through
74 Columns 22 through Columns 29 through Columns 36 through Columns 43 through Columns 50 through Columns 57 through
75 Columns 64 through Columns 71 through Columns 78 through Columns 85 through Columns 92 through Columns 99 through
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79 Magnitude of Fundamental nd Harmonic in db Res 24 No. points 1024 fsig = No.DFT Periods 5.00 No Sig Periods fcl/fsig Nsamp = 6.83 Rectangular Window Pyyt = Columns 1 through Columns 8 through Columns 15 through Columns 22 through
80 Columns 29 through Columns 36 through Columns 43 through Columns 50 through Columns 57 through Columns 64 through
81 Columns 71 through Columns 78 through Columns 85 through Columns 92 through Columns 99 through Columns 106 through
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85 Magnitude of Fundamental nd Harmonic in db Res 6 No. points 1024 fsig = No.DFT Periods 5.00 No Sig Periods fcl/fsig Nsamp = 6.83 Rectangular Window Pyyt = Columns 1 through Columns 8 through Columns 15 through Columns 22 through
86 Columns 29 through Columns 36 through Columns 43 through Columns 50 through Columns 57 through Columns 64 through
87 Columns 71 through Columns 78 through Columns 85 through Columns 92 through Columns 99 through Columns 106 through
88 DAC Comparisons with Quantization N θ Nsam n A 1 A 2 A 3 32K K
89 Comparison of DAC resolution levels 12-bit resolution DFT = bit resolution 24-bit resolution
90 Quantization Effects N Q =6, 12 and 14 DFT = 16,384
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95 Rectangular Window Pyyt = Columns 1 through Columns 8 through Columns 15 through Columns 22 through Columns 29 through
96 Columns 36 through Columns 43 through Columns 50 through Columns 57 through Columns 64 through Columns 71 through
97 Columns 78 through Columns 85 through Columns 92 through Columns 99 through Columns 106 through
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102 Res 24 No. points fsig = No.DFT Periods 5.00 No Sig Periods fcl/fsig Nsamp = Rectangular Window Pyyt = Columns 1 through Columns 8 through Columns 15 through Columns 22 through
103 Columns 29 through Columns 36 through Columns 43 through Columns 50 through Columns 57 through Columns 64 through
104 Columns 71 through Columns 78 through Columns 85 through Columns 92 through Columns 99 through Columns 106 through
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109 Res 6 No. points fsig = No.DFT Periods 5.00 No Sig Periods fcl/fsig Nsamp = Rectangular Window Pyyt = Columns 1 through Columns 8 through Columns 15 through Columns 22 through
110 Columns 29 through Columns 36 through Columns 43 through Columns 50 through Columns 57 through Columns 64 through
111 Columns 71 through Columns 78 through Columns 85 through Columns 92 through Columns 99 through Columns 106 through
112 Comparison of DAC resolution levels DFT = 16, bit resolution 24-bit resolution 12-bit resolution
113 Comparison of DAC resolution levels DFT = 16, bit resolution 24-bit resolution 12-bit resolution
114 DAC Comparisons with Quantization N θ Nsam n A 1 A 2 A 3 32K K K K K
115 DFT Length Effects DFT = 8,10,12, 14, and 16 bits
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118 Res 18 No. points 256 fsig = No.DFT Periods 5.00 No Sig Periods fcl/fsig Nsamp = 1.71 Rectangular Window Pyyt = Columns 1 through Columns 8 through Columns 15 through Columns 22 through
119 Columns 29 through Columns 36 through Columns 43 through Columns 50 through Columns 57 through Columns 64 through
120 Columns 29 through Columns 36 through Columns 43 through Columns 50 through Columns 57 through Columns 64 through
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124 Res 18 No. points 1024 fsig = No.DFT Periods 5.00 No Sig Periods fcl/fsig Nsamp = 6.83 Rectangular Window Pyyt = Columns 1 through Columns 8 through Columns 15 through Columns 22 through
125 Columns 29 through Columns 36 through Columns 43 through Columns 50 through Columns 57 through Columns 64 through
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129 Res 18 No. points 4096 fsig = No.DFT Periods 5.00 No Sig Periods fcl/fsig Nsamp = Rectangular Window Pyyt = Columns 1 through Columns 8 through Columns 15 through Columns 22 through
130 Columns 29 through Columns 36 through Columns 43 through Columns 50 through Columns 57 through Columns 64 through
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135 Res 18 No. points fsig = No.DFT Periods 5.00 No Sig Periods fcl/fsig Nsamp = Rectangular Window Pyyt = Columns 1 through Columns 8 through Columns 15 through Columns 22 through
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140 Magnitude of Fundamental nd Harmonic in db Res 18 No. points fsig = No.DFT Periods 5.00 No Sig Periods fcl/fsig Nsamp = Rectangular Window Pyyt = Columns 1 through Columns 8 through Columns 15 through Columns 22 through
141 Columns 29 through Columns 36 through Columns 43 through Columns 50 through Columns 57 through Columns 64 through
142 DFT Length Effects
143 DFT Length Effects
144 Comparison of DAC Resolution Levels Resolutions: = 4,6,8,10,12, 14, and 16 bits
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148 Res 4 No. points 4096 fsig = No.DFT Periods 5.00 No Sig Periods fcl/fsig Nsamp = Rectangular Window Pyyt = Columns 1 through Columns 8 through Columns 15 through Columns 22 through Columns 29 through 35
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152 Res 6 No. points 4096 fsig = No.DFT Periods 5.00 No Sig Periods fcl/fsig Nsamp = Rectangular Window Pyyt = Columns 1 through Columns 8 through Columns 15 through Columns 22 through Columns 29 through 35
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156 Res 8 No. points 4096 fsig = No.DFT Periods 5.00 No Sig Periods fcl/fsig Nsamp = Rectangular Window Pyyt = Columns 1 through Columns 8 through Columns 15 through Columns 22 through Columns 29 through 35
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160 Res 10 No. points 4096 fsig = No.DFT Periods 5.00 No Sig Periods fcl/fsig Nsamp = Rectangular Window Pyyt = Columns 1 through Columns 8 through Columns 15 through Columns 22 through
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164 Res 12 No. points 4096 fsig = No.DFT Periods 5.00 No Sig Periods fcl/fsig Nsamp = Rectangular Window Pyyt = Columns 1 through Columns 8 through Columns 15 through Columns 22 through Columns 29 through 35
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168 Columns 29 through 35 Res 14 No. points 4096 fsig = No.DFT Periods 5.00 No Sig Periods fcl/fsig Nsamp = Rectangular Window Pyyt = Columns 1 through Columns 8 through Columns 15 through Columns 22 through
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172 Res 16 No. points 4096 fsig = No.DFT Periods 5.00 No Sig Periods fcl/fsig Nsamp = Rectangular Window Pyyt = Columns 1 through Columns 8 through Columns 15 through Columns 22 through
173 Comparison of DAC Resolution Levels
174 Comparison of DAC Resolution Levels
175 DAC Comparisons with Quantization N θ Nsam n A 1 A 2 A 3 32K K K K K K
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179 Res 12 No. points fsig = No.DFT Periods 1.00 No Sig Periods 1.00 fcl/fsig Nsamp = Rectangular Window Pyyt = Columns 1 through Columns 8 through Columns 15 through Columns 22 through
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183 Res 16 No. points 4096 fsig = No.DFT Periods No Sig Periods fcl/fsig Nsamp = Rectangular Window Pyyt = Columns 1 through Columns 8 through Columns 15 through Columns 22 through
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187 Res 16 No. points 4096 fsig = No.DFT Periods No Sig Periods fcl/fsig Nsamp = 6.95 Rectangular Window Pyyt = Columns 1 through Columns 8 through Columns 15 through Columns 22 through
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191 Res 16 No. points 4096 fsig = No.DFT Periods 5.00 No Sig Periods fcl/fsig Nsamp = Rectangular Window Pyyt = Columns 1 through Columns 8 through Columns 15 through Columns 22 through
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195 Res 16 No. points 4096 fsig = No.DFT Periods 3.00 No Sig Periods 9.00 fcl/fsig Nsamp = 4.55 Rectangular Window Pyyt = Columns 1 through Columns 8 through Columns 15 through Columns 22 through Columns 29 through 35
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199 Res 16 No. points 4096 fsig = No.DFT Periods 1.00 No Sig Periods 3.00 fcl/fsig Nsamp = Rectangular Window Pyyt = Columns 1 through Columns 8 through Columns 15 through Columns 22 through Columns 29 through 35
200 End Skip
201 Summary of time and amplitude quantization assessment Time and amplitude quantization do not introduce harmonic distortion Time and amplitude quantization do increase the noise floor
202 Duty Cycle Effects on Spectral Performance of DACS File: DAC Quantization with RTZ.m
203 Consider N P =1 N SIG =11 N CL =70 f sig =50 n res =10 Thus, f CLK =f SIG (N CL /N SIG )=318Hz The fft spectrum should be nominally symmetric around f CLK /2=159Hz so will get only the fundamental, second harmonic, and third harmonic in the fundamental frequency half-period which occurs at fft coefficient number 36 and the clock frequency will be at fft coefficient number 71 (and thus the fundamental will appear at fft coefficient numbers 11+1=12 and 71-11=60) The relationship between fft coefficient number and frequency is given by n-1 f= f NSIG SIG or by n=1+f N f SIG SIG
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208 Magnitude of Fundamental nd Harmonic in db Res 10 No. points fsig = No.DFT Periods 1.00 No Sig Periods fcl/fsig 6.36 Nsamp = DutyCycle = 1.0 Rectangular Window Pyyt = Columns 1 through Columns 9 through Columns 17 through
209 Columns 25 through Columns 33 through Columns 41 through Columns 49 through Columns 57 through Columns 65 through
210 Columns 73 through Columns 81 through Columns 89 through Columns 97 through Columns 105 through
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215 Magnitude of Fundamental nd Harmonic in db Res 10 No. points fsig = No.DFT Periods 1.00 No Sig Periods 11.0 fcl/fsig 6.36 Nsamp = DutyCycle = 0.5 Rectangular Window Columns 1 through Columns 9 through Columns 17 through Columns 25 through
216 Columns 33 through Columns 41 through Columns 49 through Columns 57 through Columns 65 through Columns 73 through
217 Columns 81 through Columns 89 through Columns 97 through Columns 105 through
218 DAC Comparisons with Quantization N θ Nsam n A 1 A 2 A 3 32K K K K K K K K
219 Summary of Duty Cycle Effects Duty Cycle does dot introduce harmonic distortion Duty Cycle reduction reduces signal levels thus degrades SNR
220 Number of Samples/Period One Sample per Period Multiple Samples per Period Many authors use a data acquisition system and select one sample/period Spectrum analyzer will generally measure continuous-time effects
221 Number of Samples/Period Nonlinear Settling Glitch Glitch Typical DAC Response
222 Number of Samples/Period Incorrect Settling Typical DAC Response
223 Number of Samples/Period Incorrect Settling Settling error can be multiple LSB at Nyquist Rate Multiple LSB settling error does not cause distortion if settling is linear Glitches are a significant contributor to spectral distortion (at high frequencies)
224 Typical SFDR Plot From: Y. Cong and R. L. Geiger, "A 1.5-v 14-bit 100-MS/s Self-Calibrated DAC," IEEE J. of Solid State Circuits, December 2003, vol. 38, no. 12, pp
225 Spectral Characterization of Data Converters Distortion Analysis Time Quantization Effects of DACs of ADCs Amplitude Quantization Effects of DACs of ADCs Clock Jitter
226 Effects of Jitter on Spectral Performance
227 Model of Jitter T S Ideal Clock Jittery Clock t Jk Assume t Jk are uncorrelated uniformly distributed random variables θ θ tjk U - T S, TS 2 2 Note: there can also be jitter in the ideal clock or there may be no ideal clock so zero crossings may be modeled as a random walk or a sum of a random walk and uniform jitter. Analysis more complicated in these cases.
228 Model of Jitter Assume t Jk are uncorrelated uniformly distributed random variables θ θ tjk U - T S, TS 2 2 Consider θ=.01,.001,.0001, Observe: If T S is a 100MHz clock, then T S =10nsec and θ=.0001 corresponds to 1psec (±0.5psec) of symmetric jitter
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233 Statistical Characterization of Electronic Components and Circuits Recall: Almost all data converter structures work perfectly if components are ideal Major challenges in data converter design Parasitic Resistances and Capacitances Nonlinearity in components Statistical variation in components and circuits Model uncertainties Power supply variability
234 Consider a flash ADC V REF V IN R R R R Thermometer to Binary Decoder n X OUT Resistor values and offset voltages of Comparators are all random variables at design level Variations of these RVs affect the break point and thus the yield R
235 Consider Current-Steering DAC V DD I 1 I 1 /2 I 1 /4 I 1 /8 b 3 b 2 b 1 b 0 R F V OUT Ideally n -1 b i OUT 1 F n-i i=0 2 V = -I R
236 Consider Current-Steering DAC V DD V DD M REF M n-1 M 1 M 0 I 1 I 1 /2 I 1 /4 I 1 /8 b 3 b 2 b 1 b 0 R F V R I n-1 I 1 I 0 V OUT I REF b n-1 M (n-1)s M 1S b0 b 1 M 0S Basic Implementation of Current Sources Ideally Actually I μc W V -V 2 OX k k R Tp 2 L k L k=l0 k-1 W k=2 W0 I μc W V -V 2 k OXk k k R Tpk 2 L k I k is a random variables and is a function of the model parameters μ k, C OXk, W k, L k, and V Tpk μ k, C OXk, W k, L k, and V Tpk are all random variables
237 Recall from previous lecture How important is statistical analysis? Example: 7-bit FLASH ADC with R-string DAC V REF V IN Assume R-string is ideal, V REF =1V and V OS for each comparator must be at most +/- ½ LSB Case 1 Standard deviation is 5mV Case 2 P COMP = Y = ADC -32 R R R R Thermometer to Binary Decoder n X OUT Standard deviation is 1mV P COMP Y =0.988 ADC R Statistics play a key role in the performance and consequently yield of a data converter
238 End of Lecture 7
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EE 435 Lecture 32 Spectral Performance Windowing Spectral Performance of Data Converters - Time Quantization - Amplitude Quantization Quantization Noise . Review from last lecture. Distortion Analysis
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