Enhanced Time Base JitterCompensation of

Sine Waves.

Vrije Universiteit BrusselFaculteit IngenieurswetenschappenVakgroep ELECPleinlaan 2, B-1050 Brussels, Belgium

Frans VerbeystYves RolainRik PintelonJohan Schoukens

2

Motivation

LSNA phase calibration

requires

requires

a calibrated oscilloscope

a calibrated HPR

3

Sampling oscilloscopes “reality”

drift

jitter

mismatches, connector saver

time base errors

distortiontk k.t

vertical errors

offset

nonlinearity

dynamics

measure,estimate,compensate

vertical cal plug-in

avoid: usesmall signal

measure and compensate

nose2noseEOS

4

Amplitude verification setup

VNA/LSNA

calibrationelementsscope

stepped sine wavek.600 MHz (k = 1 .. 83)

SOL + power meter

• freerun + histogram = assumptions

• normal mode = full correction

jittersine wave

5

Jitter estimation (classical)

6

Jitter estimation (new)

7

Cost functionsmeasurements models

8

Simulations

units

true value

LS WLS1 WLS2 ML

mV 75.0075.00± 0.14

75.55± 0.11

74.97± 0.12

75.00± 0.08

rad1.5708

1.5709± 0.0024

1.5705± 0.0025

1.5702± 0.0057

1.5706± 0.0025

(ps)2 1.0001.001± 0.016

0.980± 0.010

0.810± 0.019

1.001± 0.012

(mV)2 0.250

0.321± 3.260

-0.584± 1.189

-7.640± 2.068

0.199± 1.312

f = /2= 48 GHz knownti = i.dt (dt = 1.25 ps)

N = 4000 sample varof sample var

sample var

2 distributed

25 sets of 25 realizations

9

0.01 0.02 0.03 0.04timens

0.2

0.4

0.6

0.8

varx103 V20.01 0.02 0.03 0.04

timens 60

40

20

20

40

60

meanmV

t (ns)

var (x10-3 V2)

ML estimateA = 74.12 ± 0.02 mV

= -1.1166 ± 0.0005 rad

= 1.057 ± 0.002 ps

= 1.650 ± 0.083 mV

mean (mV)

Measurements 50 GHz sampling scope

48 GHz

500 realizationsincl. time base drift

and time base distortion

t (ns)

10

Conclusions

• Exact expressions do exist …

• Watch out for WLS estimators

• Prefer ML estimator … … especially for modest data sets (500)

• Thank you for your attention !

… for sine wave and Gaussian jitter