Calibration technique for calibrating high speed

equivalent time sampling scope using a

characterized high speed photo diode

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

Comb generator

Comb generator output

NIST

Traceability

Comb generator

Sampling scope

Photo diode

EOS system

Sampler

in out

50Ω

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

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

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

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

Known pulse excitation

Pulsed laser

80 fs FWHM pulse train

10 MHz repetition rate

Electrical pulse

~4-5 ps FWHM

50 Ω

V bias gnd

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

Results from EOS

Photo Diode

-5

0

5

10

15

20

25

30

0 20 40 60 80 100 120

Frequency [ GHz]

Mag

nit

ud

e [

V/(

C*H

z)]

Ph

ase [

deg

rees]

Magnitude

Phase

Pulsed

laser

pzt sync

diode

scope

RF source

trig 3dB

hybrid

loop filter HV amp

Spectrum

opt

attenuator

PLL

90° 0°

5 GHz

5 GHz

Transfer system architecture

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

Single raw measurement

Data process flow

Oscilloscope

Waveforms

TBD

Correction

Drift

Correction

Jitter

Analysis

Fourier

Transform

Mismatch

Correction Mismatch Factor VNA Data

EOS

Data

Photodiode

Response

Photodiode

Correction

Oscilloscope

Response

Time-domain

correction

Frequency domain

correction

Acquisition

Time interval: 0 to 5.1 ns

Number of points: 8192

Samples per set: 250

Repeat above 5 times between disconnects

TBC program

TBC detail algorithm

hn

k

ijijjkijjkjij ftfty1

2sin2cos

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

ijiiij hTt

ijjijiij TFy ;

n

i

iiiiiii yTFwyTFwR1

22

22

2

1121 ;;,,

Implemented using ODRPACK

Minimize with respect to θ1, θ2 and δ

random additive noise

harmonic order

model parameters

systematic timebase distortion

random jitter

model parameters

weight

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 = 4.28061076D+00

SUM OF SQUARED WEIGHTED DELTAS = 0.00000000D+00

SUM OF SQUARED WEIGHTED EPSILONS = 4.28061076D+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 = 1.68998468D-02

SUM OF SQUARED WEIGHTED DELTAS = 8.45508208D-03

SUM OF SQUARED WEIGHTED EPSILONS = 8.44476475D-03

--- RESIDUAL STANDARD DEVIATION = 1.43753303D-03

DEGREES OF FREEDOM = 8178

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:

8192;2

5

NFFT

NFFTts stNFFTT *]1:0[

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

Jitter estimate

N

N

nu

1

2

2

min

22

minmin_

ˆ

t

y

uj

2

max

22

maxmax_

ˆ

t

y

uj

2

ˆˆmin_max_ jj

j

Calibration of Sampling Oscilloscopes with high-speed photodiodes; Clement, Hale, Williams, Wang, Dienstfrey, Keenan;

2006

dy/dt

Final result after Time Base and drift correction

Zoom in on main pulse

Reflection 1.0 mm to 1.85 mm interface

Result after FFT

Mismatch correction

21

2211122122111

S

SSSSSSvv

sgsgs

h

Calibration of Sampling Oscilloscopes with high-speed photodiodes; Clement, Hale, Williams, Wang, Dienstfrey, Keenan;

2006

vs = voltage sampled

vh = corrected voltage

After mismatch correction

After mismatch correction (phase)

After photo diode de-convolution

After photo diode de-convolution (phase)

k=Σ(phase)/ Σ(f)

Comb generators

Comb generator measurement

scope

RF source

2.56 GHz trig

3dB

hybrid

90° 0° 1/16

comb generators 1/16

uut

10 dB

Time domain pulse

Pulse Impulse response magnitude

Mag

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

1

2

0.00E+00 1.00E+10 2.00E+10 3.00E+10 4.00E+10 5.00E+10 6.00E+10

Frequency [Hz]

Ma

gn

itu

de

[d

B]

Mag

Pulse impulse response phase

Phase

174

176

178

180

182

184

186

188

190

0.00E+00 1.00E+10 2.00E+10 3.00E+10 4.00E+10 5.00E+10 6.00E+10

Frequency [Hz]

Ph

as

e [

de

gre

es

]

Phase

Alternate calibration method

Self calibration

Comb gen

10 MHz out

Comb gen

PNA-X

Squaring ckt

b2

Time domain pulse

Unwrapped phase

Detrended phase compared to calibration data

Cal using photo diode

Pulsed

laser

pzt sync

diode

RF source

loop filter HV amp

Spectrum

opt

attenuator

PLL

5 GHz

5 GHz

10 MHz

Comb gen

10 MHz in 10 MHz out

Comb gen

Pulse

Unwrapped phase vs frequency

Unwrapped and detrended phase vs frequency

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

Back up

Uncertainties

Major contributors

Photo diode, data from NIST

Mismatch correction

TBC – intrinsic

Transform and interpolation

Repeatability

Rigorous method

Covariance matrix based approach

Time domain to frequency domain

t

A

δ

f

A

-f

A

t -f f

τ sinc

EOS phase uncertainty