Seminario d’Eccellenza “ITALO GORINI” Scuola di Dottorato

Seminario d’Eccellenza “ITALO GORINI”Scuola di Dottorato

METODOLOGIE E DISPOSITIVI DI MISURA

Linea di Ricerca A6:

MISURE PER LA CARATTERIZZAZIONE DI COMPONENTI E SISTEMI

Responsabile: Prof. Gregorio Andria, Politecnico di Bari

Siena, 5-9 settembre 2011

Seminario d’Eccellenza “ITALO GORINI”

Le Misure ad Alta Frequenza per le Applicazioni di Signal Integrity

MISURE PER LA CARATTERIZZAZIONE DI COMPONENTI E SISTEMI

Prof. Andrea FerreroDip. Elettronica- Politecnico di Torino

Le Misure ad Alta Frequenza per la Applicazioni di Signal Integrity. A. Ferrero- Scuola di Dottorato I.Gorini 2011

Summary

• Signal Integrity and Microwave• S-parameter: so what?• VNA Hardware Evolution• Error Models and Calibration Techniques• Interconnection and Fixture Design • Calibration design for the DUT


Signal Integrity and Microwave


Microwave Measurements

• Power Measurements• Time Domain Signals• Frequency Domain Linear Parameters:

– S parameters


6

Few Remainders


7

Few Remainders• Linear Network: The ratio among voltages and currents

on the n ports DOES NOT depend on signal levels thus the behaviour can be described as linear relationship ie:

• Where M can be any relationship among any linear combination of voltages and currents ie:– V=Z * I– I = Y * VHere Y and Z are two examples of possible M matrix but

anyone is acceptable

[M] [M] becomes a 4x4 matrix

1

2

3

4


Scattering Paremeters Demystified

• Let’s take the following combinations of I and V:

• Where ZR is a parameter called Reference Impedance than the Ohm law equivalent becomes:

R

R

R

R

ZIZVb

ZIZVa

,

R

R

ZRZR

abRIV

is called Reflection Coefficient


Scattering Paremeters Demystified

• Let’s move to n-ports everything become vectors and matricies:

SabZiv

baiv

nnnn b

bb

a

aa

i

ii

v

vv

.,

.,

.,

.2

1

2

1

2

1

2

1

S is called Scattering matrix


Signal Trasmission at High Frequency

• A structure where the Electromagnetic field can propagate along an axis with a UNIFORM transversal section is called Trasmission Line

Coax cable Waveguide Bifilar Line Microstrip

EEE

E

IT’S ALL ABOUT FIELD CONFINEMENT


11

So why S and not Z or Y?

Let’s take a transmission line:

z

I(z)

V(z)

Plane A Plane B• V and I are complex function of the position

while if:• Zr = Appropriate constant of the

propagation called Line Characteristic impedance then:

• a and b function along the line become simply:

Z

jkzjkz ebzbeaza )0()(,)0()(

l

Reflected signalIncident signal


12

Some usefull propertiesNote that:

I(z)

V(z) Z

0)()(

)0()0()0(

0)0()(0)()()(

2

jkl

R

R

R

R

R

elalb

ab

blbZZZZ

ZRZR

lalbl

ZZZif

a(z)

b(z)


The S-matrix of a transmission line

zPort 1 Port 2

RZZ

l

00jkl

jkl

ee

S

So to completely describe the propagation along a trasmission line we will need:REFERENCE PLANESREFERENCE IMPEDANCES-MATRIX

0,,,002

222

02

112

01

221

01

111

2221212

2121111

2

1

2221

1211

2

1

1122

a

jkl

a

jkl

aaabse

abse

abs

abs

asasbasasb

aa

ssss

bb

Sab

a1

b1

a2

b2


14

Differential S-parameters

• What if instead of single ended voltages and currents we wish to use differential ones and associate the information to a couple of wires ?

V1

I1

V2

I2

V3

I3

V4

I4

)(2/)(

2/)(

kIjIcjkIkIjIdjkIkVjVcjkVkVjVdjkV

For Each Couple


WHY differential S-parameters?

• The differential mode Ed propagates mainly in the air thus it suffers much less of dielectric loss and anysotrtopy

• FR4 is a must for Digital application but FR4 is lossy and anysotropic thus…

• Differental propagation became a must for high speed digital systems

E Ec

Ed


16

Differential S-parameters

• What are the propagation properties and is it usefull to have an “S-parameter equivalent”?

• Use a linear combination of V and I it’s just another convention but to link it to propagation became more tricky:– Which Reference impedance we need to take?– What if we wish to have some port left single

ended, i.e. an Operational Amplifier?– Which are the properties of the new parameters?


17

Mixed Mode S-parameter

• Traditional definitions are:

1MSMS

)(

21

)(2

1

)(2

1

)(2

1

c

c

d

d

kjjk

kjjk

kjjk

kjjk

bbb

aaa

bbb

aaa

Only Real R2Z

Only Real 2RZ

d

c

jk

jk

BUT THESE ARE VALID ONLY IF


18

Generalized Mixed Mode

• In general we may have Vd12

Id12

Vc12

Ic12

Vd(p-1)p

Id(p-1)p

Vc(p-1)p

Ic(p-1)p

n-portsp differential ports

n-p single ended ports

Vp-1

Vp+1

Ip+1

Ip

Vn

In

I2

V2

I1

V1

Ip-1

Vp

1)121)(222(

2

2

2

2

c

ccccc

c

ccccc

d

ddddd

d

ddddd

SΞ1ΞSΞ1ΞS

jk

jkjkjkjkjk

jk

jkjkjkjkjk

jk

jkjkjkjkjk

jk

jkjkjkjkjk

ZZIV

Rb

ZZIV

Ra

ZZIV

Rb

ZZIV

Ra

BILINEAR MATRIX TRANSFORM


Impedance Measurements

R ?

| |,F

Z


Let’s move to microwave

DownConversion and Digitizing

ADCADC

Directional Coupler

aa bb

a<-b

Microwave Source


2 port Measurements

02

222

02

112

01

221

01

111

2

1

2221

1211

2

1

1122

,,,

iiiiivz

ivz

ivz

ivz

ii

zzzz

vv

ZIV


2 port Measurements

02

222

02

112

01

221

01

111

2

1

2221

1211

2

1

1122

,,,

aaaaabs

abs

abs

abs

aa

ssss

bb

Sab

S11 S21a1

b2

a1

b1


The old questions of S-parameter Measurements

• How can we generate microwave signals?• How can we sample microwave signals?• Where’s the reference plane ?• What’s the reference impedance?


Plus new problems… for digital Low cost application

• How do I keep reasonable microwave signals on non microwave substrate ?

• How can I make proper interconnections to measure these signals ?

• How much accuracy can I accept ?


26

VNA BASIC SCHEME

REFLECTOMETER

bm1am1 bm2 am2

FOUR-CHANNEL MICROWAVE RECEIVER

PORT 1 PORT 2

DUT

MICROWAVESOURCE

BIAS 1 BIAS 2

IF Digitizer

SIGNAL SEPARATION


27

VNA Source

Agilent PNA Source block

• Synthetised Source (PLL+DDS)• Very Broadband• Very Fast Sweeping• Power Leveled• Low Phase Noise Not really Necessary

• High Repeatability


Signal Separation

MICROWAVESOURCE

bm1

am1

bm2

am2

Receiver Block

• Provides a and b waves separation

• Provides signal excitation at DUT ports

• It may have also bias tee and attenuators


Receiver Block

• Typically two or three downconversion

• Digital vectorial measurement of mag and phase

• Phase lock of the internalsource through receiversignals


Phase Lock through its receiver

Unlike the old VNA where thesource was autonomuos lockedand the receiver could be lock to any microwave signal, modernVNAs cannot work unlesstheir internal source is used.As example:You cannot use a VNA to measurethe signal coming out from a chipwhere it’s clock cannot be lock toan external refenrence


Today VNA Hardware:

31

2-ports2 Ref2 Rec

4 Ports4 Ref4 Rec


Are 4 ports VNA enough?

Differential pairs are used so:12-port data is required for channel modelingData for a fully characterized 12-port DUT results in a completely

filled 12x12 matrix

Ex. Package/Socket footprint

Port 1 & Port 7

Port 3 & Port 9

Port 5 & Port 11

Port 2 & Port 8

Port 4 & Port 10Port 6 & Port 12

Ports 1-6 are on the socket bottomPorts 7-12 are on the socket top

GNDs


12 ports VNA

33

2 Ref2 Switched Rec

LEFTPORTS

RIGHTPORTS


12 ports VNA

2 Ref2 Switched Rec

LEFTPORTS

RIGHTPORTS


Interfacing

• Repeatibility• Standard Availability• Custom Fixtures


On Wafer


Let’s summarize up to now

1. Directional Couplers have finite directivity and frequency depend behaviour

2. Switches are not ideal and frequency dependent3. Reference Plane position depends on cable, adapter

interconnections and so on4. DownConversion and Digitizing problems like:

1. Source Phase Noise2. Frequency accuracy and repeatibility3. Non linearity of mixer/sampler4. ADC Dynamic Range & Speed

37

ACCURACY ???


Lab Care

Calibration

Cause of Uncertainty

• Systematic Errors (85%)– Microwave Components – Interconnections– Incorrect Standard Modeling– Calibration Algorithm

• Random Error (10%)– Connection Repeatibility – Frequency Stability– Noise

• Drift (5%)

38


Is Calibration fundamental?

• What if we would measure 30g of Ham with

the scale plate of 1 ton?

THIS IS THE SAME EFFECT OF 1m cable at 10GHz if we are

looking for 1 degree of phase shift on S11


Raw vs. Corrected Data


How does the calibration work?

An error model

A Specific Algorithm

A Standard Sequence

ExampleTRLThru

ReflectLine


Error Model • Ipothesis

1. sampler (mixer),and all the other system components are linear and invariant parts

2. The two half are independent 4-port networks which “talk” only through the DUT

42

DUT

b2

a2

a3

b1

a1

a0

b0

b3 a4b4

• Let the half • 8 unknowns:

a0, b0, a1, b1,a3, b3, a4, b4

• The two acquire data are proportional to b3, b4 :

• am1=k1b3 , bm1=k2b4

am1 bm1


Error Model Definition II

0 011 12 13 14

1 121 22 23 24

31 32 33 343 3

41 42 43 444 4

b aS S S Sb aS S S S

S S S Sb aS S S Sb a

43

4 port equation

Reflection Coefficients of the downconversion part and reading vs. wave

3 3

4 4

a ba b

3

4

ΓΓ

1 3 3

2 4 4

m

m

V k bV k b

8 eq. with 10 unknowns. (a0, b0, a1, b1, a3, b3, a4, b4, Vm1, Vm2):Let use Vm1 e V m2 as independent variables and called them:

am1=Vm1, bm1=Vm2, a1= a1DUT e b1= b1DUT we find the following model


Error Model Definition III

0 011 12 13 14

1 121 22 23 24

31 32 33 343 3

41 42 43 444 4

b aS S S Sb aS S S S

S S S Sb aS S S Sb a

44

4440414

0313

0211

4143131120110

....

....

....

aSaSbaSbaSb

aSaSaSaSb

444433430414

443433330313

442433230211

441433131120110

....

....

....

bSbSaSbbSbSaSbbSbSaSbbSbSaSaSb

3 3

4 4

a ba b

3

4

ΓΓ


Error Model Definition IV

45

44443343142041

44343323132031

442433231112021

441433131120011

)1()1(

bSbSaSaSbSbSaSaSbSbSbaSaSbSbSaSbaS

4

3

444343

434333

424323

414313

1

1

0

0

4241

3231

2221

1211

)1()1(

00001001

bb

SSSSSSSS

baba

SSSSSSSS

4

3

1

1

0

0

bb

baba

QW

4412

3311

bkbVbkaV

mm

mm

If we call am1 and bm1

4

3

2

1

1

1

00

bb

kk

ba

m

m


The famous error box

46

4

3

1

1

0

0

bb

baba

QW

4

3

4

3

2

1

1

1

00

bb

bb

kk

ba

m

m K

1421411

1321311

1221210

1121110

mm

mm

mm

mm

bDaDbbDaDabDaDbbDaDa

1

1

1

11

1

1

0

0

m

m

m

m

ba

ba

baba

DQKW 1

1221211

1121111

beaeabeaeb

m

mm

Shuffle the last 2 Equations and rename as


The birth of the famous error box

47

am1 a1

IdealVNA

bm1

ErrorBoxE

b1

DUT

1221211

1121111

beaeabeaeb

m

mm

Since we are in the S-parameter world the LINEAR RELATIONSHIP WHICH LINKS THE MEASUREMENT TO THE ACTUAL WAVES WILL BE


Error Box Property

• It’s not an actual network but only a linear system model• Every parameter is frequency dependent but time invariant• Since the E parameters are more or less link with some

specifications of the coupler they are also called:

48

TrackingEeehSourceMatcEeyDirectivitEe

R

S

D

1221

22

11


Two Port Error Model

49

To apply this model, 4 independent readings on each source position are required

NOT POSSIBLE

TA TDUT T-1B

a1m

b1m

a1DUT

b1DUT

b2DUT

a2DUT

b2m

a2m

Two error boxes on the right and left

2

1

2

1

m

m

m

m

aa

bb

Sm

' ' " "1 1 1 111 12 11 12' ' " "

21 22 21 222 2 2 2,m m m mm m m m

m m m mm m m m

b a b aS S S SS S S Sb a b a

1' " ' "11 12 1 1 1 1

' " ' "21 22 2 2 2 2

m m m m m m

m m m m m m

S S b b a aS S b b a a

2-ports Measured S-matrix

0m

m

m

jiaj

ai

bijSm


FULL 2-Ports Error Model

11 1 1111 12

21 221 1 1

DUT m mA AA

A ADUT m m

b b bT T TT Ta a a

50

12 2 2111 12

21 222 2 2

DUT m mB BB

B BDUT m m

a a aT TT

T Tb b b

TA, TB are the transmission matrix equivalent of the two E matrices of left and right side while Tm is the transmission matrix equivalent of Sm

1 21

1 2

m mA DUT B

m m

b aT T T

a b

2

2

1

1

m

m

m

m

ba

ab

Tm

8 error terms, but7 UNKNOWS TO GET Tdut


51

Most USED 2-port Calibrations

• TSD-TRL (Thru, Short, Delay or Thru, Reflect, Line)

• LRM (Line, Reflect, Match) • SOLR (Short, Open, Load, Reciprocal)• SOLT (Short, Open, Load, Thru)

MANDATORY FOR 3 samplers VNAs


52

SOLT• The old good cal: Short, Open, Load and Thru• It measures 3 standards at port 1, 3 at port 2

and the THRU.• It obviously overdetermed with the 8 port

model (10 equations for 8 unknows)but it’s the proper choice for the 3-sampler architecture


53

Thru Reflect Line

• The Thru and Line must have the same geometryI.e. REFERENCE IMPEDANCE

• Normally the Reference plane it’s placed in the middle of the THRU

• The system Reference impedance IS THE Characteristic impedance of the LINE

• Known 1 port Standard TSD• Unknown 1 port standard -> TRL

54

TSD-TRL II

• The length diff from the THRU and the LINE should avoid l/2 and its multiple

• To have broadband TRL more line are usefull (different line lenght)

• Side Result: The propagation constant of the line comes from free


55

Coax On-Board Simple Calibration Structures

Thru and Line Structures

Reflect and Match Structures


VNA Noise

THE GOOD OLD 8510:RAW DATA NOISE-50dB ->

-50dB ->


Repeatability an example:APC7mm

58

A close look to theconnector


Repeatibility Model


Multifinger On wafer probes

• Probe landing repeatibility

• Probe Coupling


Standard Accuracy

• Standard Model• Model Identification• Parameter Accuracy


Standard Model: Open

t,g

33

2210 fCfCfCCC

• How do we get Cj ?• FEM Methods which are based on mechanical dimensions


Apc7mm Open

Repeatability effects


Standard Model: 40ps line


Multiport VNA Calibration

• A new errror model is necessary• Multiport standard may be required• Calibration Algorithm must be found• Cannot be a simple extension of the 2 port

ones


Multiport Calibration

We do not have multiport standards

We cannot connect one port

to any others

We may not have Thrus

What if:

?Calibration cannot be based on

a fixed sequence A general formulation must be

found !


Classical multiport error model

67

nnm

mm

000

000

22

11

M

nnk

k

000

0001

22

K

nnh

hh

000

000

22

11

H

nnl

ll

000

000

22

11

L

Complete reflectometer multiport architecture: two directional couplers @ each port

Error box extension as

4n -1 unknowns


Partial Reflectometer error model

68

Partial reflectometer multiport architecture: two directional couplers @ each port are not always available

This architecture has the advantages of costs (n-2 couplers are saved) and speed

The model for these case must be: of general validity (i.e. not valid for only one calibration algorithm and scalable) compatible with the complete reflectometer one easy to be calibrated


The new formulation

69

The partial reflectometer multiport system has two states, for each i port:

STATE A STATE B


The cal equation becomes

• And the de-embedding is:

70

“A Novel Calibration Algorithm for a Special Class of Multiport Vector Network Analyzers”,Ferrero, A.; Teppati, V.; Garelli, M.; Neri, A.IEEE Transactions on Microwave Theory and Techniques, Volume 56, Issue 3, March 2008

6n -1 unknowns

Based on S parameters Always defined for any standardsCan be used to find H,L,M,K,F,G during the cal As well as to find dut S matrix during the measurement


Dynamic Calibration

Since no constrains are given on the standard type and the math can combine whatever sequence, the calibration becomes dynamic i.e. the software can generate the standard sequence which gives a set of enough linear independent equations as well as it accomplished for:

– Connectors at each ports– Available standards USE ONLY 1 or 2 ports ONES !!– User interconnection description– Use of particular two port pairs self calibration

71

Let’s combine everything and design

a cal to fit the DUT


Example: Design CAL for the DUT

72

P_1

P_2

P_3

P_4


An Example a Socket Measurement


8-ports Socket Setup


Calibration Design

P1 P5

P2 P6

P3 P7

P4 P8

LSM

LSM

LSM

LSM

Rec

Rec

Rec

8-Port LRM/LSM Multi-Calibration Matrix with Reciprocal Thrus

Port 1 Port 2 Port 3 Port 4 Port 5 Port 6 Port 7 Port 8

Port 1 X Recip X X 2P_LSM X X X

Port 2 Recip X X X X 2P_LSM X X

Port 3 X X X Recip X X 2P_LSM X

Port 4 X X Recip X X X X 2P_LSM

Port 5 2P_LSM X X X X X X X

Port 6 X 2P_LSM X X X X Recip X

Port 7 X X 2P_LSM X X Recip X X

Port 8 X X X 2P_LSM X X X X

• Calibration Procedure:– Thru Port 1, 5– Thru Port 2, 6– Thru Port 3, 7– Thru Port 4, 8– Recip 1, 2– Recip 3, 4– Recip 6, 7– Reflect Port 1, Reflect Port 5– Reflect Port 2, Reflect Port 6– Reflect Port 3, Reflect Port 7– Reflect Port 4, Reflect Port 8– Load Port 1, Load Port 5– Load Port 2, Load Port 6– Load Port 3, Load Port 7– Load Port 4, Load Port 8

Structure 1

Structure 2

Structures 3

Structures 4

4 separate 2-port LSM/LRM calibrations linked with reciprocal thru standards

• No wasted probe touchdowns• Never move probe tips in x or y direction• Full characterization of every port• Could provide more accurate calibrations


1

2

3

4

5

6

7

8

Probe Touchdown 4

GND SIG TERM

8-Port LRM/LSM Standards (Probe tip Calibration)

Minimize probe tip Xtalk

1

2

3

4

5

6

7

8

Probe Touchdown 1

X Length

1

2

3

4

5

6

7

8

Probe Touchdown 3

X Length

1

2

3

4

5

6

7

8

Probe Touchdown 2


Socket/Board Setup Close-up

Cal StandardsOn Socket PROBESLand Places

On Board PROBESLand Places


Socket-Board Data

SDD11-SDD22-SDD33-SDD44


Socket-Board Data

SDD12 - SDD34


Socket-Board Data

SD14 – SD23 (Far End Xtalk)


Socket-Board Data

SD13 – SD24 (Near End Xtalk)

Bottom Board

Top Board


Conclusion

• Modern Calibration Technology solves manyissues in multiport structure S parameter measurements

• Proper design of the measurement bench dramatically improves data accuracy

• Modern Software are today available to handle the measurement complexity

83


Acknoledgements

• Valeria Teppati, Serena Bonino Politecnico of Torino

• Marco Garelli HFE

• Brett Grossmann, Tom Ruttan, Evan FledellIntel Corp

• Jon MartensAnritsu Corp

• Dave BlackhamAgilent

THANK YOU

Seminario d’Eccellenza “ITALO GORINI” Scuola di Dottorato

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