EECS 247 Lecture 14: Data Converters © 2005 H.K. Page 1EE247Lecture 14• Administrative issuesq To avoid having EE247 & EE 142 or EE290C midterms on the same day, EE247 midterm moved from Oct. 20thto Thurs. Oct. 27thq Homework # 4 due on Thurs. Oct. 20thq H.K.‘s office hours changed from 3-4 to 2:30 to 3:30EECS 247 Lecture 14: Data Converters © 2005 H.K. Page 2EE247Lecture 14• Data Converters0Spectral testing including windowing0Practical aspects of converter testing§ Signal source § Clock generator§ Evaluation board considerations§ Evaluation set-up§ DebuggingEECS 247 Lecture 14: Data Converters © 2005 H.K. Page 3ADC Testing (Continued)• Need to find "decision levels", i.e. input voltages at all code boundaries– One way: Adjust voltage source to find exact code trip points "code boundary servo"– More versatile: Histogram testingØApply a signal with known distribution (ramp or sinusoid) and analyze digital code distribution at ADC output• Spectral testing- Reveals ADC errors associated with dynamic behavior i.e. ADC performance as a function of frequency§Direct Discrete-Fourier-Transform (DFT) based measurements§ Feasable when input signal can be locked to sampling frequency§ Resticts input signal frequency§DFT measurements including windowingEECS 247 Lecture 14: Data Converters © 2005 H.K. Page 4Direct DFTChoice of Number of Cycles & Number of SamplesTo overcome frequency spectrum leakage problem:– Number of Cycles à integer– N/cycles = fs/ fxà non-integer– Preferable to have N à power of 2 (FFT instead of DFT)N/cycles = fs / fx=6 à integer-1-0.500.51Signal Amplitude-1-0.500.51Signal AmplitudeN/cycles = fs / fx=5.55 à non-integeTimeTimeEECS 247 Lecture 14: Data Converters © 2005 H.K. Page 5Windowing• Spectral leakage can be virtually eliminated by “windowing” time samples prior to the DFT– Windows taper smoothly down to zero at the beginning and the end of the observation window– Time samples are multiplied by window coefficients on a sample-by-sample basis• Windowing sinusoidal waveforms places the window spectrum at the sinewave frequency– Convolution in frequencyEECS 247 Lecture 14: Data Converters © 2005 H.K. Page 6Window• Time samples are multiplied by window coefficients on a sample-by-sample basis• Multiplication in the time domain corresponds to convolution in the frequency domain• Example: Nuttall window100 200 300 400 500 600 700 800 900 10000.20.40.60.811.21.41.61.82TimeEECS 247 Lecture 14: Data Converters © 2005 H.K. Page 7Windowed Data• Signal before windowing• Signal after windowing– Windowing removes the discontinuity at block boundaries0 0.2 0.4 0.6 0.8 1-1-0.500.51TimeSignal Amplitude0 0.2 0.4 0.6 0.8 1x 10-3-2-1012TimeWindowed Signal Amplitudex 10-3EECS 247 Lecture 14: Data Converters © 2005 H.K. Page 8Nuttall Window DFT• Only first 20 bins shown• Response attenuated by -120dB for bins > 5 • Lots of windows to choose from (go by name of inventor-Blackman, Harris…)• Various window trade-off attenuation versus width (smearing of sinusoids)2 4 6 8 10 12 14 16 18 20-120-100-80-60-40-20DFT BinNormalized Amplitude [dB]EECS 247 Lecture 14: Data Converters © 2005 H.K. Page 9DFT of Windowed Signal• Spectra of signal before and after windowing• Window gives ~ 100dB attenuation of sidelobes(use longer window for higher attenuation)• Signal energy “smeared” over several (approximately 10) bins0 0.1 0.2 0.3 0.4 0.5-70-60-50-30-20-100Frequency [ fx/ fs]Spectrum not Windowed [ dBFS ]0 0.1 0.2 0.3 0.4 0.5-140-120-100-80-60-40-200Windowed Spectrum [ dBFS ]Frequency [ fx/ fs]-40Before windowingAfter windowingEECS 247 Lecture 14: Data Converters © 2005 H.K. Page 10Integer Cycles versus Windowing• Integer number of cycles– Signal energy for a single sinusoid falls into single DFT bin– Requires careful choice of fx– Ideal for simulations– Measurements à need to lock fxto fs(PLL)• Windowing– No restrictions on fxàno need to have the signal locked to fsà ideal for measurements– Signal energy (and harmonics) distributed over several DFT bins– Requires more data points for a fixed accuracyEECS 247 Lecture 14: Data Converters © 2005 H.K. Page 11Spectral ADC Testing• ADC with B bits• ±1 full scale inputB = 10;delta = 2/(2^B-1);th = -1+delta/2:delta:1-delta/2;x = sin(…);y = adc(x, th) * delta - 1;s = abs(fft(y)/N*2);s = s(1:N/2);f = (0:length(s)-1) / N;EECS 247 Lecture 14: Data Converters © 2005 H.K. Page 12ADC Output Spectrum•Signal amplitude:– Bin: N * fx/fs + 1(Matlab arrays start at 1)– A = 0dBFS•SNR?0 0.1 0.2 0.3 0.4 0.5-120-100-80-60-40-200N=2048Ampliutde [dbFS]f/fsEECS 247 Lecture 14: Data Converters © 2005 H.K. Page 13ADC Simulated Output Spectrum• Noise bins: all except signal binbx = N*fx/fs + 1;As = 20*log10(s(bx))s(bx) = 0;An = 10*log10(sum(s.^2))SNR = As - An• SNR = 62dB (10 bits)• Computed SQNR = 6.02xN+1.76dBNote: In a real circuit including thermal/flicker noise à the measured total noise is the sum of quantization & noise associated with the circuit0 0.1 0.2 0.3 0.4 0.5-120-100-80-60-40-200N=2048Amplitude [dbFS]f /fsEECS 247 Lecture 14: Data Converters © 2005 H.K. Page 14Why is noise floor not @ 62dB ?• DFT bins act like an analog spectrum analyzer with bandwidth of fs/N, rather than fs/2• The DFT noise floor is 10log10(N/2)dB below the actual noise floor (assuming white noise)• For N=2048: 30dB0 0.1 0.2 0.3 0.4 0.5-120-40-200Amplitude [dbFS]N=204830dB-100-80-60f /fsEECS 247 Lecture 14: Data Converters © 2005 H.K. Page 15DFT Plot Annotation1. Specify how many DFT points (N) are used, or2. Shift DFT noise floor by 10log10(N/2)dB, or3. Normalize to "noise power in 1Hz bandwidth"EECS 247 Lecture 14: Data Converters © 2005 H.K. Page 16Spectral Performance MetricsADC Including Nonlinearities• Signal S• DC• Distortion D• Noise N• Signal-to-noise ratioSNR = S / N• Signal-to-distortion ratioSDR = S / D• Signal-to-noise+distortion ratio SNDR = S / (N+D)• Spurious-free dynamic rangeSFDREECS 247 Lecture 14: Data Converters © 2005 H.K. Page 17Harmonic Components• At multiples of fx• Aliasing:– fsignal= fx= 0.18 fs– f2= 2 f0= 0.36 fs– f3= 3 f0= 0.54 fsà 0.46 fs– f4= 4 f0= 0.72 fsà 0.28 fs– f5= 5 f0= 0.90 fsà 0.10 fs– f6= 6 f0= 1.08 fsà 0.08 fsEECS 247 Lecture 14: Data Converters © 2005 H.K. Page 18Spectrum versus INL,
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