1. Enhanced Time Base Jitter Compensation of Sine Waves. Vrije Universiteit Brussel Faculteit Ingenieurswetenschappen Vakgroep ELEC Pleinlaan 2, B-1050 Brussels, Belgium Frans Verbeyst Yves Rolain Rik Pintelon Johan Schoukens

2. 2 Motivation LSNA phase calibration requires a calibrated oscilloscope a calibrated HPR

3. 3 Sampling oscilloscopes “reality” drift jitter mismatches, connector saver time base errors distortion t k  k.  t vertical errors offset nonlinearity dynamics measure, estimate, compensate vertical cal plug-in avoid: use small signal measure and compensate nose2nose EOS

4. 4 Amplitude verification setup VNA/LSNA calibration elements scope stepped sine wave k.600 MHz (k = 1.. 83) SOL + power meter freerun + histogram = assumptions normal mode = full correction jitter sine wave

5. 5 Jitter estimation (classical)

6. 6 Jitter estimation (new)

7. 7 Cost functions measurementsmodels

8. 8 Simulations units true value LSWLS1WLS2ML mV75.00 ± 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 1.000 1.001 ± 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 known t i = i.dt (dt = 1.25 ps) N = 4000 sample var of sample var sample var  2 distributed 25 sets of 25 realizations

9. 9 t (ns) var ( x 10 -3 V 2 ) ML estimate A = 74.12 ± 0.02 mV  = -1.1166 ± 0.0005 rad = 1.057 ± 0.002 ps = 1.650 ± 0.083 mV mean ( m V) Measurements 50 GHz sampling scope 48 GHz 500 realizations incl. time base drift and time base distortion t (ns)

10. 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