Perfect data reconstruction algorithm of interleaved adc

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Interleaving 12 14-bit ADC's to achieve >80dB SFDR at 1.5Gs/s

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Perfect data reconstruction algorithm of interleaved adc

  1. 1. Perfect data reconstructionPerfect data reconstructionalgorithm of interleaved ADCalgorithm of interleaved ADCDr. Fang XuTeradyne, Inc. Boston, MA, U.S.A.
  2. 2. Presentation OutlinePresentation Outline Purpose Time Interleaved ADC The reconstruction algorithm Experiment Conclusions
  3. 3. PurposePurposeTest instruments are built with available partsInstrument development time is longInstruments are designed for testing future productsPerformance gap needs be solved by designYearPerformance(frequency, bits)InstrumentarchitecturereducesPerformance gapState of art device performanceFutureProductInstrumentDesign-in
  4. 4. Time Interleaved ADC’sTime Interleaved ADC’sCapture of a continuous time domain waveformADC7ADC6ADC5ADC4ADC3ADC2ADC1ADC0Clock generationInterleavedsamples
  5. 5. Time Interleaved Real ADC’sTime Interleaved Real ADC’sADC’s and analog sections have differentoffset, gain and phaseGain and phase vary with frequencyUp-to 20 dB measured for gain !Samples are not uniformly distributedNeed advanced algorithm to reconstruct signalRelative gain/phase (timing) error vs. 1stADC @199.99 MHz5 dB/div 50 ps/div
  6. 6. Time Interleaved Real ADC’sTime Interleaved Real ADC’sADC’s and analog sections have differentoffset, gain and phaseGain and phase vary with frequencyUp-to 20 dB measured for gain !Samples are not uniformly distributedNeed advanced algorithm to reconstruct signalADC7ADC6ADC5ADC4ADC3ADC2ADC1ADC0InputClock generationDatacorrectionreconstruction
  7. 7. FFT of Capture Before CorrectionFFT of Capture Before CorrectionH2offsetgain/phase-120-80-40Fi = 199.990200 MHz,Fs = 1.494220800Gsamples/sSNR=20 dBc,Non harmonic spur=-25dBc100 200 300 400 500 600 700
  8. 8. Offset Discrepancy ArtifactsOffset Discrepancy Artifacts100 200 300 400 500 600 700Repetitive noise pattern Spurs at integer FsEasy to removeH2offset-120-80-40gain/phase
  9. 9. Gain Discrepancy ArtifactsGain Discrepancy Artifacts0Repetitive amplitude modulation Spur at ± input tone to integer FsNeed advanced algorithm100 200 300 400 500 600 700H2offset-120-80-40gain/phase
  10. 10. Phase/Timing Discrepancy ArtifactsPhase/Timing Discrepancy Artifacts0Repetitive phase modulation Spur at ± input tone from integer FsNeed advanced algorithmH2offset-120-80-40gain/phase100 200 300 400 500 600 700
  11. 11. Sampling and Aliasing at FsSampling and Aliasing at FsAliased in frequency domain without HermitiansymmetryRedundant information with Hermitian symmetryAliasAlias
  12. 12. Family of Mutually Aliased FrequenciesFamily of Mutually Aliased FrequenciesRepetitive amplitude/phase modulation Spur at ± input tone from integer Fs That is a subset of whole spectrum-40gain/phase100 200 300 400 500 600 700We call this subset of frequencies including that of signal A family of mutually aliased frequencies (FMAF) Frequencies number equals the number of ADCs Vector notation: iNMiMNiNkNikNiNi XXXXXX +−−−++− )12/(*)2/(*)(*,,,,,-20
  13. 13. Frequency Domain ReconstructionFrequency Domain ReconstructionFsInput signal spectrumto be reconstructedADC7ADC6ADC5ADC4ADC3ADC2ADC1ADC0Clock generationFs/2Spectrum at output of each ADCMatrix of linear system FMAFOrthogonal components outside FMAFPorous matrix (lot of 0)Sampling with Hermitian symmetrySmall matrix for each FMAF
  14. 14. =+−−+−−−−−−+−+−−+−+−−iNMMikNMiMiNMiMNMiNMmikNmimiNmiMNmiNMikNiiNiMNRHHHHHHHHHHHHHHH)12/,(1,1,1*,1*2/,1)12/,(,,*,*2/,)12/,(0,0,0*,0*2/,0..........HMatrix RepresentationMatrix RepresentationADC7ADC6ADC5ADC4ADC3ADC2ADC1ADC0Clock generationFs/2=+−+−−+−iNMikNiiNiNkNiMNRXXXXXX)12/(**)(*)2/(ˆX=− iMimiRXXX,1,,0~.~.~~XRRR XXH~ˆ =FsTo be reconstructed Input signal spectrumWithin a family of mutually aliased frequenciesHm,j
  15. 15. Unknowns and Knowns in EquationUnknowns and Knowns in EquationFsComponent at frequency i=+−+−−+−iNMikNiiNiNkNiMNRXXXXXX)12/(**)(*)2/(ˆX=− iMimiRXXX,1,,0~.~.~~XUnknown:All frequencycomponents withina FMAFCaptureddata of allconvertersFs/2Captured dataof converter mat frequency iiXimX ,~
  16. 16. =+−−+−−−−−−+−+−−+−+−−iNMMikNMiMiNMiMNMiNMmikNmimiNmiMNmiNMikNiiNiMNRHHHHHHHHHHHHHHH)12/,(1,1,1*,1*2/,1)12/,(,,*,*2/,)12/,(0,0,0*,0*2/,0..........HInterpretation of Matrix CoefficientsInterpretation of Matrix CoefficientsEach coefficient is complex gain relative to systemclock of a converter at a specific frequencyIt includes information on amplitude (flatness)and phase (group delay, clock delay)To solve equation, each coefficient needs to bemeasuredHm,jComplex gain of converterm for input frequency i
  17. 17. ADC7 FFTFsADC6 FFTADC5 FFTADC4 FFTADC3 FFTADC2 FFTADC1 FFTADC0 FFTInputN/2 timesMxM linearequationsOrder of dataFrequency Domain ReconstructionFrequency Domain ReconstructionSolving linear equations for each FMAFReorder data according to Hermitian symmetryRRR XHX~ˆ 1−=
  18. 18. -120-100-80-60-40-20Magnitude(dBFS)Correction Result of Captured SignalCorrection Result of Captured SignalFi = 199.9902 MHz, Fs = 1.4942208Gmples/sBefore correctionSNR= 20dBc, Non harmonic spur= -25dBcAfter correctionSNR= 54dBc, Non harmonic spur= -78dBc100 200 300 400 500 600 700
  19. 19. DiscussionsDiscussionsPerformance54dBc SNR @750MHZ BW = 142dBc/Hzlimited by signal generator-78dBc Spur –20dB dispersion better thanSFDR of ADCHardware stability limitationEx: A 0.1% converter gain change will limitperformance level to about -60dBThis does not cover non-linear distortionApplication limitationDFT can only start when entire segment ofwaveform has been capturedThis method is a better fit for applicationswhich do not need real time capture
  20. 20. ConclusionsConclusionsSolution based on general model of ADCGain and phase are functions of frequencyComplete mathematical resolutionValidation by data captured on hardwareResults exceed expectationBase of high-performance instruments
  21. 21. Perfect data reconstructionPerfect data reconstructionalgorithm of interleaved ADCalgorithm of interleaved ADCQuestions and Answers? And !

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