Passive components in MMIC technology

1

Passive components in MMIC technology

Evangéline BENEVENT

Università Mediterranea di Reggio Calabria

DIMET

2


Introduction

Design cycle of passive components in MMIC technology


Distributed components

Inductor, capacitor

Localized components

Resistor, capacitor, inductor

Microwave characterization of passive devices

S-parameters

Extraction of device’s characteristics from measurements

De-embedding and calibration

3


Introduction




Inductor, capacitor




S-parameters



4


Introduction

Maxwell’s equations

All electromagnetic behaviors can ultimately be explained by Maxwell’s four

basic equations:

However, it isn’t always possible or convenient to use these equations directly.

Solving them can be quite difficult. Efficient design requires the use of

approximations such as lumped and distributed models.

Why are models needed?

Models help us predict the behavior of components, circuits and systems.

Lumped models are useful at lower frequencies, where some physical effects

can be ignored. Distributed models are needed at higher frequencies to

account for the increased behavioral impact of those physical effects.

ρ=∇ D. 0. =∇ Bt

BE

∂

∂−=×∇

t

DjH

∂

∂+=×∇

5


Introduction

Two ports models

Two-port, three-port, and n-port models simplify the input/output response of

active and passive devices and circuits into “black boxes” described by a set

of four linear parameters.

Lumped models use representations such as admittances (Y) and resistances

(R). Distributed models use S-parameters (transmission and reflection

coefficients).

Limitations of lumped models

At low frequencies most circuits behave in a predictable manner and can be

described by a group of replaceable, lumped-equivalent black boxes.

6


Introduction

Limitations of lumped models

At microwave frequencies, as circuit element size approaches the

wavelengths of operating frequencies, such a simplified type of model

becomes inaccurate. The physical arrangements of the circuit components

can no longer be treated as black boxes. We have to use a distributed circuit

element model and S-parameters.

S-parameters

S-parameters and distributed models provide a means of measuring,

describing, and characterizing circuits elements. They are used for the design

of many high-frequency products.

7


Introduction




Inductor, capacitor




S-parameters



8



Choice (or no choice!) of the substrate respect to the application or the specifications

Choice of additional key materials such as dielectric and magnetic materials

Analytical models ⇒⇒⇒⇒ approximated size and performance of passive components

EM simulation (numerical modeling) ⇒⇒⇒⇒ performance of passive components

Performance = specifications?NO

YES

Fabrication of a prototype, Characterization, Test

Performance = specifications?NO

YES

GOOD JOB !

DESIGN COST !

9


Introduction




Inductor, capacitor




S-parameters



10


From transmission lines, it is possible to realize low values passive components

like capacitances or inductances, provided that the length of the line is less than

λ/10.

Theory of transmission lines:

Zc ZL

ℓ)(

)()(

l

ll

β

β

tgjZZ

tgjZZZZ

Lc

cLc

+

+=


A section of a transmission line without losses

(or with low losses), with a length ℓ, with a

characteristic impedance Zc, and terminated

by a impedance (load) ZL presents an

impedance Z(ℓ), on the input, equal to:

[1] C. Algani, “Composants passifs”, Support de cours du CNAM, Spécialité Electronique-Automatique.

11


If the length of the transmission line is small respect to the wavelength:

Then:

This input impedance is a complex impedance so:

If Re(Z(ℓ)) << Im(Z(ℓ)): Z(ℓ) → pure imaginary

⇒ One can realize a capacitor or an inductor !

βℓ < π/6 or ℓ < λ/12

l

ll

β

β

Lc

cLc

jZZ

jZZZZ

+

+=)(


12


Inductor:

If ZL = 0 or ZL << Zctg(βℓ):

By identification:

The synthesized inductance L (H) has a value equal to:

This inductance can be realized by a short-circuited line or by a line with a

characteristic impedance Zc high respect to the impedance of the load.

)()( ll βtgjZZ c≈

)( lβω

tgZ

L c≈


ωjLZ =

13


Real realization of distributed inductor:

Series inductance:

Z0 >> Z01, Z02

Shunt inductance:


ℓ

Z01 Z02

Z0

ℓ

Z01

Z0

Short-circuit

14


Capacitor:

If ZL = ∞ or ZL >> Zctg(βℓ):

By identification:

The synthesized capacitance C(F) has a value equal to:

This capacitance can be realized by a open-circuit line or by a line with a

characteristic impedance Zc low respect to the impedance of the load.

)()(

ll

βjtg

ZZ c≈

cZ

tgC

ω

β )( l=


ωjCZ

1=

15


Real realization of distributed capacitor:

Series capacitance:

Shunt capacitance:

Z0 << Z01, Z02


gZ0 Z0

ℓ

Z01 Z02

Z0

16


Introduction




Inductor, capacitor




S-parameters



17


The localized components have higher values than the distributed components.

However, due to parasitic elements at high frequency, the dimensions of localized

components must be small compared to the wavelength (ℓ < λ/30). In this way, the variations of phase are negligible.

Localized components can be described by analytical models which take into

account the frequency-dependent parasitic effects and different kinds of losses by

adding other localized components.


18


Resistor

Structure:

The resistance R (Ω) of a conductor strip is defined by the following equation:

substrate

metallization

resistor

ground plane

tWR

⋅=

l

σ

1

where σ is the conductivity of the conductor, ℓ the length, W the width, and t the thickness of the conductor strip.

If the conductor strip is square, the resistance does not depend on the

dimensions of the strip and the “square resistance” (Ω/square) is equal to:

tRs

11

σ=


19


Resistor

At high frequency, the current circulates only in a thin thickness of the resistive

layer called “skin depth” and not in the total thickness t. The skin depth δ (m) depends on the frequency:

σωδ

cµµ0

2=

where ω=2πf is the pulsation (rad/s), µ0 and µc are the conductivities of the

vacuum and conductor respectively, σ is the conductivity.

The square resistance becomes:

δσ

11=Rs


Typical values: 20 to 500 Ω/square.

20


Resistor

Resistor model:

R is the resistance, depending on the skin-effect,

The distributed nature of the resistor is taken into account with the series

inductance L,

C1, C2 are the parasitic shunt capacitances to ground of the resistor and

its contact pads,

C3 is the end-to-end feedback capacitance.


L

C3

C1 C2

R (f)

[2] Frank Ellinger, “RF Integrated Circuits and Technologies”, Springer, 2007.

21


Capacitor

Interdigital capacitor

The capacitance increases with the number of fingers.


Port 1 Port 2

22


Capacitor


Equivalent circuit:

C is the interdigital capacitance.

R corresponds to the resistive losses.

L is the parasitic inductance of the fingers.

C1, C2 are the parasitic capacitances to the ground.


CL

C2

R

C1

23


Capacitor


Advantages:

Only one metallization plane,

Easy to manufacture.

Drawback:

Too small capacitance: typically C = 0.5 to 2 pF/mm².


24


Capacitor

MIM (Metal-Insulator-Metal) capacitor

ε0 is the vacuum permittivity.

εr is the relative permittivity of the insulator.

W is the width of the capacitor.

ℓ is the length of the capacitor.

e is the thickness of the insulator

layer.


e

W

e

SFC rr

MIM

lεεεε 00)( ==

25


Capacitor


MIM capacitor model:

C is the MIM capacitance,

R corresponds to the losses of the capacitor,

C1, C2 are the parasitic capacitances to ground from bottom, top plate,

L1, L2 are the parasitic inductances of bottom, top plate.


L1 L2C

C1 C2

R

26


Capacitor


Choice of the dielectric material:

The higher the relative permittivity of the material is, the higher the

value of the capacitance is (C = εdielectric.C0). So one can choose a high permittivity material.

But in a MMIC circuit, the capacitors must support various DC

polarization voltages. So one have to also consider the breakdown voltage (or breakdown electric field).


[3] C. Rumelhard, “MMIC Composants”, Techniques de l’Ingénieur.

27



Capacitor


For example, in order to the titanium dioxide (TiO2) supports the same

voltage than the tantalum pentoxide (Ta2O5), it is necessary to multiple

the thickness by five, so to reduce the capacitance by five.

4905055TiO2 (titanium dioxide)

88520025Ta2O5 (tantalum pentoxide)

3902508.8Al2O3 (alumina)

2902506.5Si3N4 (silicon nitride)

2653005SiO2 (silica)

Capacitance density for Vmax = 50 V (pF/mm²)

Breakdown electric field (V/µm)

Relative permittivityDielectric material

28



Capacitor


This is summarized in the third column with the capacitance density for a maximum voltage. Regarding this parameter, the best dielectric

material is now the tantalum pentoxide instead of the titanium dioxide.

4905055TiO2 (titanium dioxide)

88520025Ta2O5 (tantalum pentoxide)

3902508.8Al2O3 (alumina)

2902506.5Si3N4 (silicon nitride)

2653005SiO2 (silica)

Capacitance density for Vmax = 50 V (pF/mm²)

Breakdown electric field (V/µm)

Relative permittivityDielectric material

29



Capacitor


Because of the leakage area, in real topology, it is necessary to add an

air bridge.

Leakage area

2nd thick metalFirst metal

Silicon nitride Si3N4

SubstrateSubstrate

Air bridge (deck)

Air bridge(pillar)

2nd thick metal

First metal

Silicon nitride Si3N4

30



Inductor

Rectangular plate inductor

In order to reduce the area occupied by the inductor, one can:

Fold down the conductor,

Make loops.

W

ℓ

t

+++

+=

l

ll

35.0

2ln2 0

tW

tWµL

31



Inductor

Loop inductor

W is the width of the conductor,

t is the thickness of the conductor,

ℓ is the circumference of the loop equal to:

−

+= − 76.1ln.10.2 9

tWL

ll

Rπ2=l

32



Inductor

Meander inductor


t is the thickness of the conductor,

ℓ is the length of the meander.

Typical values: 0.4 to 4 nH.

+

++

+= − 19.122.0ln.10.2 9

l

ll

tW

tWL

33



Inductor

Circular spiral inductor

n is the number of turns,


h is the height of the substrate,

Do is the outer diameter,

Di is the inner diameter.

Typical values: 0.2 to 15 nH.

Kca

naL

118

²²394.10 9

+= −

h

WnK l145.057.0 −= 05.0>

h

W

4io DD

a+

=2

io DDc

−=

34



Inductor

Square spiral inductor

There are many ways to layout a planar spiral inductor. The optimal structure is the circular spiral. This structure places the largest amount of

conductors in the smallest possible area, reducing the series resistance of

the spiral.

This structure, however, is often not used because it is not supported by

many mask generation systems. Many of these systems are able to only

generate Manhattan geometries (and possibly 45° angles as well).

Manhattan-style layouts only contain structures with 90°angles.

[4] R.L. Bunch, D.I. Sanderson, S. Raman, Application Note, “Quality factor and inductance in differential IC implementations”, IEEE Microwave Magazine, June 2002.

35



Inductor


So a simple solution is to approximate a circle by a

polygon. An octagonal spiral as a Q that is slightly

lower than the circular structure but is much easier

to lay out. Octagonal inductor

The square spiral structure does not have the best performance, but it is

one of the easiest structure to lay out and simulate.

36



Inductor


n is the number of turns,

davg represents the average

diameter of the spiral,

ρ represents the percentage of the inductor area that is

filled by metal traces.

++

= ²125.0178.0

067.2ln

²2 0ρρ

ρπ

avgdnµL

37



Inductor with magnetic material

When a high permeability material is placed near a conductor carrying

electrical current, the inductance of the conductor is know to increase.

Ideally, if a conductor is enclosed in an infinite magnetic medium, the

inductance is increased by a factor of µr, the relative permeability of the

medium. If µr is purely real (no magnetic loss) and large, then the inductance

as well as the quality factor Q of the structure are significantly enhanced.

It also means that, for the same inductance value, a much smaller substrate

area would be needed. Furthermore, since the magnetic flux is confined

within the magnetic material, cross-talk between the inductors on the same

chip would be reduced.

[5] V. Korenivski, R.B. van Dover, “Magnetic film inductors for radio frequency applications”, J. Appl. Phys. 82 (10), Nov. 1997, pp. 5247-5254.

38




Thin film solenoid with a magnetic core

What’s a solenoid?

39





Cross section of thin film rectangular solenoid

conductor/coil

magnetic core

insulator

µr

µ0

tm

ti

ts

W

tc

40





Top view of thin film rectangular solenoid

1 2 3 … N turnsWc

ℓ

W

41





Inductance:

Quality factor:

l

mr tWNµµ

I

NL

.²0=Φ

=

where N is the number of turns, Φ the magnetic flux, µ0 the vacuum permeability, µr the relative

permeability of the magnetic material, tm its

thickness, W the width of the solenoid, ℓ its length.

ρ

ωω

l20 ccmr tWNtµµ

R

LQ ==

where Wc is the width of the conductor strip, tc its

thickness, ρ its resistivity..

42





Parasitic capacitance:

where ε = ε0.εr is the permittivity of the insulator, ti its thickness.

Resonance frequency:

i

c

t

WWNC ε2≈

2/13

0 ²²8

2

1−

==

li

cmrr

t

WtWNµµ

LCf

επ

π

43




Magnetically sandwiched stripe inductor

Where µ0 is the vacuum permeability, µr the relative permeability of the

magnetic material, ℓ the length of the strip, tm the thickness of the

magnetic, W the width of the structure, g the gap between the two

magnetic layers.

Conductor strip

Magnetic layer

tc= g

tm

µr

µ0

−=

K

W

W

K

W

tµµL m

r2

tanh2

12

0 l

2rm µgt

K =

44




Magnetically wrapped stripe inductor

The magnetically wrapped stripe inductor is an improved version of the

magnetically sandwiched stripe inductor as the factor:

was removed.

This is due to the enclosure of the magnetic flux in the wrapped version.

Conductor strip

Magnetic layer

tc= g

tm

µr

µ0W

tµµL m

r2

0 l=

−

K

W

W

K

2tanh

21

45


Introduction




Inductor, capacitor




S-parameters



46


S-parameters

Two-port model

Any device can be described by a set of four variables associated with a two-port model. Two of these variables represent the excitation (independent variables), and the remaining two represent the response of the device to the excitation (dependent variables).

If the device is excited by voltage sources V1 and V2, the currents I1and I2 will be related by the following equations:

2121111 VyVyI +=

2221212 VyVyI +=Two-port devicePort 1 Port 2V2V1

I1 I2

[6] Test & Measurement Application Note 95-1, Hewlett Packard, “S-parameters techniques for faster, More accurate network design”, 1997.

47


S-parameters

Two-port model

In this case, with port voltages selected as independent variables and port currents taken as dependent variables, the relating parameters are called short-circuit admittance parameters, or y-parameters. Four measurements are required to determine the four parameters y11, y12, y21, y22. Each measurement is made with one port excited by a voltage source, while the other port is short-circuited. For example:

At high frequencies, lead inductance and capacitance make short and open circuits difficult to obtain. So the characterization of microwave devices by S-parameters is more convenient.

01

221

2 =

=V

V

Iy

48


S-parameters

Using S-parameters

“Scattering parameters” which are commonly referred as S-parameters, are

a parameter set that relates to the traveling waves that are scattered or

reflected when an n-port network is inserted into a transmission line.

S-parameters are usually measured with the device imbedded between a

50 Ω load and source.

Two-port device ZLVS

a1 a2

b2b1

ZS

∼∼∼∼

49


S-parameters

Incident and reflected waves

The independent variables a1 and a2 are normalized incident voltages:

The dependent variables b1 and b2 are normalized reflected voltages:

The parameters are referenced to Z0 (supposed real and positive)

generally equal to 50 Ω

0

1

00

0111

1 port on incident wavevoltage

2 Z

V

ZZ

ZIVa i==

+=

0

2

00

0222

2 port on incident wavevoltage

2 Z

V

ZZ

ZIVa i==

+=

0

1

00

0111

1 port from reflected wavevoltage

2 Z

V

ZZ

ZIVb r==

−=

0

2

00

0222

2 port from reflected wavevoltage

2 Z

V

ZZ

ZIVb r==

−=

50


S-parameters

Definition of S-parameters

The linear equations describing the two-port device are then:

Under the matrix form:

a1 a2

b2b1

S21

S11

S12

S22

2121111 aSaSb +=

2221212 aSaSb +=

=

2

1

2221

1211

2

1

a

a

SS

SS

b

b

51


S-parameters

Definition of S-parameters

S11 is the input reflection coefficient with the output port terminated by a

matched load (ZL = Z0 sets a2 = 0):

S22 is the output reflection coefficient with the input port terminated by a

matched load (ZS = Z0 sets VS = 0):

S21 is the forward transmission coefficient with the output port terminated by

a matched load (ZL = Z0 sets a2 = 0):

S12 is the reverse transmission coefficient with the input port terminated by

a matched load (ZS = Z0 sets VS = 0):

01

111

2 =

=a

a

bS

02

222

1=

=a

a

bS

021

221

=

=a

a

bS

02

112

1=

=a

a

bS

52


S-parameters

Cascade of several two-port devices

The ABCD matrix:

=

2

2

1

1

b

a

DC

BA

a

b

Two-port device 1

[A1B1C1D1]

a1 a2

b2b1

Two-port device 2

[A2B2C2D2]

Two-port device 3

[A3B3C3D3]

a1 a2

b2b1

Equivalent two-port device 2[ABCD]

=

=

2

2

33

33

22

22

11

11

2

2

1

1

b

a

DC

BA

DC

BA

DC

BA

b

a

DC

BA

a

b

53


S-parameters

Two other matrix are widely used:

Y-matrix (admittance matrix)

Z-matrix (impedance matrix)

Two-port devicePort 1 Port 2V2V1

I1 I2

[ ]

=

=

2

1

2221

1211

2

1

2

1.

I

I

ZZ

ZZ

I

IZ

V

V

[ ]

=

=

2

1

2221

1211

2

1

2

1.

V

V

YY

YY

V

VY

I

I

54


S-parameters

Relations between the matrix of a two-port device

55


S-parameters

Relations between the matrix of a two-port device

56


S-parameters

ABCD matrix and S-parameters matrix of useful two-port devices

Z1 Z2

Z3

Z

Y

57


S-parameters

ABCD matrix and S-parameters matrix of useful two-port devices

Y1 Y2

Y3

αααα

Zc, γγγγ

ℓ

58


Introduction




Inductor, capacitor




S-parameters



59


Extraction of the device’s characteristics from measurements

How to compare analytical and experimental (measurements) results?

Analytical study: Measurements:

Propagation constant γ

Characteristic impedance Zc

S-parameters

S11, S12, S21, S22

“conversion”

S-parameters

S11, S12, S21, S22

Propagation constant γ

Characteristic impedance Zc

“conversion”

Comparison

is now

possible!

60



Experimental results:

During measurements, the device is placed between two 50 Ω ports.

Two-port device50 ΩΩΩΩ port 50 ΩΩΩΩ port

50 ΩΩΩΩ port50 ΩΩΩΩ port ΓΓΓΓ -ΓΓΓΓ ΓΓΓΓ-ΓΓΓΓ

T

T

1+ΓΓΓΓ

1-ΓΓΓΓ

1-ΓΓΓΓ

1+ΓΓΓΓ

Graph of fluency

61



Extraction of the characteristic impedance and the propagation constant from

the S-parameters (for a reciprocal device):

Transmission coefficient:

Propagation constant:

Reflection coefficient:

Characteristic impedance:

Γ−=

11

21

1 S

ST

)ln(1

Tl

−=γ

1² +±=Γ KK11

2111

2

1²²

S

SSK

+−= 1≤Γ

Γ−

Γ+=

1

10ZZc

62



Calculation of S-parameters from analytical evaluation of the propagation

constant and the characteristic impedance (for a reciprocal device):

Transmission coefficient:

Reflection coefficient:

S-parameters:

)exp( lγ−=T

0

0

ZZ

ZZ

c

c

+

−=Γ

²²1

²)1(2211

Γ−

−Γ==

T

TSS

²²1

²)1(2112

Γ−

Γ−==

T

TSS

63


Introduction




Inductor, capacitor




S-parameters



64



Vector network analyzer (VNA)

Vector Network Analyzer are commonly used to measure S-parameters of a

DUT (Device Under Test).

VNA are available for measurements from 45 MHz up to 220 GHz.

The DUT is excited on one port by a sinusoidal signal of constant

magnitude and a frequency range defined by the user. The transmitted and

reflected signals are measured by the VNA. The operation is repeated for

each port, and then the scattering matrix (S-parameters) can be evaluated

for each point of frequency.

[7] B. Bayard, “Contribution au développement de composants magnétiques pour l’électronique hyperfréquence”, Thèse de Doctorat, 2000.

65




In case of a two-port device, the VNA automatically excites first the port 1 of

the DUT and measures the parameters S11 and S21, and second excites the

port 2 and measures the parameters S22 and S12. In this way, it is not

necessary to reverse the DUT.

When one of the two port is excited, the VNA divides the signal in two parts.

The first one will be the excitation source of the DUT, the second one will

be needed as a reference. The reflected and transmitted signals should be

compared to this reference.

The DUT is linked to the VNA by coaxial cables. The bandwidth of the

cables and the VNA must be greater than the frequency range study of the

DUT.

66




Screen display

Port 1Port 2

Digit

keypad

Thin

frequency

sweeping

Command

buttons

67



Measurement benchmark

VNA

DUT

Ground Signal

Port 1 Port 2Coaxial cable

GSG coplanar probes Substrate

68



Calibration permits to suppress the parasitic effects of the cables, the probes

and the VNA.

VNA

DUT



CALIBRATION

69



Calibration:

Two categories of errors:

Random errors:

Can not be corrected,

Supposed negligible respect to the systematic errors,

Example: noise, temperature drift, user manipulation …

To use the maximal power source without saturate the DUT to

optimize the SNR (Signal/Noise Ratio).

Systematic errors:

Reproducible errors,

Must be corrected by the calibration.

70



Calibration

Systematic errors:

Directivity error: error due to the imperfect separation of reflected and transmitted signals.

Impedance mismatching of the generator output: a part of the signal reflected by the DUT is reflected by the generator.

Impedance mismatching of the load: a part of the signal transmitted by the DUT to the load is reflected by the load.

Tracking error: this error is due to the path difference between the measured (external) signals and the reference (internal) signals.

Error due to the dissymmetry of the switch that orients the signals from the generator to the ports 1 or 2.

Insulation error: this is due to the coupling between the two ports.

71



Calibration

The goal of the calibration is to obtain a perfect measurement system by

removing the errors introduced by the experimental benchmark.

The calibration consists on the measurement of special components called

“standards” in order to obtain data to evaluate the elements of the error

model. The standards take place in a “calibration kit” or a calibration

substrate.

Three models exist:

The model with 12 error elements,

The model with 10 error elements,

The model with 8 error elements.

Complexity Accuracy

72



Calibration

The model with 12 error elements:

Forward (F) model ⇒ 6 elements

EIF

EDF

1

EGF

ERF

ELF

ETF

Incident wave

Reflected wave

Transmission measurement

S21

S12

S11 S22

Sij: intrinsic S-parameters of the DUT

EIF: insulation error

EGF: generator impedance mismatching

ELF: load impedance mismatching

EDF: directivity error

ERF: reflection error

ETF: transmission error

73



Calibration

The model with 12 error elements:

Reverse (R) model ⇒ 6 elements

Sij: intrinsic S-parameters of the DUT

EIR: insulation error

EGR: generator impedance mismatching

ELR: load impedance mismatching

EDR: directivity error

ERR: reflection error

ETR: transmission error

EIR

ELR

ETR

EGR EDR

ERR

1

S11

S21

S12

S22

Transmission measurement

Reflected wave

Incident wave

74



OSTL calibration (open-short-thru-load calibration)

Commonly used calibration based on the model with 12 error elements.

4 standards are required: open, short, thru, and load.

Large bandwidth calibration.

OST (open-short-thru) or OSL (open-short-line) calibration

Based on the model with 8 error elements.

⇒ 3 standards are needed instead of 4.

The standard “load” is eliminated, this is the hardiest to manufacture.

75



TRL calibration (thru-reflect-line)

High accuracy calibration.

Initially based on the model with 8 error elements.

Standard “thru”: the two ports are directly linked together. The standard “thru”

must be perfect.

Standard “reflect”: each port is connected to a unknown device with a high

reflection level.

Standard “line”: the two ports are linked by a transmission line. The length of the

line could be unknown.

LRL calibration (line-reflect-line)

Identical to the TRL calibration, but it could be convenient for the calibration of

planar lines since they can not be directly linked together (the standard “thru” is

not feasible).

76



Schematic of a calibration substrate

Probes positioned on a calibration substrate

2 probes on the same support

Probes positioning on the contact pads of an ICGSG probes positioning on the contact pads of an inductor

Transition from probes to coaxial cable

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Manual probe system

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De-embedding permits to suppress the parasitic effects of the transition

between the probes and the DUT, and the access of the DUT.

VNA

DUT



DE-EMBEDDING

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De-embedding techniques fall into two broad categories:

Modeling based approach,

Measurement based approach.

The de-embedding approach starts with the knowledge (by measurements or

simulation) of the S-parameters of a structure containing the discontinuity to be

studied and other auxiliary part such as traces, adapters, etc. The S parameters of

these parts are evaluated by means of simulation or measurements.

The S matrix of the discontinuity is extracted from the S matrix of the complete

structure by means of the information on the auxiliary parts.

More exactly, the ABCD matrix is used for the calculation.

[8] S. Agili, A. Morales, “De-embedding techniques in signal integrity: a comparison study”, 2005 Conference on Information Sciences and Systems.

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De-embedding step-by-step:

Measurement of the S-parameters of the complete structure and conversion in ABCD matrix.

Evaluation by measurement or simulation of the S-parameters of the auxiliary parts and conversion in ABCD matrix.

Evaluation of the ABCD matrix of the DUT, and conversion in S-parameters:

1

22

22

1

11

11..

−−

=

DC

BA

DC

BA

DC

BA

DC

BA

totaltotal

totaltotal

DUTDUT

DUTDUT

DUT

Substrate

[A1B1C1D1] [A2B2C2D2][ADUT BDUT

CDUT DDUT]

[AtotalBtoitalCtotalDtotal]

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De-embedding

Example with a planar spiral inductor:

[9] S. Couderc, “Etude de matériaux ferromagnétiques doux à forte aimantation et à résistivité élevée pour les radio-fréquences, applications aux inductances spirales planaires sur silicium pour réduire la surface occupée”, Thèse de Doctorat, 2006.

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On-wafer de-embedding:

Short-open de-embedding

The open-short de-embedding method is a two-step de-embedding

method and is considered as the industry standard. Shunt and series

parasitic elements are removed by using open and short dummy

structures, respectively.

Consequently, a short and an open circuits are added on the wafer for

each device to be measured.

[10] M. Drakaki, A.A. Hatzopoulos, S. Siskos, “De-embedding method fro on-wafer RF CMOS inductor measurements”, Microelectronics Journal 40 (2009) 958-965.

[11] T.E. Kolding, “On-wafer calibration techniques for GHz CMOS measurements”, Proc. IEEE 1999 Int. Conf. on Microelectronic Test Structures, Vol. 12, March 1999, pp. 105-110.

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From the measurement of the short-circuit, the open circuit, and the two-

port device, it is possible to extract the intrinsic characteristics of the

DUT:

DUT

Zshort

Yopen Yopen

Zshort

( ) ( ) 1111 −−−− −−−= shortopenshorttotalDUT ZYZYY

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Example of a coplanar transmission line:

De-embedding reference planes Open circuit Short circuit

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Example of a planar spiral inductor:

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Evangéline BENEVENT

Università Mediterranea di Reggio Calabria

DIMET

Thank you for your attention!

Documents

Passive components in MMIC technology