Download Passive components in MMIC technology

Passive components
in MMIC technology
Evangéline BENEVENT
Università Mediterranea di Reggio Calabria
DIMET
1
Passive components in MMIC technology
Introduction
Passive components in MMIC technology
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
2
Passive components in MMIC technology
Introduction
Passive components in MMIC technology
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
Passive components in MMIC technology
Introduction
Maxwell’s equations
All electromagnetic behaviors can ultimately be explained by Maxwell’s four
basic equations:
∂B
∂D
∇.D = ρ
∇.B = 0
∇×E = −
∂t
∇×H = j +
∂t
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.
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Passive components in MMIC technology
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.
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Passive components in MMIC technology
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.
6
Passive components in MMIC technology
Introduction
Passive components in MMIC technology
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
7
Passive components in MMIC technology
Design cycle of passive components in MMIC technology
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?
DESIGN COST !
NO
YES
GOOD JOB !
8
Passive components in MMIC technology
Introduction
Passive components in MMIC technology
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
9
Passive components in MMIC technology
Distributed components
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:
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:
Z (l ) = Z c
Z L + jZ c tg ( βl )
Z c + jZ L tg ( βl )
Zc
ZL
ℓ
[1] C. Algani, “Composants passifs”, Support de cours du CNAM, Spécialité Electronique-Automatique.
10
Passive components in MMIC technology
Distributed components
If the length of the transmission line is small respect to the wavelength:
βℓ < π/6 or ℓ < λ/12
Then:
Z (l ) = Z c
Z L + jZ c βl
Z c + jZ L βl
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 !
11
Passive components in MMIC technology
Distributed components
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.
Z ( l ) ≈ jZ c tg ( β l )
Z = jLω
L≈
Zc
ω
tg ( βl )
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Passive components in MMIC technology
Distributed components
Real realization of distributed inductor:
Series inductance:
ℓ
Z01
Z02
Z0 >> Z01, Z02
Z0
Z01
Shunt inductance:
Z0
ℓ
Short-circuit
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Passive components in MMIC technology
Distributed components
Capacitor:
Zc
jtg ( β l)
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.
Z=
Z (l) ≈
1
jCω
C=
tg ( β l )
ωZ c
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Passive components in MMIC technology
Distributed components
Real realization of distributed capacitor:
Series capacitance:
Z0
Shunt capacitance:
Z0 << Z01, Z02
Z0
g
ℓ
Z01
Z02
Z0
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Passive components in MMIC technology
Introduction
Passive components in MMIC technology
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
16
Passive components in MMIC technology
Localized components
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.
17
Passive components in MMIC technology
Localized components
Resistor
Structure:
resistor
metallization
substrate
ground plane
The resistance R (Ω) of a conductor strip is defined by the following equation:
R=
1
l
σ W ⋅t
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:
Rs =
11
σ t
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Passive components in MMIC technology
Localized components
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:
δ=
2
ωµ 0 µ c σ
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:
Rs =
11
σδ
Typical values: 20 to 500 Ω/square.
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Passive components in MMIC technology
Localized components
C3
Resistor
R (f)
Resistor model:
L
C1
C2
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.
[2] Frank Ellinger, “RF Integrated Circuits and Technologies”, Springer, 2007.
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Passive components in MMIC technology
Localized components
Capacitor
Interdigital capacitor
The capacitance increases with the number of fingers.
Port 1
Port 2
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Passive components in MMIC technology
Localized components
Capacitor
Interdigital capacitor
Equivalent circuit:
C
C1
R
L
C2
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.
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Passive components in MMIC technology
Localized components
Capacitor
Interdigital capacitor
Advantages:
Only one metallization plane,
Easy to manufacture.
Drawback:
Too small capacitance: typically C = 0.5 to 2 pF/mm².
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Passive components in MMIC technology
Localized components
Capacitor
MIM (Metal-Insulator-Metal) capacitor
C MIM (F ) =
ε 0ε r S
e
=
ε 0 ε r Wl
e
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.
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Passive components in MMIC technology
Localized components
Capacitor
MIM (Metal-Insulator-Metal) capacitor
MIM capacitor model:
L1
C
C1
R
L2
C2
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.
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Passive components in MMIC technology
Localized components
Capacitor
MIM (Metal-Insulator-Metal) 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.
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Passive components in MMIC technology
Localized components
Capacitor
MIM (Metal-Insulator-Metal) 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.
Dielectric material
Relative permittivity
Breakdown electric field
(V/µm)
Capacitance density for
Vmax = 50 V (pF/mm²)
5
300
265
Si3N4 (silicon nitride)
6.5
250
290
Al2O3 (alumina)
8.8
250
390
Ta2O5 (tantalum pentoxide)
25
200
885
TiO2 (titanium dioxide)
55
50
490
SiO2 (silica)
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Passive components in MMIC technology
Localized components
Capacitor
MIM (Metal-Insulator-Metal) 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.
Dielectric material
Relative permittivity
Breakdown electric field
(V/µm)
Capacitance density for
Vmax = 50 V (pF/mm²)
5
300
265
Si3N4 (silicon nitride)
6.5
250
290
Al2O3 (alumina)
8.8
250
390
Ta2O5 (tantalum pentoxide)
25
200
885
TiO2 (titanium dioxide)
55
50
490
SiO2 (silica)
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Passive components in MMIC technology
Localized components
Capacitor
MIM (Metal-Insulator-Metal) capacitor
Because of the leakage area, in real topology, it is necessary to add an
air bridge.
Air bridge
(deck)
Air bridge
(pillar)
2nd thick
metal
First metal
2nd thick metal
Silicon nitride Si3N4
Silicon nitride Si3N4
Leakage area
First metal
Substrate
Substrate
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Passive components in MMIC technology
Localized components
Inductor
Rectangular plate inductor
  2l 
W +t
L = 2 µ 0 l ln
 + 0.5 +
3l 
 W + t 
ℓ
t
W
In order to reduce the area occupied by the inductor, one can:
Fold down the conductor,
Make loops.
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Passive components in MMIC technology
Localized components
Inductor
Loop inductor
  l 

L = 2.10 −9.l ln
 − 1.76
 W + t 

W is the width of the conductor,
t is the thickness of the conductor,
ℓ is the circumference of the loop equal to:
l = 2πR
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Passive components in MMIC technology
Localized components
Inductor
Meander inductor
  l 

W + t 
L = 2.10 −9.l ln
 + 0.22
 + 1.19
 l 
 W + t 

W is the width of the conductor,
t is the thickness of the conductor,
ℓ is the length of the meander.
Typical values: 0.4 to 4 nH.
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Passive components in MMIC technology
Localized components
Inductor
Circular spiral inductor
L = 10 −9.
394a ²n ²
K
8a + 11c
K = 0.57 − 0.145ln
W
h
W
> 0.05
h
a=
Do + Di
4
c=
Do − Di
2
n is the number of turns,
W is the width of the conductor,
h is the height of the substrate,
Do is the outer diameter,
Di is the inner diameter.
Typical values: 0.2 to 15 nH.
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Passive components in MMIC technology
Localized components
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.
34
Passive components in MMIC technology
Localized components
Inductor
Square spiral 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.
35
Passive components in MMIC technology
Localized components
Inductor
Square spiral inductor
L=
2 µ 0 n ²d avg   2.067 

 + 0.178 ρ + 0.125 ρ ²
ln
π
  ρ 

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.
36
Passive components in MMIC technology
Localized components
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.
37
Passive components in MMIC technology
Localized components
Inductor with magnetic material
Thin film solenoid with a magnetic core
What’s a solenoid?
38
Passive components in MMIC technology
Localized components
Inductor with magnetic material
Thin film solenoid with a magnetic core
Cross section of thin film rectangular solenoid
W
conductor/coil
magnetic core
µr
insulator
µ0
ts
tm
ti
tc
39
Passive components in MMIC technology
Localized components
Inductor with magnetic material
Thin film solenoid with a magnetic core
Top view of thin film rectangular solenoid
1
2
3
Wc
…
N turns
W
ℓ
40
Passive components in MMIC technology
Localized components
Inductor with magnetic material
Thin film solenoid with a magnetic core
Inductance:
L=
NΦ µ 0 µ r N ²W .t m
=
I
l
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.
Quality factor:
Q=
ωL
R
=
ωµ 0 µ r Nt mW c t c
2lρ
where Wc is the width of the conductor strip, tc its
thickness, ρ its resistivity..
41
Passive components in MMIC technology
Localized components
Inductor with magnetic material
Thin film solenoid with a magnetic core
Parasitic capacitance:
C ≈ 2Nε
W cW
ti
where ε = ε0.εr is the permittivity of the insulator, ti its thickness.
Resonance frequency:
 8π ² µ 0 µ r εN 3W ²t mWc
fr =
=
ti l
2π LC 
1




−1/ 2
42
Passive components in MMIC technology
Localized components
Inductor with magnetic material
Magnetically sandwiched stripe inductor
L = µ0 µr l
tm
2W
Magnetic layer
µr
Conductor strip
µ0
 2K
 W 
1 −
tanh
 
 2K  
 W
K=
tm
tc= g
gt m µ r
2
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.
43
Passive components in MMIC technology
Localized components
Inductor with magnetic material
Magnetically wrapped stripe inductor
L = µ0 µr l
Magnetic layer
µr
Conductor strip
µ0
tm
tc= g
The magnetically wrapped stripe inductor is an improved version of the
magnetically sandwiched stripe inductor as the factor:
1−
tm
2W
2K
W 
tanh

W
 2K 
was removed.
This is due to the enclosure of the magnetic flux in the wrapped version.
44
Passive components in MMIC technology
Introduction
Passive components in MMIC technology
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
45
Passive components in MMIC technology
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 I1
and I2 will be related by the following equations:
I1 = y 11V1 + y 12V2
I 2 = y 21V1 + y 22V2
I1
Port 1
V1
I2
Two-port device
V2
Port 2
[6] Test & Measurement Application Note 95-1, Hewlett Packard, “S-parameters techniques for faster, More accurate
network design”, 1997.
46
Passive components in MMIC technology
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:
y 21 =
I2
V1 V
2 =0
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.
47
Passive components in MMIC technology
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.
ZS
VS
∼
a1
a2
Two-port device
b1
b2
ZL
48
Passive components in MMIC technology
S-parameters
Incident and reflected waves
The independent variables a1 and a2 are normalized incident voltages:
a1 =
a2 =
2 Z0
V2 + I 2 Z 0
2 Z0
voltage wave incident on port 1
=
Z0
=
=
voltage wave incident on port 2
Z0
Vi 1
Z0
Vi 2
=
Z0
The dependent variables b1 and b2 are normalized reflected voltages:
b1 =
b2 =
V1 + I1Z 0
V1 − I1Z 0
2 Z0
V2 − I 2 Z 0
2 Z0
=
voltage wave reflected from port 1
=
Z0
=
voltage wave reflected from port 2
Z0
Vr 1
Z0
=
Vr 2
Z0
The parameters are referenced to Z0 (supposed real and positive)
generally equal to 50 Ω
49
Passive components in MMIC technology
S-parameters
Definition of S-parameters
S21
a1
b1
S11
a2
S22
S12
b2
The linear equations describing the two-port device are then:
b1 = S11a1 + S12 a2
b2 = S21a1 + S22a2
Under the matrix form:
 b1  S11 S12   a1 
b  = S
 
 2   21 S22  a2 
50
Passive components in MMIC technology
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):
b1
S11 =
a2
a1 = 0
S21 is the forward transmission coefficient with the output port terminated by
a matched load (ZL = Z0 sets a2 = 0):
b2
S 21 =
a2 =0
S22 is the output reflection coefficient with the input port terminated by a
matched load (ZS = Z0 sets VS = 0):
b2
S 22 =
a1
a1
a 2 =0
S12 is the reverse transmission coefficient with the input port terminated by
a matched load (ZS = Z0 sets VS = 0):
S12 =
b1
a2
a1 = 0
51
Passive components in MMIC technology
S-parameters
Cascade of several two-port devices
The ABCD matrix:
a1
b1
b1   A B  a2 
a  = C D  b 
 2 
 1 
Two-port
device 1
Two-port
device 2
Two-port
device 3
[A1B1C1D1]
[A2B2C2D2]
[A3B3C3D3]
Equivalent
two-port
device 2
[ABCD]
a2
a1
b1
b1   A B  a2   A1 B1   A2
a  = C D  b  = C D  C
 2   1
1 2
 1 
a2
b2
b2
B2   A3
D2  C3
B3  a2 
D3  b2 
52
Passive components in MMIC technology
S-parameters
Two other matrix are widely used:
Y-matrix (admittance matrix)
I1 
V1  Y11 Y12  V1 
I  = [Y ].V  = Y
 
 2
 2   21 Y22  V2 
Z-matrix (impedance matrix)
V1 
I1  Z11 Z12  I1 
V  = [Z ].I  = Z
 
 2
 2   21 Z 22  I 2 
I1
Port 1
V1
I2
Two-port device
V2
Port 2
53
Passive components in MMIC technology
S-parameters
Relations between the matrix of a two-port device
54
Passive components in MMIC technology
S-parameters
Relations between the matrix of a two-port device
55
Passive components in MMIC technology
S-parameters
ABCD matrix and S-parameters matrix of useful two-port devices
Z
Y
Z1
Z2
Z3
56
Passive components in MMIC technology
S-parameters
ABCD matrix and S-parameters matrix of useful two-port devices
Y3
Y1
Y2
α
Zc, γ
ℓ
57
Passive components in MMIC technology
Introduction
Passive components in MMIC technology
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
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Passive components in MMIC technology
Extraction of the device’s characteristics from measurements
How to compare analytical and experimental (measurements) results?
Analytical study:
Propagation constant γ
Characteristic impedance Zc
“conversion”
Comparison
is now
possible!
Measurements:
S-parameters
S11, S12, S21, S22
“conversion”
S-parameters
Propagation constant γ
S11, S12, S21, S22
Characteristic impedance Zc
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Passive components in MMIC technology
Extraction of the device’s characteristics from measurements
Experimental results:
During measurements, the device is placed between two 50 Ω ports.
50 Ω port
Two-port device
1-Γ
Γ
50 Ω port
T
-Γ
Γ
Γ
1+Γ
Γ
50 Ω port
1+Γ
Γ
-Γ
Γ
T
Γ
50 Ω port
1-Γ
Γ
Graph of fluency
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Passive components in MMIC technology
Extraction of the device’s characteristics from measurements
Extraction of the characteristic impedance and the propagation constant from
the S-parameters (for a reciprocal device):
Transmission coefficient:
T=
S 21
1 − S11Γ
Propagation constant:
1
l
γ = − ln(T )
Reflection coefficient:
Γ = K ± K² + 1
K=
S11 ² − S 21 ² + 1
2S11
Γ ≤1
Characteristic impedance:
Zc = Z0
1+ Γ
1− Γ
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Passive components in MMIC technology
Extraction of the device’s characteristics from measurements
Calculation of S-parameters from analytical evaluation of the propagation
constant and the characteristic impedance (for a reciprocal device):
Transmission coefficient:
T = exp( −γl )
Reflection coefficient:
Γ=
Zc − Z0
Zc + Z0
S-parameters:
S11 = S 22 =
Γ(1 − T ²)
1 − T ²Γ ²
S12 = S 21 =
T (1 − Γ ²)
1 − T ²Γ ²
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Passive components in MMIC technology
Introduction
Passive components in MMIC technology
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
63
Passive components in MMIC technology
De-embedding and calibration
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.
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Passive components in MMIC technology
De-embedding and calibration
Vector network analyzer (VNA)
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.
65
Passive components in MMIC technology
De-embedding and calibration
Thin
frequency
sweeping
Vector network analyzer (VNA)
Digit
keypad
Screen display
Port 1
Port 2
Command
buttons
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Passive components in MMIC technology
De-embedding and calibration
Measurement benchmark
VNA
Port 1
Coaxial
cable
Port 2
DUT
GSG
coplanar
probes
Substrate
Ground
Signal
67
Passive components in MMIC technology
De-embedding and calibration
Calibration permits to suppress the parasitic effects of the cables, the probes
and the VNA.
VNA
Port 1
Coaxial
cable
Port 2
DUT
GSG
coplanar
probes
Substrate
CALIBRATION
68
Passive components in MMIC technology
De-embedding and calibration
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.
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Passive components in MMIC technology
De-embedding and calibration
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.
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Passive components in MMIC technology
De-embedding and calibration
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
71
Passive components in MMIC technology
De-embedding and calibration
Calibration
The model with 12 error elements:
Forward (F) model ⇒ 6 elements
EIF
Sij: intrinsic S-parameters of the DUT
EIF: insulation error
Transmission
measurement
Incident wave
1
EGF: generator impedance mismatching
ELF: load impedance mismatching
EDF
EDF: directivity error
ERF: reflection error
Reflected wave
S21
EGF
ERF
S11
ETF
S22
ELF
S12
ETF: transmission error
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Passive components in MMIC technology
De-embedding and calibration
Calibration
The model with 12 error elements:
Reverse (R) model ⇒ 6 elements
Reflected
wave
Sij: intrinsic S-parameters of the DUT
S21
EIR: insulation error
EGR: generator impedance mismatching
ELR
ELR: load impedance mismatching
ETR: transmission error
S22
S12
EDR: directivity error
ERR: reflection error
S11
Transmission
measurement
ETR
ERR
EGR
EDR
1
Incident
wave
EIR
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Passive components in MMIC technology
De-embedding and calibration
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.
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Passive components in MMIC technology
De-embedding and calibration
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).
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Passive components in MMIC technology
De-embedding and calibration
Schematic of a calibration substrate
Probes positioned on a
calibration substrate
Transition from probes to coaxial cable
GSG probes positioning on the
contact pads of an inductor
2 probes on the same support
Probes positioning on the contact pads of an IC
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Passive components in MMIC technology
De-embedding and calibration
Manual probe system
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Passive components in MMIC technology
De-embedding and calibration
De-embedding permits to suppress the parasitic effects of the transition
between the probes and the DUT, and the access of the DUT.
VNA
Port 1
Coaxial
cable
Port 2
DUT
GSG
coplanar
probes
Substrate
DE-EMBEDDING
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Passive components in MMIC technology
De-embedding and calibration
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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Passive components in MMIC technology
De-embedding and calibration
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 Sparameters:
 ADUT
C
 DUT
B DUT   A1
=
D DUT  C1
−1
B1   Atotal
.
D1  C total
B total   A2
.
D total  C 2
B2 
D 2 
Substrate
DUT
[A1B1C1D1]
−1
[ADUT BDUT
CDUT DDUT]
[A2B2C2D2]
[AtotalBtoitalCtotalDtotal]
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Passive components in MMIC technology
De-embedding and calibration
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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Passive components in MMIC technology
De-embedding and calibration
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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Passive components in MMIC technology
De-embedding and calibration
On-wafer de-embedding:
Short-open de-embedding
From the measurement of the short-circuit, the open circuit, and the twoport device, it is possible to extract the intrinsic characteristics of the
DUT:
(
−1
YDUT = Ytotal
− Z short
)
−1
(
−1
− Yopen
− Z short
)
−1
Zshort
Zshort
DUT
Yopen
Yopen
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Passive components in MMIC technology
De-embedding and calibration
On-wafer de-embedding:
Short-open de-embedding
Example of a coplanar transmission line:
De-embedding reference planes
Open circuit
Short circuit
84
Passive components in MMIC technology
De-embedding and calibration
On-wafer de-embedding:
Short-open de-embedding
Example of a planar spiral inductor:
85
Passive components
in MMIC technology
Evangéline BENEVENT
Università Mediterranea di Reggio Calabria
DIMET
Thank you for your attention!
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