Phase Calibration,
an Overview from a
Large-Signal Network Analysis
Point of View
Frans Verbeyst
© 2007
Some slides courtesy of Agilent Technologies
Why accurate phase ?
0.2
0.2
0.1
-0.1
0.5
1
1.5
2
t HnsL
0.1
0.5
-0.1
-0.2
-0.2
-0.3
-0.3
-0.4
-0.4
-0.5
-0.5
1
same amplitude
different phase
dBm
-16
-18
-20
-22
-24
-26
-28
5
10
2
15
20
f HGHzL
1.5
2
t HnsL
Large-signal network analysis: what?
accurate and complete measurement
of the nonlinear behaviour
of your active device
under realistic conditions
realistic with respect to:
• excitation
• mismatch conditions
3
Why realistic conditions ?
picture courtesy of NASA
picture courtesy of NASA
4
Why realistic conditions ?
picture courtesy of NASA
5
Why realistic conditions ?
the unreleased picture
6
LSNA relative calibration
K
Acquisition
1
γ
 1
0

0
β1
δ1
0
0
0
0
α2
γ2
0
0 
β2 

δ2 
{f0, 2 f0, …, n f0}
50 Ohm
{f0, 2 f0, …, n f0}
f0 = 1GHz
50 Ohm
Load
Open
Short
50 Ohm
Acquisition
Thru
50 Ohm
Calibration for fundamental and harmonics
One frequency at the time
7
LSNA power calibration
K
Amplitude
{f0, 2 f0, …, n f0}
1
γ
 1
0

0
β1
δ1
0
0
0
0
α2
γ2
Acquisition
{f0, 2 f0, …, n f0}
Power Meter
f0 = 1GHz
Calibration for fundamental and harmonics
One frequency at the time
8
50 Ohm
0
0 
β2 

δ2 
LSNA phase calibration
K
Phase
{f0, 2 f0, …, n f0}
1
γ
 1
0

0
β1
δ1
0
0
0
0
α2
γ2
0
0 
β2 

δ2 
Acquisition
{f0, 2 f0, …, n f0}
50 Ohm
...
50 Ohm
f0
HPR
Harmonic Phase Reference
f0 = 1GHz
Calibration for fundamental and harmonics
All frequencies applied simultaneously !
9
Harmonic Phase Reference
HPR Amplifier Unit
HPR Pulse Generator
Output
dBm
0.2
-16
0.1
-18
f0 = 1GHz
Power
Meter
-20
-0.1
-22
-0.2
-24
0.3
-26
0.4
28
-0.5
0.5
1.5
2
“known” phase relationship
5
10
1
10
15
20
t HnsL
f HGHzL
LSNA and phase calibration
LSNA phase calibration
requires
a calibrated HPR
requires
a calibrated oscilloscope
11
Sampling oscilloscopes “reality”
time base errors
distortion
offset
tk ≠ k.∆t
drift
vertical errors
measure,
estimate,
compensate
jitter
nonlinearity
dynamics
mismatches, connector saver
vertical cal
plug-in
avoid: use
small signal
nose2nose
EOS
measure and compensate
12
Sampling oscilloscope calibration
nose2nose
EOS-based
plug-in 1
impulse
laser
plug-in 2
O/E calibrated using
EOS system @ NMI
plug-in 2
assumption:
kickout pulse ÷ impulse response
assumption:
no anomalies in O/E calibration
Hmeas(f) ÷ H1(f). H2(f)
Hmeas(f) = HO/E(f). H2(f)
after compensation of
time base errors
(and mismatches)
13
More details on nose2nose
plug-in 1
plug-in 2
14
Origin of nose2nose
±∆
±∆
• sampler topology pulse generator topology
• offset applied to sampler
⇒ unbalance
⇒ generation of pulse: “kickout”
• “kickout” proportional to “impulse response” of plug-in
15
Basic setup for nose2nose
sampling scope A
sampling scope B
±∆
± 100 mV
offset
±∆
H1 H2
plug-in 1
50 ps
plug-in 2 M ÷ H .H
21
2
1
M21 ÷ H2.H1
M21.M13
M23 ÷ H2.H3
M23
M13 ÷ H1.H3
16
÷ H1
nose2nose in practice: from Mij …
Mij (V)
30
0.06
align (time base drift)
subtract
average
0.04
Mij (mV)
0.02
64
-0.02
-50
67
t HnsL
67
Mij (V)
positive and negative kickout
50
66
reflection
-0.04
t (ns)
63
65
0.06
0.04
0.02
Mij (mV)
63.4
63.5
t HnsL
63.7
63.6
-0.02
-0.04
-50
t (ns)
63
64
17
nose2nose in practice: from Mij to Hi
Mij (dB)
Hi (dB)
-72
-73
0.5
-74
10
-75
20
30
40
50
f HGHzL
-0.5
-76
-1
-77
10
20
30
40
50
f HGHzL
-1.5
Mij (deg)
Hi (deg)
40
20
20
10
10
20
30
40
50
f HGHzL
10
-10
-20
-20
-40
-30
-60
-40
18
time base distortion compensation
proper combination of Mij
jitter compensation
mismatch compensation
20
30
40
50
f HGHzL
Appl#1: Harmonic Phase Reference
simplified schematic (trigger required)
HPR Amplifier Unit
HPR Pulse
Generator
ideal sample scope:
• no time base errors
• no vertical errors
• perfect 50 Ohm input
f0 = 1GHz
Power
Meter
capture time-domain signal
apply Fourier transform
to obtain phase relationships
19
Appl#1: Harmonic Phase Reference
HPR Pulse
Generator
1 HHPR
f0 = 1GHz
Power
Meter
scope plug-in
Hscope
ΓHPR
M
Γscope
real sample scope:
after compensation of time base errors (!)
HHPR . Hscope
M=
1 - ΓHPR . Γscope
20
n2n
HHPR
Appl#1: Harmonic Phase Reference
HPR Pulse
Generator
1 HHPR
Equivalent
Scheme
f0 = 1GHz
ΓHPR
Power
Meter
dBm
-16
-18
HHPR
-20
-22
-24
-26
-28
“known” phase relationship
5
10
15
20
f HGHzL
21
Appl#2: LCA O/E
LCA O/E
impulse
ideal glasses
Fourier transform
amplitude
phase
frequency
frequency
HO/E : O/E impulse response
22
Appl#2: LCA O/E
scope plug-in
LCA O/E
500
fs
1 HO/E
fiber (im)pulse laser
Hscope
ΓO/E
M
200
ps
Γscope
real sample scope:
after compensation of time base errors (!)
M=
HO/E . Hscope
n2n
HO/E
1 – ΓO/E . Γscope
23
EOS
scope plug-in
O/E calibrated using
EOS system @ NMI
1 HO/E
fiber (im)pulse laser
Hscope
ΓO/E
M
Γscope
real sample scope:
after compensation of time base errors (!)
M=
HO/E . Hscope
1 – ΓO/E . Γscope
24
EOS
Hscope
Ampl. characteristic verification (1)
amp H(dB)
dB L
amp
1
0.5
10
20
30
40
50
freq
freq
HGHz L
(GHz)
-0.5
-1
-1.5
-2
-XX
+
nose2nose
EOS
power meas – freerun trigger – histogram meas
power meas – triggered mode - normal meas
25
Ampl. characteristic verification (2)
diff HdB
L
ampamp
diff
(dB)
1
0.8
0.6
0.4
0.2
10
20
30
40
50
freq
freq
H GHz L
(GHz)
- 0.2
-XX
+
nose2nose
EOS
power meas – freerun trigger – histogram meas
power meas – triggered mode - normal meas
26
Phase characteristic comparison
nose2nose versus EOS
phasediff
diff Hdeg
L
phase
(deg)
10
20
30
40
50
freq H GHz L
freq
(GHz)
-5
- 10
- 15
- 20
- 25
∆ within 95% conf. interval up to 20 GHz
∆ ≈ 25 degrees @ 50 GHz
27
Harmonic Phase Reference
HPR Pulse
Generator
1 HHPR
f0 = 1GHz
Power
Meter
scope plug-in
Hscope
ΓHPR
M
Γscope
real sample scope:
after compensation of time base errors (!)
HHPR . Hscope EOS
M=
1 - ΓHPR . Γscope
28
HHPR
Time base error compensation
time base errors
distortion
tk ≠ k.∆t
measure,
estimate,
compensate
drift
IQ
x(t)
type #1: no additional channels
perform separate measurements
e.g. to estimate time base distortion
jitter
type #2: additional channels
IQ detection to retrieve time
time base distortion + jitter
starting values by type #1
methods enhanced over time
29
Summary
• Phase is important
• Large-Signal Network Analysis is important
“We cannot afford to destroy life on Mars”
• Phase calibration of LSNA requires
• Calibrated HPR
• Calibrated sample scope
• Deal with
• Time base errors
• Vertical errors
Vertical dynamics = n2n Æ EOS
• Mismatch (reflections)
30