Examensarbete
LITH-ITN-ED-EX--06/007--SE
Design of a balanced X-band
low-noise amplifier using a
GMIC process
Rikard Eliasson
LITH-ITN-ED-EX--06/007--SE
Design of a balanced X-band
low-noise amplifier using a
GMIC process
Examensarbete utfört i Elektronikdesign
vid Linköpings Tekniska Högskola, Campus
Norrköping
Rikard Eliasson
Handledare Anders Wall
Handledare Anders Sundberg
Examinator Shaofang Gong
Norrköping 2006-02-24
Rapporttyp Report category Examensarbete B-uppsats C-uppsats D-uppsats _ ________________ Språk Language Svenska/Swedish Engelska/English _ ________________ Titel Title Författare Author Sammanfattning Abstract ISBN _____________________________________________________ ISRN _________________________________________________________________ Serietitel och serienummer ISSN
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URL för elektronisk version
Avdelning, Institution
Division, Department
Institutionen för teknik och naturvetenskap Department of Science and Technology
2006-02-24
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LITH-ITN-ED-EX--06/007--SE
Design of a balanced X-band low-noise amplifier using a GMIC process
Rikard Eliasson
This report is the result of a master thesis work done at SAAB Bofors Dynamics AB between September 2005 and January 2006. The purpose of the work was to design a balanced low-noise amplifier covering the X-band (8 12 GHz) using the GMIC (Glass Microwave Integrated Circuit) process provided by M/A-COM, Tyco Electronics UK Limited.
This thesis work has resulted in an approved and functional balanced low-noise amplifier design. The manufacturer, M/A-COM, reviewed the design for manufacturability only and takes no responsibility for the electrical performance. The amplifier has been designed to have a flat frequency response and low reflections on the input and output. Of course, the noise performance has also been taken into
consideration during the design process. This thesis report covers the whole design flow in a chronological order.
The layout work and most of the simulations were accomplished by using the design tool Microwave Office from Applied Wave Research. For complex structures such as Lange couplers and spiral inductors, more accurate simulation models were obtained by using HFSS (High Frequency Structure Simulator) from Ansoft.
Glass Microwave Integrated Circuit, X-band, Low-noise amplifier, RF, Microwave Office, HFSS, 3dB hybrid, Balanced amplifier, Lange coupler, SAAB Bofors Dynamics
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Abstract
This report is the result of a master thesis work done at SAAB Bofors Dynamics AB between September 2005 and January 2006. The purpose of the work was to design a balanced low-noise amplifier covering the X-band (8 – 12 GHz) using the GMIC (Glass Microwave Integrated Circuit) process provided by M/A-COM, Tyco Electronics UK Limited.
This thesis work has resulted in an approved and functional balanced low-noise amplifier design. The manufacturer, M/A-COM, reviewed the design for manufacturability only and takes no responsibility for the electrical performance. The amplifier has been designed to have a flat frequency response and low reflections on the input and output. Of course, the noise performance has also been taken into consideration during the design process. This thesis report covers the whole design flow in a chronological order.
The layout work and most of the simulations were accomplished by using the design tool Microwave Office from Applied Wave Research. For complex structures such as Lange couplers and spiral inductors, more accurate simulation models were obtained by using HFSS (High Frequency Structure Simulator) from Ansoft.
Sammanfattning
Den här rapporten är resultatet utav ett examensarbete genomfört på SAAB Bofors Dynamics AB mellan september 2005 och januari 2006. Det övergripande syftet med examensarbetet har varit att konstruera en balanserad lågbrusförstärkare på X-bandet (8 – 12 GHz) med GMIC-processen som tillhandahålls av M/A-COM, Tyco Electronics UK Limited.
Det här examensarbetet har resulterat i en godkänd och fungerande balanserad lågbrusförstärkarkonstruktion. Tillverkaren, M/A-COM, har enbart granskat att konstruktionen går att tillverka och avsäger sig allt ansvar för elektrisk prestanda. Förstärkaren har konstruerats för att ha ett platt frekvenssvar samt låga reflektioner på in- och utgången. Brusegenskaperna har givetvis beaktats under hela konstruktionsprocessen. Den här rapporten följer hela konstruktionsprocessen i en kronologisk ordning.
All skapad layout och större delen utav simuleringarna har genomförts i konstruktionsverktyget Microwave Office, som tillhandahålls av Applied Wave Research. Komplexa strukturer, såsom Langekopplare och spiralinduktanser, har simulerats i HFSS från Ansoft för att erhålla mer exakta simuleringsmodeller.
Acknowledgements
This thesis work has been carried out at SAAB Bofors Dynamics AB in Linköping as a part of a Master of Science degree in Electronics Design Engineering at Linköping University. I would like to thank all persons who have helped and encouraged me during the work. Especially, I would like to thank following persons:
• My supervisors Anders Wall and Anders Sundberg at SAAB Bofors Dynamics
AB, for all support and assistance during the thesis work.
• Mats Eriksson at MTT AB, for providing the Microwave Office license.
• Robert Smith at M/A-COM Ltd, for validating the manufacturability of the
created amplifier layout.
• The staff at Excelics Semiconductors Inc., for contributing the s-parameter files. • Björn Peterson at SAAB Bofors Dynamics AB, for all help with the simulation
software HFSS.
• My examiner Shaofang Gong at the Department of Science and Technology,
Linköping University, for valuable comments on the report.
• My opponent Anna-Maria Lann for her valuable comments and feedback on my
thesis report.
Rikard Eliasson February 2006
Contents
Terminology IX 1 Introduction 1 1.1 Background ... 1 1.2 Task... 1 1.3 Purpose... 2 1.4 Method ... 2 1.5 Delimitations... 2 1.6 Outline... 2 2 Design specification 5 3 Theory 7 3.1 General microwave theory... 73.1.1 Transmission-line concept ... 7
3.1.2 Terminated lossless transmission line... 10
3.1.3 Microstrip transmission line ... 12
3.2 Scattering parameters... 14
3.3 Microwave transistor amplifiers ... 15
3.3.1 DC bias... 15
3.3.2 Stability... 17
3.3.3 Gain... 18
3.3.4 Noise ... 20
3.3.5 1-dB compression point ... 20
3.3.6 Third-order intercept point... 21
3.4 Broadband amplifiers... 22
3.4.1 Frequency compensated networks ... 23
3.4.2 Balanced amplifiers ... 24
4 The GMIC process 27 4.1 The GMIC substrate... 27
4.1.1 Conductor traces ... 27 4.1.2 Airbridge interconnections... 28 4.1.3 Pedestals... 28 4.2 Passive elements ... 29 4.2.1 MIM Capacitor... 29 4.2.2 Thin-film resistor ... 31 4.2.3 Spiral inductor... 33 4.3 Lange coupler... 36 5 Design process 39 5.1 The transistor ... 39
5.1.1 Small-signal model ... 39 5.1.2 Large-signal model ... 40 5.1.3 Footprint... 40 5.2 DC bias... 41 5.3 Stability... 49 5.4 Impedance matching ... 53
5.4.1 Input matching network ... 53
5.4.2 Output matching network ... 55
5.5 The balanced amplifier ... 59
6 Results 63 6.1 Simulations ... 63
6.1.1 Gain... 63
6.1.2 Noise ... 64
6.1.3 Stability... 64
6.1.4 Reflections and reverse transmission... 65
6.1.5 1-dB compression point ... 66
6.1.6 Third-order output intercept point ... 67
6.2 Temperature behavior ... 67 6.3 Yield analysis... 68 6.3.1 Table ... 68 6.3.2 Graphs ... 70 7 Discussions 75 8 Conclusions 77 9 Further work 79 References 81
A Microwave Office schematics 83
B Stress sheets 87
List of figures
Figure 3.1: Lumped element model of a transmission line... 8
Figure 3.2: Terminated transmission line ... 10
Figure 3.3: Microstrip line ... 12
Figure 3.4: Incident and reflected waves in a two-port network ... 14
Figure 3.5: Operating points ... 16
Figure 3.6: Unipolar biasing network for FET ... 17
Figure 3.7: Transistor with input and output matching networks... 18
Figure 3.8: Definition of the 1-dB compression point... 21
Figure 3.9: Definition of the third-order intercept point... 22
Figure 3.10: Frequency behavior of |S21|, |S12| and |S12S21|... 23
Figure 3.11: Increase and decrease of the transducer gain ... 24
Figure 3.12: Balanced amplifier using 3-dB 90˚ hybrids ... 25
Figure 3.13: Lange coupler with port 4 terminated to 50 ... 26
Figure 4.1: Cross-sectional view of an airbridge ... 28
Figure 4.2: MWO layout of an Airbridge ... 28
Figure 4.3: MWO layout of a pedestal... 29
Figure 4.4: MWO layout of a MIM capacitor... 30
Figure 4.5: 3-D HFSS model of a MIM capacitor... 31
Figure 4.6: Comparison between capacitor models... 31
Figure 4.7: MWO layout of a thin-film resistor... 32
Figure 4.8: 3-D HFSS model of a thin-film resistor ... 32
Figure 4.9: Comparison between resistor models... 33
Figure 4.10: MWO layout of a spiral inductor ... 34
Figure 4.11: 3-D HFSS model of a spiral inductor... 34
Figure 4.12: Comparison between inductor models ... 35
Figure 4.13: Input impedance of the spiral inductor... 35
Figure 4.14: MWO layout of a Lange coupler... 36
Figure 4.15: S21 and S31 for the Lange coupler ... 36
Figure 4.16: Phase difference between ports 2 and 3 ... 37
Figure 5.1: Transistor footprint... 41
Figure 5.2: Transistor footprint with bond wires, capacitors and bond pads... 41
Figure 5.3: Biasing network... 43
Figure 5.4: IV-curve... 43
Figure 5.5: Resistor network... 44
Figure 5.6: DC supply network... 45
Figure 5.7: Layout of DC supply network ... 46
Figure 5.8: Isolation ... 47
Figure 5.9: Complete biasing network... 48
Figure 5.10: Currents and voltages through the transistors, A: upper and B: lower... 48
Figure 5.11: Stability factors of the unstable amplifier ... 49
Figure 5.12: Noise figure of the unstable amplifier... 50
Figure 5.14: Stability factors of the stable amplifier ... 51
Figure 5.15: Noise figure of the stable amplifier... 51
Figure 5.16: Stabilized amplifier branches ... 52
Figure 5.17: S21 of unmatched amplifier branch... 53
Figure 5.18: Input matching network... 54
Figure 5.19: Field radiation, A: un-mitered, B: optimal mitered... 54
Figure 5.20: Comparison between HFSS and MWO models... 55
Figure 5.21: Output matching network... 56
Figure 5.22: Comparison between HFSS and MWO models... 56
Figure 5.23: Matched amplifier branches ... 57
Figure 5.24: S21 of matched amplifier branch... 58
Figure 5.25: Noise figure of matched amplifier branch... 58
Figure 5.26: S11 and S22 of matched amplifier branch ... 59
Figure 5.27: Circuit schematic of the balanced amplifier... 59
Figure 5.28: The balanced amplifier... 61
Figure 6.1: Gain ... 63
Figure 6.2: Noise figure ... 64
Figure 6.3: Stability factors... 65
Figure 6.4: S11, S12 and S22... 65
Figure 6.5: S11 and S22 represented in Smith chart... 66
Figure 6.6: 1-dB compression point and power gain at f = 12 GHz ... 66
Figure 6.7: Third-order output intercept point at f = 12 GHz ... 67
Figure 6.8: S21, five linear models, 100 yield runs... 70
Figure 6.9: Stability factors, five linear models, 100 yield runs... 71
Figure 6.10: Stability factors, one nonlinear model, 100 yield runs... 71
Figure 6.11: S12, Reverse isolation, five linear models, 100 yield runs... 72
Figure 6.12: S11, five linear models, 100 yield runs... 72
Figure 6.13: S22, five linear models, 100 yield runs... 73
Figure 7.1: Input impedance of spiral inductors ... 76
Figure 9.1: Further work ... 79
Figure A.1: Resistor network... 83
Figure A.2: DC supply... 84
Figure A.3: Grounded tune stub... 85
Figure A.4: Matched amplifier branch... 85
List of tables
Table 2.1: Design specification... 5
Table 4.1: Current ratings for conductors ... 27
Table 5.1: Maximum ratings... 39
Table 5.2: Resistance values ... 44
Table 5.3: Stabilization resistors... 52
Table 6.1: 1-dB compression points ... 67
Table 6.2: Third-order output intercept points... 67
Table 6.3: Gain variations with respect to the temperature ... 68
Table 6.4: Yield analysis... 68
Table B.1: Active component stress sheet ... 87
Table B.2: Capacitor stress sheet ... 87
Table B.3: Resistor stress sheet ... 88
Terminology
Abbreviation Explanation
3-D Three Dimensional ABRIDGE Airbridge
dBm Power level in decibel (dB) relative to 1 mW DC Direct Current
CAD Computer-Aided Design FEM Finite Element Method FET Field Effect Transistor GaAs Gallium Arsenide
GMIC Glass Microwave Integrated Circuit HEMT High Electron Mobility Transistor HFSS High Frequency Structure Simulator Ids Drain current
Idss Saturated drain current
IMN Input Matching Network LNA Low-Noise Amplifier MIM Metal-Insulator-Metal
MMIC Monolithic Microwave Integrated Circuit
MRINDSBR Rectangular Microstrip Inductor with Strip Bridge MWO Microwave Office
NF Noise Figure
OIP3 Third-order Output Intercept Point
OMN Output Matching Network
Pout, 1 dB 1-dB compression point
RF Radio Frequency
RFC Radio-Frequency Choke SWR Standing Wave Ratio
TFCM Thin-Film Capacitor for MMIC TFR Thin-Film Resistor
Vds Drain-source Voltage
1 Introduction
This chapter serves as an introduction to this master thesis work. It starts with describing the background to why this project was initiated and is followed by the task, purpose, method, delimitations and report outline.
1.1 Background
A balanced low-noise amplifier that covers the entire X-band (8 – 12 GHz) is a strategically important microwave component in a future project at SAAB Bofors Dynamics AB. The wanted balanced low-noise amplifier is needed in an X-band radar application. X-band radar systems are of great interest at SAAB Bofors Dynamics AB, since the short wavelengths make possible high-resolution radars for target identification and target detection.
Before the summer 2005, all GMIC design work at SAAB Bofors Dynamics was accomplished by manually implemented layouts. An adaptation of the GMIC process provided by M/A-COM, Tyco Electronics UK Limited to the design tool Microwave Office was needed. The author of this thesis report adapted parts of the GMIC process to Microwave Office during the summer 2005. Dynamic layouts of GMIC elements were written in the programming language C++ and linked together with suitable simulation models in Microwave Office. To validate the adapted GMIC process to Microwave Office by designing the wanted balanced low-noise amplifier, this thesis work was initiated.
1.2 Task
The task of this master degree project was to design a balanced low-noise amplifier covering the frequency range 8 – 12 GHz using the GMIC process provided by M/A-COM, Tyco Electronics UK Limited. The thesis work involved component selection and layout work. It was also required that the design should be optimized with respect to temperature and parameter variations, i.e., a yield analysis was performed. The thesis work was finished by submitting the amplifier layout to the manufacturer. The manufacturer M/A-COM reviewed the layout for manufacturability only and takes no responsibility for the electrical performance.
Section 1.3 Purpose Chapter 1 Introduction
1.3 Purpose
The main objective for the thesis work was to accomplish an approved balanced low-noise amplifier layout and thus strengthen SAAB Bofors Dynamics AB’s design experience and expand the existing component library. Another important objective was to validate the adapted GMIC process to Microwave Office by submitting the amplifier layout to the manufacturer, which is equipped with a design rule violation checker.
1.4 Method
The theoretical ground of the required knowledge was obtained by reading selected chapters in books and by useful discussions with the supervisors at SAAB Bofors Dynamics AB.
The performed simulations were accomplished with the design tools Microwave Office from Applied Wave Research and HFSS (High Frequency Structure Simulator) from Ansoft. HFSS was used to obtain accurate simulation models for complex structures such as Lange couplers and spiral inductors. All layout work has been done by the adapted GMIC process to Microwave Office.
The final balanced amplifier layout was submitted to M/A-COM and will be realized as hardware in a future project at SAAB Bofors Dynamics AB.
1.5 Delimitations
Since the s-parameters for the selected transistor were measured on an Al2O3 carrier, the
behavior may vary when a glass substrate is used. This effect has not been covered in this thesis work.
1.6 Outline
The report is organized in the following chapters:
• Chapter 2 contains the design specification. All specified parameter values are
given in this chapter.
• Chapter 3 covers most of the theory used in this thesis work. It also contains an
introduction to general RF and microwave theory.
• Chapter 4 describes the GMIC process. Passive elements, such as MIM
capacitors, spiral inductors and thin-film resistors, are described in this chapter.
• Chapter 5 covers the entire design process from component selection to the final
Section 1.6 Outline Chapter 1 Introduction
• Chapter 6 contains the simulated results for the balanced amplifier. It also
contains temperature behavior and yield analysis.
• Chapter 7 contains the discussions regarding the results obtained by this project. • Chapter 8 contains the conclusions drawn by this master thesis work.
2 Design specification
All specified requirements of the balanced low-noise amplifier are given in Table 2.1.
Table 2.1: Design specification
Parameter Desired value Comments
Process technology GMIC M/A-COM
Supply voltage +4 V Unipolar supply voltage Current consumption < 50 mA
Frequency range 8 – 12 GHz The X-band Gain variation within frequency range ±1 dB
S11 < -15 dB Input reflection
S21 > 8 dB Forward transmission
S12 < -20 dB Reverse transmission
S22 < -15 dB Output reflection
NF < 3 dB Noise figure
Pout, 1 dB > 5 dBm 1-dB compression point
OIP3 > 13 dBm Third-order output
intercept point Temperature range -55 – 95 ˚C
Gain variation within temperature range < 2 dB
Chapter 2 Design specification
K
B1 > 1 > 0 Requirement for unconditional stability Other requirements:
• The design should be able to handle a 20-dBm signal applied on the input within
the frequency range 7 -13 GHz.
• The amplifier should be optimized with respect to temperature and parameter
variations.
3 Theory
This chapter covers most of the theory used in this thesis report. It is assumed that the reader has a basic knowledge in electrical engineering. For further knowledge, see the books listed in references.
3.1 General microwave theory
In conventional low-frequency electronics, voltage and current follows Kirchhoff’s equations and are spatially uniform in a conductor. At higher frequencies, Kirchhoff’s voltage and current laws do not longer apply. When the wavelength of the signal becomes small, current and voltage will propagate as electromagnetic waves in the conductor. [ 1], [ 2]
3.1.1 Transmission-line concept
In RF and microwave engineering, the three most commonly used transmission lines are two-wire transmission line, coaxial transmission line and microstrip transmission line. This section focuses mainly on the microstrip transmission line, even though most of the presented equations are valid for all kinds of transmission lines. [ 2]
Since magnitude and phase vary along the transmission line, Kirchhoff’s laws cannot be applied as an analytical method on a macroscopic level. This problem can be circumvented if the length of the transmission line is divided into infinitesimally small segments, which follow Kirchhoff’s laws on a microscopic level. The segments are still large enough to contain characteristics such as loss, as well as inductive and capacitive effects. [ 1], [ 2]
Section 3.1 General microwave theory Chapter 3 Theory
Figure 3.1: Lumped element model of a transmission line
An electrical model for a transmission line is shown in Figure 3.1 [ 1]. The length of the transmission line is divided into many identical segments with length z. Each segment is modeled by a resistance R per unit length (R in /m), an inductance L per unit length (L in H/m), a capacitance C per unit length (C in F/m), and a conductance G per unit length (G in S/m). Applying Kirchhoff’s voltage and current laws to the model in Figure 3.1 gives:
( ) (
z t v z z t)
R zi( )
z t L z i( )
zt t v ∂ ∂ ∆ + ∆ = ∆ + − , , , , ( 3.1)( ) (
z t i z z t)
G zv(
z z t)
C z v(
z t z t)
i ∂ ∆ + ∂ ∆ + ∆ + ∆ = ∆ + − , , , , ( 3.2)Dividing by z, the following equations are obtained:
(
) ( )
( )
( )
t t z i L t z Ri z t z v t z z v ∂ ∂ − − = ∆ − ∆ + , , , , ( 3.3)(
) ( )
(
)
(
)
t t z z v C t z z Gv z t z i t z z i ∂ ∆ + ∂ − ∆ + − = ∆ − ∆ + , , , , ( 3.4)Taking the limits as ∆z→0results in:
( )
( )
( )
t t z i L t z Ri z t z v ∂ ∂ − − = ∂ ∂ , , , ( 3.5)( )
( )
( )
t t z v C t z Gv z t z i ∂ ∂ − − = ∂ ∂ , , , ( 3.6) [ 1], [ 2]Section 3.1 General microwave theory Chapter 3 Theory
The partial differential equations (3.5) and (3.6) describe the voltages and currents along the transmission lines. With sinusoidal steady-state condition only propagation in z-direction can be observed, the equations can therefore be simplified to:
( ) (
R j L) ( )
I z dz z dV =− + ω ( 3.7)( ) (
G j C) ( )
V z dz z dI =− + ω ( 3.8) Solving equations (3.7) and (3.8), gives the standard second-order differential equation:( )
2( )
0 2 2 = − V z dz z V dγ
( 3.9)where the complex propagation constant is given by:
(
R j L)(
G j C)
j
β
ω
ω
α
γ
= + = + + ( 3.10)The attenuation constant is given in nepers per meter and the propagation constant in radians per meter.
The general solution of equation (3.9) is:
( )
z V e z V e zV = + −γ + − +γ ( 3.11)
From equation (3.7) it follows that the current can be expressed in the form:
z z z z e I e I Z e V Z e V z I = + −γ − − +γ = + −γ + − γ 0 0 ) ( ( 3.12)
where the complex characteristic impedance Z0 of the transmission line is given by:
C j G L j R Z ωω + + = 0 ( 3.13) [ 1], [ 2]
Equations (3.11) and (3.12) represent the voltage and current along the transmission line as a pair of waves traveling in opposite directions, with phase velocity vp = / and
Section 3.1 General microwave theory Chapter 3 Theory
decreasing in amplitude according to e- z or e z. The wave e- z = e- ze-j z is called the incident wave and the wave ez = e zej z is called the reflected wave. [ 1], [ 2]
3.1.2 Terminated lossless transmission line
At high frequencies, the conductive and resistive terms in (3.13) become insignificant compared to the frequency dependent inductive and capacitive terms and can therefore be neglected. The equation for the characteristic impedance when R = G = 0 (a lossless transmission line) is:
C L
Z0 = ( 3.14)
When the transmission line is lossless, the propagation constant is purely complex and can be related to the wavelength as:
λπ
ω β
γ = j = j LC = j2 ( 3.15)
[ 1], [ 2]
Figure 3.2: Terminated transmission line
A finite lossless transmission line of length l connected to a load impedance of ZL is
shown in Figure 3.2 [ 2]. If an incident wave of the form V+e- z is generated at z = -l, the wave will propagate in the positive z-direction. When the incident wave hits the load impedance ZL Z0 located at z = 0, some part of the wave will reflects back in the
negative z-direction. The reflected wave has the form V-ez and the ratio between incident wave and reflected wave at z = 0 is known as the reflection coefficient given by:
+ − = Γ V V 0 ( 3.16) [ 1], [ 2]
Section 3.1 General microwave theory Chapter 3 Theory
Equations (3.11) and (3.12) for the voltage and the current in the transmission line can be re-expressed in terms of the reflection coefficient as:
(
e z e z)
V z V ( ) = + −γ + Γ0 γ ( 3.17)(
e z ez) (
I e z ez)
Z V z I γ 0 γ γ 0 γ 0 ) ( = + − −Γ = + − −Γ ( 3.18)If (3.17) is divided by (3.18), an impedance function of space is given as:
( )
( )
( )
z z z z e e e e Z z I z V z Z γ γ γ γ 0 0 0 −Γ Γ + = = −− ( 3.19)At location z = 0, the exponential terms in (3.19) cancels and the impedance becomes the load impedance. The impedance function of space at z = 0 becomes:
( )
0 0 01 1 0 Γ − Γ + = =Z Z Z L ( 3.20)Solving (3.20) for the reflection coefficient 0 gives:
0 0 0 Z Z Z Z L L + − = Γ ( 3.21) [ 1], [ 2]
An infinite load impedance, i.e., an open line, results in 0 = 1. It means that the reflected
voltage wave returns with the same polarity as the incident voltage wave. For a short circuit (ZL = 0) the reflection coefficient becomes 0 = -1 and the reflected voltage wave
returns with opposite polarity as the incident voltage wave. A load impedance equal to the characteristic impedance results in 0 = 0. When this occurs, the impedances are
matched and the entire incident voltage wave is absorbed by the load and there is no reflected voltage wave. To quantify the degree of mismatch, the standing wave ratio is given as: 0 0 1 1 Γ − Γ + = SWR ( 3.22) [ 1], [ 2]
Section 3.1 General microwave theory Chapter 3 Theory
In microwave and RF applications, it is important to know how a load impedance is transformed along a transmission line. The input impedance at a distance d of a lossless transmission line terminated to ZL is given by the equation:
( )
( )
( )
d jZ Z d jZ Z Z d Z L o L inβ
β
tan tan 0 0 + + = ( 3.23) [ 1], [ 2]Using equation (3.23) it is obvious to see that a transmission line with the length of a quarter wavelength ( /4) terminated to a load represented by a short circuit results in an infinite input impedance, hencetan
( )
β
d →∞ifβ
d →π
2. With equation (3.23) it is possible to design impedances by using transmission lines. Impedances designed with transmission lines are known as distributed components.[ 1], [ 2]3.1.3 Microstrip transmission line
A microstrip transmission line is a conductor of thickness t and width w at a distance h from a ground plane. The distance between the conductor and the ground plane is defined by a substrate height h with the dielectric constant r. Figure 3.3 shows a cross-sectional
view of a microstrip line. [ 2]
Figure 3.3: Microstrip line
The ground plane below the conductor helps prevent excessive field leakage and thus reduces radiation loss. On one hand, the field leakage and cross coupling between adjacent conductor traces depends on the dielectric constant of the substrate. It is therefore good to use a substrate with as high dielectric constant as possible. On the other hand, substrates with a low dielectric constant offer a broad range of characteristic impedances when thin substrates are used. To avoid cross coupling, there is a rule of thumb saying that the spacing between adjacent microstrip lines should be twice the substrate thickness. [ 2]
If the conductor thickness is negligible compared to the substrate height, the characteristic impedance of a microstrip line is only dependent of the conductor width,
Section 3.1 General microwave theory Chapter 3 Theory
the substrate height and the dielectric constant. For narrow lines, w/h<1, the characteristic impedance is given by:
+ = h w w h Z Z eff f 4 8 ln 2 0
ε
π
( 3.24)where Zf =
µ
0ε
0 =376.8Ω is the wave impedance in free space, and eff is theeffective dielectric constant given by:
− + + − + + = 2 1 04 . 0 12 1 1 2 1 2 1 h w w h r r eff
ε
ε
ε
( 3.25)For wide lines, w/h>1, the line impedance is given by:
+ + + = 444 . 1 ln 3 2 393 . 1 0 h w h w Z Z eff f
ε
( 3.26) with w h r r eff 12 1 1 2 1 2 1 + ⋅ − + + =ε
ε
ε
( 3.27)With knowledge of the effective dielectric constant it is possible to calculate the wavelength of the strip line by the expression:
eff p f c f v
ε
λ
= = ( 3.28)Section 3.2 Scattering parameters Chapter 3 Theory
3.2 Scattering parameters
Scattering parameters, or s-parameters, are normalized power wave descriptors that define input-output relations of a network in terms of incident and reflected power waves. Figure 3.4 [ 2] shows a two-port network with normalized incident and reflected power waves defined as follows:
(
n n)
n V Z I Z a 0 0 2 1 + = ( 3.29)(
n n)
n V Z I Z b 0 0 2 1 − = ( 3.30) [ 1], [ 2]where the index n refers either to port 1 or port 2. The incident power wave at port n is given by (3.29) and the reflected power wave at port n is given by (3.30). Vn and In are the
voltage and current at port n and Z0 is the characteristic impedance of the two-port
network. [ 1], [ 2]
Figure 3.4: Incident and reflected waves in a two-port network
Based on the directional convention shown in Figure 3.4, the s-parameters are defined as the matrix: = 2 1 22 21 12 11 2 1 a a S S S S b b ( 3.31) where the terms are:
0 1 1 11 2= = a a b S (Input reflection) ( 3.32)
Section 3.2 Scattering parameters Chapter 3 Theory 0 1 2 21 2= = a a b S (Forward transmission) ( 3.33) 0 2 2 22 1= = a a b S (Output reflection) ( 3.34) 0 2 1 12 1= = a a b S (Reverse transmission) ( 3.35) [ 1], [ 2]
The term S11 represents the input reflection coefficient and is measured as the ratio
between b1 and a1 when a2 = 0. The incident power wave on port 2 is equal to zero if the
output port is properly terminated to an impedance equal to the characteristic impedance of the two-port network. This means that a traveling incident wave on the load will be totally absorbed and no energy will be returned to the output port. The term S21 represents
the transmission from port 1 to port 2, S12 the transmission from port 2 to port 1 and S22
represents the output reflection coefficient of the network [ 1], [ 2]
The advantage of measuring the ratio between normalized power waves instead of the total voltage or current is obvious. At high frequencies, accurate system characterizations can no longer be accomplished by measuring the total voltage or current through a two-port network. S-parameters are measured using matched terminations, i.e., no undesired reflections occur at the ports. The s-parameters for transistors are measured under specific bias conditions at small-signal levels. [ 1], [ 2]
3.3 Microwave transistor amplifiers
RF and microwave amplifier design differ quite much from traditional low-frequency design. The most important design considerations in high-frequency amplifier design are stability, power gain, bandwidth, noise and DC requirements. The first step in a design is usually to obtain a model of a transistor. A non-linear, large-signal model is needed for the DC settings and the output-power characteristics. For parameters such as gain, noise and stability, a signal model of the transistor is required for the analysis. The small-signal model is usually represented as a set of s-parameters measured at a specific bias point. [ 1], [ 2], [ 3]
This section focuses only on GaAs hetero junction field effect transistors (FETs) because of its outstanding frequency response and noise performance at frequencies above 4 GHz. [ 1], [ 2]
3.3.1 DC bias
Biasing provides an appropriate operating point for the transistor under specified conditions. The choice of operating point depends upon the desired application. Different choices of operating points are shown in Figure 3.5 [ 1], [ 3]
Section 3.3 Microwave transistor amplifiers Chapter 3 Theory
Figure 3.5: Operating points
The lowest noise figure is obtained when the current through the transistor is small; approximately 10 % of the saturated drain current IDSS. A low noise amplifier is
commonly designed for low power gain and the operating point is set to P1 shown in
Figure 3.5. [ 3]
Lower voltage on the gate, VGS, results in higher current, IDS, through the transistor. The
operating point P2 results in a higher gain than the point P1. [ 3]
To get as high output power as possible, an increase of the voltage is required. The operating point P3, shown in the figure, is biased to 50 % of IDSS and is recognized as a
class A power amplifier. A class A amplifier has good linearity and the transistor is in a conducting state the whole signal period. The main disadvantage with a class A stage is its poor DC to RF efficiency, which has a theoretical maximum value of 50 %.[ 3]
If the gate voltage, VGS, is increased to the operating point P4, the transistor has reached a
non-conducting state and thus consumes no energy when no input signal is applied. The behavior of the transistor at this operating point is known as a class B power amplifier, which has similar output power as the class A stage but with lower gain and higher noise figure. [ 3]
A compromise between the class A and class B power amplifiers is the class AB stage with the operating point P5. This type of amplifier is employed when a high-power linear
amplification is required.[ 2], [ 3]
Section 3.3 Microwave transistor amplifiers Chapter 3 Theory
biasing networks for FETs. The only biasing network that satisfies the required power supply is shown in Figure 3.6.
Figure 3.6: Unipolar biasing network for FET
The voltage drop over the resistance Rs limits the current in the transistor and gives the
required bias setting on the gate. A DC blocking capacitance CB is connected in parallel
over the resistance to prevent RF signal going through the resistance. At DC, all blocking capacitors CB represent an open circuit and all RFCs (radio frequency chokes) behave
like short circuits. The voltage drop over Rs is determined with the expression:
s DS s I R
V = ( 3.36)
The disadvantage with a resistance connected to the source of the transistor is a slight increase of the noise figure and poorer efficiency.[ 1], [ 2], [ 3]
3.3.2 Stability
When designing amplifiers, one must ensure that the device is stable, i.e., no oscillations occur at any frequency. The amplifier can start to oscillate if the amplified signal is fed back to the input. If this occurs, the fed back signal may combine with reflections already present on the transistor to produce effective reflection coefficients whose magnitudes exceeds unity. The feedback can occur by the transistor itself and by the biasing network. [ 1], [ 2], [ 3]
An amplifier is unconditionally stable, i.e., stable for all passive termination impedances on the input and output, if the following conditions are satisfied:
1 2 1 21 12 2 2 22 2 11 − + ∆ > − = S S S S K ( 3.37)
Section 3.3 Microwave transistor amplifiers Chapter 3 Theory and 0 1 11 2 22 2 2 1 = + S − S − ∆ > B ( 3.38) where 21 12 22 11S S S S − = ∆ ( 3.39) [ 1], [ 2]
The criterions for unconditional stability should be satisfied for all frequencies, i.e., it also includes frequencies outside the desired bandwidth. At low frequencies, the transistor has high gain and can readily start to oscillate. To ensure unconditional stability, the analysis should be done from DC to frequencies above the specified frequency range. [ 3]
One way to stabilize an unstable transistor is to add resistances in series or in parallel to the input or output. Since a resistance produces thermal noise, it is preferable to put it on the output of the transistor. Placing it before the transistor will result in amplified noise. The series resistances should be as small as possible, since it reduces the gain and increases the noise figure of the amplifier.[ 1], [ 2], [ 3]
3.3.3 Gain
An amplifier can be designed for maximum gain using matching networks on the input and output. The functionality of a matching network is to transform a given impedance to another value and thus reduce undesired reflections on the input and output. Maximum gain is achieved if the input and output ports of the transistor are conjugate matched to the source and load terminations. Figure 3.7 shows a transistor with input and output matching networks. [ 1], [ 2], [ 3]
Section 3.3 Microwave transistor amplifiers Chapter 3 Theory
If the feedback parameter S12 of the transistor is neglected, the transistor is unilateral.
Since there is no interaction between the input and output ports, the reflection coefficients are IN = S11 and OUT = S22. The maximum power flow is obtained when ΓS =S11*
and *
22
S
L =
Γ , where a * indicates the complex conjugate of the parameters. The maximum
unilateral transducer gain, which defines the gain of the amplifier placed between source and load, is given by:
2 22 2 21 2 11 2 22 2 2 21 2 11 2 max , 1 1 1 1 1 1 1 1 S S S S S S G L L s s TU − − = Γ − Γ − Γ − Γ − = ( 3.40) [ 1], [ 2]
In reality, the transistors feedback parameter cannot be neglected. The interaction between the input and output makes the reflection coefficients dependent on each other. The optimal values of the reflection coefficients in the bilateral case (S12 0) are given
by: 1 2 1 2 1 1 2 4 C C B B MS − ± = Γ ( 3.41) 2 2 2 2 2 2 2 4 C C B B ML − ± = Γ ( 3.42) where 2 2 22 2 11 1 =1+ S − S − ∆ B ( 3.43) 2 2 11 2 22 2 =1+ S − S − ∆ B ( 3.44) and * 22 11 1 S S C = −∆ ( 3.45) * 11 22 2 S S C = −∆ ( 3.46) [ 1], [ 2]
Section 3.3 Microwave transistor amplifiers Chapter 3 Theory
The maximum gain is obtained when the matching networks have the reflection coefficients MS and ML. When the reflection coefficients are found, matching networks
can be designed with distributed or lumped components. The maximum transducer gain in the bilateral case is given by:
(
) (
)
(
)(
)
2 12 21 22 11 2 2 21 2 max , 1 1 1 1 MS ML ML MS MS ML T S S S S S G Γ Γ − Γ − Γ − Γ − Γ − = ( 3.47) [ 1], [ 2], [ 4]3.3.4 Noise
Noise can be defined as any random interference unrelated to the signal of interest. In many applications it is essential to minimize the generated noise since the signal level at the input may be extremely low. Three main causes of electrical noise in an amplifier are:
• Thermal noise, caused by the thermal agitation of free electrons in conductors. • Shot noise, caused by the random fluctuation of current flow in semiconductors. • Flicker noise, caused by fluctuation in the conductivity of the medium.[ 5]
An amplifier produces noise even if no input signal is applied and the noise performance is determined with the expression:
(
2)
2 2 0 min 1 1 4 opt S opt S n Z R F F Γ + Γ − Γ − Γ + = ( 3.48) [ 1], [ 2], [ 3]The minimum noise figure Fmin, equivalent noise resistance Rn and optimum reflection
coefficient opt are given in the transistor data sheet or measured by the manufacturer. [ 2]
If an amplifier is designed for maximum gain, it might not give the best noise performance. For best noise performance, the input reflection coefficient S is
transformed to opt using a matching network. Matching or mismatching the output does
not have any effect on the signal-to-noise ratio and noise figure. A trade-off between gain, noise and VSWR has to be done when designing amplifiers.[ 1], [ 2], [ 4]
3.3.5 1-dB compression point
When the input power is increased, the gain begins to fall off. The amount of input power that causes the small-signal gain of the amplifier to drop by 1 dB is called the 1-dB compression point. This is an important parameter when characterizing the nonlinear behavior of an amplifier. To obtain the 1-dB compression point, a nonlinear model of the
Section 3.3 Microwave transistor amplifiers Chapter 3 Theory
transistor is needed. The definition of the 1-dB compression point is shown in Figure 3.8 and can be calculated as:
) ( 1 ) ( ) ( ) ( ,1 0 ,1 1 1 , G dB P dBm G dB dB P dBm Pout dB = dB + in dB = − + in dB ( 3.49)
where G1dB is the gain where the small-signal gain G0 has dropped by 1 dB. [ 2], [ 5]
Figure 3.8: Definition of the 1-dB compression point
3.3.6 Third-order intercept point
Since the amplifier begins to work in a nonlinear region when the input power is increased, the small-signal assumption is no longer valid. The input-output relationship of the nonlinear amplifier can be described with the Taylor expansion:
( )
( )
( )
( )
3 ... 3 2 2 1 + + + = xt x t xt t yα
α
α
( 3.50) [ 1], [ 5]A sinusoidal input signal x(t)= A1cos(
ω
1t)+A2cos(ω
2t)applied to (3.50) gives anoutput signal containing frequency components at DC, 1, 2, 2 1, 2 2, 3 1, 3 2, 1± 2, 2 1± 2 and 2 2± 1. The frequencies 1 and 2 are the fundamentals, 2 1, 2 2,
3 1 and 3 2 are the harmonics, 1± 2 are the second-order intermodulation products and
Section 3.3 Microwave transistor amplifiers Chapter 3 Theory
If the frequencies 1 and 2 are close to each other, the third-order intermodulation products at 2 1- 2 and 2 2- 1 might fall within the amplifiers bandwidth and cause
distortion. Figure 3.9 [ 1] shows the output powers of the third-order intermodulation product P2 1- 2 and the fundamental component P 1 versus the input power. If the two
curves are extrapolated in the linear region, the point where they intercept is defined as the third-order intercept point. [ 1], [ 5]
Figure 3.9: Definition of the third-order intercept point
The third-order output intercept point OIP3 is a quantity that characterizes the linearity of
an amplifier. It is therefore good to have as high OIP3 as possible.[ 1], [ 5]
3.4 Broadband amplifiers
An amplifier is considered to be broadband if its bandwidth is greater than 20 % of the center frequency. The transistor s-parameters vary with frequency, as shown in Figure 3.10 [ 1]. Typically, |S21| decreases with frequency at a rate of 6 dB/octave and |S12|
increases with frequency at the same rate. The frequency variation of the product |S12S21|
Section 3.4 Broadband amplifiers Chapter 3 Theory
Figure 3.10: Frequency behavior of |S21|, |S12| and |S12S21|
There are two commonly used methods to compensate the frequency variations of the transistor s-parameters in broadband amplifiers. One is to use frequency compensated matching networks, and the other is to use negative feedback. The technique of negative feedback is not covered in this thesis report since it tends to limit the maximum power gain and increase the noise figure of the amplifier.[ 1], [ 2]
3.4.1 Frequency compensated networks
The frequency variations of |S21| can be compensated by introducing frequency
compensated matching networks. The technique involves mismatching the output and input at low frequencies to compensate for the variations. As shown in Figure 3.11 [ 4], the gain is decreased at low frequencies and increased at high frequencies. Design of frequency compensated matching networks requires a CAD tool since it is almost impossible to obtain the networks in an analytical way. [ 1], [ 2], [ 4]
Section 3.4 Broadband amplifiers Chapter 3 Theory
Figure 3.11: Increase and decrease of the transducer gain
The main disadvantage with this technique is the poor impedance match. Since the gain is decreased at some frequencies, more power is reflected. According to the design specification, the input and output reflections of the amplifier should be less than -15 dB. These requirements are not possible to achieve by only using frequency compensated networks. One practical way to achieve good impedance match is to use a balanced amplifier configuration. [ 1], [ 2], [ 4]
3.4.2 Balanced amplifiers
A good impedance match on the input and output is achieved if two identical amplifier branches are placed between two 3-dB 90˚ hybrids. This thesis report focuses only on the Lange coupler since it is the smallest microstrip realization of a 3-dB 90˚ hybrid and is possible to fabricate with the GMIC process. Signals reflected from the input and output ports of amplifiers A and B in Figure 3.12 are summed together and dissipated in the
terminations on the hybrids. As a result, the balanced amplifier is completely isolated from reflected signals and matched to 50 . Figure 3.12 shows a balanced amplifier configuration using two 3-dB 90˚ hybrids. [ 1], [ 2], [ 4], [ 6]
Section 3.4 Broadband amplifiers Chapter 3 Theory
Figure 3.12: Balanced amplifier using 3-dB 90˚ hybrids
The 3-dB 90˚ hybrid on the input works as a power divider and the one on the output works as a power combiner. The incident power wave on the input in Figure 3.12 is equally divided in magnitude but with a phase shift of 90˚ between the input ports of amplifiers A and B. The output 3-dB 90˚ hybrid combines the output signals from amplifiers A and B by introducing an additional 90˚ phase shift, thus bringing them in phase again. The s-parameters for a balanced amplifier are given by:
B A B A B A B A S S S S S S S S S S S S 22 22 22 12 12 12 21 21 21 11 11 11 2 1 2 1 2 1 2 1 − = + = + = − = ( 3.51) [ 1], [ 2], [ 4], [ 6]
If the two amplifier branches are identical, then S11 = S22 = 0. The forward and reverse
transmissions, S21 and S12,are equal to one branch of the amplifier. The main advantages
with a balanced amplifier are:
1. Good impedance match if the amplifiers in both branches have similar
characteristics.
2. The output power is twice that obtained from a single amplifier.
Section 3.4 Broadband amplifiers Chapter 3 Theory
4. Easy to cascade with other units, since the amplifier is isolated by the 3-dB 90˚
hybrid.
5. One of the two amplifiers continues to operate even if the other one fails.
The drawbacks with a balanced amplifier are that it is larger and contains two amplifiers, thus consumes more DC power. [ 1]
A microstrip realization of a 3-dB 90˚ hybrid is the Lange coupler. When the Lange coupler is used as a 3-dB hybrid, port 4 is terminated to 50 . The Lange coupler has interconnections between the microstrip lines to achieve half of the incident power from port 1 to ports 2 and 3, i.e., transmissions of -3 dB. Design of a Lange coupler involves specification of the length l, conductor width w and spacing d. The length l should be /4 at the center frequency to achieve the phase shift of 90˚ between ports 2 and 3. Figure 3.13 [ 2] shows a Lange coupler with port 4 terminated to 50 . [ 1], [ 2], [ 4], [ 6]
4 The GMIC process
The GMIC (Glass Microwave Integrated Circuit) process is a circuit technology, which has been under development at M/A-COM since 1985. GMIC provides a broad range of hybrid applications as well as efficient integration. GMIC is an extremely reproducible and robust fabrication technology capable of meeting the needs for high performance, complex microwave circuits in space, defense and other high reliability applications. M/A-COM offers different techniques of manufacturing GMIC applications. The amplifier in this thesis report uses the full glass process since it provides the highest performance and highest design flexibility.
Due to the confidentiality of the GMIC process, no comprehensive process overview can be given in this thesis report. This chapter is written under permission from M/A-COM.[ 7], [ 8]
4.1 The GMIC substrate
The GMIC substrate consists of a glass wafer laminated to a silicon wafer. The glass layer serves as the microstrip transmission medium and the silicon layer provides mechanical support and creates an integral carrier. Since glass has poor thermal conductivity, the silicon layer provides good heat transfer through the substrate. Other reasons why silicon is used are that it has thermal expansion match to glass, smooth surface and is cheap to manufacture. The glass and silicon layers have thicknesses of 200 µm and 400 µm respectively. [ 7], [ 8]
The composite microwave structure allows the use of standard silicon chemical processing, photolithographic and thin-film deposition techniques. By this method it is possible to produce two layers of metallization, resistors, capacitors, inductors, conductors, air bridges and plated via holes. [ 7], [ 8]
4.1.1 Conductor traces
Conductor traces are formed by one of the metallization layers on the GMIC substrate. Table 4.1 contains current ratings for different conductor widths. The minimum width of a conductor is limited to 10 µm. [ 7], [ 8]
Table 4.1: Current ratings for conductors Width ( m) Current limit (mA)
25 40
50 75
75 100
A conductor with the width W = 407 µm results in a characteristic impedance of 50 at 10 GHz. The value of the characteristic impedance was calculated with the utility TXLine in
Section 4.1 The GMIC substrate Chapter 4 The GMIC process Microwave Office. Measurements have shown losses to be 0.02 dB/mm at 18 GHz for a 50-
line. [ 7], [ 8]
4.1.2 Airbridge interconnections
Airbridge interconnections are used when conductor cross-unders are needed and when interconnecting elements. An airbridge consists of support pillars at the interface between two metallization layers. Figure 4.1 shows a cross-sectional view of an airbridge. The yellow areas in the figure represent the microstrip metallization layer. [ 7], [ 8]
Figure 4.1: Cross-sectional view of an airbridge
Calculations have showed that a force >100,000 g would be required to lift a typical airbridge due to the low mass and the relatively large area of the support pillars. Figure 4.2 shows the Microwave Office layout of an airbridge. The airbridges are modeled by the ABRIDGE model in Microwave Office. [ 7], [ 8], [ 9]
Figure 4.2: MWO layout of an Airbridge
4.1.3 Pedestals
The silicon wafer in the GMIC substrate is highly doped thus provides good electrical connection between the glass-silicon interface and the ground plane when pedestals are used. Pedestals are via holes that maintain access from the glass layer to the ground plane. Since glass has poor thermal conductivity, active devices is mounted on pedestal to increase the heat transfer from the substrate. Figure 4.3 shows the Microwave Office layout of a pedestal. The pedestals are modeled in Microwave Office by a resistance R = 1x10-4 connected to ground. [ 7], [ 8], [ 9]
Section 4.1 The GMIC substrate Chapter 4 The GMIC process
Figure 4.3: MWO layout of a pedestal
On the top of the pedestal, metal layers are plated up to maintain electrical connection to other elements. Since pedestals are created by the use of hydrofluoric etchant, an under etch is introduced. The gray area surrounding the pedestal in Figure 4.3 represents the under etch. [ 7], [ 8], [ 9]
4.2 Passive elements
The GMIC substrate offers a high level integration of passive elements, such as MIM (Metal-Insulator-Metal) capacitors, thin-film resistors and spiral inductors.
4.2.1 MIM Capacitor
A MIM capacitor consists of two parallel metal plates separated by a dielectric layer. Figure 4.4 shows the Microwave Office layout of a GMIC capacitor with width and length equal to 150 m. The bottom plate of the capacitor consists of a thin metal layer followed by a dielectric layer. The top plate of the capacitor consists of one of the metallization layers. An airbridge is used to interconnect the capacitor top-plate with the adjacent conductor. [ 7], [ 8]
Section 4.2 Passive elements Chapter 4 The GMIC process
Figure 4.4: MWO layout of a MIM capacitor
The capacitance value of a GMIC capacitor is calculated with the expression:
f
p C
C
C= + ( 4.1)
where the principal capacitance Cp is given by:
pF d LW C r p 6 0 ×10 =ε ε ( 4.2)
and the fringing capacitance Cf by:
(
W L)
pFCf =2.4×10−4 2 +2 ( 4.3)
[ 7]
The capacitor width W, length L and dielectric thickness d are in µm. A capacitor with a width W = 150 m, length L = 150 m and the dielectric thickness and relative dielectric constant of the layer in the GMIC process results in a certain capacitance value. If the capacitance value is divided by the capacitor area, a certain sheet capacitance in F/m2 is obtained. This value is required when using the TFCM (thin-film capacitor for MMIC) in Microwave Office. [ 9] To evaluate the Microwave Office model of a thin-film capacitor, the layout has been exported to HFSS (High Frequency Structure Simulator) from Ansoft. The HFSS simulation tool utilizes FEM (Finite Element Method) to solve Maxwell’s equations in the 3-D structure. To avoid boundary effects, de-embedded conductor traces with the length 1000 m have been added to the ports of the capacitor. Figure 4.5 shows the 3-D HFSS model of the MIM capacitor.
Section 4.2 Passive elements Chapter 4 The GMIC process
Figure 4.5: 3-D HFSS model of a MIM capacitor
The results from HFSS have been exported to Microwave Office as a set of s-parameters. Figure 4.6 shows S11 and S21 for the Microwave Office and HFSS models.
0 1. 0 1 . 0 -1 . 0 1 0 . 0 10.0 -1 0. 0 5 . 0 5.0 -5 .0 2 . 0 2.0 -2 .0 3 . 0 3.0 -3 .0 4 . 0 4.0 -4 .0 0 . 2 0. 2 -0.2 0 . 4 0. 4 -0.4 0 . 6 0. 6 -0 .6 0 . 8 0 . 8 -0 .8 C Swp Max 15GHz Swp Min 5GHz S(1,1) C_HFSS_MODEL S(2,1) C_HFSS_MODEL S(1,1) C_MWO_MODEL S(2,1) C_MWO_MODEL
Figure 4.6: Comparison between capacitor models
The simulated results presented in Figure 4.6 show that the accuracy of the Microwave Office model is excellent in the desired frequency range. Since the good accuracy, it was decided to use the Microwave Office model TFCM in this thesis work
4.2.2 Thin-film resistor
Thin-film resistances are implemented on the substrate by a layer with a certain resistivity. Connections to the resistive layer are achieved by the metallization layer used when implementing conductors. The width and length of the thin-film resistor correspond to the
Section 4.2 Passive elements Chapter 4 The GMIC process width of the metallization layer and the length of the resistive layer. The resistance value is calculated with the expression:
W L R
R= s⋅ ( 4.4)
[ 7], [ 8]
where L is the length, W is the width and Rs is the sheet resistivity in / . Figure 4.7 shows
the Microwave Office layout of a 50- thin-film resistor with the width W = 407 µm. [ 9]
Figure 4.7: MWO layout of a thin-film resistor
To validate the Microwave Office model of a thin-film resistor, the layout has been exported to HFSS. The model that is used in Microwave Office is the TFR model. Figure 4.8 shows the 3-D HFSS model of the thin-film resistor.
Figure 4.8: 3-D HFSS model of a thin-film resistor
The simulation results from HFSS have been exported to Microwave Office and compared to the TFR model. Figure 4.9 shows the input reflections and the forward transmissions of the two models.
Section 4.2 Passive elements Chapter 4 The GMIC process 0 1. 0 1 . 0 -1 . 0 1 0 . 0 10.0 -1 0. 0 5 . 0 5.0 -5 .0 2 . 0 2.0 -2 .0 3 . 0 3.0 -3 .0 4 . 0 4.0 -4 .0 0 . 2 0. 2 -0.2 0 . 4 0. 4 -0.4 0 . 6 0 . 6 -0 .6 0 . 8 0 . 8 -0 .8 R Swp Max 15GHz Swp Min 5GHz S(1,1) R_MWO_MODEL S(1,1) R_HFSS_MODEL S(2,1) R_HFSS_MODEL S(2,1) R_MWO_MODEL
Figure 4.9: Comparison between resistor models
The simulated results in Figure 4.9 show that the Microwave Office TFR model is valid for the GMIC thin-film resistors. Since the good accuracy between the models, it was decided to use the Microwave Office model TFR in this thesis work.
4.2.3 Spiral inductor
Spiral inductors are implemented on the substrate as loops by one of the metallization layers. The inner turn is brought to the outside by a cross-under. A cross-under is constructed as a thin conductor with a dielectric layer above overlapped by an airbridge. Figure 4.10 shows the Microwave Office layout of a spiral inductor with 13 segments, the dimensions 575 m x 575 m, the conductor width W = 50 m and the conductor spacing S = 25 m. These dimensions resulted in the best performance at 10 GHz. According to the design specification, the current consumption should be less than 50 mA. A conductor with a width of 50 m allows a maximum current of 75 mA, as given in Table 4.1. [ 7], [ 8], [ 9]
Section 4.2 Passive elements Chapter 4 The GMIC process
Figure 4.10: MWO layout of a spiral inductor
To analyze the behavior, the spiral inductor has been exported to HFSS. Figure 4.11 shows the 3-D HFSS model and Figure 4.12 shows the comparison with the Microwave Office model MRINDSBR.
Section 4.2 Passive elements Chapter 4 The GMIC process 0 1. 0 1 . 0 -1 . 0 1 0 . 0 10.0 -1 0. 0 5 . 0 5.0 -5 .0 2 . 0 2.0 -2 .0 3 . 0 3.0 -3 .0 4 . 0 4.0 -4 .0 0 . 2 0. 2 -0.2 0 . 4 0. 4 -0.4 0 . 6 0 . 6 -0 .6 0 . 8 0 . 8 -0 .8 L Swp Max 15GHz Swp Min 5GHz S(2,1) L_HFSS_MODEL S(2,1) L_MWO_MODEL S(1,1) L_MWO_MODEL S(1,1) L_HFSS_MODEL
Figure 4.12: Comparison between inductor models
The simulated results presented in Figure 4.12 show that S11 and S21 differ between the
models. To get as accurate model as possible in the amplifier design, it was decided to use the HFSS model.
The spiral inductors will be used as RF chokes, i.e., to create large impedances at the center frequency. Figure 4.13 shows the input impedance of the spiral inductor modeled by HFSS. It can be seen that the inductor has an impedance peak of 1169 at 10.2 GHz.
5 10 15 Frequency (GHz) Spiral inductor 0 500 1000 1500 Im pe da nc e (O hm ) |ZIN(1)| (Ohm) L_HFSS_MODEL
