Calibration technique for calibrating high speed equivalent time sampling scope using a characterized high speed photo diode

Transcription

1 Calibration technique for calibrating high speed equivalent time sampling scope using a characterized high speed photo diode

2 Motivation PNA-X Non-linear network analyzer application Measurement technique uses a phase reference Implemented as a pulse generator Non ideal magnitude and phase characteristics Traceability to known standard needed, especially phase

3 Comb generator

4 Comb generator output

5 Traceability Comb generator Sampling scope Photo diode EOS system NIST

6 Sampler in out 50Ω

7 Equivalent time sampling scope Real time scope have limited bandwidth Equivalent time sampling scope samples a short window in time by opening closing the switch Re-triggers a small amount of time later Piece by piece filling in the picture

8 Jitter, drift and time base distortion Inaccuracies in the time base Drift (time base reference) Jitter (random and systematic) Imperfections in the switch Finite opening and closing time Leakage Mismatches in the transmission line All leads to finite impulse response

9 Measurement methods Three classes of methods Swept sine calibration magnitude only method Nose to Nose calibration depends on reciprocal pulse kick out and impulse response assumption research has shown this has limitations above 25 GHz * Calibration with known pulse source Our method described here is in the latter * Systematic error of the nose-to-nose sampling oscilloscope calibration; Williams, K. Remley, Paul D. Hale; 2007

10 Known pulse source Need to be sufficiently fast, 90 GHz bandwidth Ideal system, pulse source is de-convolved from measurement by sampling scope impulse response or complex frequency response In practice there are many imperfections that need our attention Drift Time base distortion Jitter Impedance mismatch

11 Known pulse excitation Electrical pulse ~4-5 ps FWHM Pulsed laser 50 Ω 80 fs FWHM pulse train 10 MHz repetition rate V bias gnd

12 Electro Optical Sampling EOS system at NIST Calibrating electro-optical sampling systems; D. Williams, P. Hale, T. Clements, J.M. Morgan; IEEE MTT-S digest 2001

13 Magnitude [V/(C*Hz)] Phase [degrees] Results from EOS Photo Diode Magnitude Phase Frequency [ GHz]

14 Transfer system architecture Pulsed laser opt attenuator diode scope 0 90 pzt sync trig 5 GHz 3dB hybrid 5 GHz PLL Spectrum RF source HV amp loop filter Correcting sampling oscilloscope timebase errors with a passively mode-locked laser phase locked to a microwave oscillator; A. Jargon, Paul D. Hale, C.M. Wang; 2010

15 Single raw measurement

16 Data process flow Oscilloscope Waveforms TBD Correction Drift Correction Time-domain correction Jitter Analysis Fourier Transform VNA Data EOS Data Mismatch Factor Photodiode Response Mismatch Correction Photodiode Correction Frequency domain correction Oscilloscope Response

17 Acquisition Time interval: 0 to 5.1 ns Number of points: 8192 Samples per set: 250 Repeat above 5 times between disconnects

18 TBC program

19 TBC detail algorithm y t ij ij R model parameters j T i n h jk cos2 ftij jk sin2 ftij k1 h i harmonic order ij n Minimize with respect to θ 1, θ 2 and δ Uncertainty of Timebase Corrections; C.M. Wang, Paul D. Hale, Dylan Williams; 2009 Compensation of random and systematic timing errors in sampling oscilloscopes; P. Hale, C. Wang, D. Williams, K. Remley, D. Wepman; 2006 ij y ij T i ij j ij F ; , 2, w F Ti i; 1 yi 1 w F Ti i; 2 yi2 i i1 random jitter systematic timebase distortion weight Implemented using ODRPACK random additive noise model parameters

20 TBC output --- STOPPING CRITERIA: SSTOL = 1.49D-08 (SUM OF SQUARES STOPPING TOLERANCE) PARTOL = 3.67D-11 (PARAMETER STOPPING TOLERANCE) MAXIT = 200 (MAXIMUM NUMBER OF ITERATIONS) --- INITIAL WEIGHTED SUM OF SQUARES = D+00 SUM OF SQUARED WEIGHTED DELTAS = D+00 SUM OF SQUARED WEIGHTED EPSILONS = D+00 *** FINAL SUMMARY FOR FIT BY METHOD OF ODR *** --- STOPPING CONDITIONS: INFO = 1 ==> SUM OF SQUARES CONVERGENCE. NITER = 4 (NUMBER OF ITERATIONS) NFEV = 9 (NUMBER OF FUNCTION EVALUATIONS) NJEV = 5 (NUMBER OF JACOBIAN EVALUATIONS) IRANK = 0 (RANK DEFICIENCY) RCOND = 4.49D-06 (INVERSE CONDITION NUMBER) ISTOP = 0 (RETURNED BY USER FROM SUBROUTINE FCN) --- FINAL WEIGHTED SUMS OF SQUARES = D-02 SUM OF SQUARED WEIGHTED DELTAS = D-03 SUM OF SQUARED WEIGHTED EPSILONS = D RESIDUAL STANDARD DEVIATION = D-03 DEGREES OF FREEDOM = 8178

21 Read the files and interpolate TBC produces a file for every sample, plus final interpolated Samples are moved to the correct time, but out of order Sort and linear interpolate to new constant spaced time grid To achieve 200 MHz frequency grid: t s 5 NFFT ; NFFT T [ 0: NFFT 1] * t s

22 Simple naïve drift correction - cross correlate every sample against first sample - Find maximum and index at maximum - Shift time index using circshift() {MATLAB} Alignment of noisy signals; Kevin J. Coakley, Paul D. Hale; 2001; IIIA Naïve cross correlation

23 Jitter estimate N N n u min 2 2 min _ min ˆ t y u j 2 max 2 2 max _ max ˆ t y u j 2 ˆ ˆ min _ max _ j j j Calibration of Sampling Oscilloscopes with high-speed photodiodes; Clement, Hale, Williams, Wang, Dienstfrey, Keenan; 2006 dy/dt

24 Final result after Time Base and drift correction

25 Zoom in on main pulse

26 Reflection 1.0 mm to 1.85 mm interface

27 Result after FFT

28 Mismatch correction v h v s 1 g S 11 s S 22 S 21 g s S 21 S 12 S 11 S 22 v s = voltage sampled v h = corrected voltage Calibration of Sampling Oscilloscopes with high-speed photodiodes; Clement, Hale, Williams, Wang, Dienstfrey, Keenan; 2006

29 After mismatch correction

30 After mismatch correction (phase)

31 After photo diode de-convolution

32 After photo diode de-convolution (phase) k=σ(phase)/ Σ(f)

33 Comb generators

34 Comb generator measurement scope RF source 2.56 GHz comb generators 1/16 1/16 uut 10 db trig dB hybrid

35 Time domain pulse

36 Magnitude [db] Pulse Impulse response magnitude Mag E E E E E E E Mag Frequency [Hz]

37 Phase [degrees] Pulse impulse response phase Phase Phase E E E E E E E+10 Frequency [Hz]

38 Alternate calibration method

39 Self calibration PNA-X 10 MHz out Squaring ckt b2 Comb gen Comb gen

40 Time domain pulse

41 Unwrapped phase

42 Detrended phase compared to calibration data

43 Cal using photo diode 10 MHz in 10 MHz out Pulsed laser opt attenuator diode 10 MHz pzt sync 5 GHz Comb gen PLL Spectrum 5 GHz RF source Comb gen HV amp loop filter

44 Pulse

45 Unwrapped phase vs frequency

46 Unwrapped and detrended phase vs frequency

47 Summary Traceability path for phase reference in NVNA measurements Sampling scope impulse response measurements using high speed photo diode Comb generator impulse response measurements using similar process Proposed direct calibration of comb generators using NVNA More work is needed

48 Back up

49 Uncertainties Major contributors Photo diode, data from NIST Mismatch correction TBC intrinsic Transform and interpolation Repeatability Rigorous method Covariance matrix based approach

50 Time domain to frequency domain A A δ t -f f A τ sinc t -f f

51 EOS phase uncertainty