Perfect data reconstruction algorithm of interleaved adc
- 1. Perfect data reconstructionPerfect data reconstruction algorithm of interleaved ADCalgorithm of interleaved ADC Dr. Fang Xu Teradyne, Inc. Boston, MA, U.S.A.
- 2. Presentation OutlinePresentation Outline Purpose Time Interleaved ADC The reconstruction algorithm Experiment Conclusions
- 3. PurposePurpose Test instruments are built with available parts Instrument development time is long Instruments are designed for testing future products Performance gap needs be solved by design Year Performance (frequency, bits) Instrument architecture reduces Performance gap State of art device performance Future Product Instrument Design-in
- 4. Time Interleaved ADC’sTime Interleaved ADC’s Capture of a continuous time domain waveform ADC7 ADC6 ADC5 ADC4 ADC3 ADC2 ADC1 ADC0 Clock generation Interleaved samples
- 5. Time Interleaved Real ADC’sTime Interleaved Real ADC’s ADC’s and analog sections have different offset, gain and phase Gain and phase vary with frequency Up-to 20 dB measured for gain ! Samples are not uniformly distributed Need advanced algorithm to reconstruct signal Relative gain/phase (timing) error vs. 1st ADC @199.99 MHz 5 dB/div 50 ps/div
- 6. Time Interleaved Real ADC’sTime Interleaved Real ADC’s ADC’s and analog sections have different offset, gain and phase Gain and phase vary with frequency Up-to 20 dB measured for gain ! Samples are not uniformly distributed Need advanced algorithm to reconstruct signal ADC7 ADC6 ADC5 ADC4 ADC3 ADC2 ADC1 ADC0 Input Clock generation Data correction reconstruction
- 7. FFT of Capture Before CorrectionFFT of Capture Before Correction H2 offset gain/phase -120 -80 -40 Fi = 199.990200 MHz, Fs = 1.494220800 Gsamples/s SNR=20 dBc, Non harmonic spur=-25 dBc 100 200 300 400 500 600 700
- 8. Offset Discrepancy ArtifactsOffset Discrepancy Artifacts 100 200 300 400 500 600 700 Repetitive noise pattern Spurs at integer Fs Easy to remove H2 offset -120 -80 -40 gain/phase
- 9. Gain Discrepancy ArtifactsGain Discrepancy Artifacts 0 Repetitive amplitude modulation Spur at ± input tone to integer Fs Need advanced algorithm 100 200 300 400 500 600 700 H2 offset -120 -80 -40 gain/phase
- 10. Phase/Timing Discrepancy ArtifactsPhase/Timing Discrepancy Artifacts 0 Repetitive phase modulation Spur at ± input tone from integer Fs Need advanced algorithm H2 offset -120 -80 -40 gain/phase 100 200 300 400 500 600 700
- 11. Sampling and Aliasing at FsSampling and Aliasing at Fs Aliased in frequency domain without Hermitian symmetry Redundant information with Hermitian symmetry Alias Alias
- 12. Family of Mutually Aliased FrequenciesFamily of Mutually Aliased Frequencies Repetitive amplitude/phase modulation Spur at ± input tone from integer Fs That is a subset of whole spectrum -40 gain/phase 100 200 300 400 500 600 700 We 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. Frequency Domain ReconstructionFrequency Domain Reconstruction Fs Input signal spectrum to be reconstructed ADC7 ADC6 ADC5 ADC4 ADC3 ADC2 ADC1 ADC0 Clock generation Fs/2 Spectrum at output of each ADC Matrix of linear system FMAF Orthogonal components outside FMAFPorous matrix (lot of 0) Sampling with Hermitian symmetrySmall matrix for each FMAF
- 14. = +−−+−−−−−− +−+−− +−+−− iNMMikNMiMiNMiMNM iNMmikNmimiNmiMNm iNMikNiiNiMN R HHHHH HHHHH HHHHH )12/,(1,1,1 * ,1 * 2/,1 )12/,(,, * , * 2/, )12/,(0,0,0 * ,0 * 2/,0 ..... ..... H Matrix RepresentationMatrix Representation ADC7 ADC6 ADC5 ADC4 ADC3 ADC2 ADC1 ADC0 Clock generation Fs/2 = +− + − −+ − iNM ikN i iN iNkN iMN R X X X X X X )12/( * * )( * )2/( ˆ X = − iM im i R X X X ,1 , ,0 ~ . ~ . ~ ~ X RRR XXH ~ˆ = Fs To be reconstructed Input signal spectrum Within a family of mutually aliased frequencies Hm,j
- 15. Unknowns and Knowns in EquationUnknowns and Knowns in Equation Fs Component at frequency i = +− + − −+ − iNM ikN i iN iNkN iMN R X X X X X X )12/( * * )( * )2/( ˆ X = − iM im i R X X X ,1 , ,0 ~ . ~ . ~ ~ X Unknown: All frequency components within a FMAF Captured data of all converters Fs/2 Captured data of converter m at frequency i iX imX , ~
- 16. = +−−+−−−−−− +−+−− +−+−− iNMMikNMiMiNMiMNM iNMmikNmimiNmiMNm iNMikNiiNiMN R HHHHH HHHHH HHHHH )12/,(1,1,1 * ,1 * 2/,1 )12/,(,, * , * 2/, )12/,(0,0,0 * ,0 * 2/,0 ..... ..... H Interpretation of Matrix CoefficientsInterpretation of Matrix Coefficients Each coefficient is complex gain relative to system clock 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 be measured Hm,j Complex gain of converter m for input frequency i
- 17. ADC7 FFT Fs ADC6 FFT ADC5 FFT ADC4 FFT ADC3 FFT ADC2 FFT ADC1 FFT ADC0 FFT Input N/2 times MxM linear equations Order of data Frequency Domain ReconstructionFrequency Domain Reconstruction Solving linear equations for each FMAF Reorder data according to Hermitian symmetry RRR XHX ~ˆ 1− =
- 18. -120 -100 -80 -60 -40 -20 Magnitude(dBFS) Correction Result of Captured SignalCorrection Result of Captured Signal Fi = 199.9902 MHz, Fs = 1.4942208 Gmples/s Before correction SNR= 20dBc, Non harmonic spur= -25dBc After correction SNR= 54dBc, Non harmonic spur= -78dBc 100 200 300 400 500 600 700
- 19. DiscussionsDiscussions Performance 54dBc SNR @750MHZ BW = 142dBc/Hz limited by signal generator -78dBc Spur –20dB dispersion better than SFDR of ADC Hardware stability limitation Ex: A 0.1% converter gain change will limit performance level to about -60dB This does not cover non-linear distortion Application limitation DFT can only start when entire segment of waveform has been captured This method is a better fit for applications which do not need real time capture
- 20. ConclusionsConclusions Solution based on general model of ADC Gain and phase are functions of frequency Complete mathematical resolution Validation by data captured on hardware Results exceed expectation Base of high-performance instruments
- 21. Perfect data reconstructionPerfect data reconstruction algorithm of interleaved ADCalgorithm of interleaved ADC Questions and Answers ? And !