EE247 Lecture 14 Administrative issues q To avoid having EE247 EE 142 or EE290C midterms on the same day EE247 midterm moved from Oct 20th to Thurs Oct 27th q q Homework 4 due on Thurs Oct 20th H K s office hours changed from 3 4 to 2 30 to 3 30 EECS 247 Lecture 14 Data Converters 2005 H K Page 1 EE247 Lecture 14 Data Converters 0Spectral testing including windowing 0Practical aspects of converter testing Signal source Clock generator Evaluation board considerations Evaluation set up Debugging EECS 247 Lecture 14 Data Converters 2005 H K Page 2 ADC 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 testing Apply 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 windowing EECS 247 Lecture 14 Data Converters 2005 H K Page 3 Direct DFT Choice of Number of Cycles Number of Samples N cycles fs fx 6 integer Signal Amplitude To overcome frequency spectrum leakage problem Number of Cycles integer 1 0 5 0 0 5 1 Time Preferable to have N power of 2 FFT instead of DFT Signal Amplitude N cycles fs fx non integer 1 N cycles fs fx 5 55 non intege 0 5 0 0 5 1 Time EECS 247 Lecture 14 Data Converters 2005 H K Page 4 Windowing 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 frequency EECS 247 Lecture 14 Data Converters 2005 H K Page 5 Window Time samples are multiplied by window coefficients on a sample by sample basis 2 1 8 1 6 1 4 1 2 Multiplication in the time domain corresponds to convolution in the frequency domain 1 0 8 0 6 0 4 0 2 100 Example Nuttall window EECS 247 Lecture 14 Data Converters 200 300 400 500 600 700 800 900 1000 Time 2005 H K Page 6 Windowed Data 1 Signal Amplitude Signal before windowing 0 5 0 0 5 Windowed Signal Amplitude 1 Signal after windowing Windowing removes the discontinuity at block boundaries 0 0 2 0 4 0 6 Time 0 8 0 0 2 0 4 0 6 Time 0 8 1 3 x 10 2 1 0 1 2 EECS 247 Lecture 14 Data Converters 1 3 x 10 2005 H K Page 7 Only first 20 bins shown Response attenuated by 120dB for bins 5 Lots of windows to choose from go by name of inventorBlackman Harris Various window trade off attenuation versus width smearing of sinusoids Normalized Amplitude dB Nuttall Window DFT 20 40 60 80 100 120 2 4 6 8 10 12 14 16 18 20 DFT Bin EECS 247 Lecture 14 Data Converters 2005 H K Page 8 0 10 Before windowing 20 30 40 50 60 70 0 0 1 0 2 0 3 0 4 0 5 Frequency fx fs Windowed Spectrum dBFS 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 bins Spectrum not Windowed dBFS DFT of Windowed Signal 0 20 After windowing 40 60 80 100 120 140 0 0 1 0 2 0 3 0 4 0 5 Frequency fx fs EECS 247 Lecture 14 Data Converters 2005 H K Page 9 Integer 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 need to lock fx to fs PLL Windowing No restrictions on fx no need to have the signal locked to fs ideal for measurements Signal energy and harmonics distributed over several DFT bins Requires more data points for a fixed accuracy EECS 247 Lecture 14 Data Converters 2005 H K Page 10 Spectral ADC Testing ADC with B bits 1 full scale input B 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 11 ADC Output Spectrum 0 N 2048 Signal amplitude 20 Ampliutde dbFS Bin N fx fs 1 Matlab arrays start at 1 A 0dBFS 40 60 80 SNR 100 120 0 0 1 0 2 0 3 0 4 0 5 f fs EECS 247 Lecture 14 Data Converters 2005 H K Page 12 ADC Simulated Output Spectrum 0 N 2048 Amplitude dbFS Noise bins all except signal bin bx N fx fs 1 As 20 log10 s bx s bx 0 An 10 log10 sum s 2 SNR As An 20 40 60 80 SNR 62dB 10 bits Computed SQNR 6 02xN 1 76dB 100 120 0 f fs 0 1 0 2 0 3 0 4 0 5 Note In a real circuit including thermal flicker noise the measured total noise is the sum of quantization noise associated with the circuit EECS 247 Lecture 14 Data Converters 2005 H K Page 13 Why is noise floor not 62dB 0 The DFT noise floor is 10log10 N 2 dB below the actual noise floor assuming white noise For N 2048 30dB EECS 247 Lecture 14 Data Converters N 2048 20 Amplitude dbFS DFT bins act like an analog spectrum analyzer with bandwidth of fs N rather than fs 2 40 60 30dB 80 100 120 0 f fs 0 1 0 2 0 3 0 4 0 5 2005 H K Page 14 DFT Plot Annotation 1 Specify how many DFT points N are used or 2 Shift DFT noise floor by 10log10 N 2 dB or 3 Normalize to noise power in 1Hz bandwidth EECS 247 Lecture 14 Data Converters 2005 H K Page 15 Spectral Performance Metrics ADC Including Nonlinearities Signal S DC Distortion D Noise N Signal to noise ratio SNR S N Signal to distortion ratio SDR S D Signal to noise distortion ratio SNDR S N D Spurious free dynamic range SFDR EECS 247 Lecture 14 Data Converters 2005 H K Page 16 Harmonic Components At multiples of fx Aliasing fsignal fx 0 18 fs f2 2 f0 0 36 fs f3 3 f0 0 54 fs 0 46 fs f4 4 f0 0 72 fs 0 28 fs f5 5 f0 0 90 fs 0 10 fs f6 6 f0 1 08 fs 0 08 fs EECS 247 Lecture 14 Data Converters 2005 H K Page 17 Spectrum versus INL …
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