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1

Wafer-Level S-Parameter Calibration Techniques

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

Gavin Fisher

Cascade Microtech


Content

Error Modeling of a two-port setup

Calibration methods

– SOLT

Self-calibration routine:

– SOLR

– LRM/LRM+

– LRRM

Conclusion

•Slide 2

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

•Slide 4

where :

N - number of receivers

n - number of ports

3


Double Reflectometer VNA

N=2n receivers

7(8)-term or 10-term (converted) model

•Slide 5

where :

N - number of receivers

n - number of ports


10-Term Model

Reflection terms:

– Directivity, ED

– Source match, ES

– Reflection tracking, ER

•Slide 6

Transmission terms:- Transmission tracking, ET

- Load match, EL

- Crosstalk, EX

Forward direction:

4


SOL Calibration

Reflection measurements:

•Slide 7

( )R

ED

EM

SS

E

DE

MS

AS

+−

−=

11

1111

( ) I

MRSD

I

AR

I

M

I

ADSEEESESSE

11111111=−−+

( ) II

MRSD

II

AR

II

M

II

ADSEEESESSE

11111111=−−+

( ) III

MRSD

III

AR

III

M

III

ADSEEESESSE

11111111=−−+

1:

2:

3:

• Three independent measurement conditions:

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


Experiment

Error Correction

•Slide 8

5


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

6



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

7



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

8



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

9



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

10


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

11


SOL Calibration – Recap..

Reflection measurements:

•Slide 21

( )R

ED

EM

SS

E

DE

MS

AS

+−

−=

11

1111

( ) I

MRSD

I

AR

I

M

I

ADSEEESESSE

11111111=−−+

( ) II

MRSD

II

AR

II

M

II

ADSEEESESSE

11111111=−−+

( ) III

MRSD

III

AR

III

M

III

ADSEEESESSE

11111111=−−+

1:

2:

3:

• Three independent measurement conditions:

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


SOLT Calibration

10 unknowns have to be defined

– Step 1. SOL on Port 1 and 2:

•Slide 22

- Step 2. Connect two port together (“Thru”):

,D

E′ ,S

E′ ,R

E′R

E ′′,S

E ′′,D

E ′′and

( )RSDSM

DM

L

EEEES

ESE

′−′′−′

′−′=′

11

11 ( )LSMT

EESE ′′−=′ 121

,L

E ′′F

E ′′- From reverse direction:

prime, double-prime parameters correspond to the forward

and reverse measurement directions respectively.

12


Calibration Standard Requirements

•Slide 23

THRU OPEN SHORT LOAD

Known:

S11, S21, S12, S22

Known:

S11 (S22)

Known:

S11 (S22)

Known:

S11** (S22)

Example:

THRU OPEN SHORT LOAD

Z0=50Ω

α=0, τ=0.5pS

R=inf

C=0.3fF

R=0

L=9pH

R=50

L=10.6pH


Experiment

SOLT

•Slide 24

13


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

14


SOLT Experiment

•Slide 27


SOLT Experiment

Looking at coefficients

•Slide 28

15


SOLT Experiment

Open / Load standards look as they should

•Slide 29


SOLT Experiment

But Lines look terrible

•Slide 30

16


SOLT Experiment

Load inductance now set to correct value

•Slide 31


SOLT Experiment

Comparison between same line different calibration

•Slide 32

17


Content


Calibration methods

– 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

•Slide 34

=

−

''

4

'

4

''

3

'

3

1

2221

1211

2221

1211

2221

1211

''

2

'

2

''

1

'

1

mm

mm

BB

BB

TT

TT

AA

AA

mm

mm

18


Self Calibration (cont.)

Measured matrix:

•Slide 35

1−= BATM

XX,

1

''

4

'

4

''

3

'

3

''

2

'

2

''

1

'

1

−

=

mm

mm

mm

mmM

• 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.


SOLR

Standards used:

– Reflection: Short, Open, Load

– Transmission: Reciprocal

•Slide 36


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.

19


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

20


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

21


Content


Calibration methods

– SOLT


– SOLR

– LRM/LRM+

– LRRM

Conclusion

•Slide 41


LRM and LRM+

Standards used:

– Transmission: Thru (Line)

– Reflection: Load (Match), Reflect

•Slide 42


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.

22


LRM vs. LRM+

Differ in requirements for Load standard:

– LRM for coaxial applications

– LRM+ for on-wafer calibration

•Slide 43

Method Load R X

LRM Known R1=R2=50Ω 0

LRM+ Known R1, R2

Arbitrary

X1, X2

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.


Experiment

LRM/LRM+

•Slide 44

23


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

24



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

25


LRRM

Standards used:

– Transmission: Thru (Line)

– Reflection: Reflect(Open), Reflect(Short), Load(Match)

•Slide 49


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.


LRRM(cont.)

Requirements to the Load standard

•Slide 50

Load Impedance R L

Inductance approximation

Z = R+jωL

Known Arbitrary,

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.

26


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

27


Probes in normal position

•Slide 53


Probes misplaced

•Slide 54

28


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!

•Slide 56

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

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