S-Parameter Calibration of Two-Port Setup

S-Parameter Calibration of Two-Port Setup:
How to choose the optimal calibration method?

Gavin Fisher
Cascade Microtech

Wafer-Level S-Parameter Calibration Techniques

Content

 Error Modeling of a two-port setup
 Calibration methods
– SOLT
 Self-calibration routine:
– SOLR
– LRM/LRM+
– LRRM
 Conclusion

•Slide 2

Error Modeling of a Two Port Setup

 Influencing Factors:
– VNA architecture
– Crosstalk between ports

 Commonly used models:
– 10(12) Terms
– 7(8) Terms
– 15(16) Terms

•Slide 3

Reference Channel VNA

 N=n+1 receivers
 10(12)-term error model

m1 a1
1
[E] 1
I m2 b1 DUT
II m2 m3 a2
[Sx]
2
m1, m2 [F] 2
m4 b2
m4
where :
N - number of receivers
n - number of ports

•Slide 4

Double Reflectometer VNA

 N=2n receivers
 7(8)-term or 10-term (converted) model

m1 a1
1
[A] 1
m2 b1 DUT
I
m1 m2 m3 a2
[Tx]
II 2
[B1]-1 2
m4 b2
m3 m4
where :
N - number of receivers
n - number of ports

•Slide 5

10-Term Model
Reflection terms: Transmission terms:
– Directivity, ED - Transmission tracking, ET
– Source match, ES - Load match, EL
– Reflection tracking, ER - Crosstalk, EX

Forward direction: EX
m1 ' a1 b2 m4'

1 S21 ET
ED ES S11 S22 EL
m2' b1 a2
ER S12

•Slide 6

SOL Calibration
m1 a
 Reflection measurements: 1
ED
S11M  E D ES SA
S11A 
 
m2
ER b
E S S11M  E D  E R

• Three independent measurement conditions:
1: ED  S11A S11M ER  S11A ED ES  E R   S11M
I I I I

II II II II

III III III III

• Commonly used standards:
- Short, Open, Load (SOL)

•Slide 7

Experiment

Error Correction

•Slide 8

Wincal / SOL demonstration

 Objective:
– To show how calibration (and Wincal) works
 Verification conditions
– Verification series: same standards
 Experimental Conditions:
– Regular SOL calibration and measurement of standard
 Observation:
– How to use Wincal to apply calibration and show use of
Wincal processing raw data directly

•Slide 9


 In this example we will be using Wincal with
measured data to perform the measurement, but the
data has been measured previously
 Screen shots are shown in case existing Wincal
users may want to use the same techniques for off
line processing of raw measurement

•Slide 10


 Folder set-up is done in order for Wincal to find the raw data for process under
calibration.
 Note - MeasFiles folder used to store raw measurements
 Files have Vmeas_ as start of file name to denote Wincal will process the raw
measurement.

•Slide 11

 Wincal system set-up
restores default conditions of
instrument, probes, stimulus
etc

•Slide 12


 Opening the calibration set-up allows the old
calibration state to be restored, including
measurements if present

•Slide 13


 With the cal loaded we can hit compute which calculates the error
terms as discussed. Normally we would send these to the instrument

•Slide 14


 Hitting the measure button brings up a new blank report
 We can store hundreds of individual measurements in a single report

•Slide 15


 From the report window we can open pre-saved
reports with preset viewing and processing options

•Slide 16


 Wincal can either take a measurement from an instrument or use the
currently applied cal to correct a named raw measurement in the
measurement folder

•Slide 17


 Here we have S-parameter measurements of the SOL standards used
for the calibration and also an additional open standard which is on
wafer and has positive capacitance

•Slide 18

Wincal / SOL errors

 Objective:
– To show effect of standard misplacement and other
errors
 Verification conditions
– Verification series: same standards for cal
 Experimental Conditions:
– Regular SOL calibration and measurement of standard
 Observation:
– How SOL is only as good as the standards you
measure

•Slide 19

Wincal / SOL errors
 New calibration loaded
 Same standards for cal re-measured (Short / Open iss)
 Independent standard re-measured (Air open)
 Spot the problem.....

•Slide 20

SOL Calibration – Recap..
m1 a
 Reflection measurements: 1
ED
S11M  E D ES SA
S11A 
 
m2
ER b
E S S11M  E D  E R

• Three independent measurement conditions:
I I I I

II II II II

III III III III

• Commonly used standards:
- Short, Open, Load (SOL)

•Slide 21

SOLT Calibration
 10 unknowns have to be defined
– Step 1. SOL on Port 1 and 2:

  
ED , ES , ER , and  
ED , ES , ER


- Step 2. Connect two port together (“Thru”):

S11M  ED

EL  ET  S21M 1  ES EL 
  
S11M ES  ED ES  ER 
   

- From reverse direction: EL , EF
 

prime, double-prime parameters correspond to the forward
and reverse measurement directions respectively.

•Slide 22

Calibration Standard Requirements

THRU OPEN SHORT LOAD

Known: Known: Known: Known:
S11, S21, S12, S22 S11 (S22) S11 (S22) S11** (S22)

Example:
THRU OPEN SHORT LOAD

Z0=50Ω R=inf R=0 R=50
α=0, τ=0.5pS C=0.3fF L=9pH L=10.6pH

•Slide 23

Experiment

SOLT

•Slide 24

SOLT Experiment

 Objective:
– To prove sensitivity to standard models
 Verification conditions:
– Series of CPW different length
 Experimental Conditions A:
– Define wrong OSL coefficients (different probe type/pitch)
 Observation:
– Accuracy decreases with the frequency, RF “noise” on S21
 Experimental Condition B:
– Define extracted data-file models for OSL standards
 Observation
– SOLT is as good as you know your standards
•Slide 25

SOLT Experiment

 Wincal settings loaded from file
 Calibration settings loaded from file
 Calibration populated with measurements and
calculated
 Measurements of line standards carried out

•Slide 26

SOLT Experiment

•Slide 27

SOLT Experiment

 Looking at coefficients

•Slide 28

SOLT Experiment

 Open / Load standards look as they should

•Slide 29

SOLT Experiment

 But Lines look terrible
•Slide 30

SOLT Experiment

 Load inductance now set to correct value

•Slide 31

SOLT Experiment

 Comparison between same line different calibration
•Slide 32

Content

– SOLT
– SOLR
– LRM/LRM+
– LRRM
 Conclusion

•Slide 33

Self Calibration
 Requires double reflectometer VNA
 Two error matrices [A] and [B] of [T] parameters
 7 error terms are in use (normalized to A22)
 More information is measured than required
 This additional information allows some parameters to be calculated from
within the calibration routine
m1 a1
1 [A] 1
Ideal m2 b1 DUT
VNA m3 a2
[Tx]
-1
2 [B ] 2
m4 b2

1
 m1' m1''   A11 A12  T11 T12  B11 B12   m3
'
m3' 
'
 '      ' 
m
 2 m2   A21
'' 
 A22  21 T22  B21
 T
 B22 

m
 4
'' 
m4 

•Slide 34

Self Calibration (cont.)

 Measured matrix:
1
m '
m ''
 m '
m ''

M  1 1
 3 3
 , M X  ATX B 1
m ' ''  m ' '' 
 2 m 2  4 m 4 

• Three measurement conditions give [A] and [B]:

Standard Requirements Definitions
T1 Fully known 4
T2 Maximum of two free parameters 2
T3 Maximum of three free parameters 1

H. J. Eul and B. Schiek, "A generalized theory and new calibration procedures for network analyzer self-calibration," Microwave Theory and
Techniques, IEEE Transactions on, vol. 39, pp. 724-731, 1991.

•Slide 35

SOLR

 Standards used:
– Reflection: Short, Open, Load
– Transmission: Reciprocal

Short S11, S22 : known 2
Open S11, S22 : known 2
Load S11, S22 : known 2
Reciprocal unknown, S21=S12 1

A. Ferrero and U. Pisani, "Two-port network analyzer calibration using an unknown `thru'," Microwave and Guided Wave Letters, IEEE, vol. 2,
pp. 505-507, 1992.

•Slide 36

Experiment

SOLR

•Slide 37

SOLR Experiment

 Objective:
– To prove sensitivity to standard models
– Series of CPW different length
– Define wrong OSL coefficients (different probe type/pitch)
 Observation:
– Accuracy decrease with the frequency

 Experimental Condition B:
– Define extracted data-file models for OSL standards
 Observation
– SOLR is as good as you know your OSL standards
•Slide 38

SOLR Experiment

 SOLR line measurements using initial value for load
inductance

•Slide 39

SOLR Experiment

 Calibration carried out again with correct probe
definitions. Correction applied to original data

•Slide 40

Content

– SOLT
– SOLR
– LRM/LRM+
– LRRM
 Conclusion

•Slide 41

LRM and LRM+

 Standards used:
– Transmission: Thru (Line)
– Reflection: Load (Match), Reflect

Thru/Line Fully known 4
Load/Match S11, S22 : known 2
Reflect unknown, S11=S22 1

H. J. Eul and B. Schiek, "Thru-Match-Reflect: one result of a rigorous theory for de-embedding and network analyzer calibration," in European
Microwave Conference, 18th, B. Schiek, Ed., 1988, pp. 909-914.

•Slide 42

LRM vs. LRM+

 Differ in requirements for Load standard:
– LRM for coaxial applications
– LRM+ for on-wafer calibration

Method Load R X

LRM Known R1=R2=50Ω 0

LRM+ Known R 1, R 2 X1, X2
Arbitrary Arbitrary

R. F. Scholz, F. Korndorfer, B. Senapati, and A. Rumiantsev, "Advanced technique for broadband on-wafer RF device characterization," in
ARFTG Microwave Measurements Conference-Spring, 63rd, 2004, pp. 83-90.

•Slide 43

Experiment

LRM/LRM+

•Slide 44

LRM/LRM+ Experiment 1

 Objective:
– To prove sensitivity to the Load
– Open, Short, Load, CPW’s
– Asymmetrical Load
 Observation:
– Offset in reflection coefficient for high-reflective
elements

•Slide 45


 Calibration applied for LRM+ and measurements computed
 LRM is calculated and the same raw data is computer with LRM
 For both calibrations Reflect was short so open makes good validation structure
 Loads were assymetric – RH was 49 ohms which LRM+ is set up for

•Slide 46


 LRM shows divergence in Port1 and Port 2 Open (not
used in cal) due to load inductance assymetry
•Slide 47


 Objective:
– To prove sensitivity to the Load
– Open, Short, Load, CPW’s
– Load as a resistor (50 Ohm)
 Observation:
– Impact of Zref

•Slide 48

LRRM

 Standards used:
– Transmission: Thru (Line)
– Reflection: Reflect(Open), Reflect(Short), Load(Match)

Thru/Line Fully known 4
Reflect (Open) unknown, S11=S22 1
Reflect(Short) unknown, S11=S22 1
Load(Match) S11 (or S22) known 1

A. Davidson, K. Jones, and E. Strid, "LRM and LRRM calibrations with automatic determination of load inductance," in ARFTG Microwave
Measurements Conference-Fall, 36th, 1990, pp. 57-63.

•Slide 49

LRRM(cont.)

 Requirements to the Load standard

Load Impedance R L

Inductance approximation Known Arbitrary,
Z = R+jωL unknown

• Unknown L can be found by the automated load
inductance extraction algorithm

L. Hayden, "An enhanced Line-Reflect-Reflect-Match calibration," in ARFTG Microwave Measurements Conference-Spring, 67th, 2006, pp.
143-149.

•Slide 50

Experiment

LRRM

•Slide 51

LRRM Experiment 1

 Objective:
– To show LRRM relative immunity to probe
misplacement
– CPW’s
 Observation:
– Line measurements comparatively immune to probe
misplacement

•Slide 52

Probes in normal position

•Slide 53

Probes misplaced

•Slide 54

LRRM Experiment 1

 SOLT based calibrations show much more noise in
line measurement
•Slide 55

Choosing Calibration Strategy

 Understanding of strengths and limitations is essential!
 Re-measuring of calibration standards ≠ verification!

Method Application
SOLT • Well defined conditions
• Frequencies < 40GHz

SOLR • Rectangular configurations
• Double-side probing

LRM • Not recommended for wafer-level applications

LRM+ • Broadband on-wafer calibration

LRRM • Broadband ISS calibration

•Slide 56

S-Parameter Calibration of Two-Port Setup

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