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