Design of Radio Frequency Power Amplifiers for

Design of Radio Frequency Power Amplifiers for
Design of Radio Frequency Power Amplifiers for
Cellular Phones and Base Stations in
Modern Mobile Communication Systems
Von der Fakultät Informatik, Elektrotechnik und Informationstechnik
der Universität Stuttgart
zur Erlangung der Würde eines Doktor-Ingenieurs
(Dr.-Ing.) genehmigte Abhandlung
Vorgelegt von
Lei Wu
aus der Volksrepublik China · Shandong
Hauptberichter: Prof. Dr.-Ing. Manfred Berroth
Mitberichter: Prof. Dr.-Ing. Joachim Burghartz
Tag der mündlichen Prüfung: 29.06.2009
Institut für Elektrische und Optische Nachrichtentechnik
2009
Acknowledgments
Acknowledgements
My foremost appreciation goes to Professor Berroth who has given me the chance to finish
my PhD at the Institute of Electrical and Optical Communications Engineering, University of
Stuttgart. Thanks for his numerous and professional instructions in the last years. I also would
like to thank my colleagues and my students for their great technical and personal help
through the years.
Thanks also go to my parents who have supported me for so long time. They are not with
me in Germany; however, they have given me very strong mental supports for many many
years. I also would like to thank my dear wife who is just alone in China and waiting for me
patiently. Her existence and her love let me always know that I must work hard to win a
wonderful future. Finally, I wish to acknowledge family Mueller for the great private help in
the last ten years.
Contents
Symbols ………………………………………………………………………………………. I
Glossary ……………………………………………………………………………….….... III
Zusammenfassung ...………………………………………………………………………….1
1. Introduction ………………………………………………………………………..….….5
2. Fundamentals to the power amplifier design ....….…………..….……….……….........9
2.1 Current source mode power amplifiers ..….…………………………………………...9
2.1.1 The class A power amplifier ...…………………………………………………11
2.1.2 The class B power amplifier ...…………………………………………………12
2.1.3 The class C power amplifier ...…………………………………………………13
2.1.4 Comparison of the different classes of power amplifiers ………………………14
2.2 Switching mode power amplifiers …………………………………………………...16
2.2.1 The class D power amplifier ……….………………………………………..…16
2.2.2 The class E power amplifier ……………………………………………………18
2.2.3 The class F power amplifier ……………………………………………………20
2.3 Active devices for the power amplifier design …………..…………………………..23
2.3.1 CMOS devices ……………………………………………………………...….23
2.3.2 HiVP configuration …………………………………………………………….26
2.3.3 LDMOS devices ………………………………………………………………..28
2.4 Introduction and analyses of conventional circuit design concepts ……………….....30
2.4.1 Common-source single-ended stage …………………………………………...30
2.4.2 Estimation of the high-frequency bandwidth …………………………………..31
2.4.3 High frequency response and Miller effect …………………………………….32
2.4.4 Cascode circuits ………………………………………………………………..33
2.4.5 Differential amplifier …………………………………………………………..35
2.5 Impedance matching ……………………...………………………………………….37
2.5.1 Discrete matching networks ……………………………………………………37
2.5.2 Impedance transforming property of a transmission line ………………………39
2.5.3 Microstrip geometry and characteristic parameters ……………………………40
2.5.4 Single-stub tuning ……………...………………………………………………42
2.5.5 Quarter-wave and multi-section matching networks ……………..……………42
2.6 Biasing network ……………………………………………………………………...45
2.7 Design parameters of the power amplifier …………………………………………...47
2.7.1 Power gain ….……………………………………………………….………….47
2.7.2 Stability ………………………………………………………………………...47
2.7.3 Gain compression and 1-dB compression point ……………………………….49
2.7.4 Intermodulation distortion ……………………………………………………...50
2.7.5 Intercept point ………………………………………………………………….52
2.7.6 ACPR …………………………………………………………………………..52
2.7.7 Power added efficiency ………………………………………………………...53
3. Design of the CMOS driver and power amplifiers …………………….……………..55
3.1 A logarithmic programmable-gain amplifier ………………………………….……..55
3.1.1 Introduction of the PGA and VGA ……...……………………………………..56
3.1.2 Design concept of the radio frequency PGA …………………………..……….60
Contents
3.1.3 Simulation and measurement results …………………………………………...62
3.1.4 Conclusion ……………………………………………………………………..67
3.2 A High Voltage/High Power class A power amplifier ……………..………………..68
3.2.1 Design and simulation of a CMOS HiVP power amplifier ………………...….68
3.2.2 Measurement results …….……….…………………………………………….75
3.2.3 HiVP design concept with adjustable DC power consumption …….…...……..79
3.2.4 Conclusion ……………………………………………………………………..81
4. Design of broadband LDMOS power amplifiers ……...............…………………...…83
4.1 Design of a broadband LDMOS single-ended class AB power amplifier …………...83
4.1.1 Selection of the simulation model for LDMOS transistors …….........……..…..83
4.1.2 DC simulation and selection of operating points …………………………...….84
4.1.3 Advanced stability improvement ………………………………………………85
4.1.4 Design of the matching networks and the S-parameter simulation …………….88
4.1.5 Simulation for large signal response of the broadband power amplifier ………91
4.1.6 Experiments and measurement results …………………………………………93
4.2 Design of a broadband LDMOS balanced class AB power amplifier ……...………..98
4.2.1 Balanced structure ………………………………..…………………………….98
4.2.2 Simulation of the LDMOS balanced power amplifier ……………………..…..99
4.2.3 Experiments and measurement results ……………………………………..…102
5. Summary ……………………………………………………………………………….107
Appendix …………………………………………………………………...………………111
A1. Logic of the 5-to-18 demultiplexer ……………..……………………………….....111
A2. Schematic of the 5-to-18 demultiplexer ……………………………………………112
Reference …………………………………………………………………………………...113
Symbols
Symbols
Symbol
Description
a0, a1…an
C
Cb
Cc
Cs
Cds
Cgd
Cgs
Csb
Cp
Csh
Cox
Cth
Ci
Co
c
D
Dds
Ec
EC
EV
EF
f
fres
f0
∆f
G
GT
GP
GA
gm
gmb
gm,d
gds
h
Iq
Idc
In
I1
Id
ID
Imax
IR
IS
K
L
Ls
Taylor coefficients
capacitance
bypass capacitor
coupling capacitors
series capacitor
drain-source-capacitance
gate-drain capacitance
gate-source capacitance
source-bulk capacitance
parallel capacitance
shunt capacitance
gate oxide capacitance per unit area
thermal capacitance
center of the input stability circle
center of the output stability circle
speed of light
distance of the metal traces
drain-source diode
energy loss per cycle
conduction band
valence band
fermi-level
operating frequency
resonant frequency
center frequency
band width
gain
transducer power gain
operating power gain
available power gain
transconductance
transconductance caused by bulk potential
the transconductance of the differential pair
drain-source admittance of the transistor
substrate thickness
quiescent current
DC component of the current
nth harmonic of the current
fundamental component of the current
drain current
current distribution
the maximum value of the current
current on the shunt resistor
current source
parameter of the Rollet’s condition
inductance
series inductor
Unit
,
F
F
F
F
F
F
F
F
F
F
F/m2
F
m/s
m
J
eV
eV
eV
Hz
Hz
Hz
Hz
dB
dB
dB
dB
S
S
S
S
m
A
A
A
A
A
mA/µm2
A
A
A
H
H
I
Symbols
Lw
Ln
l
N
PL
P1dB
PAVS
PIN
Pin
Pout
Q
Rds
RCgd 1
wiring-inductor
channel length of the n-channel transistor
length of the microstrip line
number of sections of quarter-wave transmission lines
power delivered to the load
1 dB compression point
power available from the source
power input to the network
RF input power; RF drive power
RF output power
quality factor
drain-source resistance
series resistance facing Cgd1
Ropt
Rth
Rg
RL
Rl
Rload.opt
Ri
Ro
Rp
rds-p
Tn
t
tox
Udd
Uds
Ud6
Ui
Uo
Ugg
Ugs
Uds-ON
UK
Umax
Uth
UB
Ubr
vp
vi
vo
W
Wn
WD,cell
WS,cell
XL, XC
Z0
ZL
Zopt
Zin_opt
optimum load
thermal resistance
source resistance
load resistance to be matched
load resistance
optimum load in the class E amplifier
radius of the input stability circle
radius of the output stability circle
shunt resistance
drain-source resistance of PMOS transistors
Chebyshev polynomials
conductor thickness
oxide thickness
supply voltage
drain-source voltage
drain voltage of the top device
input voltage
output voltage
biasing voltage
gate-source voltage
“on” drain-source voltage
knee voltage
maximum voltage
threshold voltage
bulk voltage
breakdown voltage
phase velocity
input voltage
output voltage
conductor width
channel width of the n-channel transistor
width of the metal lines connected at the drain
width of the metal lines connected at the source
reactance of the reactive elements
characteristic impedance
load impedance to be matched
optimum impedance
input optimum impedance
H
m
m
W
dBm
W
W
dBm
dBm
Ω
Ω
Ω
K/W
Ω
Ω
Ω
Ω
Ω
Ω
m
m
V
V
V
V
V
V
V
V
V
V
V
V
V
m/s
V
V
m
m
m
m
Ω
Ω
Ω
Ω
Ω
II
Glossary
Zout_opt
Z1…Zn
α
β
∆
∆G
ε0
εeff
η
Γ
Γin
Γout
ΓS
ΓL
Γm
Γn
λ
µ
µn
ω
ω0
π-θm
τ
τi
θ
θm
output optimum impedance
characteristic impedance of transmission lines
conduction angle
imaginary part of the propagation constant
auxiliary parameter of the Rollet’s condition
gain offset
vacuum dielectric constant
effective relative dielectric constant
output efficiency
voltage reflection coefficient
input reflection coefficient
output reflection coefficient
source reflection coefficient
load reflection coefficient
maximum voltage reflection coefficient
partial reflection coefficients
channel-length modulation coefficient
unconditional stability factor
mobility of the electrons
angular frequency
center frequency
upper edges of the passband
period of the sinusoidal signal
time constants
an arbitrary angle between –α/2 and α/2
lower edges of the passband
Ω
Ω
degree
1/m
dB
F/m
%
1/V
m2/V·s
Hz
Hz
s
Glossary
2DEG
3GPP
π/4-DQPSK
ACLR
ACPR
AGC
AlGaAs
CDMA
CM
CMOS
CS
DC
DCW
ETSI
FET
FDD
FDMA
GaAs
GMSK
GPRS
GSM
two-dimensional electron gas
3rd generation partnership project
π/4 differential quadrature phase shift keying
adjacent channel leakage ratio
adjacent channel power ratio
automatic gain control
aluminium-gallium-arsenide
code division multiple access
common-mode
complementary metal-oxide-semiconductor
common-source
directional current
digital control words
european telecommunications standardisation institute
field-effect transistor
frequency division duplex
frequency division multiple access
gallium-arsenide
Gaussian minimum shift keying
general packet radio service
global system for mobile communication
III
Glossary
HBT
HEMT
HiVP
IF
IMD
IMD3
IMD5
InP
IP3
IIP3
LDMOS
MIM
MI
MO
MODEM
MOS
MOSFET
M1; M2
NADC
NMOS
OCTC
OIP3
PA
PAE
PAR
PCB
PCS
PGA
PMOS
RF
SCTC
SiGe
SMA
SMD
T
TEM
TD-CDMA
TDMA
UMTS
VGA
VSWR
WCDMA
ZCS
ZVS
heterojunction bipolar transistor
high electron mobility transistor
high voltage/high power
intermediate frequency
intermodulation distortion
third order intermodulation distortion
fifth order intermodulation distortion
indium phosphide
third order intercept point
input IP3
lateral double diffused metal-oxide-semiconductor
metal-insulator-metal
input matching network
output matching network
modulator/demodulator
metal-oxide-semiconductor
metal-oxide-semiconductor field-effect transistor
metal traces
north American digital cellular
n-type metal-oxide-semiconductor
open-circuit time constants
output third order intercept point
power amplifier
power added efficiency
peak to average ratio
printed circuit board
personal communication system
programmable gain amplifier
p-type metal-oxide-semiconductor
radio frequency
short-circuit time constants
silicon germanium
straight medium adaptors
surface mount devices
transistor
transverse electromagnetic mode
time division code division multiple access
time division multiple access
universal mobile telecommunication system
variable gain amplifier
voltage standing wave radio
wideband code division multiple access
zero current switching
zero voltage switching
IV
Zusammenfassung
Zusammenfassung
Die Bereitstellung von Informationen und Dienstleistungen zu jeder Zeit an jedem Ort wird
durch eine rasante Weiterentwicklung der Mobilkommunikation unterstützt. Wo immer
drahtlose Kommunikation existiert, gibt es Funksender und viele Funksender benötigen
Leistungsverstärker. Deshalb wurden Hochfrequenz (HF)-Leistungsverstärker in den letzten
Jahren weltweit intensiv untersucht. In dieser Arbeit werden Leistungsverstärker and ihre
Vorverstärker nicht nur für die Basisstationen, sondern auch für die Mobiltelefone entworfen
und gemessen, die in den Mobilkommunikationssystemen verwendet werden. Sowohl die
hybriden als auch die integrierten Verstärker werden mit MOS-Transistoren entworfen, da sie
wegen billiger Materialien und relativ einfacher Herstellungsprozesse als kostengünstigste
Technologie angesehen werden. Dank der Entwicklung der modernen Halbleitertechnologie
sind die MOS-Transistoren nun genügend schnell, um in HF-Schaltungen eingesetzt zu
werden, die bei einigen Gigahertz arbeiten. Aber die MOS-Transistoren zeigen auch Nachteile
bei manchen HF-Schaltungen. Zum Beispiel ist es schwierig, ein logarithmisches Verhalten in
einer CMOS-Technologie zu realisieren. Außerdem nimmt die Durchbruchspannung der
CMOS-Transistoren mit der verkleinerten Dimension stark ab. Die Fähigkeit, bei hohen
Spannungen betrieben zu werden, sinkt und die Schwierigkeit, einen Leistungsverstärker in
der CMOS Technologie zu entwerfen, steigt. Um die Durchbruchspannung der MOS
Transistoren zu erhören, wird ein zusätzliches niedrigdotiertes n-Diffusionsgebiet bei dem
Drainanschluss in einem LDMOS-Transistor verwendet. Die Durchbruchspannung dieser
Transistoren wird sogar bis auf 70 V erhöht, so dass die Leistungsverstärker, die in den
Basisstationen verwendet werden, auch in einer MOS-Technologie realisiert werden können.
Aber auf der anderen Seite ist die optimale Ausgangsimpedanz von den LDMOS-Transistoren
meistens sehr niedrig. Sie sind deshalb nicht geeignet für breitbandige Leistungsverstärker.
Um die oben genannten Probleme zu lösen, werden einige neu entwickelte
Schaltungskonzepte in dieser Arbeit präsentiert. Deren Funktionsprinzipien werden bei den
Schaltungsentwürfen ausführlich diskutiert. Die Simulationsergebnisse und die
Messergebnisse der entworfenen Schaltungen werden verglichen.
Heute wird die komplementäre MOS-Technologie (CMOS) weitgehend für integrierte
Schaltungen verwendet. Sie ist bereits, bedingt durch extrem hohe Integrationsdichte und die
Möglichkeit einer kostengünstigen Fertigung, in digitalen Schaltungen dominant. In dieser
Arbeit wird nun versucht, die in den Mobiltelefonen verwendete Leistungsverstärker und ihre
Vorverstärker auch in den Standard-CMOS-Technologien zu entwerfen.
Die Verstärkungsvariation ist eine unverzichtbare Funktion für viele Kommunikationssysteme.
Diese Funktion kann durch einen einstellbareren Verstärker (PGA) realisiert werden. Es gibt
in der Praxis PGAs, die entweder bei einer Zwischenfrequenz (üblicherweise bei 70 MHz)
oder direkt bei der Operationsfrequenz des Systems funktionieren. Man nennt sie IF-PGA
bzw. RF-PGA. Der Letztere kann auch als Vorverstärker des Leistungsverstärkers verwendet
werden, wenn er genügend hohe Ausgangsleistung liefert. In dieser Arbeit wird ein
logarithmischer CMOS-RF-PGA präsentiert. Ein MOS-Transistor hat eine exponentielle
Funktion nur in dem Bereich der schwachen Inversion. Da der Strom in diesem Bereich
jedoch sehr klein ist, ist es schwierig, einen logarithmischen PGA mit hoher Ausgangsleistung
und großem Variationsbereich der Verstärkung in einer CMOS-Technologie zu realisieren. In
dieser Arbeit wird ein neues Schaltungskonzept entworfen, bei welchem mehrere
Verstärkerzellen parallel verschaltet sind. Der Schaltplan ist in Abb. 3.8 dargestellt. Die
parallelen Verstärkerzellen werden durch einen Demultiplexer kontrolliert. Es wird jeweils
nur eine Zelle eingeschaltet. Die unterschiedliche Verstärkung und der adaptive
Leistungsverbrauch werden erzeugt, indem die Verstärkerzellen verschiedene
1
Zusammenfassung
Transistorgrößen besitzen. Um eine hohe Immunität gegen das Rauschen von der Umgebung
zu erlangen, wird die differentielle Operation in den Verstärkerzellen eingesetzt. Die
Kaskode-Konfiguration wird auch in der Schaltung verwendet, um den Miller-Effekt zu
unterdrücken. Statt der aktiven Last wird ein LC-Schwingkreis als die gemeinsame Last für
alle Verstärkerzellen eingesetzt. Die Simulation zeigt, dass der LC-Schwingkreis einen viel
kleineren Spannungsabfall als die aktive Last benötigt, so dass eine höhere Ausgangsleistung
erzielt wird. Der Testchip wurde mit einer 0,12-µm CMOS-Technologie hergestellt. Die
Messergebnisse zeigen, dass die Verstärkung des PGAs zwischen - 43 dB und 8 dB mit
Kontrollschritten von 3 dB geändert werden kann. Es wird somit ein Variationsbereich von 51
dB erreicht. Das ist der größte HF-logarithmische Variationsbereich für die Verstärkung, von
dem bisher berichtet wird. Außerdem wird auch ein adaptiver Leistungsverbrauch erhalten.
Die maximale Ausgangsleistung erreicht 9 dBm, während der 1-dB Kompressionspunkt bei 8
dBm liegt. Der oIP3 Punkt liegt bei 22 dBm.
Des Weiteren wird in dieser Arbeit ein HF-CMOS-Klasse-A-Leistungsverstärker demonstriert.
Die größte Schwierigkeit beim Entwurf eines Leistungsverstärkers in einer modernern
CMOS-Technologie ist, dass die Durchbruchspannung ständig mit der verkleinerten
Transistordimension sinkt, aber auf der anderen Seite die Ausgangsspannung genügend groß
bleiben muss. Deshalb gibt es bisher weltweit ganz wenige Versuche, Leistungsverstärker in
einer Technologie moderner als 0,18-µm CMOS zu realisieren. Um dieses Problem zu lösen,
wird die High Voltage/High Power (HiVP) Technik (s. Abb. 2.19) in dieser Arbeit eingesetzt,
wo mehrere identische Transistoren DC und HF übereinander verbunden sind. Der größte
Vorteil der HiVP Struktur ist, dass eine hohe Ausgangsspannung auf mehrere Transistoren
verteilt werden kann, damit die Spannung zwischen zwei beliebigen Anschlüssen jedes
Transistors nicht höher als die Durchbruchspannung wird. Jedoch auch die Beschränkungen
der HiVP Struktur werden in dieser Arbeit ausführlich diskutiert. Erstens kann die Anzahl der
Transistoren, die in der HiVP Struktur verwendet werden, nicht unbegrenzt erhöht werden.
Die DC-Simulation zeigt, dass die HiVP Struktur ein ähnliches Verhalten wie ein einzelner
Transistor hat. Aber der maximale Schwingungsbereich für die HF-Spannung wird verkleinert,
wenn die Anzahl der Transistoren sich erhöht (s. Abb. 3.21). Ferner erhöht sich die
Schwierigkeit mit der ansteigenden Transistoranzahl, die Versorgungsspannung gleichmäßig
auf alle Transistoren zu verteilen. Zweitens wird die HF-Eigenschaft des Leistungsverstärkers
dramatisch verschlechtert, wenn ein Serienwiderstand zum Source-Anschluss der HiVP
Struktur vorkommt. Da der Strom, der durch die Transistoren fließt, sehr groß ist (mehr als
1 A), kann ein kleiner Serienwiderstand einen starken Abfall der Gate-Source-Spannung aller
Transistoren verursachen. Die Transistoren arbeiten dann im Abschnürbereich. Die
Ausgangsleistung wird dementsprechend stark reduziert. Schließlich wird eine weitere
0,13-µm CMOS-Technologie für den geplanten Leistungsverstärker ausgewählt, bei welcher
drei Wannen verfügbar sind. Die NMOS-Transistoren können durch P-Wanne von dem
Substrat isoliert werden und deshalb wird der Leistungsverlust durch das Substrat verkleinert.
Außerdem kann der Bulk-Anschluss eines Transistors mit dem Source verbunden werden, so
dass die Bulk-Spannung mit der Source-Spannung schwingen kann. Ein anderes wichtiges
Thema in dieser Arbeit ist, ein kompaktes Layout für die großen Transistoren zu zeichnen.
Gleichzeitig muss der große Strom, der durch die HiVP Struktur fließt, berücksichtigt werden.
Alle sechs Metallschichten, die in der CMOS-Technologie zur Verfügung stehen, werden
deshalb in dem Layout verwendet. In Abbildung 3.24 wird ein neues gestaffeltes
Transistorlayout vorgestellt, das die gesamte Chipfläche effektiv verkleinert. Dieses neue
Layoutkonzept hat noch weitere Vorteile, wie z.B. keinerlei Überlappung zwischen dem
Drainanschluss und dem Sourceanschluss, gleichmäßige Verteilung des aktiven Bereichs, etc.
Eine so genannte H-Struktur wird in diesem Layout für die Gateleitungen eingesetzt. Der
Phasenunterschied zwischen den Eingängen der Transistorzellen wird dadurch minimiert. Bei
2
Zusammenfassung
dem erstellten Testchip wird eine maximale Ausgangsleistung von 29,5 dBm (0,9 W) bei
einer Frequenz von 900 MHz gemessen, während die Klein-Signal-Verstärkung ca. 11 dB
beträgt. Die maximale Effizienz erreicht 34,5 %. Ferner wird in dieser Arbeit die Methode
vorgestellt, mit der die Effizienz des Leistungsverstärkers bei niedrigen Leistungen erhöht
wird. Ein Transistor mit großer Gateweite kann in mehrere Zweige aufgeteilt werden (s. Abb.
3.37). Jeder Zweig kann auf digitale Weise ein- oder ausgeschaltet werden. Im Fall, dass die
Ausgangsleistung klein ist, werden die meisten Zweige deaktiviert. Der gesamte DC-Strom
des Verstärkers wird verkleinert und die Effizienz wird dann erhöht.
In dieser Arbeit werden Leistungsverstärker auch für die Basisstationen in den
Mobilkommunikationssystemen entworfen. Heute werden die LDMOS-Transistoren
weitgehend in den Basisstationen verwendet wegen der niedrigen Kosten und der besserer
Linerarität verglichen mit den anderen konkurrierenden Technologien. Der LDMOSTransistor MRF21030SR3 wird in dieser Arbeit genutzt. Die geplanten Leistungsverstärker
sollen breitbandig sein, damit sie sowohl im UMTS-System als auch im GSM1800-System in
Europa eingesetzt werden können.
Zuerst wird ein einphasiger Klasse-AB-Leistungsverstärker entworfen. Die Stabilität der
Schaltung gehört zu den wichtigsten Themen beim Entwurf eines breitbandigen
Leistungsverstärkers, da die meisten Transistoren in einem großen Frequenzband potentiell
instabil sind. In dieser Arbeit wird eine neue Methode für die Stabilitätsverbesserung
vorgestellt, bei der ein serieller Kondensator mit einem parallelen Widerstand direkt am Drain
des LDMOS-Transistors verwendet wird (s. Abb. 4.5). Dieser Kondensator schützt den
Widerstand gegen einen großen DC-Strom, damit wird die Stabilitätsverbesserung
gewährleistet, die durch den parallelen Widerstand erzielt wird. Außerdem wird der gesamte
Leistungsverbrauch der Verstärkerschaltung durch den Kondensator verringert. Die
Leistungseffizienz wird erhöht. Die Durchbruchspannung eines LDMOS-Transistors wird
wegen des zusätzlichen nieder-dotierten Bereiches beim Drainanschluss dramatisch erhöht.
Aber auf der anderen Seite wird eine große Ausgangskapazität durch diesen Dotierungsbereich erzeugt. Die optimale Ausgangsimpedanz des Transistors wird durch diese
Ausgangskapazität auf einen sehr niedrigen Wert transformiert. Eine breitbandige Anpassung
ist aus diesem Grund für einen LDMOS-Transistor schwer zu erreichen. Um dieses Problem
zu beheben, werden verschiedene Anpassungsnetzwerke in dieser Arbeit entworfen und
jeweils in die Verstärkerschaltung eingesetzt. Anhand der S-Parameter-Simulation wird
schließlich festgelegt, dass nur die Ein- und Ausgangsanpassungsnetzwerke, die aus MultiSektions-Übertragungsleitungen bestehen, eine genügende Bandbreite bieten können. Die
Struktur und die Entwurfsparameter der optimalen Ein- und Ausgangsanpassungsnetzwerken
werden in Abb. 4.7 und in der Tabelle 4.2 präsentiert. Eine λ/4-Übertragungsleitung wird in
dem Versorgungsnetzwerk verwendet. Die Länge der Leitung wird bei einer Frequenz von
2 GHz festgelegt. Die zweite Harmonische des Ausgangssignals, die die größte Signalverzerrung verursacht, wird durch diese λ/4-Leitung effektiv unterdrückt. Der entworfene
Leistungsverstärker wird auf dem Substrat RO4003 aufgebaut und gemessen. Mit einer
Versorgungsspannung von 26 V und einer Gate-Source-Spannung von 3,8 V wird eine 3-dB
Bandbreite von etwa 1 GHz bei der Messung erzielt. Die Mittenfrequenz liegt bei etwa 2,1
GHz. Das ist die größte Bandbreite, die bisher von einem LDMOS-Leistungsverstärker
berichtet wird. Die Breitbandigkeit wird auch bei der Großsignal-Messung nachgewiesen.
Eine maximale Ausgangsleistung von 43,5 dBm wird sowohl in dem UMTS-Band als auch in
dem GSM1800-Band erzielt. Eine Leistungseffizienz höher als 30 % bzw. 37 % wird bei 1,85
GHz und bei 2,14 GHz erzielt. Hohe Linearität, die mit einem NachbarkanalLeistungsverhältnis (ACPR) niedriger als - 40 dB gekennzeichnet ist, wird in den gesamten
Leistungsebenen erreicht.
3
Zusammenfassung
Ein wesentlicher Nachteil von einem einphasigen Leistungsverstärker ist, dass die
Reflektionskoeffizienten sowohl am Eingang als auch am Ausgang schlecht sind. Grund dafür
ist, dass die Ein- und Ausgangsanpassungsnetzwerke für die Leistungsanpassung und nicht
für die konjugiert komplexe Anpassung entworfen werden. Um bessere Reflektionskoeffizienten zu erreichen und deshalb eine hohe Kaskade-Fähigkeit von der Schaltung zu
gewinnen, wird ein balancierter Leistungsverstärker in dieser Arbeit entwickelt. Die maximal
erreichbare Ausgangsleistung soll weiterhin erhöht werden. Zwei identische Transistoren sind
mit zwei hybriden Kopplern parallel verbunden (s. Abb. 4.20). Die zwei von den beiden
einzelnen Transistoren reflektierten Signale haben am Eingang des gesamten Leistungsverstärkers die gleiche Amplitude und 180° Phasenunterschied. Sie kompensieren sich
gegeneinander, deshalb soll das gesamte reflektierte Signal am Eingang des balancierten
Leistungsverstärkers einen Betrag von null haben. Genau das Gleiche gilt auch für die
reflektierten Signale am Ausgang. Die gleichen Transistoren, die gleichen Arbeitspunkte und
die gleichen Anpassungsnetzwerke, die beim Design des einphasigen Leistungsverstärkers
benutzt wurden, werden auch hier in den beiden individuellen Leistungsverstärken verwendet.
Der balancierte Leistungsverstärker wird auch auf RO4003 aufgebaut. Bei der Messung wird
eine Bandbreite von etwa 830 MHz mit der Mittenfrequenz von 2 GHz erzielt. Die maximale
Ausgangsleistung erreicht 50 W (47 dBm) sowohl im UMTS-Band als auch in dem
GSM1800-Band. Eine Leistungseffizienz höher als 35 % bzw. 42 % wird jeweils bei 1,85
GHz und bei 2,14 GHz erreicht. Hohe Linearität, die mit einem NachbarkanalLeistungsverhältnis (ACPR) niedriger als - 40 dB gekennzeichnet ist, wird in den gesamten
Leistungsebenen erzielt. Der in dieser Arbeit erreichte balancierter Leistungsverstärker ist ein
aussichtsreicher Kandidat für Multistandard-Multiband-Mobilkommunikationssysteme.
4
Introduction
1. Introduction
The mobile radio communication has begun with Guglielmo Marconi’s and Alexander
Popov’s experiments with ship-to-shore communication in the 1890’s. Land mobile radio
telephone systems have been used since the Detroit City Police Department installed the first
wireless communication system in 1921 [1]. Since that time, radio systems have become more
and more important for both voice and data communication.
The modern mobile communication systems are mainly designed in high frequency ranges
due to the larger available bandwidth at these frequencies. Today, the mostly used mobile
communication systems in the United States are cellular telephone systems operating at 800 –
900 MHz and personal communication systems (PCS) at 1800 – 2000 MHz. In Europe, these
include the Global System for Mobile Communication (GSM) and Universal Mobile
Telecommunications System (UMTS). China now has GSM/GPRS and Code Division
Multiple Access (CDMA) networks. For the third generation services, China has been
planning a 3G standard called Time Division Synchronous CDMA (TD-SCDMA) since 1999,
which is planned to operate at 2010 MHz - 2025 MHz.
In this work, attentions are paid on the uplink and downlink applications in the GSM and
the UMTS systems adopted in Europe. The frequency bands of these mobile communication
systems are depicted in Fig. 1.1 and listed in Table 1.1.
Uplink
Downlink
800
900
1000
Uplink
Uplink
Downlink
1700
GSM
1800
GSM1800
Downlink
1900
2000
2100
2200 [MHz]
UMTS
Fig. 1.1. Frequency bands of the mobile communication systems in Europe.
Table 1.1
Frequency bands of the mobile communication systems in Europe
GSM
Uplink [MHz]
Downlink [MHz]
890 - 915
935 - 960
GSM1800
UMTS
1710 - 1785 1920 - 1980
1805 - 1880 2110 - 2170
The GSM system is commonly referred to as the second generation mobile phone standard.
In the GSM system, time division multiple access (TDMA) is applied. It allows several users
to share the same frequency by dividing it into different time slots. The synchronisation of the
mobile phones is achieved by sending timing offset commands from the base station which
instructs the mobile phones to transmit earlier or later. In radio systems, TDMA is almost
always used alongside frequency division multiple access (FDMA) and frequency division
duplex (FDD); the combination is referred to as FDMA/TDMA/FDD. FDMA is used in radio
systems to share the radio spectrum. This means that users are allocated with different carrier
frequencies of the radio spectrum.
Using the code division multiple access (CDMA) modulation process, the UMTS system is
aimed as the third generation of mobile communication system, whose standards have first
been developed by European Telecommunications Standardisation Institute (ETSI). CDMA is
5
Introduction
a form of multiplexing and a method of multiple accesses that does not divide up the channel
by time, or frequency, but by encoding the data with a special code associated with each
channel and uses the constructive interference properties of the special codes to perform the
multiplexing. It usually also refers to digital cellular telephony systems. Compared to the
GSM system, the UMTS system has more advantages like longer talk time due to lower
power consumption, better quality, larger capacity and cheaper equipment etc. Therefore, the
UMTS system is capable of offering new and much more services including multimedia and
the access to internet.
No matter which system is discussed, a wireless communication link usually includes a
transmitter, a receiver, and a channel as shown in Fig. 1.2 [2]. The functions of the
quantization, of the coding and of the decoding are only performed in digital systems. Most
links are fully duplex and include a transmitter and a receiver or a transceiver at each end of
the link. Obviously, to send or receive large enough signals, power amplifiers and their
driving amplifiers are necessary on both sides of the link.
Fig. 1.2. The block diagram of a wireless communication link.
A radio frequency (RF) power amplifier (PA) is a circuit for converting directional current
(DC) input power into a significant amount of RF output power. One of the principal
differences between a small-signal amplifier design and a power amplifier design is that the
main purpose of the latter is the maximum output power, not the maximum gain. However, a
power amplifier cannot simply be regarded as a small-signal amplifier driven into the
saturation. There is a great variety of different power amplifiers, while most of them employ
techniques beyond simple linear amplification. In other words, RF power can be generated by
a wide variety of techniques using a wide variety of devices.
In this work, the fundamental theories used for the design of RF power amplifiers are
systematically introduced. Using these theories, power amplifier circuits are designed both for
the base stations and for the cellular phones adopted in the modern mobile communication
systems in Europe. Not only current source mode but also switching mode power amplifiers
are considered and attempted.
The basic techniques for RF power amplification are classes A, B, C, D, E, and F modes. In
sections 2.1 and 2.2, the functional principles of these different power amplifier modes are
first introduced. The most important component of an RF power amplifier circuit is the
transistor used as the power device. Today, LDMOS, GaAs, HBT transistors are widely
6
Introduction
adopted as commercial power devices for the base station applications, which offer an output
power level up to several hundred Watt. In cellular phones, GaAs technology is widely used
due to its low loss substrate and high breakdown voltage. On the other hand, standard digital
technology sees a breakthrough in both performance and size in case that deep-submicron
CMOS devices are used. For certain highly-integrated, low-power, wireless transceivers
operating at several GHz, CMOS is now very attractive. However, the most significant
drawback of the deep-submicron CMOS transistors, namely the low breakdown voltage, is a
limitation for the power amplifier design. To solve this problem, the high voltage/high power
(HiVP) structure is adopted, which can also be regarded as a single active device. The features
of these semiconductor technologies and constructions are introduced in section 2.3. In this
work, MOSFETs are applied for the developments of both the hybrid and the integrated
power amplifier circuits. Several conventional design concepts for MOSFET circuits, for
instance, the common-source stage, the differential amplifier and the cascode stage, are
introduced in section 2.4. In order to obtain the maximum output power, the reference
impedance (usually 50 Ohm) must be transformed to the optimum input and output
impedance of the selected transistor. Matching networks are therefore necessary at the input
and at the output of a power amplifier circuit. The design methods for different matching
concepts, such as discrete matching networks or distributed matching networks are provided
in section 2.5. Another important issue for a power amplifier design is to select the proper
quiescent point and holding the quiescent point constant over variation in transistor
parameters and temperature. This can be realized by selecting a suitable biasing network.
Moreover, the other topics must also be taken into account in the designing of the biasing
network, for example, the output power, amount of distortion, the efficiency, the voltage
headroom, the gain of the stage, the noise of the stage, and the class of operation, etc.
Additionally, a biasing network is also helpful for suppressing the higher harmonics and
controlling the DC power consumption in dependence on the power level. All these
considerations are introduced in section 2.6. Finally, in section 2.7, the design parameters in
terms of developing the microwave power amplifiers are described. They are the power gain,
the stability, the 3-dB bandwidth, the 1-dB compression point, the power added efficiency
(PAE), the intermodulation distortion (IMD) and the adjacent channel power ratio (ACPR).
Today, the design and analysis of integrated RF and microwave circuits is receiving a
considerable interest by the research community due to the continuous growth in the wireless
telecommunication market. In particular, many ongoing efforts are focused on the integration
of RF circuits in standard CMOS technologies. This is necessary in order to allow the
implementation of RF front-ends with digital signal processors and enable low-cost singlechip fully integrated solutions. The evolution of CMOS technologies and the high level of
integration they offer have made the CMOS circuits attractive candidates for RF and
microwave applications.
In section 3.1, the design of an RF CMOS logarithmic programmable gain amplifier (PGA)
is first demonstrated which is realized in the Infineon 0.12-µm CMOS technology. CMOS
devices perform an exponential or logarithmic function only in the subthreshold region. Since
the current in this region is very small, it is generally difficult to realize a logarithmic PGA
with high output power in CMOS technology. This work presents a novel circuit concept
employing parallel amplifier cells. In this manner, the logarithmic gain variation and adaptive
power consumption can easily be obtained. Moreover, a large gain control range of 51 dB,
high output power of 9 dBm as well as high linearity are also achieved at the radio
frequencies.
Section 3.2 presents the design of an RF class A CMOS power amplifier. To overcome the
problem of low breakdown voltage, the HiVP structure is employed, in which several
transistor devices are connected DC and RF in series. Therefore, the large output voltage can
be divided by all the cascaded devices. In this section, the design approaches to obtain an
7
Introduction
equal voltage division and to draw a compact layout for the large transistors used in the HiVP
structure are described in detail; the simulation and experimental results of the proposed
power amplifier are presented. A small signal gain of 11 dB is obtained in the measurement,
whereas the maximum output power reaches 29.5 dBm. The maximal power added efficiency
reaches 34.5 %. They are comparable with the other works reported over the world in recent
years, or even better. On the other hand, the limitation of using the HiVP structure is also
described, while lots of methods to improve the HiVP-performance are provided in this
chapter, not only for the circuit design but also for more adopted transistor layout. Finally, the
design concept for transistors with adjustable gate width is introduced in this work, so that the
power added efficiency of the HiVP power amplifier can significantly be increased in the low
power levels.
In chapter 4, the design of broadband power amplifiers for base station applications is
demonstrated. These amplifiers can simultaneously be used in the GSM1800 and in the
UMTS systems in Europe. Motorola LDMOS transistors are employed for these works.
Section 4.1 presents the design of a single-ended class AB power amplifier. Firstly, a novel
modification for the stability improvement is introduced, with which the conditional stability
of the proposed power amplifier circuit is obtained in the whole frequency band. Simulations
also show that this modification can greatly reduce the total DC power consumption; hence
the power added efficiency is enhanced. Secondly, different impedance matching networks
described in chapter 2 are attempted in order to fulfil the specification of large bandwidth.
The S-parameters of power amplifiers with these different matching networks are simulated.
Comparing the simulation results, the impedance matching networks consisting of multisection transmission lines are determined to be the best candidate to realize a broadband
power amplifier. Finally, the proposed power amplifier circuit is fabricated in the laboratory
and measured. Good agreements between the simulations and the measurements are obtained.
The measurement results show that this power amplifier has a 3-dB bandwidth of 1 GHz at
the center frequency of 2.1 GHz. To the best of the author’s knowledge, this is the largest
bandwidth reported so far at these frequencies in an LDMOS technology. The maximum
output power of this circuit reaches 43.5 dBm. High efficiency and high linearity are also
achieved over large frequency range.
Using the same LDMOS transistors and the same matching networks obtained in the design
of the single-ended one, a broadband LDMOS balanced class AB power amplifier is
presented in section 4.2. Two power devices are connected in parallel, hence an even higher
output power up to 50 W (47 dBm) is achieved. Simultaneously, the balanced structure also
provides perfect voltage standing wave ratio (VSWR) performance. Measurement results
show that S11 and S22 smaller than -10 dB are obtained in large frequency range.
Finally, the most important design processes, technical innovations and simulation as well
as experimental results for developments of RF power amplifiers and their driving stages
obtained in this work are summarized and presented in chapter 5.
8
Fundamentals to the Power Amplifier Design
2. Fundamentals to the Power Amplifier Design
The general design concept of a power amplifier is given in Fig. 2.1. Ordinarily, it consists
of the transistor T, the input and output matching networks MI and MO, the biasing networks
and the alternating current (AC) couplings Cg and Cd. Ui and Uo in Fig. 2.1 indicate the input
and the output voltages, while Udd and Ugg are the supply voltage and the biasing voltage,
respectively.
Fig. 2.1. General design concept of a RF power amplifier.
The main purpose of a power amplifier design is to provide sufficiently high output power,
while another very important aim is to achieve high efficiency. Therefore, there are generally
two types of power amplifiers: the current source mode power amplifiers and the switching
mode power amplifiers. Different kinds of each mode of power amplifiers and their functional
principles are introduced in detail in sections 2.1 and 2.2. The active devices are the basic
components in a power amplifier circuit. Different technologies, e.g. CMOS, LDMOS, etc are
used in practice. They are concisely described in section 2.3. Moreover, the HiVP structure,
which can also be regarded as a single active device is demonstrated here. In this work, MOS
transistors are used as the active devices. Several typical circuit concepts using MOS devices
are introduced in section 2.4. In section 2.5, different matching networks used at the input and
the output of power amplifier circuits are described. For a current source mode power
amplifier, a so-called load-line matching [3] at the output is often used, which is a
compromise to extract the maximum power from the RF transistors and at the same time to
keep the RF voltage swing within the available DC supply. On the other hand, a complex
conjugate matching is usually used at the input. For a switching mode power amplifier, fixed
structures of the output matching network have been developed, in order to obtain determined
waveforms of the output voltage and the output current. Theoretically, there is no overlap
between the output voltage and output current in the time domain, so that a high efficiency of
the power amplifier could be ensured. In Fig. 2.1, the inductors L1 and L2 serve as RF choke
which block the RF signals and simultaneously feed DC power to the device. This is the
simplest configuration of biasing networks. Various structures of biasing networks are
provided in section 2.6, which have different functions, as well as different benefits and
drawbacks. The AC coupling Cg and Cd pass the RF signals and cut off the power supply. In
section 2.7, the most important design parameters for a power amplifier circuit are presented,
which are frequently used to describe the specifications of the power amplifiers.
2.1 Current Source Mode Power Amplifiers
Obviously, in a current source mode power amplifier, the power device is regarded as a
current source, which is controlled by the input signal. The most important current source
9
Fundamentals to the Power Amplifier Design
mode power amplifiers are class A, class B, class AB and class C power amplifiers. They
differ from each other in the operating points. Figure 2.2 illustrates the different classes of
current source mode power amplifiers in the transfer characteristic of a field-effect transistor
(FET) device. The drain current Id exhibits pinch-off, when the channel is completely closed
by the gate-source voltage Ugs and reaches the saturation, in which further increase of gatesource voltage results in no further increase in drain current.
Fig. 2.2. Operating points of the different classes of current mode power amplifiers [3].
The other very important concept to define the different classes of current source mode
power amplifier is the conduction angle α. As illustrated in Fig. 2.3, the conduction angle
depicts the proportion of the RF cycle for which conduction occurs, where ω is the angular
frequency and ωt is the radian. Iq in Fig. 2.3 denotes the quiescent current, while Imax denotes
the maximum value of the current. The conduction angles of different classes are summarized
in Table 2.1.
Fig. 2.3. The conduction angle of the current source mode power amplifiers [3].
Table 2.1
Conduction angle of the different classes of current mode power amplifiers [3]
Class
Conduction angle
A
AB
B
C
2π
π-2π
π
0-π
The general schematic of a current source mode power amplifier is already depicted in Fig.
2.1. Usually, matching networks are used to realise a conjugate complex matching at the input
10
Fundamentals to the Power Amplifier Design
and a load-line matching at the output. The load-line matching at the output takes both the
maximum current Imax that the device can supply and the maximum voltage that the device
can sustain across its terminals into consideration. It has the task of transforming the load
impedance to the optimum output resistance Ropt, which can be calculated using the load-line
method as shown below.
Fig. 2.4 shows the output characteristic of a FET, where Ubr and UK denote the breakdown
voltage and the knee-voltage of the transistor, respectively.
Fig. 2.4. The load-line method.
The optimum output resistance Ropt can be obtained using the following equation.
Ropt =
(U br − U K )
I max
(2.1)
However, the calculated Ropt can normally not directly be used in practice, since it will be
transformed by the output capacitance of the power devices (e.g. the drain-source-capacitance
Cds of a MOS transistor) and the output wiring-inductance Lw to the practical optimum
impedance Zopt, which has unfortunately a much smaller magnitude than Ropt. Zopt for
different frequencies of the commercial power devices are usually provided by the
manufacturers, which are extended to the frequency-dependent optimum input impedance
Zin_opt and optimum output impedance Zout_opt determined through the load-pull measurements
[3]. The load-pull data has been the mainstay of RF and microwave power amplifier design
for many years. It gives the power amplifier designer a simple target area in the Smith chart
on which to base the strategy for suitable matching network design. Usually, output matching
networks are designed as low pass filters; hence the harmonics generated by the
transconductive nonlinearities will be greatly attenuated.
2.1.1 The Class A Power Amplifier
As shown in Fig. 2.2, the operating point of a class A power amplifier is just located at the
midpoint of the region between the cutoff and the saturation. The conduction angle of a class
A power amplifier is 2π. Therefore, the output waveforms of a class A power amplifier using
FET devices can be shown in Fig. 2.5. The drain current having an amplitude of Imax /2
sweeps the entire range from zero to the maximum current Imax. The drain-source voltage can
swing over its maximum range of zero to 2Udd [3], where Udd is the supply voltage of the
11
Fundamentals to the Power Amplifier Design
power amplifier circuit as shown in Fig. 2.1. The drain voltage drops while the drain current
increases, and vice versa.
Fig. 2.5. Waveforms of a class A power amplifier.
Ideally, if a sinusoidal signal is fed at the input, the waveform of the output current remains
also sinusoidal for a limited range and no harmonic occurs. Therefore, a class A power
amplifier is theoretically the most linear power amplifier. However, in practice, the linear
region contains weak nonlinearities. On the other side, it is not negligible that a class A power
amplifier consumes the most DC power resulting in a lower efficiency compared to the other
classes of power amplifiers. The maximum drain efficiency of a class A power amplifier is
theoretically 50 % [3]. The heat dissipation is therefore an essential problem which must be
considered.
2.1.2 The Class B Power Amplifier
As shown in Fig. 2.2, the operating point of a class B power amplifier is just located at the
pinch off point in the transfer characteristic of a FET device. The conduction angle of a class
B power amplifier is π, just half of that of a class A amplifier. The output waveforms of a
class B power amplifier using FET devices are shown in Fig. 2.6. Clearly, the negative part of
its drain current is cut off, while the drain-source voltage can also swing over its maximum
range of zero to 2Udd [3].
Due to the much lower operating point, the DC power consumption of a class B power
amplifier can significantly be reduced. Much higher efficiency can therefore be expected. The
maximum drain efficiency of a class B power amplifier is theoretically 78.5 % [3]. However,
due to the loss of the negative part of its drain current, harmonics of the output current occur,
which should be diminished by suitable output matching network or biasing network as
shown later.
12
Fundamentals to the Power Amplifier Design
Fig. 2.6. Waveforms of a class B power amplifier.
In practice, class AB power amplifier is widely used. It has the operating point between
those of the class A and class B operation modes; therefore, a class AB power amplifier has
moderate waveforms and features. Part of the negative drain current is cut off. The drainsource voltage swings from zero to the voltage level even higher than 2Udd [3], depending on
the resonance circuit used at the output. Theoretically, the linearity of a class AB power
amplifier is worse than that of a class A power amplifier. However, since the section of the
transfer characteristic of the power devices, which locates between the cutoff and the
saturation points, is usually not linear in practice, simulations and also the experiments often
show that the linearity of a class AB power amplifier can even be better than that of a class A
power amplifier. On the other hand, due to the relatively low operating point, class AB power
amplifiers have higher efficiency than class A power amplifiers. The maximum drain
efficiency of a class AB power amplifier can theoretically also reach 78.5 % [3]. Therefore, as
a good compromise of linearity and efficiency, class AB power amplifiers are very popular
and widely adopted in the practical applications.
2.1.3 The Class C Power Amplifier
As shown in Fig. 2.2, the operating point of a class C power amplifier is located between
zero and the pinch-off point in the transfer characteristic of an enhancement FET device. The
conduction angle of a class C power amplifier is between 0 and π. The output waveform of a
class C power amplifier using FET devices is shown in Fig. 2.7. Clearly, the drain-source
voltage can also swing over its maximum range of zero to 2Udd [3]. On the other hand, the
entire negative part and a fraction of the positive part of the drain current are cut off; the
current waveform is reduced to a train of short pulses, which have lower DC component
compared to the other classes of power amplifiers mentioned above, but also a lower
fundamental RF component. Consequently, very high efficiencies can be obtained, but at the
expense of lower RF output power and heavy input drive requirements. The maximum drain
13
Fundamentals to the Power Amplifier Design
efficiency of a class C power amplifier can even reach 100 % [3], if the operating points close
to the zero point are selected.
Fig. 2.7. Waveforms of a class C power amplifier.
One of the major problems with utilizing class C modes in solid state applications is the
large negative swing of the input voltage, which coincides with the output voltage peaks. This
is precisely the worst condition for reverse breakdown in any kind of transistor, and even
small amounts of leakage current flowing at this point of the cycle can degrade the efficiency.
For this reason, class C power amplifiers are not often used in solid state amplification at
higher RF and microwave frequencies.
2.1.4 Comparison of the Different Classes of Power Amplifiers
As mentioned above, different classes of the current source mode power amplifier have
different operating points. Observing Fig. 2.3, it is intuitive that the mean component will
decrease as the conduction angle is reduced. Additionally, harmonics will occur as well.
Using Fourier analysis, the mean current, i.e. the DC component Idc can be given as follows [3]
I dc =
I max 2sin(α / 2) − α ⋅ cos(α / 2)
⋅
.
2π
1 − cos(α / 2)
(2.2)
The nth harmonic In can be described by
In =
1
π
α /2
−
I max
[cos θ − cos(α / 2)] ⋅ cos nθ dθ ,
1 − cos(α / 2)
/2
∫
α
(2.3)
where θ is an arbitrary angle between –α/2 and α/2. The fundamental component I1 is therefore
14
Fundamentals to the Power Amplifier Design
I1 =
I max
α − sin α
⋅
.
2π 1 − cos(α / 2)
(2.4)
The amplitudes of the DC component and of the different harmonics |A| in dependence on
the conduction angle is shown in Fig. 2.8. Obviously, the DC component decreases
monotonically as the conduction angle is reduced. According to equation (2.2), the DC
components Idc of the class A and the class B power amplifiers can be calculated, resulting in
the results of Idc(class A)= Imax/2 and Idc(class B)= Imax/π, respectively. Therefore, it is clear
that the class B power amplifier has the same fundamental component as the class A power
amplifier, while its DC supply power is reduced by a factor of π/2, hence the efficiency
increases from 1/2 in the class A mode to π/4 (about 78.5%) in class B. Compared to the class
A operation, the class AB operation shows benefits of even higher fundamental component
and lower DC power consumption.
As mentioned above, the linearity of the class B operation is degraded, compared to the
class A power amplifier. Note in Fig. 2.8 that throughout the class AB range and up to the
midway class B condition the only significant harmonic, other than the fundamental signal, is
the second harmonic. This however, can be shorted by using suitable low pass or band pass
matching networks at the output of the power amplifier circuit. Therefore, the class AB
operation sometimes could have even better linearity than the class A operation, depending on
the selected operating point and the actual shape of the transfer characteristic.
Fig. 2.8. The Fourier analysis of the DC component and the harmonics.
For conduction angles lower than π, corresponding to class C operation, the DC component
continues to drop, but the fundamental component of the current also starts to drop below the
level of class A and class B operations. However, it can mathematically be proven that the
efficiency of the class C operation continues to increase.
15
Fundamentals to the Power Amplifier Design
2.2 Switching Mode Power Amplifiers
The switching mode power amplifiers are widely used in different frequency ranges and
output power levels beginning from several kilowatts at low frequencies and up to one watt at
microwaves. In these power amplifiers, the transistors operate as an on-to-off switch and the
waveforms of the output current and the output voltage fulfill the condition that they do not
overlap at any given time. Therefore, the power dissipation is minimized and the efficiency is
maximized. Such an operation mode can be realized by an appropriate choice of the values for
the reactive elements in the output load network.
The first possibility of increasing the efficiency of the single-ended power amplifier by
modifying of the output matching circuit was experimentally described by Lohrmann in 1966
[4]. Three years later Artym [5] and Gruzdev [6] provided the theoretical analysis of the
operating conditions of the single-ended switching mode power amplifiers with the
calculation of their circuit parameters. Analysis is carried out for the operation conditions of
switching mode power amplifiers not only with the shunt capacitance but also with the
resonant circuit tuned on the fundamental to provide the sinusoidal signal flowing into the
load. Later, the generalized analysis of the electrical performance and circuit parameters of
the single-ended switching mode power amplifiers with shunt capacitance C and series
inductance L, as well as with a parallel LC circuit was presented by Popov [7] and Kozyrev
[8]. The schematics of them are separately shown in Fig. 2.9 (a) and Fig. 2.9 (b). These two
general design models have been used even up to now.
Fig. 2.9. Switching-mode power amplifiers with
(a) shunt capacitance and series inductance and (b) parallel LC circuit.
The most significant benefit of switching mode power amplifier is the high efficiency of up
to 100 %. But since the transistors are used as switches, the largest disadvantage of a
switching mode power amplifier is the nonlinearity. Therefore the signal spectrum can be
degraded and severe adjacent channel interference will occur.
The typical switching mode power amplifiers are class D and class E power amplifiers. The
class F power amplifiers are often used as the driving stages of the class E power amplifiers.
2.2.1 The Class D Power Amplifier
The original class D power amplifier is the voltage mode class D power amplifier. Using a
MOSFET device, the simplified circuit of this power amplifier and its waveforms of the drain
voltage and the drain current are shown in Fig. 2.10. Two transistors are connected in parallel
and a series filter comprising the inductor L and the capacitor C is employed. This filter is
tuned at the fundamental frequency. The two transistors T1 and T2 are driven 180° out-ofphase. That means, the input connection guarantees that only one transistor is driven on at a
given time, with one transistor handling the positive half-cycles and the other one the negative
half-cycles. It works just like a push-pull class B power amplifier. The difference here is that
16
Fundamentals to the Power Amplifier Design
the transistors are driven hard enough and hence act like switches. The voltage across the
transistors is a square wave and the transistor current becomes a half-wave rectified sine wave.
A Zero-Current-Switching (ZCS) is realized, which means that the drain current is zero, if a
transistor is turned on. Ideally, there is no overlap of the drain voltage and the drain current.
Therefore, the DC power consumption should theoretically be zero.
Fig. 2.10. The voltage mode class D power amplifier and its waveforms.
Unfortunately, a real transistor has always parasitic capacitors, e.g. the drain-source
capacitor in a field-effect transistor. The transistor must be charged or discharged to the
supply voltage Udd or ground through the transistor. That means, the voltage waveform can
not have a perfect square wave shape and some transient current spikes occur when the
transistor turns on. The overlap of voltage and current can not be avoided. The energy loss Ec
per cycle can be calculated with the following equation [9]
1
Ec = Cds ⋅U ds2 −ON ,
2
(2.5)
where Cds is the drain-source capacitance and U ds −ON is the drain-source voltage when the
transistor is turned on. This energy loss on the output capacitance is independent on the
channel resistance of the transistor and becomes the dominant loss mechanism at high
frequencies.
To overcome the problem of energy loss, a new design concept of class D power amplifier,
namely current-mode class D power amplifier is given, which is shown in Fig. 2.11. Two
transistors are also connected in parallel, but instead of a voltage source we use a current
source in this design. Instead of a series filter a shunt filter is employed, which is also tuned at
the fundamental frequency. The voltage across the transistors is a half-wave rectified sine
wave and the transistor current becomes a square wave. Due to the filter resonance, there is no
voltage across the transistors when a transistor is turned on; therefore, a so-called Zero-
17
Fundamentals to the Power Amplifier Design
Voltage-Switching (ZVS) is realized. Even if the transistors have some output capacitance,
they can be regarded as a part of the parallel filter, so that an overlap of the drain voltage and
the drain current can theoretically be avoided.
Fig. 2.11. The current mode class D power amplifier and its waveforms.
2.2.2 The Class E Power Amplifier
Another important kind of switching-mode power amplifier is the class E power amplifier,
which is introduced by Socal in 1975 [10]. The schematic of a class E power amplifier is
shown in Fig. 2.12. A shunt capacitor Cp is used to provide the charge-discharge function of
the switching-mode operation. It ensures that the voltage across the switch still remains
relatively low, when the switch is turned off, until the drain current reaches zero.
Fig. 2.12. The schematic of a class E power amplifier.
18
Fundamentals to the Power Amplifier Design
A series filter is adopted which consists of a series inductor Ls and a series capacitor Cs. This
filter is tuned at the fundamental frequency to ensure a sine waveform on the load. Rl ,opt is the
optimum load of the class E power amplifier, to which the 50 Ohm reference load should be
transformed.
The waveforms of the voltage across the transistor and the current flowing through it are
shown in Fig. 2.13. Clearly, the amplitude of the drain-source voltage can even reach 4.5Udd
[3]; therefore, the supply voltage of a class E power amplifier is usually lower than those used
in the other classes.
Fig. 2.13. Voltage and current waveforms for an optimum class E power amplifier.
The switch alternately opens and closes at the operating frequency, and the common choice of
the duty cycle is 50 %. During the ON state, the transistor is overdriven and should provide a
resistance as low as possible, while sustaining the current running through it. The voltage
across the switch is zero and the current flows totally through the switch. Conversely, during
the OFF state the transistor is in cut-off region and should provide very high impedance. It
should also be able to sustain the voltage rise across its terminals. The entire current is
flowing through the shunt capacitor Cp, charging and discharging it, and the switch voltage
has a characteristic asymmetric waveform. The voltage and the current waveforms never
simultaneously have non-zero values, so that no power is dissipated in the switch and the
efficiency of this operation can theoretically be set to 100 %. However, on the other hand, this
operation is clearly an extremely non-linear regime.
To realize the so-called soft switching, which means that the shunt capacitor will not be
discharged through the switch resulting power loss, two conditions should be fulfilled [11],
[12]. The first one is that the voltage returns to zero at the switch turn-on. The second one is
zero voltage slope at the switch turn-on. These two conditions can mathematically be
described by the following two equations:
U ds (t = τ / 2) = 0 ,
dU ds
dt
= 0,
(2.6)
(2.7)
t =τ / 2
where Uds is the drain-source voltage of the transistor as shown in Fig. 2.12 and t denotes the
time; the time constant τ is equal to 2π/ω. These two conditions can be fulfilled by an
appropriate choice of the reactive elements applied in the output network of the proposed
amplifier circuit. These reactive elements can be described by the following equations [13]:
19
Fundamentals to the Power Amplifier Design
Rl ,opt ≈ 0.577
Cp =
Ls =
U dd2
,
Pout
0.1837
,
ω ⋅ Rl ,opt
Q ⋅ Rl ,opt
ω
(2.8)
(2.9)
,
(2.10)
.
(2.11)
and
Cs =
1
ω 2 ⋅ Ls
Therefore, the mostly used reference impedance, namely 50 Ohm should first be transformed
to Rl ,opt given in equation (2.8), according to the required output power. The other
components can then be calculated in turn. The values of Ls and Cs are not uniquely
determined; they depend on the chosen quality factor Q. The shunt capacitance Cp in equation
(2.9) includes the output capacitance of the active device.
Unfortunately, the transistors used as switches always have a finite on-resistance, and the
transition times from the off-state to the on-state and vice-versa are not negligible. In order to
avoid power loss from the finite on-resistance of the switch, the FET is designed with a large
gate width. On the other hand, the transition time of the input signal is increased in this way
due to the enhanced parasitic capacitance. To obtain the shortest transition time from one state
to the other, it is necessary to use a driving stage in the power amplifier, which feeds a
squarewave-like signal to the input of the class E power amplifier. Class F power amplifiers
are good candidates to generate such squarewave-like periodic signal.
In order to yield good performance in a class E power amplifier, suitable technology should
be selected. Due to low substrate power loss and low parasitic capacitance and resistance,
GaAs FET is frequently used. On the other hand, standard digital technology has seen a
breakthrough in both performance and size through the use of device scaling to deepsubmicron CMOS. For highly integrated, low-power, wireless transceivers operating near
1 - 2 GHz, CMOS may also prove to be a useful process to realize switching-mode power
amplifiers. A CMOS class E power amplifier is proposed in this work.
2.2.3 The Class F Power Amplifier
The class F power amplifier was introduced at the end of the 1950s [14]. The basic idea of
this operation mode is loading the active device output with appropriate terminations at
fundamental and harmonic frequencies to improve the efficiency. Basically, open- and shortcircuit terminations at odd and even harmonics are presented at the output of the transistors to
shape the drain waveforms. This can be done with an output network including a load and
harmonic resonators. Ideally, infinite number of resonators should be used, which is however
not feasible in practice. Fig. 2.14 shows the schematic of a class F power amplifier using a
field-effect transistor as the active device. This circuit has a band rejection filter tuned to the
second harmonic in the output matching network, which consists of the inductors L1, L2, L3
and the capacitors C1, C2 and C3. Such a configuration will give a close approximation to a
20
Fundamentals to the Power Amplifier Design
square wave for the output voltage [15], hence can be used as the driving stage for a class E
power amplifier.
Fig. 2.14. The schematic of a class F power amplifier.
Another possibility to shorten several determined harmonics is to use the corresponding
resonators in the biasing networks as shown later.
The waveforms of the drain voltage and the drain current are illustrated in Fig. 2.15 for the
ideal case [16], i.e. the output matching network includes infinite number of resonators.
Obviously, the drain-source voltage has a square waveform, while the drain current regularly
presents a half sine waveform. In Fig. 2.15, the peak value of the drain-source current Im is
equal to πIq, where Iq is the quiescent current of the amplifier circuit. The quiescent current is
defined using the following equation:
AS = Aq ,
(2.12)
where AS is the area covered by the half sine waveform and Aq is the area covered by the
quadrate shown in Fig. 2.16. The area AS can be calculated as following
π
AS = ∫ I m sin xdx
0
π
= I m ⋅ − cos x 0
= I m (− cos(π ) + cos(0))
= 2I m .
(2.13)
On the other side, the quadrate area Aq can be calculated as following:
Aq = I q ⋅ 2π .
(2.14)
Using (2.13) and (2.14) in (2.12), we obtain
Im = Iq ⋅π .
(2.15)
21
Fundamentals to the Power Amplifier Design
Fig. 2.15. Ideal waveforms of a class F power amplifier.
Fig. 2.16. Calculation of the quiescent current.
A class F power amplifier has in practice only limited number of resonators; hence the
drain-source voltage waveform includes one or more odd harmonics and approximates a
squarewave-like waveform. The current waveform includes even harmonics and approximates
a half-wave rectified sine wave. Theoretically, the efficiency of a class F power amplifier
increases as more harmonics are tuned. It approaches the ideal value of 100% in case that all
the harmonics are rejected.
22
Fundamentals to the Power Amplifier Design
2.3 Active Devices for the Power Amplifier Design
A wide range of semiconductor technologies are being applied for RF power transistor
applications between 500 MHz - 2.5 GHz. In practice, CMOS, LDMOS, HBT, and GaAsHEMT are the mostly used technologies for the microwave power amplifier development. In
this section, concise introductions of some of these technologies are provided. The novel
HiVP configuration is also applied in practice for the power amplifier design; especially in
case that a high supply voltage is used. The HiVP configuration can be considered as a single
transistor as shown later, hence an analytical overview of it is given in this section.
2.3.1 CMOS Devices
The concept of metal-oxide-silicon field-effect transistors (MOSFETs) was generated in the
early 1930s [17] [18]. In the mid-1960s, the complementary MOS (CMOS) devices (i.e. both
n-type and p-type transistors) were introduced [19] [20], initiating a revolution in the
semiconductor industry. Today, CMOS technology dominates the digital market, due to its
low fabrication cost and low power consumption which happens only during the switching.
The dimensions of MOS devices can be scaled down; hence their speed can be increased.
CMOS technology is attractive for modern communication also due to the possibility of the
monolithic-integration of the digital and analog circuits, which improve the overall
performance and reduce the cost of packaging.
Fig. 2.17 illustrates a simplified structure of an n-type MOS transistor. Fabricated on a ptype substrate (also called the “bulk” or the “body”), the device consists of two heavily-doped
n-regions forming the source (S) and drain (D) terminals. Note that the structure is symmetric
with respect to S and D. A heavily-doped piece of polysilicon operates as the gate (G), which
is insulated from the substrate by a layer of silicon dioxide (SiO2) with a thickness of tox. Ln
and Wn are the effective gate length and gate width, respectively. In reality, the substrate
potential must generally be considered, which also influences the device characteristics. The
connection to the substrate is usually realized through an additional p+ region indicated as the
bulk (B) in Fig. 2.17. Therefore, a MOSFET is normally regarded as a four-terminal device.
In CMOS technologies, both NMOS and PMOS transistors are available. The PMOS devices
are obtained by negating all of the doping types. They are usually placed in a “local substrate”
called n-well, since they are fabricated on the same wafer as the NMOS devices [21].
Fig. 2.17. The structure of an n-channel MOS device.
The output characteristic of an enhancement NMOS transistor [22], which indicates the
relationship between the drain current Id and the voltages can be described in Fig. 2.18.
Obviously, there are two different regions, namely the triode region and the saturation region,
before the device enters the breakdown region. They can be distinguished by U ds < U gs − U th
23
Fundamentals to the Power Amplifier Design
and U ds > U gs − U th , where Ugs and Uds denote the voltage difference between the gate and
source terminals, as well as between the drain and source terminals, respectively. Uth is the
threshold voltage of the MOSFET. The threshold voltage of a MOSFET is usually defined as
the gate voltage where an inversion layer forms at the interface between the insulating layer
(oxide) and the substrate of the transistor. In case of U gs = 0 V , there is no conductive
connection between the drain and the source. With a positive gate voltage U gs > U th an nconductive channel is generated, hence the current flows between the drain and the source,
which rises with an increased Uds. However, this channel is “pinched off ” [22], if Uds is larger
than Ugs-Uth. That means the drain current remains constant as Uds further increased.
Fig. 2.18. The output characteristic of an enhancement MOS device.
In the triode region, the drain current Id is given by [22]
I d = µnCox
Wn 
1

U gs − U th ) ⋅ U ds − U ds2  ,
(

Ln 
2

(2.16)
where µ n is the mobility of the electrons and Cox is the gate oxide capacitance per unit area.
Ugs – Uth is usually called as the “overdrive voltage”, while Wn/Ln denotes the “aspect ratio”.
Obviously, in the triode region, Id increases with the enhanced Ugs and Uds, if Ugs excesses the
threshold voltage.
In the saturation region, Id can be expressed by
Id =
2
W
1
µ nCox n (U gs − U th ) ,
2
Ln
(2.17)
indicating that the drain current is independent on Uds in the ideal case. Since a MOSFET
operating in saturation produces a current in response to its gate-source overdrive voltage, a
figure of merit that indicates how well a device converts a voltage to a current can be defined.
This figure of merit, which is called the “transconductance” and denoted by gm, can be
obtained by using the derivation of the drain current by the change in the gate-source voltage
as shown below
gm =
24
∂I d
∂U gs
= µn Cox
U ds = const .
W
(U gs − U th ) .
L
(2.18)
Fundamentals to the Power Amplifier Design
In a sense, gm represents the sensitivity of the device: for a high gm, a small change in Ugs
results in a large change in Id. The direct relationship between gm and Id can be described with
the following equation:
g m = 2 µ n Cox
W
Id .
L
(2.19)
Though Id is theoretically independent on Uds in the saturation region, the maximum
allowable Uds is limited by the avalanche-effect. With an oversized Uds, the MOSFET can be
destroyed rapidly. The breakdown appears first on the side of drain, since the largest
difference between the gate-potential and the channel-potential exists at this point. Today, the
breakdown voltage of a MOSFET, which is denoted by Ubr, drops dramatically with the
decreased dimensions of transistors. The typical value of a 120 nm CMOS technology is, for
instance, only about 2.5 V.
In reality, for a MOS transistor, several second-order effects are not negligible. The “body
effect” must first be considered, which means that the threshold voltage Uth of a MOS device
can be varied by a bulk-voltage UB. As UB drops, Uth increases. Furthermore, the effective
channel length gradually decreases as the potential difference between the gate and the drain
increases, resulting in an enhanced Id with an increased Uds. Therefore, the expression of the
Id in the saturation region should be corrected and given as
Id =
2
W
1
µ nCox n (U gs − U th ) ⋅ (1 + λU ds ) ,
2
Ln
(2.20)
where λ is the channel-length modulation coefficient. This effect is called the “channel-length
modulation”.
The small-signal model of a MOSFET is given in Fig. 2.19. It can be seen from the output
characteristic that a MOS device operates as a voltage-controlled current source in the
saturation region. Therefore, a voltage-dependent current source equal to g m ⋅U gs is
incorporated at the output. The channel-length effect is modelled by the drain-source
resistance Rds, whose value is approximately 1/ ( λ ⋅ I d ) . The bulk potential, which influences
the threshold voltage and hence the gate-source overdrive, is modelled by a second current
source g mb ⋅ U bs , where g mb is the secondary transconductance caused by bulk potential. That
is, the bulk is regarded here as the second gate. Furthermore, to predict the RF behaviour, the
device capacitances between every two of the four terminals are also included in the complete
small-signal model of a transistor.
Fig. 2.19. The complete MOS small-signal model.
25
Fundamentals to the Power Amplifier Design
2.3.2 HiVP Configuration
As mentioned above, CMOS technology is widely used due to lots of benefits. However,
the bottleneck of this technology is the breakdown voltage. The gate-drain voltage of a MOS
transistor is especially critical due to the field distribution along the channel and the extreme
thin gate oxide. Therefore, a single MOS device, especially one of the deep-submicron CMOS
technologies, is not suitable for power amplifier design. Recently, the HiVP configuration [23]
becomes attractive to solve this problem. The HiVP is a high voltage and high power device
configuration in which several devices are connected DC and RF in series, so that the large
output voltage can be divided by all the cascaded devices. With some methods it is even
possible to share the large voltage equally [24].
Figure 2.20 illustrates the schematic of a CMOS HiVP configuration. Several devices (e.g.
three devices as shown here in Fig. 2.20) are connected in series. Therefore, the currents
flowing through the transistors are all the same. Ideally, the transistors have the same
operating points. The resistors R1-R3 are used as the voltage divider to ensure that Uds of all
the transistors are exactly the same. Clearly, the DC voltage Uds of T1-T3 are equal to the DC
voltage drop of R1-R3, respectively, However, the DC voltage Uds of T3 is equal to the DC
voltage drop of R3 plus the gate-source voltage of T3. Therefore, R1 and R2 should have the
same value while R3 must be much smaller than the others. The DC voltages between gate
and source of all the devices are always the same and equal to Ugg, because the transistors are
absolutely identical and the same current flows through them. The resistor R3 serves
simultaneously as a feedback to allow the gate voltages of T1 – T3 to swing with the RF
output signal. Therefore, the voltages between the gate and the drain of each device can
remain smaller than the maximum allowable voltage for the transistors. The two inductors L1
and L2 serve as RF chokes which feed DC power to the gate and drain, respectively.
Fig. 2.20. A HiVP configuration with three transistor devices.
As mentioned above, the main function of a HiVP structure is to realize a voltage division.
That means the drain voltages of the transistors are different. Since the same current flows
through all the transistors in a row, the voltage difference can only be fulfilled by the
increasing drain impedance from the lower transistor to the upper one. In this sense, the HiVP
configuration operates also as a power combiner. The output power of this configuration is the
26
Fundamentals to the Power Amplifier Design
combined sum of all the power achieved from each individual transistor. In this manner, a
high output power is achievable.
The impedance level seen at the drains of T2 and T1 can be adjusted by the capacitors C2
and C1, which are connected between the gates of the floating MOS transistors and the ground.
Noting that the drain impedance of these two transistors is equal to the impedance at the
source input of the upper device, the calculation of this impedance can be done by using a
current source at the source of the device as shown in Fig. 2.21 (a). The small-signal
equivalent circuit is shown in Figure 2.21 (b). Csh symbolizes C1 and C2 in Fig. 2.20 and
Zsource indicates the impedance seen at the source.
(a)
(b)
(a) Calculation of the source impedance using a current source
(b) The small-signal equivalent circuit of a)
Fig. 2.21. The calculation of the impedance seen at the drain.
(Csh: The shunt capacitance between gate and ground)
Noting that
U 1 = −U X ,
(2.21)
following equations can be obtained
U gs =
1/ jω Cgs
1/ jω Cgs + 1/ jω Csh
=−
⋅U 1
Csh
⋅U X .
Csh + Cgs
(2.22)
On the other hand
I x = −U gs ⋅ ( g m + jω C gs ) .
(2.23)
Substituting equation (2.22) into equation (2.23) yields
IX =
Csh
⋅ ( g m + jω C gs ) ⋅ U X .
Csh + Cgs
(2.24)
27
Fundamentals to the Power Amplifier Design
This leads to the impedance at the source input of the device
Z source =
Csh + Cgs
UX
1
=
⋅
.
IX
g m + jω Cgs
Csh
(2.25)
If the transistor has a gate width of several millimetres, the gate-source capacitance normally
has a value in the range of several pikofarad. Therefore, jωCgs at several Gigahertz is much
smaller than gm (normally > 1). The equation above can approximately be rewritten in
Z source ≈
1 Csh + Cgs
1  Cgs 
⋅
=
⋅ 1 +
.
gm
Csh
g m  Csh 
(2.26)
Observe from equation (2.26) that Csh is the unique but useful variable to adjust the
impedance level seen at the drains of each individual transistor. The smaller Csh, the larger is
Zsource. For a high output power, the voltage swing of the drain of the top device must be large
enough (e.g. peak-peak voltage > 10 V). On the other hand, the voltage swing of the drain of
the bottom device must remain small (peak value smaller than 1.5 V) because the source of
the bottom device is directly connected to the ground. For an equal distribution of the large
drain voltage of the top device, the higher devices must have a larger voltage swing. As
mentioned above, the larger voltage swing can only be obtained with a higher impedance
level seen at the drain. According to equation (2.26), the gate of a higher device must be
connected with a smaller capacitor, which means that the following condition must be
fulfilled [24].
C2 < C1
(2.27)
The HiVP configuration can be regarded as a single transistor [23]. The gate of the first
transistor can be considered as the input and the drain of the top transistor can be considered
as the output. The difference between such a configuration and a conventional single device is
the ability to carry a larger voltage. Therefore, a large supply voltage can be applied to
generate a larger output power.
2.3.3 LDMOS Devices
The lateral double diffused MOS (LDMOS) power transistor is a development of the MOStechnology, which has an increased breakdown voltage. Today, silicon LDMOS technology
has a strong position in base station applications due to its benefits, which are improved
efficiency; higher peak-power capability and lower cost-per-watt performance. Furthermore,
LDMOS power amplifiers are widely used in modern wireless communication systems also
due to their better intermodulation distortion (IMD) performance compared to other
competing technologies [25].
The operating theories of an LDMOS transistor are based on those of a conventional MOS
device. However, compared to a conventional MOS transistor, the breakdown voltage of an
LDMOS transistor is significantly increased by using a long n-drift region at the drain
terminal. Fig. 2.22 shows the device structure of a LDMOS transistor [26]. The drift region is
low doped and hence has relatively high resistivity. Therefore, the high electrical field
strength at the drain can be degraded. The usage of this drift region can boost the breakdown
voltage of the transistor, even up to 70 V, so that a higher supply voltage can be used for a
power amplifier design to obtain a large output power. Today, the commercial LDMOS
28
Fundamentals to the Power Amplifier Design
transistors typically have a supply voltage of 26 V and are available with power outputs of
more than 100 W at 2 GHz.
Fig. 2.22. The cross section of an LDMOS transistor [26].
On the other hand, the additional n-drift region involves a relatively large output
capacitance which leads to an optimum output impedance of the device well below 50 Ohm.
Therefore, a broadband output matching is quite difficult using an LDMOS device. The short
channel region, called the p-base, is formed by lateral diffusion of a p-type implantation that
will enhance RF performance of the transistor [27]. The source terminal is directly structured
on the back side of the wafer, so that bonding wire of the source terminal can be eliminated,
thus the source inductance can be greatly reduced. A thicker gate oxide is implemented,
which reduces the feedback capacitor between the drain and the gate, so that the transit
frequency is enhanced.
29
Fundamentals to the Power Amplifier Design
2.4 Introduction and Analyses of Conventional Circuit Design Concepts
In this section, the design concept as well as the functional principle of the common-source
(CS) single-ended stage is first introduced. According to open-circuit time constants method,
the high-frequency response of this circuit is discussed. It can be proven, that the problem
often occurring in analog circuits, the Miller effect, causes the limitation for the bandwidth.
Therefore, this effect should be diminished in the radio frequency circuits. The cascode
circuit is introduced on this account, which effectively eliminates the Miller effect. The
functional principle of the cascode circuit is provided in subsection 2.4.4. Today, the
differential circuit is widely used in practice, its benefits and drawbacks are described in
subsection 2.4.5.
2.4.1 Common-Source Single-Ended Stage
In case of a common-source single-ended stage, the gate and the drain of the MOS
transistor are separately used as the input and the output of the circuit, while the source and
the bulk of the transistor are directly connected to the ground. The schematic of such a
configuration is depicted in Fig. 2.23, where Ui and Uo denote the input and the output voltage,
respectively. The supply voltage is indicated by Udd.
Fig. 2.23. The schematic of a common-source single-ended stage.
The MOSFET converts variations in its gate-source voltage to a variation of the drain
current, which can pass through the load Rl to generate an amplified output voltage. Both the
large-signal and the small-signal analysis show, that the gain (G) of this common-source stage
is proportional to the transconductance of the transistor gm and the load impedance as
expressed below [22]
G = − g m Rl ,
(2.28)
when the body effect is neglected. The minus sign in equation (2.28) indicates that the input
and the output voltage are just 180° out-of-phase.
In practice, the load Rl shown in Fig. 2.23 is generally a resistive load, which can directly
be realized with a resistor. It can also be realized by using a MOSFET that operates in the
deep triode region. Moreover, the load can also be a diode-connected MOSFET to obtain a
relatively linear gain, or be a current-source load to maximise the output voltage swing etc.
Sometimes, the load is connected at the source of the transistor device to form a source
degeneration circuit. In this manner, a linear behaviour of a common-source stage can be
obtained.
30
Fundamentals to the Power Amplifier Design
2.4.2 Estimation of the High-Frequency Bandwidth
In microwave region, it is sometimes desired to approximately predict the bandwidth of the
proposed radio frequency circuits. Leastwise, it is demanded to have the insight to find the
components which are responsible for the limitation of the circuit bandwidth. Two such
approximate methods are open-circuit time constants (OCTC) and short-circuit time constants
(SCTC), which are used to estimate the high-frequency 3-dB point and the low-frequency 3dB point, respectively [28].
Fig. 2.24. A two-port network.
Using OCTC, let’s consider the high-frequency bandwidth of an arbitrary two-port network
shown in Fig. 2.24. This network consists only of sources, n resistors Ri and n capacitors Ci ,
where i is an arbitrary integer between 1 and n. The resistor Ri in Fig. 2.24 denotes the
effective resistance facing ith capacitor Ci with all the other capacitors removed (opencircuited). The all-pole transfer function F(ω) of this two-port network can approximately be
described as
F (ω ) =
a0
Uo
,
=
U i (τ 1 jω + 1)(τ 2 jω + 1) ⋅⋅⋅ (τ n jω + 1)
(2.29)
whereas τi are the various time constants, determined by the product of the resistors and
capacitors Ri ⋅ Ci . Multiplying out the terms in the denominator leads to the following
polynomial
bn ⋅ ( jω ) n + bn −1 ⋅ ( jω ) n −1 + ⋅ ⋅ ⋅b1 ⋅ ( jω )1 + 1 ,
(2.30)
where the coefficient bn is the product of all the time constants and b1 is the sum of them.
Generally, near the 3-dB limit-frequency, the first-order term in equation (2.30) dominates
over the higher-order terms, therefore, the reasonable approximation of the transfer function
can be simplified as
Uo
≈
Ui
a0
(
)
∑ i=1τ i ⋅ jω + 1
n
.
(2.31)
As shown later, (2.31) could further be simplified if only the dominant RC-constant arising
from the input is considered. The estimated high-frequency bandwidth of the system ω3-dB is
then simply the reciprocal of the effective time constant, given as
31
Fundamentals to the Power Amplifier Design
ω3− dB ≈
1
(∑ τ )
n
.
(2.32)
i =1 i
Thus, each time constant represents a local bandwidth degradation term. Naturally, not all
capacitors in a network belong to the OCTC calculation. For instance, the large coupling
capacitors used to connect the output of one stage to the input of the next stage is not counted
to such calculation. As a consequence, the removal of a capacitor that belongs to the OCTC
calculation should lead to an increase of the high-frequency power gain.
2.4.3 High Frequency Response and Miller Effect
The gain of a single-ended common-source stage expressed in equation (2.28) is only valid
for low-frequency application. To show the frequency response of the circuit in the highfrequency region, the capacitance of the MOSFETs given in Fig. 2.19 must also be taken into
account. The complete small-signal equivalent circuit of a single-ended common source stage
is depicted in Fig. 2.25, where Rg and Rl are the gate and load resistance of the transistor,
respectively.
Fig. 2.25. The small-signal equivalent circuit of a single-ended common source stage.
Known from the OCTC method, the effective resistance Ri facing each capacitor should
first be calculated, under the condition that all the other capacitors are open-circuited.
Obviously, only Rg is connected to Cgs, as well as the parallel circuit of Rds and Rl to Cds. An
important phenomenon that occurs in many analog circuits, namely the “Miller effect” [22],
arises from Cgd. Usually, the Miller effect is caused by connecting a capacitance across two
nodes that have an inverting gain between them. Using a test current source, the resistance
facing Cgd can be calculated as follows [28]
RCgd = Rg + ( Rl Rds ) + g m ⋅ Rg ⋅ ( Rl Rds ) .
(2.33)
According to equation (2.31), the gain of the common-source stage in dependence of the
frequency can approximately be described as follows.
− g m ⋅ Rl
Uo
=
Ui
Cgs ⋅ Rg + Cds ⋅ ( Rl Rds ) + Cgd ⋅ RC  ⋅ jω + 1
gd 

(2.34)
The largest limit-factor in equation (2.34) for the bandwidth is associated with Cgd. Even
though the value of Cgd is conventionally small, however, its effect is Miller-multiplied by the
gain gm and the resistances.
32
Fundamentals to the Power Amplifier Design
Actually, the gate-drain capacitor Cgd in Fig. 2.25 provides a feedforward path that
conducts the input signal to the output at very high frequencies, resulting in a slope in the
frequency response. Therefore, Cgd is a significant capacitor which belongs to the OCTC
calculation. It is worth to invest some effort to mitigate its effect by somewhat improved
circuit topologies.
2.4.4 Cascode Circuits
As mentioned in section 2.4.3, the Miller effect is the most significant factor for the
degradation of the bandwidth. Therefore, it is important for RF circuits design to figure out
how to mitigate the Miller effect. One possibility is to prevent the coupling-capacitance
between the input and the output across the gain stage. The cascode circuit is such a candidate,
which effectively eliminates the Miller effect and therefore is widely used for microwave
circuit design. The schematic of a cascode circuit is depicted in Fig. 2.26.
Fig. 2.26. The schematic of a cascode circuit.
Obviously, the cascode topology is a cascade of a common-source stage (T1) and a commongate stage (T2). The input device T1 generates a small-signal drain current proportional to Ui
and the cascode device T2 simply routes the current to Rl. Therefore, the voltage gain of a
cascode stage is just equal to that of a common-source single-ended stage.
Intuitively, the output is now at the drain of the T2 while the input is at the gate of T1. There
is no capacitance directly across these two nodes; hence the Miller multiplication is
dramatically reduced. Using the high-frequency mode of the cascode circuit, which is
depicted in Fig. 2.27, the suppression of the Miller effect is analytically presented. In this
figure, the main parasitic capacitances of both transistors are shown. Though Cgd1 is still
connected between the gate and the drain of the input device, the resistance facing it has been
partially changed. In this case, the gate resistance Rg facing it remains, however, the other
resistance facing it is now the resistance of the parallel circuit comprising Rds1 and the
resistance seen looking toward the source of T2. Similar to the calculation of the resistance
seen at the source of the upper device in the HiVP configuration, the resistance seen looking
toward the source of T2 can be calculated with the result of (1/ g m 2 ) Rds 2 , neglecting the
body effect of the devices. The total resistance facing Cgd1 can now be expressed as

 1

 1

RCgd 1 = Rg + Rds1 
Rds 2  + g m1 ⋅ Rg ⋅  Rds1 
Rds 2   .


 gm2

 gm2


(2.35)
33
Fundamentals to the Power Amplifier Design
Since 1/gm2 has a much smaller value than Rds1 and Rds2, the equation above can
approximately be rewritten in
RCgd 1 = Rg +
1
1
.
+ g m1 ⋅ Rg ⋅
gm2
gm2
(2.36)
Compared to the parallel resistance Rl Rds in equation (2.33) for the common source singleended stage, 1/gm2 also has a much smaller value, leading to a significant degradation of the
Miller effect caused by Cgd1.
Fig. 2.27. The small-signal circuit of a cascode circuit.
Clearly, since one more transistor is applied, the cascode circuit has more parasitic
capacitances than the single-ended stage. However, since the Miller multiplication is
definitively removed from the entire configuration, every capacitance in the cascode circuit
makes only a small contribution to the effective time constant, resulting in a relatively small
sum. Therefore, the bandwidth of the circuit is increased.
Another important benefit of the cascode circuit is its higher output impedance, compared
to a single-ended common-source stage. The output impedance of a cascode circuit can be
described as follows [29]
Rout = (1 + g m 2 ⋅ Rds 2 ) ⋅ Rds1 + Rds 2
≈ g m 2 ⋅ Rds 2 ⋅ Rds1 ,
(2.37)
assuming g m 2 Rds 2 >> 1 . This result can be regarded that the output impedance of T1 is greatly
increased by a factor of g m 2 ⋅ Rds 2 . Therefore, the attenuation of the RF signal at the output of
the circuit is reduced.
Despite the benefits of a cascode circuit mentioned above, the drawbacks of such a
configuration are not negligible. Assuming both transistors T1 and T2 operate in saturation
region, the output voltage swing of the cascode circuit is decreased by at least the overdrive
voltage of T2. Therefore, the maximum achievable output power is also reduced. Just on this
account, cascode topologies extended to three or even more stacked devices are usually not
used in practice, though they have even larger output impedance than the conventional
cascode circuit.
34
Fundamentals to the Power Amplifier Design
2.4.5 Differential Amplifier
The differential operation has become an important choice in today’s high-performance
analog and mixed-signal circuits. The basic schematic of a differential pair is presented in Fig.
2.28. Two identical single-ended devices T1 and T2 are connected in parallel. They also have
the same supply voltage Udd and identical loads, i.e. Rl1 = Rl 2 = Rl . Ui1, Ui2, Uo1 and Uo2
separately denote the input as well as the output voltages of the T1 and T2. The differential
pair employs a current source IS to minimise the dependence of the sum of the bias currents
Id1 and Id2 flowing through the devices on the input common-mode level.
Fig. 2.28. The basic schematic of a differential amplifier.
The waveforms in the time domain of the input and the output voltages are given in Fig.
2.29. The two input signals have the same center potential named common-mode (CM) level,
but are 180° out of phase as shown in Fig. 2.29 (a). The input common-mode voltage level is
denoted as Ui,CM in this figure. The output signals of the two signal-ended stages are also 180°
out of phase with each other and separately with their input signals as shown in Fig. 2.29 (b).
(a) The input voltages
(b) The output voltages
Fig. 2.29. The waveforms of the input and the output signals of a differential pair.
35
Fundamentals to the Power Amplifier Design
Compared to a single-ended stage, an important advantage of differential operation is the
higher immunity to the environmental noise, since the environmental noise disturbs each
individual CM signal, but not the differential output signal. The other useful property of the
differential signalling is the doubled achievable voltage swings, as the peak to peak swing for
U o1 − U o 2 is equal to 2 ⋅ U dd − (U gs − U th )  , while the maximum output swing of Uo1 or Uo2 is
only equal to U d − (U gs − U th ) [22].
Using small-signal analysis, the voltage gain of the differential pair can be given with the
following equation, where gm,d is the transconductance of the differential pair,
U o 2 − U o1
= − g m ,d Rl .
U i1 − U i 2
(2.38)
According to equation (2.19), gm,d in equation (2.38) is 1 / 2 times that of a single-ended
stage, if the single-ended transistor has the same dimension and is also biased at IS, since the
bias current in the differential pair must be equally divided by the two parallel transistors. In
this respect, the gain of a differential pair is smaller than that of a single-ended stage. On the
other hand, a differential pair, which has the same device-dimensions and the same load
impedance as a single-ended stage, can achieve the same gain as the single-ended stage only
at the cost of twice the bias current.
Similar to the single-ended common-source stage, the load of a differential pair can also be
selected as resistive loads, diode-connected loads, or current-source loads, according to
different applications.
36
Fundamentals to the Power Amplifier Design
2.5 Impedance Matching
As mentioned in chapter 2.1, in order to obtain the maximum output power, the reference
impedance (usually 50 Ohm) must be transformed to the optimum input and output
impedance Zin_opt and Zout_opt of the transistor. Matching networks should be used at the input
and the output of the amplifier circuit. Considering the specific problems of RF power
amplifiers, the matching circuits must meet the following requirements as much as possible:
1. Transform the source and load impedance in the optimal operating impedance.
2. Maintain the specified amplitude- and phase-frequency response over a certain
frequency range.
3. Attenuate the higher harmonics. Thus, only low- or band-pass circuits are employed.
4. Have insignificant power loss, i.e. maintain high efficiency. This can be done by using
only lossless circuit elements.
5. Other requirements related to cost, size, weight, reliability and practicability.
A very useful graphical aid to the analysis of the impedance transformations is provided by
the Smith chart, which is basically a plot of all passive impedances in a reflection coefficient
chart of unit radius [30]. Furthermore, using the Smith chart, the frequency dependence of the
S-parameters and other amplifier characteristics can be presented.
In this section, discrete matching networks are first introduced, which are above all
indispensable for the integrated circuits (IC) design in the frequency region of Gigahertz. On
the other hand, microstrip lines already find extensive use as passive circuit elements.
Therefore, characteristics of microstrip transmission lines are also presented here. Based on
the knowledge of microstrip matching networks, the multi-section transmission line
impedance transformer is discussed.
2.5.1 Discrete Matching Networks
There are several different methods for the design of matching networks with lumped
elements. The simplest lumped matching networks are the two-reactance matching networks,
typically the L-circuits shown in Fig. 2.30.
(a) L-matching network for R < RL
(b) L-matching network for R > RL
Fig. 2.30. The discrete L-matching networks.
Assuming the impedances to be matched RL and the target impedance R are purely resistive,
and XL as well as XC are the reactance of the passive elements at the operating frequency f,
the design equations for the matching network in Fig. 2.30 (a) can be given as [31]
XL = R
RL
−1 ;
R
X C = RL /
RL
−1 .
R
(2.39)
This circuit is only used for R < RL. If R > RL, the input and output of the network of Fig.
2.30 (a) must be interchanged as shown in Fig. 2.30 (b). The design equations are then
37
Fundamentals to the Power Amplifier Design
X L = RL
R
−1 ;
RL
XC = R /
R
−1 .
RL
(2.40)
The quality factor, which denotes the ratio of the stored average energy and the energy loss, is
also an important characteristic of the matching networks. Assuming the circuit has a
bandwidth of ∆f around the center frequency f0, there is
Q=
f0
.
∆f
(2.41)
The equation above means, higher Q implies smaller bandwidth. For the L-matching networks,
the quality factor is determined by the source resistance RL and the first passive component
connected with it. For instance, the quality factor for the matching network shown in Fig. 2.30
(a) is determined by the RL and parallel connected passive component XC. It can be calculated
with
Q=
RL
.
XC
(2.42)
Similarly, the quality factor of the L-matching networks shown in Fig. 2.30 (b) is determined
by the source resistance RL and series connected passive component XL, which can be
calculated as follows
Q=
XL
.
RL
(2.43)
In practice, the three-reactance discrete matching networks are mostly used, since the
values obtained in the two-reactance matching networks may be impractical and there is no
design flexibility. For instance, there is no freedom to vary the quality factor Q, hence to
change the bandwidth. The typical three-reactance matching networks are π- and T-matching
networks as shown in Fig. 2.31.
(a) π-matching networks
(b) T-matching networks
Fig. 2.31. The three-reactance matching networks.
(
)
In case of RL 1 + Q 2 > R , the design equations for the π-matching network in Fig. 2.31 (a)
can be given as follows [31]
X C1 =
38
R
; X C2 =
Q
RL
RL
1+ Q2 −1
R
(
)
; XL =
QR  1
1 +
1 + Q2  Q

RL
1 + Q 2 − 1 .
R

(
)
(2.44)
Fundamentals to the Power Amplifier Design
The quality factor Q can be chosen according to the circuit bandwidth, harmonic attenuation
and efficiency. Increasing Q can enhance the filtering effect of the matching network, but
reduces the bandwidth and efficiency. Under the condition R 1 + Q 2 > RL , the design
equations for the T-matching network shown in Fig. 2.31 (b) can be given as [31]
X L1 = QR ; X L 2 = RL
R
1 + Q2 − 1 ; X C =
RL
(
)
(
)
(
)
R 1 + Q2
.
R
2
Q+
1+ Q −1
RL
(
(2.45)
)
Also here, the quality factor Q can in principal be chosen arbitrarily, but the recommended
values of Q usually range from 1 to 10.
2.5.2 Impedance Transforming Property of a Transmission Line
Microstrip lines are used extensively in building microwave transistor amplifiers because
they are easily fabricated using printed-circuit techniques. Network interconnections and the
placement of passive and transistor devices are easily realized on its metal surface. The
superior performance characteristics of the microstrip line make it one of the most important
mediums of transmission in microwave transistor amplifiers. Since the microstrip line belongs
to the most relevant members of transmission lines, the impedance transforming property of a
transmission line is first discussed in this subsection.
Fig. 2.32 illustrates a lossless transmission line terminated in an arbitrary load impedance
Z L , where the characteristic resistance Z0 indicates the ratio of voltage to current for such a
travelling wave and β is the imaginary part of the propagation constant. The transmission line
has a length of l. The relationship between the to be matched impedance Z L , the goal
impedance Z in and all these parameters is to be found. In order to simplify the following
calculation, the position of Z L is defined as zero, so that the transmission line is located in the
negative axis as shown in Fig. 2.32.
Zin
U(x), I(x)
ZL
Z0, β
0
l
x
Fig. 2.32. The lossless transmission line impedance transformer.
Assume that an incident wave of the form U 0+ e − ßx is generated from a source at x < 0 . In
case that Z L ≠ Z 0 , a reflected wave is excited. The total voltage on the line is then the sum of
the incident and the reflected waves and is described by the following equation [32]
+
−
U ( x) = U 0 e − j β x + U 0 e j β x ,
(2.46)
39
Fundamentals to the Power Amplifier Design
where U 0+ and U 0− indicate the magnitudes of the incident and the reflected voltages,
respectively. The total current on the line is
+
I ( x) =
−
U 0 − jβ x U 0 jβ x
e
−
e .
Z0
Z0
(2.47)
The total voltage and current at the load are related by the load impedance, so, at the point of
x = 0 , we must have the following relationship
+
ZL =
−
U (0) U 0 + U 0
=
Z0 .
I (0) U 0+ − U 0−
(2.48)
Solving for U 0− from the above equation, leads to
−
U0 =
Z L − Z0 +
U .
Z L + Z0
(2.49)
We define the voltage reflection coefficient Γ as the amplitude of the reflected voltage wave
normalized to the amplitude of the incident voltage wave. From equation (2.49), we obtain
−
Z − Z0
U
Γ = 0+ = L
.
U 0 Z L + Z0
(2.50)
According to equations (2.46) and (2.47), the input impedance seen looking toward the load is
+
Z in =
−
U ( −l )
U 0 e− jβ ( −l ) + U 0 e j β ( −l )
=
I ( −l ) (1/ Z 0 ) ⋅ U 0+ e − j β ( − l ) − U −0 e j β ( − l )
(
U 0 ( e j β l + Γe − j β l ) ⋅ Z 0
+
=
U 0 ( e j β l − Γe − j β l )
+
=
1 + Γe −2 j β l
Z0 .
1 − Γe −2 j β l
)
(2.51)
Using equation (2.50), the above equation can be rewritten as
Z in = Z 0
Z L + jZ 0 tan β l
.
Z 0 + jZ L tan β l
(2.52)
This equation denotes the most important impedance transforming property of a transmission
line, which is frequently used for many circuit developments. In practice, there are several
different types of transmission line, e.g. strip line, waveguide, coax, etc. In this work,
microstrip line is applied.
2.5.3 Microstrip Geometry and Characteristic Parameters
A microstrip line is a transmission line consisting of a strip conductor and a ground plane
separated by a dielectric medium. Fig. 2.33 (a) illustrates the microstrip geometry. The
40
Fundamentals to the Power Amplifier Design
dielectric material serves as a substrate and is sandwiched between the strip conductor and the
ground plane. The substrate has a thickness of h while the conductor has a width of w and a
thickness of t. The dielectric constant ε and the relative dielectric constant of the substrate ε r
are related by ε = ε r ⋅ ε 0 , where ε 0 = 8.855 ×1012 F / m denotes the vacuum dielectric constant.
The approximated electromagnetic field lines distributed in the microstrip lines are shown in
Fig. 2.33 (b).
Fig. 2.33. The microstrip geometry (a) and the field configuration (b) [32].
Clearly, the electromagnetic field lines in the microstrip are not contained entirely in the
substrate. Therefore, the propagating mode in the microstrip is not a pure transverse
electromagnetic mode (TEM) but a quasi-TEM. Assuming a quasi-TEM mode of propagation
in the microstrip line, the phase velocity is given by
c
vp =
ε eff
.
(2.53)
The parameter c is the velocity of the electromagnetic wave in the free space (299792458 m/s)
and ε eff is the effective relative dielectric constant of the microstrip, which is dependent on
the substrate thickness and the conductor width. Since some of the field lines are in the
dielectric region and some are in air, the relation 1 < ε eff < ε r always exist. The design
formulas for ε eff is given by [32]
ε eff =
εr +1 εr −1
2
+
2
⋅
1
,
1 + 12h / W
(2.54)
and the characteristic impedance Z0 of microstrip line is
60
 8h W 
ln + 
 W 4h 
for W / h ≤ 1 ,
(2.55)
120π
for W / h ≥ 1 .
⋅ [W / h + 1.393 + 0.667 ln (W / h + 1.444 )]
(2.56)
Z0 =
ε eff
whereas
Z0 =
ε eff
41
Fundamentals to the Power Amplifier Design
These results are curve-fit approximations to rigorous quasi-static solutions [33].
2.5.4 Single-Stub Tuning
The impedance transforming properties of microstrip lines shown in equation (2.52) can be
used in the design of matching networks. A microstrip line can be applied as a series
transmission line, as an open-circuited stub, or as a short-circuited stub. There are mainly two
variables to define a microstrip line, namely the length l and the characteristic impedance Z0,
if the substrate is determined. Therefore, there are typically two types of combinations of a
series transmission line and a shunt stub as shown in Fig. 2.34. Both of these two
combinations can transform a 50 Ω resistor into any value of the input impedance.
(a) with fixed characteristic impedance
(b) with fixed length
Fig. 2.34. Two typical microstrip matching networks
using a series transmission line and a shunt stub.
In Fig. 2.34 (a), a short- or an open-circuited stub with the length of l 1 is connected in
parallel with the 50 Ohm load ZL. It is followed by a series microstrip transmission line,
which has a length of l 2 . The characteristic impedance of these two sections of lines is fixed
on 50 Ohm, only the lengths of them are varied.
The other possibility of the microstrip matching network is shown in Fig. 2.34 (b). This
network uses a series quarter-wave line with characteristic impedance Z1 followed by a shortor open-circuited shunt stub having a length of λ/8 or 3λ/8 and the characteristic impedance
Z2, where λ is the wave-length at the given frequency and substrate. Clearly, in this
configuration, the lengths of the lines are determined, only their characteristic impedances are
variable.
Design processes for the microstrip matching networks mentioned above are introduced in
[34]. There are also matching networks with combinations of a series transmission and a
series stub [32], however, the shunt stub is especially easy to fabricate in microstrip form.
2.5.5 Quarter-Wave and Multi-Section Matching Networks
The quarter-wave transmission line, indicated by l in Fig. 2.32 equalling to λ / 4 , is a
very useful impedance transformer. From (2.52), the characteristic impedance Z0 of a quarterwave transmission line can be calculated with
Z 0 = Z in ⋅ Z L .
(2.57)
Obviously, such a transformer can easily be realized. However, it can match a real load only
to real input impedance. If the center frequency f0 is given, the bandwidth of a quarter-wave
transmission line can be calculated as follows [32]
42
Fundamentals to the Power Amplifier Design
 Γ
2 Z0Z L
∆f
4
t
= 2 − cos −1 
⋅
f0
π
 1 − Γ t2 Z L − Z 0

,

(2.58)
where Γt is the maximum value of voltage reflection coefficient that can be tolerated as shown
in Fig. 2.35. The parameter θ in the figure is equal to π f / 2 f 0 , while θt and π-θt are the
lower and the upper edges of the passband, respectively; θt can be calculated using the
following equation.
cos θt =
Γt
1− Γ
2
t
⋅
2 Z0 Z L
Z L − Z0
(2.59)
The maximum voltage reflection coefficient Γm depends on the ratio of ZL/Zin.
Fig. 2.35. The definition of the bandwidth of a microstrip line.
In practice, multi-section transformers are widely used. As shown in Fig. 2.36, N sections
of quarter-wave transmission lines are connected in a row. They have different characteristic
impedances Z1…ZN. Typically, all values of Zn [n ∈ (1 : N)] increase or decrease
monotonically across the transformer. Γn are the partial reflection coefficients. Just like multireactance discrete matching networks shown above, the main conception of such matching is
retaining a lower quality factor Q, which implies a broader bandwidth for a given resonance
frequency. Therefore, the bandwidth of the matching networks can theoretically be increased
if more sections of transmission lines are used.
Fig. 2.36. Multi-section microstrip matching networks.
As the length of each section of transmission lines is fixed on λ/4 at a given frequency, the
different characteristic impedances of all the sections must be determined. There are mainly
43
Fundamentals to the Power Amplifier Design
two types of multi-section transformer, namely, the binomial multi-section transformer and
the Chebyshev multi-section transformer. For the binomial multi-section transformer, the
characteristic impedance can be defined with the following equations [32]
ln
Z1
Z
≈ 2 − N C1N ln L
Z in
Z in
and
ln
Z n +1
Z
≈ 2 − N C nN ln L for n ≥ 1 .
Zn
Z in
(2.60)
The bandwidth of the binomial N-section transformer can be given by
1  Γ
∆f
4
= 2 − cos −1   m
f0
π
2  A





1/ N

,


(2.61)
with
A = 2 −N
Z L − Z in
.
Z L + Z in
(2.62)
To define the characteristic impedance of a Chebyshev N-section transformer, θm should first
be calculated with the following equation [32]
1
 ln ( Z L / Z in )
sec θ m ≈ cosh  cosh −1 

2Γ m
 N


  ,
 
(2.63)
if Γm is fixed. Let the overall reflection coefficient Γ be equal to the Chebyshev polynomials
Tn(x), resulting in
Γ(θ ) = 2e− jNθ [ Γ 0 cos Nθ + Γ1 cos( N − 2)θ + ⋅⋅⋅ + Γ n cos( N − 2n)θ + ⋅⋅⋅] = Γ m e− jNθ TN (sec θ m cos θ ) .
(2.64)
Equating similar terms in cosnθ, Γn can be obtained. The following work is to determine the
characteristic impedance of the N section transmission lines with
1 Z
Γ0 ≈ ln 1
2 Z in
and Γn ≈
1 Z n +1
ln
for n ≥ 1 .
2
Zn
(2.65)
The bandwidth of the Chebyshev N-section transformer can be given by
∆f
4θ
=2− m .
f0
π
(2.66)
The binomial multi-section transformer provides the best flatness of the response near the
design frequency, while the Chebyshev multi-section transformer has a poorer flatness but a
larger bandwidth.
There are also other methods of determining the characteristic impedance of cascaded
quarter-wavelength impedance transformer, typically by means of checking the available
tables [35]. Another possibility is to use different software, one of which is LLsmith used in
this work.
44
Fundamentals to the Power Amplifier Design
2.6 Biasing Network
The purpose of a DC bias is to select the proper quiescent point and hold the quiescent
point constant over variation in transistor parameters and temperature. It determines the
output power, amount of distortion, voltage headroom, efficiency, gain of the stage, noise of
the stage, and class of operation (class A, AB, etc.). For some classes of power amplifiers, it
is also expected that the biasing network is helpful to suppress the higher harmonics. The
proper bias point is therefore a trade-off between all of these factors. Selecting the optimum
bias point can sometimes be difficult, and it will vary depending on the requirements of the
amplification stage.
The DC bias point can be set in a number of ways. The fundamental biasing network for
power amplifier design is already shown in Fig. 2.1. Generally, a sufficiently high output
power is required by a power amplifier design, the supply voltage Udd can therefore not be fed
to the drain of the MOSFET through a resistive load or any active load as mentioned in
section 2.4.1, since such loads consume relatively large voltage headroom. Hence an inductor
(L2 in Fig. 2.1) is mostly used between Udd and the drain of the MOSFET, which serves as RF
choke and simultaneously feeds DC power to the power device. The inductance must be large
enough so that the current flowing through the power device remains substantially constant.
Such a biasing concept is primarily suitable for the power amplifier circuits used in cellular
phones, where usually only a low power supply is available.
As introduced before, the different classes of the power amplifiers, especially of the current
source mode power amplifiers are mainly determined by the gate-source-voltage of the
MOSFET. The gate voltage Ugg is likewise fed to the gate through another large inductor L1,
as shown in Fig. 2.1. Another possibility to determine the gate voltage is using a resistive
voltage divider, which allocates a part of Udd to be used as Ugg, where the resistors must also
be large enough to avoid the RF power loss.
Due to lots of merits, class AB power amplifiers are widely used. As shown in Fig. 2.8, the
most critical harmonic to deal with in a class AB power amplifier is the second one. So the
removal of the second harmonic voltage at the transistor output is of significant importance.
This can be realized by using a low- or band-pass output matching network, or by using a
suitable biasing network, e.g. the quarter-wave short-circuited stub. The quarter-wave shortcircuited, high impedance line provides the DC path for the supply voltage and presents an
open circuit to the RF signals at the fundamental frequency. Simultaneously, the second
harmonic is shorted by it. The narrowest practical line, which means the line having the
largest characteristic impedance, should be used for the λ/4 short-circuited stub to avoid
unwanted RF coupling. On the other hand, the maximum allowable current must also be
considered, since it is desired, that a large DC current flows through this line to the drain of
the transistor. The bypass capacitors Cb shown in Fig. 2.1 are used as RF short circuits.
Several parallel bypass capacitors between 1 pF and 100 nF can be applied to couple RF
signals of different frequencies to the ground.
(a) series resonator
(b) parallel resonator
Fig. 2.37. The resonators used in the bias network.
45
Fundamentals to the Power Amplifier Design
Another method to realize the harmonic removal by the biasing is the use of the series or
parallel LC-resonant circuits [32] between Udd and the drain of the MOSFET as shown in Fig.
2.37. Theoretically, such biasing networks also consume no voltage headroom. The resonant
frequency fres for both the series and the parallel resonators can be calculated with the
following equation
f res =
1
2π LC
.
(2.67)
The quality factors Q of them are separately given with
Q=
1
L
⋅
R C
for series resonance,
(2.68)
for parallel resonance.
(2.69)
and
Q = R⋅
C
L
In practice, fres is just defined at the operating frequency of the amplifier circuit. Therefore,
the resonant circuit provides an open circuit to the RF signal at the fundamental frequency and
simultaneously shorts all the other harmonics of the output signal. Additional LC-resonant
circuits tuned to the higher harmonics can also be used in the biasing network to form a
determined waveform of the output voltage. Such biasing concepts are often used, e.g. in the
class F power amplifiers as shown below.
To meet the high requirement of linearity, power amplifiers of CDMA transmitters
normally operate 6 dB backed off from the saturation. It is therefore an important issue to
increase the PAE in lower output power levels. The Doherty amplifier was attempted to
improve the efficiency using the technique of load-line modulation of a carrier amplifier
through a peaking amplifier attached to a quarter-wave transmission line [36] [37]. Another
possibility developed in recent years is to use a so-called adaptive biasing network [38] [39],
which supplies a low quiescent current at the low output power level for high efficiency, and a
higher quiescent current at high output power level for high linearity.
46
Fundamentals to the Power Amplifier Design
2.7 Design Parameters of the Power Amplifier
This chapter introduces some basic concepts and parameters in the analysis and design of
the microwave transistor power amplifiers. The most important considerations in a microwave
power amplifier design are power gain, stability, bandwidth, 1-dB compression point,
intermodulation distortion (IMD), adjacent channel power ratio (ACPR) and power added
efficiency (PAE).
2.7.1 Power Gain
There are several different power gain equations appearing in the literature and are used in
the design of microwave amplifiers [34], namely the transducer power gain GT, the operating
power gain GP and the available power gain GA. They are defined as follows
GT =
power deliverd to the load
PL
=
PAVS
power available from the source
(2.70)
power deliverd to the load
PL
=
PIN
power input to the network
(2.71)
GP =
GA =
power available from the network
PAVN
=
.
PAVS
power available from the source
(2.72)
These definitions are all the same, if the input and output of the power amplifier circuit are
both conjugately matched to the source impedance and to the load impedance respectively. In
this case, the maximum power gain can be obtained.
2.7.2 Stability
Stability is an extremely important issue for the power amplifier design. Oscillation can
occur if either the input or the output impedance has a negative real part. This is a serious
problem, because the power device used in the power amplifier circuit can be destroyed under
such a condition.
Defining Γ as the reflection coefficient, the case of negative real part of the input and
output impedance can be denoted by |Γin| > 1 and |Γout| > 1. According to Fig. 2.38, the input
reflection coefficient Γin and the output reflection coefficient Γout of a two port network can be
described with the following equations [32].
Fig. 2.38. A two-port network with reflection coefficient.
47
Fundamentals to the Power Amplifier Design
Γin =
Γout =
ΓL =
ZL − Z0
ZL + Z0
(2.73)
ΓS =
ZS − Z0
ZS + Z0
(2.74)
Z in − Z 0
S S Γ
= S11 + 12 21 L
Z in + Z 0
1 − S 22 ΓL
(2.75)
Z out − Z 0
S S Γ
= S 22 + 12 21 S ,
Z out + Z 0
1 − S11ΓS
(2.76)
where the S-parameters are those of the power amplifier circuit. Because Γin and Γout depend
on the source and load matching networks, the stability of the amplifier depends on ΓS and ΓL.
Two types of stability, namely unconditional and conditional stability can be defined as
follows [32]:
1. Unconditional stability: The network is unconditionally stable if |Γin| < 1 and |Γout| < 1
are fulfilled for all passive source and load impedances.
2. Conditional stability: The network is conditionally stable if |Γin| < 1 and |Γout| < 1 are
fulfilled only for a certain range of passive source and load impedances.
Since the S-parameters of the circuits are dependent on the frequency, it is possible for an
amplifier to be stable at some frequencies but unstable at other frequencies.
Applying equation (2.75), the condition of |Γin| = 1 can be rewritten as follows
ΓL −
( S 22 − ∆ ⋅ S11* )*
2
S 22 − ∆
S12 ⋅ S 21
=
2
2
S 22 − ∆
2
,
(2.77)
with ∆ = S11S22 – S12S21. The signs of * indicate the conjugate complex number. In the
complex Γ plane, equation (2.77) can be regarded as a circle with the center of Co and a radius
of Ro, which are described by
Co =
Ro =
( S 22 − ∆ ⋅ S11* )*
2
S 22 − ∆
S12 S 21
2
S 22 − ∆
(2.78)
2
2
.
(2.79)
This circle is named output stability circle. Similarly, the input stability circle can be given
with its center of Ci and the radius of Ri described by
Ci =
Ri =
48
* *
( S11 − ∆ ⋅ S 22
)
2
S11 − ∆
S12 S 21
2
S11 − ∆
(2.80)
2
2
.
(2.81)
Fundamentals to the Power Amplifier Design
Given the S-parameters of the device, we can plot the input and output stability circles in the
Smith chart to denote where |Γin| = 1 and |Γout| = 1.
Mostly, the stability circle divides the Smith chart into two parts denoting that the circuit is
only conditionally stable. One of the two parts is inside the circle and the other is outside the
circle. The next question is then, which part belongs to the stable region, inside or outside.
The following two rules are available:
1. If |S11| < 1, the center of the Smith chart for load is in the stable region. Then, if the
stability circle includes the center point, the stable region is inside this circle.
Conversely, if the stability circle doesn’t include the center, the stable region is outside
this circle.
2. If |S11| > 1, the center of the Smith chart for load is in the instable region. Then, if the
stability circle includes the center point, the stable region is outside this circle.
Conversely, if the stability circle doesn’t include the center point, the stable region is
inside this circle.
The same relationship is also valid for |S22| and the Smith chart for source. To research
whether the circuit is conditional stable in the entire frequency band of interest, stability
circles should be plotted for all the frequencies, the rules described above are also repeated for
each frequency to see, where the circuit is stable and where not.
Similarly, the prerequisites for unconditional stability are: 1) all the stability circles for all
the frequencies are outside the Smith charts, not only for source but also for load, and 2)
|S11| < 1, as well as |S22| < 1 are fulfilled for all the frequencies.
Conveniently, there are two mathematical methods to test whether a circuit is
unconditionally stable. The first one is the so-called K – ∆ test, where it can be shown that a
circuit is unconditionally stable if Rollet’s condition, defined as
2
2
2
1 − S11 − S 22 + ∆
K=
> 1,
2 S12 S 21
(2.82)
along with the auxiliary condition that
∆ = S11S 22 − S12 S 21 < 1
(2.83)
are simultaneously satisfied. The other mathematical method applies the unconditional
stability factor µ. The circuit is unconditionally stable, if
µ=
1 − S11
2
S 22 − S11* ⋅ ∆ + S 21S12
>1
(2.84)
is obtained for the whole frequency band [40], where ∆ is given in equation (2.83). Here, only
a single parameter is used compared to the K – ∆ test. Therefore, the unconditional stability
factor µ is commonly used.
2.7.3 Gain Compression and 1-dB Compression Point
Transistors and diodes are nonlinear devices, and the nonlinearity can be used in practice
for functions like amplification, detection and frequency conversion [41] etc. However,
nonlinear device characteristics can also lead to undesired responses such as gain compression
49
Fundamentals to the Power Amplifier Design
and the generation of spurious frequency components. These effects may produce increased
losses, signal distortion and possible interference with other channels.
Assuming ui and uo are the input and the output voltage respectively, the output response
for a general nonlinear two-port network can be modeled as a Taylor series [42] shown below
uo = a0 + a1ui + a2ui2 + a3ui3 + ⋅⋅⋅ ,
(2.85)
where a0, a1, a2 ··· are the Taylor coefficients. If a sinusoidal signal ui = U0·cosω0t is applied to
the input of the nonlinear network, the output voltage is then
u0 = a0 + a1U 0 cos ω0t + a2U 02 cos 2 ω0t + a3U 03 cos3 ω0t
1
3
1
1
= (a0 + a2U 02 ) + (a1U 0 + a3U 03 ) cos ω0t + a2U 02 cos 2ω0t + a3U 03 cos 3ω0t + ⋅⋅⋅ . (2.86)
2
4
2
4
This result leads to the voltage gain at the fundamental frequency ω0 of a1 + 3 / 4 ⋅ a3 ⋅U 02 . In
most practical amplifiers a3 is typically negative, so that the gain of the amplifier tends to
decrease for large values of U0 or of Pin. This effect is called gain compression, or saturation,
which can be observed in the typical power transfer characteristic of a power amplifier as
shown in Fig. 2.39. Physically, the gain compression occurs due to the fact that the
instantaneous output voltage of an amplifier is limited by the power supply voltage used to
bias the power device. To quantify the linear operating range of the amplifier, 1 dB
compression point is defined as the power level for which the output power has decreased by
1 dB from the ideal characteristic. This point is normally denoted by P1dB and stated in terms
of either input power or output power.
Fig. 2.39. The conventional power transfer function and the 1 dB compression point.
2.7.4 Intermodulation Distortion
If a single-tone signal is applied to the input of the power amplifier, harmonics can occur
leading to a signal distortion if those components are in the passband of the amplifier. But
usually, these harmonics lie outside the passband of the amplifier, and so do not interfere with
the desired signal at the frequency of interest.
50
Fundamentals to the Power Amplifier Design
It is much more critical to consider a two-tone input voltage. Even in early radio systems,
the interfering effects of an active neighboring channel in mildly non-linear communications
systems were well known. In those simpler modulation schemes, the use of two sinusoidal
signals to represent two active channels was considered adequate. For instance, if the input
voltage is ui = U 0 (cos ω1t + cos ω2t ) , consisting of two closely spaced frequencies ω1 and ω2,
from equation (2.85), the output voltage u0 can be obtained as follows:
u0 = a0 + a1U 02
9
+ a1U 0 (cos ω1t + cos ω2t ) + a3U 03 (cos ω1t + cos ω2t )
4
1
2
+ a2U 0 (cos 2ω1t + cos 2ω2t ) + a2U 02 [ cos(ω1 − ω2 )t + cos(ω1 + ω2 )t ]
2
1
3
+ a3U 03 (cos3ω1t + cos 3ω2t ) + a3U 03 [ cos(2ω1 − ω2 ) + cos(2ω2 − ω1 ) + cos(2ω1 + ω2 ) + cos(2ω2 + ω1 )]
4
4
(2.87)
+ ⋅⋅⋅
It can be seen that the output spectrum consists of harmonics in form of mω1 ± nω2, where m
and n are integers. These combinations of the two input frequencies are called
intermodulation products, and the order of a given product is defined as |m| + |n|. The output
spectrum is shown in Fig. 2.40, assuming ω1 < ω2. Obviously, if ω1, ω2 are close, all the
second-order products will be far from ω1 or ω2, and can easily be filtered from the
fundamental signal. The critical terms come from the third-order products of equation (2.87).
They are the cubic terms of 3ω1, 3ω2, 2ω1 + ω2, 2ω2 + ω1, 2ω1 - ω2 and 2ω2 - ω1, where the
last two difference terms are located close to the two fundamental signals of ω1 and ω2, so that
they can not easily be filtered by the passband filter at the output of the power amplifier. Such
intermodulation products will generate distortion of the output signal. Therefore, the thirdorder intermodulation distortion (IMD3) is a very important specification of a power amplifier
design, which should be as low as possible. Usually, the power difference between the signals
at the frequencies 2ω1 - ω2 and ω1 is called IMD3 lower, while that between the signals at the
frequencies 2ω2 - ω1 and ω2 is called IMD3 upper.
Fig. 2.40. The output spectrum of second and third-order two-tone intermodulation products.
Naturally, the fifth-order products of 3ω1 - 2ω2 and 3ω2 - 2ω1, which also exist in the output
signal but are not shown in equation (2.87) and Fig. 2.41, are also located near to the
fundamental signals. However, they have generally much lower magnitude.
51
Fundamentals to the Power Amplifier Design
2.7.5 Intercept Point
According to equation (2.87), the voltage associated with the third-order products U 03 is
increased as the magnitude of the input voltage U 0 rises. Since the power is proportional to
the square of the voltage, the output power of third-order products must increase as the cube
of the input power. So for small input powers the third-order intermodulation products must
be very small, but will increase quickly as input power increases.
Fig. 2.41 presents this effect graphically by plotting the output power for the first- and
third-order products versus input power on logarithmic scales. The output power of the first
order product has a slope of unity, whereas the line describing the response of the third-order
products has a slope of 3. Both the first- and third-order responses will exhibit compression at
high input powers. The extension of their idealized responses which are shown with dotted
line in Fig. 2.41 will intersect, typically at a point above the 1 dB compression point. This
point is named the third-order intercept point, denoted by IP3, especially by iIP3 referred to
the input power and by oIP3 referred to the output power. In practice, many circuit
components follow the approximate rule that oIP3 is 12 to 15 dB higher than P1dB,out [42].
Fig. 2.41. The power transfer function and the third-order intercept point.
2.7.6 ACPR
As introduced in section 2.7.4, intermodulation distortion describes the interfering effects
of an active neighboring channel for the simpler modulation schemes, where two sinusoidal
signals represent two active channels. As the modulation becomes more complex, it becomes
less obvious that the sinusoidal representation will adequately simulate the problem of
interference from the neighbor channel. For many of the current and future transmission
standards, e.g. IS-95 code division multiple access (CDMA), wideband code division multiple
access (WCDMA) etc., ACPR becomes the most important test parameter for characterizing
the distortion of subsystems and the possibility that a given system may cause interference
with a neighboring radio. ACPR is the logical extension of the distortion measurement where
the two sinusoidal signals used in the IMD measurement are replaced by a given modulated
signal, which has a given bandwidth of ∆f. The bandwidth and the location are functions of
the standards being employed.
52
Fundamentals to the Power Amplifier Design
Usually, ACPR is defined as the ratio of the average power in the adjacent frequency
channel to the average power in the transmitted frequency channel. Fig. 2.42 provides the
graphic presentation of ACPR, where the output power is demonstrated in dependence of the
frequency f. In this figure, fc indicates the center frequency. Similar to IMD, we define the
ratio of the power in the left bandwidth to the power in the bandwidth of the main signal as
ACPR lower and the ratio of the right side as ACPR upper. ACPR measurements on the same
transmitter can provide different results depending on the statistics of the transmitted signal.
Different peak-to-average ratio (PAR) values of the input signal have a different impact on
the non-linear components of the transmitter, e.g. on the power amplifier, and therefore a
different impact on the ACPR as well. Higher PAR cause more interference in the adjacent
channel, and hence lower ACPR. Sometimes, ACPR is also named the adjacent channel
leakage ratio (ACLR).
Fig. 2.42. The output spectrum and ACPR
2.7.7 Power Added Efficiency
High efficiency is an important power amplifier characteristic which allows for smaller
power sources and reduced cooling requirements. The original efficiency is defined as output
efficiency which can be calculated as
η=
RF output power
.
DC power
(2.88)
This definition is also called drain efficiency, if FET transistors are used as power devices.
The other definition of the efficiency is the power added efficiency (PAE), which is in
practice mostly used and described as follows
PAE =
RF output power − RF input power Pout − Pin
=
,
DC power
Pdc
(2.89)
where Pout is the RF output power and Pin is the RF input power. This definition includes the
consideration of the RF driving power, which can be quite substantial in an RF power
amplifier. In general, if the RF power gain is less than 10 dB, the drive power requirements
will start to take a serious bite of the PAE of the power amplifier.
53
Fundamentals to the Power Amplifier Design
54
Design of the CMOS Driver and Power Amplifiers
3. Design of the CMOS Driver and Power Amplifiers
Using standard deep-submicron CMOS technology, the driving amplifiers and the power
amplifiers adopted in cellular phones are designed. The design processes are described in this
chapter. The simplified transceiver system applied in a cellular phone is shown in Fig. 3.1. To
ensure that the transmitter has sufficiently high output power, a power amplifier (PA) is
applied in the end-stage of the transmitter. Furthermore, in order to provide sufficiently high
power gain, several driving stages are necessary. On the other hand, a mobile transmitter
requires a large dynamic gain control range; hence programmable-gain amplifiers (PGA) or
variable-gain amplifiers (VGA) must be adopted. If a PGA or VGA is also designed at the
same operating frequency as that of the power amplifier, it can simultaneously be used as
driver or predriver of the power amplifier.
Fig. 3.1. Simplified transceiver system in a cellular phone.
Today, CMOS is the technology of choice for a higher integration level and lower cost
because it is capable of implementing a significant amount of digital signal processing and
because the vast majority of today’s integrated circuits are implemented in this technology.
However, it also shows drawbacks for the design of a logarithmic PGA due to its square-law
transfer characteristic in the saturation region and the design of a power amplifier with large
output power due to the low breakdown voltage. Therefore, novel circuit concepts not only
for PGAs but also for the PAs are introduced in this chapter to overcome these problems.
The design of a radio frequency logarithmic PGA using a 0.12-µm CMOS technology is
first described in section 3.1. In section 3.2, a class A HiVP power amplifier for GSM
mobile communication system is presented, which is also developed in a 0.12-µm CMOS
process.
3.1 A Logarithmic Programmable-Gain Amplifier
Using a 0.12-µm CMOS technology, two radio frequency PGAs are designed in this
section, one is designed at 1 GHz and the other is designed at 2 GHz. They should control the
overall gain of the transmitter and simultaneously be adopted as a driving stage of the power
amplifier. Following specifications should be fulfilled by these two PGAs:
-
operating frequency: 1 GHz or 2 GHz
dynamic gain control range: > 50 dB
maximum gain: at least 8 dB
logarithmic gain variation
gain control step: 3 dB
maximum output power: 10 dBm
adaptive DC power consumption
55
Design of the CMOS Driver and Power Amplifiers
The two logarithmic PGAs should be realized in a standard 0.12-µm CMOS technology.
However, in case that a MOS transistor works in the saturation region, a logarithmic gain
variation implemented in a CMOS technology can only be fulfilled, if an approximate rational
function instead of an exponential function is used [43]. However, the maximum gain control
range obtained in this manner is limited within 30 dB. For an even larger gain control range,
parasitic bipolar transistors can be used for accurate exponential transformation [44]. It has
also been attempted to develop a logarithmic PGA for a larger dynamic gain variation simply
in a CMOS technology, several cascaded PGA stages have been used [45]. However, such a
design concept has an essential drawback. Usually, the gain varies not only in the positive
range but also in the negative range. In case that a larger negative gain should be realised,
more series amplifier stages should be applied, resulting in even larger power consumption. A
more reasonable behaviour should be an adaptive power consumption, which means the DC
power consumption should be reduced when the gain becomes smaller, or in other word,
when the attenuation becomes larger. In this work, a novel parallel structure to design a
logarithmic PGA is presented.
In subsection 3.1.1, an overview of the conventional PGA and VGA design is introduced.
The new circuit configuration to design a logarithmic PGA is then described in subsection
3.1.2. Finally, the simulation results, the layout of the circuits as well as the experimental
results of the proposed PGA circuit are presented. A conclusion is given in subsection 3.1.4.
3.1.1 Introduction of the PGA and VGA
A gain variation block has become an indispensable function block for many mobile
communication systems in order to maximize the overall system dynamic range. In the
CDMA systems, for instance, the mobile transmitter is required to provide at least 80 dB
dynamic gain control range [46] - [48]. Up to now, a large gain control range is realized in
two stages, namely, in an intermediate frequency (IF) stage which is typically at 70 MHz, and
in a radio frequency (RF) stage designed at the operating frequency of the transceiver.
Mostly, a PGA has discrete gain steps as shown in Fig. 3.2 (a), since the gain of a PGA is
controlled by a discrete digital signal. Oppositely, the gain of a VGA changes continuously
with the variation of the biasing voltage or current as shown in fig. 3.2 (b). A discrete gain
variation causing indeed phase discontinuity; however, the amount of it is well below what is
currently specified in the 3GPP UMTS specifications. Therefore, it is not critical to use a
PGA designed at 2 GHz in the UMTS transmitter applications.
Fig. 3.2. Different operational functions of the PGA and VGA.
(a) discrete gain variation; (b) continuous gain variation
There are four different methods reported so far to realize the gain variation. They are
shortly introduced below.
56
Design of the CMOS Driver and Power Amplifiers
(1) Current steering technique
The gain variation can be realized by using the current steering technique [49], [50]. Fig.
3.3 shows the schematic of a conventional VGA using such technique.
Fig. 3.3. The schematic of the VGA using current steering technique.
The amplifier is composed of an input source-coupled pair (T3, T6) and the diode connected
loads (T4, T5). I1 is the current flowing through the input pair, and I2 is the current flowing
through diode-connected loads. In case that T3 – T6 have the same dimension, the differential
gain can be approximately expressed as [50]
G≈
1
I1
⋅
I2
1
rds − p µ n Cox (Wn / Ln ) ⋅ I 2
,
(3.1)
+1
where rds-p is the drain-source resistance of PMOS transistors (T7, T8). In equation (3.1), µ n is
the carrier mobility; Cox is the gate oxide capacitance per unit area; Wn and Ln are the channel
width and the channel length of T3 – T6, respectively. Obviously, the gain can be controlled
by the current ratio I1 / I 2 .
(2) Variable transconductance topology
As shown in equation (2.28), the gain of a single-ended FET amplifier is proportional to the
load R and the transconductance of the MOS transistor gm. Therefore, it is an effective method
to vary the gain by changing the transconductance of the transistors [51], [52]. There are
several different methods to control gm. An example is shown in Fig. 3.4. Two transistors T1
and T2 are connected in series. They share the same bias current, the total power consumption
of the current-reused amplifier is minimised. To achieve a higher gain, both T1 and T2 are in
common-source configuration. The gate width and the bias current of the transistors are
chosen to maximise gm while maintaining low power consumption.
The gain-controlled mechanism is achieved by adjusting the bias voltage UC at the gate of
T2. As the gate voltage of T2 decreases, the drain voltage of T1 is suppressed, moving the
transistor bias out of its high gain region.
57
Design of the CMOS Driver and Power Amplifiers
Fig. 3.4. The schematic of the VGA using variable transconductance topology.
(3) Attenuator topology
A gain variation can be obtained using additional attenuator at the input of the amplifier
stages [53], [54]. The condition is that the amplifier stages should first be developed to
possess the maximum gain. The Π or T shape attenuation circuits [53] can be applied, which
are depicted in Fig. 3.5 (a) and (b). In these circuits, low field resistance of the zero-biased
FETs are used as variable resistors, whose values are controlled by the gate voltages. The
equivalent circuits of such attenuators are presented in Fig. 3.5(c) and (d).
Fig. 3.5. Basic circuit topologies of variable attenuators (a), (b)
and their equivalent circuits (c), (d).
58
Design of the CMOS Driver and Power Amplifiers
(4) Feed back topology
A gain variation can also be achieved by a feedback topology [55], [56]. For instance, a
VGA with resistor-network feedback is shown in Fig. 3.6.
Fig. 3.6. A VGA with resistor-network feedback.
Obviously, the values of the resistors R1, R2, Rf1 and Rf2 are adjustable in this amplifier
circuit. The differential inverting configuration indicates that its voltage gain can be varied by
changing the ratios of Rf 1 / R1 and Rf 2 / R2. Thus signal amplification and attenuation can
easily be realized. High linearity can be achieved if the loop gain is very large and the resistor
network is linear [55].
Another possible feedback configuration is shown in Fig. 3.7. Clearly, Rd is the load of the
small signal amplifier circuit. A variable resistor Rs is used at the source of the MOSFET,
which indicates a feedback configuration. The gain variation can be achieved by varying this
source resistance.
Fig. 3.7. The source feedback transistor stage.
The small signal gain of the circuit shown above can be given as follows [56]
G=−
g m Rd
,
1 + g ds ( Rs + Rd ) + g m Rs
(3.2)
59
Design of the CMOS Driver and Power Amplifiers
where gds is the drain-source-admittance and gm is the transconductance of the transistor. In
case that gds is very small, equation (3.2) can be approximated as:
G=−
g m Rd
g R
R
≈− m d =− d .
1 + g m Rs
g m Rs
Rs
(3.3)
Therefore, by changing the source resistance, the gain or attenuation of this transistor stage
can be controlled.
3.1.2 Design Concept of the Radio Frequency PGA
In order to achieve a large logarithmic gain control range realized in a CMOS technology, a
new circuit configuration for the PGA design [57] is introduced in this work. In principal it
belongs to the variable transconductance topology. Several amplifier cells containing
transistor devices with different gate widths are connected in parallel. The variation of the
transconductance is therefore realized by the turning on or turning off the different amplifier
cells.
As an example, the block diagram of a PGA circuit with four amplifier cells is illustrated in
Fig. 3.8. These parallel connected amplifier cells have the common load and they are digitally
controlled by a 2 to 4 demultiplexer. B1 and B2 are the two inputs of the demultiplexer. At any
given time, only one output of the demultiplexer has a high voltage level; hence only one
amplifier cell of the four is turned on. In Fig. 3.8, the voltages UDD = 2.5 V and Udd = 1.5 V
are the power supplies used for the amplifier cells and for the demultiplexer, respectively. In
this work, 18 amplifier cells must be connected in parallel, in order to realize the
specifications of a gain control range larger than 50 dB and a gain control step of 3 dB. These
amplifier cells must be controlled by a 5 to 18 demultiplexer. The output digital control words
(DCW) of the demultiplexer are defined as 1 to 18 implying the increasing gain.
Fig. 3.8. The block diagram of the proposed PGA.
60
Design of the CMOS Driver and Power Amplifiers
Fig. 3.9 presents the schematic of a single amplifier cell. To obtain the higher immunity to
noise and crosstalk coming from substrate and power supply, differential configuration is
proposed for all the amplifier cells. Cascode structure is used in the differential pairs to
minimise the Miller effect. Guard rings are employed around the devices to reduce the
substrate noise. The transistors T1 – T4 have all the same dimensions and the gate width of
them is determined according to the gain expected from each cell. The transistor TC is used as
the control-element. It works as the current source of the differential pair and the gate of it is
connected to one of the eighteen outputs of the 5 to 18 demultiplexer. Therefore, this cell is
activated as soon as the connected demultiplexer output has a high voltage level. Moreover,
single-ended input and output are expected from this PGA, therefore, the input I2 of each
amplifier cell is connected with a 50 Ohm (the reference impedance) resistor through the
input RF coupling C2, whereas the output O2 of each amplifier cell is also connected with a
50 Ohm resistor through the output RF coupling C4 as shown in Fig. 3.8.
Fig. 3.9. The schematic of an amplifier cell.
The common load of the amplifier cells are attempted in two ways, they are the active load
comprising a current mirror and the passive load comprising an LC tank as introduced in Fig.
2.37. The active load is in many cases preferred, since it requires less chip area and it needs
no inductor which causes coupling with the other inductors used in the other circuits of the
system. However, the current mirror consumes quite large voltage headroom. For instance, a
pair of p-channel transistors having a gate width of 200 µm is first used as the load of the
PGA circuit; simulation shows that a DC voltage of 0.6 V is consumed on it. Therefore, in
case that a higher output power is demanded, passive load with LC tank is mostly preferred.
In the given components library, there is a fixed inductance of 4.7 nH. Using equation (2.67),
two different capacitances can be determined for the two different resonance frequencies.
They are 5.4 pF for the frequency of 1 GHz and 1.35 pF for the frequency of 2 GHz,
respectively. Simulations show that such a LC tank consumes voltage headroom of only
0.02 V.
The transistors of amplifier cell 1 are first dimensioned for the largest gain of 9 dB. Gate
widths of 250 µm and of 180 µm are chosen for the transistors T1 – T4 and for TC in cell 1,
respectively. Since variable transconductance topology is proposed in this PGA and gm is
nearly proportional to the gate width of the transistor known from equation (2.18), transistors
with gradually reduced gate width are selected for the other amplifier cells, according to the 3
dB gain steps.
61
Design of the CMOS Driver and Power Amplifiers
Since the bias current flowing through the transistor devices is also proportional to the gate
width, the adaptive DC power consumption can automatically be fulfilled with this
configuration of parallel connected amplifier cells. On the other hand, more parallel amplifier
cells require indeed more chip area; however, since the most amplifier cells are designed for
the attenuation, devices with only very small dimensions are used in these cells. Especially in
case that the LC tank is used and also integrated on the chip, compared to the chip area
occupied by the inductor and the capacitor applied in the LC tank, the chip area invested for
the most attenuation cells is almost negligible.
Usually, a PGA is applied in a feedback loop to form an automatic-gain control (AGC).
The PGA is implemented in an analog radio frequency transceiver IC, while the rest of the
AGC is realized in a digital base-band modem (modulator/demodulator) IC. In this design, the
input bits of the demultiplexer are used as the digital interface to the outside. The design logic
and the schematic of the 5 to 18 demultiplexer are presented in the appendix.
3.1.3 Simulation and Measurement Results
Simulation for the PGA operating at 1 GHz is first implemented with the simulation tool
Cadence. The largest gain should be obtained at the maximum digital control word, i.e. at 18
in decimal form and 10010 in binary form. The gate width of the active devices used in the
different amplifier cells are determined step by step, according to the maximum gain and the 3
dB gain steps. The forward transmission coefficient S21 is first simulated, which is used here
to indicate the gain. The simulation results are presented in Fig. 3.10.
Obviously, a maximum gain of 9 dB is obtained at the first gain step at about 1 GHz. The
following gain steps are also achievable with the reduced digital control words. The dB-linear
gain variation is realized in this manner. The 3-dB bandwidth of this circuit is about 240 MHz.
Since the bandwidth is mainly determined by the common LC-tank, all the amplifier cells
have a similar bandwidth.
10
10
00
|S
S21
, dB
21| [dB]
-10
-10
-20
-20
-30
-30
-40
-40
-50
-50
-60
-60
0.6
0.6
0.8
0.8
1.0
1.2
1.0
1.2
frequency,
f [GHz]GHz
1.4
1.4
Fig. 3.10. Simulation results of the magnitude of S21.
The power transfer function simulated at the maximum gain (9 dB) is shown in Fig. 3.11.
This simulation is implemented at 1 GHz. It can be seen that the maximum output power
reaches approximately 10 dBm, while the 1-dB compression point is located at about 7 dBm.
62
Design of the CMOS Driver and Power Amplifiers
Fig. 3.11. The simulated output power versus the input power.
The two PGAs separately designed at 1 GHz and 2 GHz actually have the same circuit
concept. They differ from each other only by the different capacitance used in the load.
Therefore, similar results have also been achieved in the simulations for the PGA operating at
2 GHz, except a much larger bandwidth obtained for it due to the lower quality factor, since
the capacitance in its LC tank is four times smaller than that used in the PGA for 1 GHz.
The layout of the PGA circuit operating at 1 GHz is shown in Fig. 3.12. The active area
occupies 0.5 x 0.4 mm2. The pads for the supply voltages UDD and Udd are also indicated in
the figure. The 5 to 18 demultiplexer is also integrated on the chip. Clearly, it only uses a very
small chip area. The pads B1 – B5 indicate the five inputs of this demultiplexer. Moreover, the
PGA designed at 2 GHz uses a smaller capacitor in its load, while all its other parts are
identical to those in the PGA designed at 1 GHz.
Udd
B5
UDD
inductor
capacitor
output
input
amplifier
cells
demultiplexer
B4
B3
B2
B1
Fig. 3.12. The layout of the PGA operating at 1 GHz.
63
Design of the CMOS Driver and Power Amplifiers
The PGA test chips are fabricated in the Infineon standard 0.12-µm CMOS technology. A
micrograph of the chip for the PGA circuit operating at 1 GHz is shown in Fig. 3.13. Due to
the passivation layer on the chip surface, only the inductor and the capacitor are observable.
The different pads are also indicated in the micrograph.
Udd
UDD
B5
I2
O2
I1
O1
B4
B2
B3
B1
Fig. 3.13. The micrograph of the PGA chip operating at 1 GHz.
|S21| [dB]
On-wafer measurements are implemented. The pads of B1 – B5, as well as the pads for the
supply voltages UDD and Udd are contacted using two GPPGPPG microprobes of the company
CASCADE MICROTECH, where G symbolizes the ground and P symbolizes the power. The
DC power and signals are fed through the P pads into the circuit. The other two microprobes
of GSSG are used to contact the input and the output pads, where S symbolizes the signals.
Not only RF signals but also the DC biasing voltages are provided through the signal pads.
DCW
Fig. 3.14. The measured gain versus digital control words at the frequency of 1 GHz.
64
Design of the CMOS Driver and Power Amplifiers
∆G [dB]
Using HP 8510B Network Analyzer, the forward transmission coefficient S21 indicating the
voltage gain is measured according to different digital control words (DCW). Fig. 3.14 shows
the measurement results obtained at 1 GHz. The gain can approximately be varied from
- 43 dB up to 8 dB with a control step of about 3 dB. A gain control range of 51 dB is
achieved. This result implies that the technique of parallel amplifier cells is effective for a dBlinear PGA design.
The measured gain offset ∆G versus digital control words is shown in Fig. 3.15.
Theoretically, an even larger dynamic range can be realized. However, the attenuation range
can sometimes be limited at a high frequency due to the direct coupling between the input und
the output of the circuit through the silicon substrate.
DCW
Fig. 3.15. The measured gain offset versus DCW at the frequency of 1 GHz.
Since all the amplifier cells have the same load, the PGA has a nearly constant bandwidth
while the gain changes. The frequency response of the PGA is shown in Fig. 3.16, which is
measured with the gain of - 4 dB and -16 dB at 1 GHz. A 3-dB bandwidth of about 200 MHz
is obtained. It is a little bit smaller than the simulated value mentioned above.
0
|S21| ,[dB]
gain
dB
-5
S21 = - 4 dB
S21 = -16 dB
-10
-15
-20
-25
-30
0.6
0.7
0.8
0.9 1.0 1.1
f [GHz]GHz
frequency,
1.2
1.3
1.4
Fig. 3.16. Measured frequency response of the PGA
with the gain of - 4 dB and -16 dB at the frequency of 1 GHz.
During the S-parameter measurements, HP 4155B Semiconductor Parameter Analyzer is
used for the DC current measurement, which simultaneously provides the DC supply voltage.
65
Design of the CMOS Driver and Power Amplifiers
The measured DC current versus the DCW is presented in Fig. 3.17. Obviously, it can be
reduced with decreased voltage gain. Adaptive power consumption is obtained.
125
112.5
100
PDC [mW]
87.5
75
62.5
50
37.5
25
7.5
0
2
4
6
8
10 12
DCW
14
16
18
20
Fig. 3.17. The DC current consumption versus the DCW at the frequency of 1 GHz.
Fig. 3.18 shows the input-referred output power and the oIP3 measured at 1 GHz and with
the gain of 8 dB. The maximum output power reaches the level higher than 9 dBm, while the
1-dB compression point is located at 8 dBm. The oIP3 is as high as 22 dBm.
IP3
Pout [dBm]
P1dB
Pin [dBm]
Fig. 3.18. Measured output power and IP3
versus the input power at the frequency of 1 GHz.
66
Design of the CMOS Driver and Power Amplifiers
IMD [dBc]
The measured results of the third-order and fifth-order intermodulation distortion (IMD3
and IMD5) are shown in Fig. 3.19, as a function of the PGA output power. IMD3 better than
- 40 dBc is accomplished when the PGA output power is lower than about 3 dBm. However,
it can be degraded if the output power increases. Compared with an IF PGA, this is a typical
critical feature of an RF PGA. Therefore, an RF PGA or VGA should usually be linearized
using a predistorter [58].
Pout [dBm]
Fig. 3.19. Measured IMD at the frequency of 1 GHz.
It can be seen; almost all the requirements of the PGA circuit are fulfilled. Similar
measurement results are also obtained for the other PGA operating at 2 GHz. The single
significant difference is that the PGA working at higher frequency has a much larger
bandwidth of about 700 MHz.
3.1.4 Conclusion
In this section, an overview of the PGA and VGA design concepts are first given. A novel
configuration using parallel amplifier cells is further introduced for the design of a PGA with
large logarithmic gain variation. Using this new circuit concept, radio frequency PGAs are
designed and fabricated in this work. A standard 0.12-µm CMOS technology is used. The
realized PGA has a gain control range of 51 dB and a gain control step of 3 dB. This is the
largest linear gain control range reported so far for a radio frequency PGA in a CMOS
technology. The maximum output power reaches 9 dBm, while the 1-dB compression point is
located at 8 dBm. A high linearity denoted by the oIP3 of 22 dBm at the maximum gain is
also achieved in the measurement. Adaptive DC power consumption is also achieved. The
configuration of parallel amplifier cells is proven to be a feasible design concept for
logarithmic programmable gain amplifiers. Certainly, it can also be applied in many other
device technologies.
67
Design of the CMOS Driver and Power Amplifiers
3.2 A High Voltage/High Power Class A Power Amplifier
The power amplifier is an indispensable component in the cellular phone, which is
simultaneously a design bottleneck in the deep-submicron CMOS process. Usually, large
output voltage is required to achieve large output power. However, on the other hand, the
maximum allowable voltage of a MOSFET in a deep-submicron CMOS process is well
limited. For instance, the supply voltage of a conventional 0.12-µm CMOS transistor is only
1.5 V and the breakdown voltage is close to 2.5 V. The gate-drain voltage of a MOS transistor
is especially critical due to the field distribution along the channel and the extreme thin gate
oxide. This restriction limits the maximum allowable output power of a single conventional
transistor. Recent years have seen worldwide efforts to develop the CMOS power amplifiers.
Almost all of them have been implemented in 0.35-µm [59] [60] or 0.18-µm [61] CMOS
processes. In this work, however, a class A power amplifier using 0.12-µm CMOS technology
is attempted.
To solve the problem of low breakdown voltage, the HiVP structure is applied in this
design. Using a 0.12-µm standard CMOS technology, a microwave class A power amplifier is
developed in this work. The original expected specification of it is the RF output power of 2
W (33 dBm), obtained with a DC power supply of 3.6 V.
In subsection 3.2.1, the design concept of the CMOS power amplifier is first demonstrated.
The simulation and experimental results of the proposed power amplifier circuit are presented
in subsection 3.2.2, where, according to the measurement results and the results of resimulation, the difficulty to design a CMOS power amplifier, especially with a low power
supply, is analysed and explicated. Suggestions to achieve even larger RF output power are
described. Moreover, to enhance the efficiency of the power amplifier circuit on lower power
levels, the technique of digitally controlled gate width is introduced in subsection 3.2.3, which
is followed by a conclusion given in subsection 3.2.4.
3.2.1 Design and Simulation of a CMOS HiVP Power Amplifier
As mentioned above, an integrated class A power amplifier using 0.12-µm CMOS
technology is proposed in this work. The simplified schematic of the power amplifier circuit
is shown in Fig. 3.20, which is mainly composed of the HiVP structure introduced in
subsection 2.3.2 and the input and the output matching networks MI and MO. The supply
voltage Udd shown in the schematic is 3.6 V.
Figure 3.20. Simplified schematic of the CMOS HiVP power amplifier.
68
Design of the CMOS Driver and Power Amplifiers
As mentioned above, the transistors should ideally have identical operating points since the
same current flows through them. Therefore, the numbers of the transistors used in the HiVP
structure must be limited since the supply voltage is limited. In this work, three NMOS
transistors are connected in series. The DC-simulation result of the HiVP structure is depicted
in Fig. 3.21 compared with that of a conventional single transistor, which has the same gate
width of 4.5 mm as those transistors used in the HiVP structure.
Id [A]
Ugs
Uds [ V ]
Output characteristic of a single transistor
Output characteristic of a HiVP structure
Fig. 3.21. DC simulation results of a single MOSFET and of a HiVP structure.
Obviously, they have the similar output characteristics, which indicate that a HiVP structure
can be considered and used as a single transistor device. The gate of the bottom transistor can
be regarded as the input and the drain of the top transistor as the output of the HiVP structure.
The difference between a HiVP configuration and a single conventional device is that the
former can carry a much larger DC voltage.
A shortcoming of the HiVP configuration can be observed in Fig. 3.21. Compared to a
single transistor, the lines of the output characteristic of the HiVP structure are shifted to the
right. Since the supply voltage Udd is divided by all the transistors in the HiVP structure, at a
small value of Udd the transistors are not turned on. According to the load-line matching
theory introduced in section 2.1, the maximum range for the voltage swing is required for the
maximum achievable output power. In case that the lines of output characteristic are shifted to
the right, this condition is definitely damaged. The more transistors are used in the HiVP
structure, the more critical is this problem. This is another important reason to limit the
number of the active devices used in the HiVP structure as far as possible.
Furthermore, the input and the output matching networks, MI and MO, are used in order to
obtain a complex conjugate matching at the input and a power matching at the output of the
circuit. To increase the matching flexibility and avoid excessive power loss of on-chip
inductors, the input and output matching networks are designed to be off chip. The output
matching network is especially important. Due to the low DC supply voltage, an impedance
transformation at the output, namely from the 50 Ohm load to a much smaller resistance, is
necessary. In case that the required output power is 2 W, the maximum value of the
transformed impedance Z max can be calculated as follows.
69
Design of the CMOS Driver and Power Amplifiers
2
Z max
( 3.6 V ) = 3.24 Ω
U dd2
=
=
2 Pmax
2⋅2 W
(3.4)
With the 3.24 Ohm load, the peak RF current will not exceed Udd / Rmax ≈ 1 A, and the DC
drain current bias must be set approximately to this value. Since the peak drain current is the
sum of the bias and peak RF current, the transistor must be designed to supply about 2 A with
minimum voltage drop. To fulfil this condition, a gate width of 3.4 mm is first selected in the
simulation. In this case, in order to obtain the output power of 2 W, the peak value of the
drain voltage of the top device must be higher than 11 V [24], which requires at least four
transistors to be used in the HiVP structure. In this work, however, it is attempted to use fewer
transistor to minimize the problems with more transistors as mentioned above. In this case,
however, the ability of the HiVP structure to sustain high voltage is degraded; hence the drain
voltage of the top device (e.g. T3 in Fig. 2.20) must be reduced. On the other hand, to
guarantee the expected output power, the current flowing through the HiVP structure must
further be increased. This means that the large output power should be obtained more by an
even larger current rather than by a higher voltage. Two modifications should be implemented
here. The first one is going on to reduce the optimum output impedance (even less than
3.24 Ohm). The ratio of the impedance transformation from the load resistance of 50 Ohm to
the optimum output impedance is enhanced. Therefore, the ratio of the voltage transformation
through the output matching network is also increased. In this case, the voltage amplitude of
14 V required on the load resistance can be accomplished by a lower drain voltage of T3. The
other modification is going on to increase the gate width of the transistors, in order to allow a
larger current to flow through the HiVP structure. Finally, transistors having a gate width of
4.5 mm are selected in this work.
Ui
Ugj
Udj
Uo
Fig. 3.22. Simulated voltage waveforms of the HiVP structure
at the frequency of 900 MHz.
A class A power amplifier is designed. The optimized gate voltage of Ugg = 0.8 V is
selected by the simulation. A large signal simulation is implemented at the frequency of 900
MHz, which is approximately the center frequency of the GSM uplink band in Europe. A
70
Design of the CMOS Driver and Power Amplifiers
sinusoidal signal having amplitude of 0.5 V is fed into the input of the HiVP structure, namely
into the gate of the bottom device T1. The simulated waveforms of the output voltage Uo as
well as the gate voltages Ugj and the drain voltages Udj of all the three transistors are presented
in the time domain as illustrated in Fig. 3.22, where j is the integer between 1 and 3.
The RF output voltage on the load resistance of 50 Ω has positive amplitude of 14 V and
negative amplitude of -13 V, a slight distortion is generated. The accomplished output power
is approximately 32 dBm, which is also shown by the power-transfer (Pout-Pin) simulation.
The voltage at the drain of the top device Ud3 is equal to the supply voltage Udd added by an
RF voltage swinging around it. The maximum value of the voltage obtained of at the drain of
the top device is 7.8 V. On the other hand, the lowest value of the Ug1 is 0.3 V. Obviously,
Ud3 can be equally divided by all the three transistors used in the HiVP structure. The gatedrain voltages of all the transistors remain smaller than 2.5 V. All the transistors operate in
safe operating area. The equal voltage division can be achieved by the optimization of the
resistances used in the voltage divider as described in [24].
As mentioned above, transistors with gate width of 4.5 mm are employed in the proposed
HiVP power amplifier. Therefore, compact layout for such large transistors is required. On
the other hand, the transistors must be able to sustain a large current. The 0.12-µm CMOS
technology used in this work has six metal layers. The materials and the thickness of these
metal layers are provided in Fig. 3.23. Obviously, the top metal layer, namely the metal 6 has
the largest thickness, compared to the other five metal layers. Therefore, it has the capability
to sustain a much larger current. To obtain a compact layout for the large transistors and
hence for the entire HiVP structure, all these metal layers must be used.
Fig. 3.23. The description of the metal layers of the Infineon 0.12-µm CMOS technology.
In Fig. 3.24, the layout concept for a transistor having a gate width of 4.5 mm is illustrated.
To realize such a large transistor, 496 small transistor cells are connected in parallel, each of
which has a gate width of 9.07 µm. They are equally distributed in a 16 x 31 matrix. In this
manner, significant voltage attenuation on a long poly-Si line is avoided. Both the drain and
the source are constructed using metal 3 – metal 6. In order to mitigate the parasitic
capacitance rising from the overlap of the different metal layers used for the drain and the
source, lots of contacts are applied to connect the metal layers.
WD,S in Fig. 3.24 indicates the maximum width of the metal lines, which connect the drain
and source of every transistor. They are determined according to the magnitude of the current
71
Design of the CMOS Driver and Power Amplifiers
flowing through the transistor and the current-carrying-ability of metal 3 – metal 6. Observing
the layout given in Fig. 3.24, the drain is arranged at the top of each transistor and the source
is located at the bottom. The current flows downward through the transistor and is allocated
by all the transistor cells. The largest drain current exists only on the top of each transistor and
can be decreased on the way. Oppositely, the source current is still relatively small on the top
of each transistor but it gathers itself top down. Therefore, the largest source current exists
only at the bottom of each transistor. As shown in Fig. 3.24, the maximum line width WD,S is
only used at the top of the transistor-layout, which is reduced top down. On the other side, the
line width for the source starts above with a very small value, increases however top down up
to WD,S at the bottom of the transistor-layout. Obviously, due to the arrangement of this
staggered form, the layout area can significantly be reduced compared to the conventional
design concept of the MOS transistors, in which the width of the metal lines used for the drain
and the source remains the same top and down.
Drain
WD,S
Gate
Source
Drain
Source
Fig. 3.24. The layout concept for NMOS transistors.
Additionally, a guard ring is used around each transistor to reduce the substrate noise.
Therefore, the lowest metal layer, namely metal 1 is reserved to connect the guard ring to the
ground. Furthermore, metal 2 is used to connect all the gates of the basic transistor cells.
Another emphasis of the layout design concerns the gate distribution. Assuming the input
signal comes from the left of the layout and runs to the right, there is a long distance between
the leftmost transistor cells and the rightmost transistor cells due to the large dimension of the
transistor layout. This results in a significant phase difference between the input signals of the
transistor cells on the left side and the input signals of the transistor cells on the right side.
Therefore, the amplified output signals of these transistor cells partly compensate each other;
a degradation of the output power is generated. In order to minimise the phase difference, the
so called H-structure is used, which is illustrated in Fig. 3.25. In this figure, a chip area is
assumed to be divided into 16 parts, which are arranged in a 4 x 4 square matrix. The small
circles in the figure indicate the inputs of every part. Apparently, the center input signal is
first fed to the middle of the chip area. It is then routed equally into all the directions. The
time delay from the center input to all the part-inputs is identical, so that no phase difference
exits between the input signals of all the 16 parts. The decisive factor of the using of Hstructure is that the entire chip area can be divided into an n x n square matrix. Since the
transistor cells used in Fig. 3.24 are distributed in a 16 x 31 matrix (not square matrix), the
phase difference between the input signals of the transistor cells can not totally be deleted.
72
Design of the CMOS Driver and Power Amplifiers
However, using the H-structure, the maximum route-difference of the input signals among all
the transistor cells is significantly reduced. The degradation of the output power due to the
phase difference is negligible.
Fig. 3.25. The H-structure.
In the HiVP structure, it is required to isolate the NMOS transistors from the substrate, so
that the bulk of every transistor can directly be connected to the source of the transistor as
shown in Fig. 2.20. In this manner, the bulk voltage can then swing with the source voltage
and the voltage difference between every two terminals of the transistors can be maintained
smaller than the breakdown voltage. The 0.12-µm CMOS technology used in this work is a
triple-well technology, where the NMOS transistors can easily be isolated from the substrate.
Fig. 3.26. The cross-section of the isolated NMOS transistors.
The cross-section of the isolated NMOS transistors is illustrated in Fig. 3.26. The NMOS
transistor is located in the p-well, which is separated by the NISO layer from the p-substrate
in the vertical direction and is embraced by the n-well layer in the horizontal sides. The p-well
has a determined width of 2 µm according to the design rules. In this manner, a NMOS
transistor is totally isolated from the substrate; hence the bulk of it can be connected with the
source terminal using metal layers. However, a p-n-junction is constructed due to the direct
contact of the n-well and the p-well, which causes additional power loss. To avoid this
secondary effect, the n-well layer must be connected to a higher positive voltage level than
73
Design of the CMOS Driver and Power Amplifiers
the p-well. Another possibility to avoid the power loss is to short the n-well and the p-well
directly, also using the metal layers as shown in Fig. 3.26. The NMOS transistors used in the
schematic must therefore be symbolized as presented in Fig. 3.27, where the transistor symbol
is complemented by the n-well. Additionally, a diode must be arranged at the border of the nwell. In this figure, the p-n-junction of the diode is shorted.
Fig. 3.27. The complete symbol of the isolated NMOS transistors.
The conclusive layout of the transistor with a gate width of 4.5 mm is demonstrated in
Fig. 3.28. This layout occupies a chip area of 250 µm x 645 µm.
Drain
250 µm
Gate
Source
645 µm
Fig. 3.28. The conclusive layout of the NMOS transistor with a gate width of 4.5 mm.
Finally, the layout of the HiVP structure using three active devices is presented in Fig. 3.29.
The different terminals and the active as well as the passive components are indicated. The
drain, source, as well as the input and the output of this configuration are also indicated in the
figure. Obviously, three large transistors are applied here, which are connected in series and
occupy most of the chip area. The voltage divider constructed by the resistors and the
capacitors used to determine the drain impedance of the different active devices are arranged
on the left of the chip. Metal-insulator-metal (MIM) capacitors are used in this design, which
perform high capacitance density, low current leakage and high breakdown. It can also be
seen, only the HiVP structure is integrated on this chip. As mentioned above, the input and
output matching networks will be realized on the printed circuit board (PCB) later. Bonding
74
Design of the CMOS Driver and Power Amplifiers
pads are therefore necessary at the terminals of the chip, which are used as connecting points
for the terminals of the HiVP and the conductor lines on the PCB.
Drain
Output
3rd Tr.
Capacitors
2nd Tr.
Input
1st Tr.
Source
Voltage divider
Fig. 3.29. The layout of the HiVP structure using the 0.12-µm CMOS technology.
Also due to the large current flowing through the active devices, numerous bonding wires are
required at the drain and source terminals of the HiVP structure, which require numerous pads
at these terminals. The total chip area is 975 µm x 970 µm.
3.2.2 Measurement Results
The micrograph of the chip with its bonding wires is shown in Fig. 3.30. In spite of the
passivation layer on the chip surface, the three transistors, the voltage divider and the
capacitors of the HiVP configuration can well be recognised, compared with the chip layout.
As mentioned above, the HiVP chip should be mounted on a PCB, where the input and the
output matching networks of the HiVP power amplifier are built. The layout the PCB is given
in Fig. 3.31. The passive components to be mounted are also indicated in the layout. The
inductor L1 and the capacitor C1 construct the input matching network, while L2, C2 construct
the output matching network. Several parallel decoupling capacitors Cb1 – Cbn distributed
between 1 pF and 100 nF are applied to couple RF signal of different frequencies to the
ground. A large inductor L3 is used as the RF choke at the drain of the HiVP device, and a
large capacitor C3 operates as the coupling capacitor at the output. All these passive
components are in the form of surface mount device (SMD) and will be soldered on the metal
75
Design of the CMOS Driver and Power Amplifiers
lines. The RF choke for the gate of the HiVP device and the coupling capacitor at the input of
the amplifier circuit are included by the Bias-Tee. The data of these passive components are
listed in Table 3.1.
Fig. 3.30. The micrograph of the HiVP chip.
Udd
Ugg
Fig. 3.31. The layout of the printed circuit board.
Table 3.1
The passive components mounted on the PCB
L1
3 nH
76
C1
4 pF
L2
2.2 nH
C2
13 pF
L3
100 nH
C3
47 pF
Design of the CMOS Driver and Power Amplifiers
Using the bias voltages Ugg = 0.8 V and Udd = 3.6 V, the output power, the power gain and
the power added efficiency are measured at 900 MHz. The measurement results are illustrated
in Fig. 3.32. It can be seen that the maximum output power reaches 29.5 dBm (0.9 W) at the
frequency of 900 MHz, while the 1-dB compression point is located at about 27 dBm. The
small-signal gain is about 11.5 dB, which is degraded with the increased power level. A
maximum power added efficiency of about 34.5 % is achieved in the high output power range.
40
Pout
gain
PAE
35
30
30
25
25
20
20
15
15
10
10
5
5
0
-5
0
5
10
Pin [dBm]
15
20
25
PAE [%]
Pout [dBm]; gain [dB]
35
40
0
Fig. 3.32. The measured output power, gain and PAE at the frequency of 900 MHz.
Comparisons are done between the power amplifier realized in this work and the other
power amplifiers achieved in recent years. Due to the most critical problem of low breakdown
voltage, the CMOS power amplifiers realized up to now are mostly implemented in 0.35-µm
or 0.6-µm technologies. Only very few works have been attempted with the technologies, in
which the gate width of the MOS transistors is smaller than 0.18-µm. Results of the
comparisons are summarized in Table 3.2. Obviously, though the expected output power of
2 W is not fulfilled, the HiVP power amplifier realized in this work performs comparable
characteristics in comparison to the other works.
Table 3.2
Comparisons of CMOS power amplifiers
Author
Sowlati et al. [62]
Reyneart et al. [63]
Knopik et al. [64]
This work
Technology
[CMOS]
0.18-µm
0.18-µm
0.13-µm
0.12-µm
Frequency
[GHz]
2.4
1.75
2
0.9
Pout
[dBm]
23
27
21
29.5
PAE
[%]
42
34
18
34.5
Udd
[V]
2.4
3.3
2.8
3.6
In the future, following efforts can be devoted in order to achieve even larger RF output
power. The RF choke L3 mounted on the PCB is selected very large in this work so that it acts
77
Design of the CMOS Driver and Power Amplifiers
like a current source. As the current flowing through the HiVP structure is very large, the
power loss in L3 can no longer be neglected. The lumped electrical model of an inductor is
shown in Fig. 3.33. It consists of an inductance Ls with a series resistance Rs and a parasitic
capacitance Cp.
Fig. 3.33. Lumped electric model of an inductor.
The series resistance Rs causes the loss of supply voltage leading to reduced output power. It
increases with the increased inductance Ls and is approximately proportional to the square
root of the frequency [65].
On the other hand, the self-resonance occurs due to the parasitic capacitance Cp. For an
inductor, only the energy stored in the magnetic field is of interest. Therefore, the electric
energy present in the parasitic capacitance has to be subtracted from the magnetic energy. At
the self-resonant frequency, the energy in the magnetic field is equal to the energy in the
electric field and the quality factor of the inductor becomes zero. For the frequencies above
the self-resonance frequency, no net magnetic energy is available from an inductor to any
external circuit. The quality factor of an inductor can be presented as follows.
ω Ls 
ω 
1 −  
Q=
Rs   ω0 

2

,

(3.5)
where ω0 is the self-resonance frequency of the inductor given in equation (2.67). Seen from
the equation above, Q increases with the frequency at lower frequencies. However, at higher
frequencies, the self-resonance effect will be responsible for a decrease of the quality factor
and at the resonance frequency, the quality factor becomes zero.
In order to reduce the parasitic resistance of the RF chock and increase its self-resonance
frequency, relatively small inductance values can be attempted to be used in the future.
However, the drawback of lowering the inductance of L3 is the current swing in it and this AC
current has to be delivered by the power supply. Of course, the voltage source itself is not able
to deliver the high frequency AC current. One solution is to use the some decoupling
capacitors Cb1 – Cbn as shown in Fig. 3.31, and the larger the current swing is; the larger
should be the capacitance. But this method requires very high quality capacitors, which are
still capacitive up to the operating frequency. The most off-chip capacitors have parasitic
inductance of their package, in series with the capacitor itself. For instance, if a capacitor of
40 pF has a parasitic inductance of about 0.6 nH, then it behaves as an inductance rather than
a capacitance at the frequencies above 1 GHz. The real solution for the problem of the AC
power supply current is the use of differential structures, which is widely used in many
commercial power amplifiers. As introduced in subsection 2.4.5, two amplifiers are placed in
parallel and are driven by two out-of-phase input signals. Therefore, the current through the
DC-feed is only DC. In case that only single-ended HiVP structure is used in this work, the
78
Design of the CMOS Driver and Power Amplifiers
RF chock L3 can only be reduced reasonably. A compromise between the parasitic resistance,
self-resonance frequency and the AC current must be found.
Additionally, gate width of 3.4 mm was selected in the previous work achieving the RF
output power of 26 dBm at 900 MHz. In this work, output power of 29.5 dBm is obtained by
using the transistors having gate width of 4.5 mm. Therefore, even larger gate width can be
attempted in the future in order to reach the expected output power of 33 dBm.
Finally, it can be attempted to measure the source resistance of the HiVP structure, namely
the resistance occurring between the source of T1 and the ground. Known from the resimulation, a reduction of the bias voltage and hence of the operating current can be caused
due to this source resistance, therefore the output power is reduced. This resistance comes
from the bonding wires which connect the source pads to the conductor lines of the PCB and
also from the conductor lines themselves. Though several bonding wires are placed in parallel,
the parasitic resistance and inductance are not significantly reduced due to the proximity
effect [65]. In case that several conductors are placed closely, the presence of nearby currents
will change the flux in and around the conductor and it will cause mutual coupling between
the conductors. For instance, two metal traces M1 and M2, which respectively have resistance
of R0 and inductance of L0, are in parallel. The currents flowing through them have the same
direction. Due to the parallel nature, the total resistance and inductance should normally be
R0/2 and L0/2, respectively. However, these values can only be obtained if the distance of
these two traces is very large. If they are close to each other, the magnetic field of the two
traces will add to each other. Therefore, though the total inductance is smaller than L0, it is
much larger than L0/2. On the other hand, the currents flowing through the two traces are
distracted by each other. This means that the currents are pushed outwards by each other and
the cross-section for the current are reduced. Therefore, though the total resistance is smaller
than R0, it is much larger than R0/2.
3.2.3 HiVP Design Concept with Adjustable DC Power Consumption
Usually, high power added efficiency is only obtained at high RF power levels. It is also
proven by the HiVP power amplifier realized above. As shown in equation (2.16), the DC
drain current is proportional to the gate width of the MOS transistors. Therefore, the DC
power consumption remains high also if the RF output power is very low, resulting in very
low power added efficiency at these power levels.
In order to improve the power added efficiency achieved at low power levels, a novel
transistor design concept with adjustable gate width is introduced in this work. A MOS
transistor having large gate width can be divided into several parallel branches, each of which
can, for example digitally, be turned on or turned off. Therefore, the DC current flowing
through the transistor is adjustable. Using the same concept, the HiVP structure is modified
and shown in Fig. 3.34.
Obviously, the HiVP structure shown in Fig. 2.20 is here equally divided into n branches.
The transistors Ti (i is an arbitrary integer between 1 and 3) having gate width of w are
respectively substituted by n transistors Ti' having gate width of w', where
w = n ⋅ w′ .
(3.6)
It can be seen that each branch of the HiVP structure includes its own voltage divider
comprising the resistors Ri' and the shunt capacitors Ci', which are used to determine the drain
impedance of the transistors. Because the voltage dividers included by all the branches are
connected in parallel, the condition of
Ri′ = n ⋅ Ri
(3.7)
79
Design of the CMOS Driver and Power Amplifiers
Fig. 3.34. The HiVP structure with n branches.
must be fulfilled, assuming Ri and Ci are the resistors and the shunt capacitors used in the
original HiVP structure depicted in Fig. 2.20. Furthermore, the relationship between Ci' and Ci
must be found out. From equation (2.26), the shunt capacitors can be described as follows.
Cshunt =
Cgs
Z source ⋅ g m − 1
(3.8)
Since the transistors used in each branch of the modified HiVP structure are n times smaller
than those used in the original one, Cgs and gm are reduced to Cgs/n and gm/n, respectively.
Similar to Ri', the impedance seen at the source of the upper transistors Z source must also be
increased to n ⋅ Z source , since all the HiVP branches are connected in parallel. Inserting these
analyses into equation (3.8), following relationship can approximately be found out:
Ci′ =
1
⋅ Ci
n
(3.9)
As shown in Fig. 3.34, the input ports, namely the gates of all the parallel HiVP branches
are connected by the switches. These switches can be digitally controlled. In case of low RF
output power, several switches can be turned off; hence the corresponding HiVP branches are
disconnected. In this manner, the DC current flowing through the HiVP structure is decreased;
the power added efficiency of the power amplifier circuit is therefore increased at the low
power levels. There are also other methods to disconnect the HiVP branches, for instance, the
disconnection at the drain of each branch. However, since the metal lines used to connect the
gates of the HiVP branches are relatively thin, it is more feasible to disconnect the gate line
than to disconnect the drain line.
In this work, the integer n equal to 10 is selected. Therefore, the gate width of the
transistors T1'-T3' used in each HiVP branch is 450 µm. Simulation is also done at the
frequency of 900 MHz. In case that all the branches are turned on, the maximum RF output
power of 2 W can also be obtained during the simulation. With the degraded output power,
80
Design of the CMOS Driver and Power Amplifiers
the HiVP branches are gradually turned off. Finally, only one branch is applied for the lowest
output power.
40
35
PAE [%]
30
25
20
15
10
5
0
15
17
19
21
23
25
27
29
31
33
Pout [dBm]
Fig. 3.35. The simulated power added efficiency obtained for the modified
HiVP power amplifier with adjustable gate width.
The simulated power added efficiency versus the output power is presented in Fig. 3.35.
Clearly, using the technique of adjustable gate width, the power added efficiency of the HiVP
power amplifier can significantly be improved in the low power range.
3.2.4 Conclusion
The most important advantage of the HiVP configuration is the equal division of a large
voltage, which solves the problem of low breakdown voltage of the transistors in deepsubmicron CMOS technology. In this work, the methods to improve the performance of the
HiVP structure are described. Moreover, using the adjustable gate width technique, the power
added efficiency of the HiVP power amplifier can clearly be improved in the low power range.
Therefore, using HiVP configuration, deep-submicron CMOS technology is theoretically a
feasible process to realize power amplifiers applied in cellular phones of mobile
communications systems. A monolithic integration of such transceiver system in a deepsubmicron CMOS technology becomes possible. In this case, the fabrication of such
transceiver systems will be simplified and the process cost will be reduced. Certainly, the
HiVP configuration can also be adopted in other ranges, e.g. satellite communication and
split-ring resonator microplasma [66], as well as in the other technologies, e.g. GaAs-FET
technology.
81
Design of the CMOS Driver and Power Amplifiers
82
Design of the Broadband LDMOS Power Amplifiers
4. Design of the Broadband LDMOS Power Amplifiers
At the beginning of the 1990s, digital mobile radio frequency communication began to
make first steps into the market. Since that time, several different generations of mobile
communications systems exist simultaneously on the market. Therefore, there is a strong
demand to design multi-frequency multi-standard transceivers, which can operate in different
systems. For a long time, such transmitters could only be implemented by replicating the
radio frequency transmitters and receivers for each operating band. Today, efforts have been
devoted to directly develop the broadband circuits and passive components used in the multifrequency multi-standard transceivers [67]-[69]. In this work, the design of the broadband
power amplifiers for several downlink applications is introduced.
Using Motorola LDMOS device MRF21030SR3, a single-ended broadband radio
frequency power amplifier is first designed and fabricated in this work. Section 4.1 describes
the design process for this amplifier in detail. Due to the compromise of the linearity and the
power added efficiency, a class AB power amplifier is proposed. Not only the simulation but
also the measurement results are presented. Furthermore, using the same power devices, the
same biasing networks, the same operating points and the same impedance matching networks,
a broadband balanced power amplifier is designed. In section 4.2, the functional principles of
the balanced structure, as well as the benefits of it are introduced. Excellent performances are
achieved during the measurements.
4.1 Design of a Broadband LDMOS Single-Ended Class AB Power Amplifier
Using Motorola LDMOS device MRF21030SR3, a single-ended broadband radio
frequency power amplifier for the base station applications is first proposed, which can
simultaneously be used in GSM1800 and UMTS systems in Europe. Known from Fig. 1.1,
this power amplifier should have a bandwidth of at least 400 MHz. Furthermore, following
specifications should also be fulfilled:
-
maximum output power larger than 43 dBm
small signal gain larger than 10 dB
maximum power added efficiency higher than 30 %
high linearity indicated by ACPR better than 40 dBc
In this section, the design process to develop such a broadband power amplifier is
introduced in detail. It includes the choice of simulation model of the power devices,
determination of the operating point, improvement of the stability and design of the
impedance matching networks, etc. Simulations are first implemented, in order to predict and
optimize the circuit performance. The proposed power amplifier circuit is then fabricated in
the laboratory and measured. Good agreements are obtained between the simulation results
and the measurement results.
4.1.1 Selection of the simulation model of LDMOS transistors
The device manufacturer Motorola provides two different models for the simulation,
namely the Root-model and the MET-model. The former is a table-form model, which is
previously derived as “HP Root FET Model” by Agilent. This model can predict the behavior
of the PA circuits in dependence on the operating point, the frequency and the power.
Naturally, it is only adapted for the simulation if the measured data are available in some
fixed ranges.
83
Design of the Broadband LDMOS Power Amplifiers
The MET-model is an electric-thermal model, in which the dynamic process of the heating
is considered. The MET-model of the Motorola LDMOS transistors is an empirical nonlinear
large-signal model. The transfer characteristic Id – Ugs as well as the transconductance gm are
modelled in terms of each operating point and each temperature. With this model, smallsignal-, large-signal-, harmonic balance-, noise- and transient-simulations can be implemented.
Therefore, such model of power devices is suitable for the design of power amplifiers used in
base stations. In this work, the MET-model of the LDMOS transistors is selected for all the
simulations. The simulation of temperature behaviour can be turned on or turned off, in
dependence on the necessity.
4.1.2 DC Simulation and Selection of the Operating Points
To obtain the high output power and simultaneously achieve the high power added
efficiency mentioned above, a class AB power amplifier is developed in this work. It is
therefore necessary to select the suitable operating points for the LDMOS transistor. Using
the transistor model, DC simulations are first implemented. The recommended drain-source
voltage Uds for MRF21030SR3 is 26 V. The simulated transfer characteristic of the transistor,
which denotes the relationship between the drain current Id and the gate-source voltage Ugs for
the given drain-source voltage U ds = 26 V , is shown in Fig. 4.1.
Fig. 4.1. The simulated transfer characteristic of MRF21030SR3 at Uds = 26 V.
Ugs = 4.6 V
Ugs = 3.8 V
Ugs = 3.5 V
Fig. 4.2. The simulated output characteristic of MRF21030SR3
for Ugs between 3.5 V and 4.6 V.
84
Design of the Broadband LDMOS Power Amplifiers
Obviously, for a class AB power amplifier the gate voltage should be tuned between 3.5 V
and 4.6 V, approximately. The simulated output characteristic, which denotes the relationship
between the drain current Id and the drain-source voltage Uds for Ugs between 3.5 V and 4.6 V,
is shown in Fig. 4.2. In this work, the optimum gate voltage is fixed by the compromise
between the linearity and the efficiency after lots of simulations, and under the condition that
the expected maximum output power must be accomplished. Finally, the optimal operating
points of U ds = 26 V and U gs = 3.8 V are selected.
4.1.3 Advanced Stability Improvement
As mentioned above, almost all the transistors are potentially unstable within a large
bandwidth. Therefore, it is important to research the stability characteristic of the used active
device, before the matching network is developed. In case that the unconditional stability is
not available by the transistor itself, actions must be taken in order to improve the conditional
stability as far as possible.
The stability characteristic of MRF21030SR3 can be simulated with the S-parameter and be
demonstrated in the Smith charts. In Fig. 4.3 (a), the simulated input and the output stability
circle, which here are also named as source and load stability circle respectively, are
presented. The simulated magnitudes of the S-parameters are also listed in it. The frequency,
at which the simulation is done, is 2140 MHz, just the center frequency of the UMTS band.
The grey areas in the Smith charts illustrate the stable regions. Obviously, this transistor is not
unconditional stable at this frequency. Therefore, effort must be devoted to improve the
conditional stability.
In Fig. 4.3 (a), a dotted circle is drawn to be tangent to the load stability circle. It crosses
the real axis at the point P, which indicates the resistance of R = 6.5 Ω in the Smith chart.
Obviously, by adding a series resistance of 6.5 Ohm, all the impedance points located in the
instable region in this Smith Chart will be shifted into the dotted circle, which is just entirely
included in the stable region. Therefore, a series resistor of 6.5 Ohm directly connected at the
output port of the transistor can improve the stability of the power amplifier circuit
dramatically. Fig. 4.3 (b) shows the resimulated results for the stability with such a resistor at
the drain of the transistor. Apparently, it now becomes unconditionally stable at the frequency
of 2140 MHz.
There are altogether four methods of resistive loading to improve the circuit stability [34].
They are series or parallel resistors connected directly at the input or at the output of the
transistors as shown in Fig. 4.4. Just like the example above, the functional principle of all the
four methods is to shift the transformed input and output impedance into the stable region by
using the additional resistors. However, the mostly used method in practice is a parallel
resistor connected at the output of the power device. A series resistor connected at the input or
at the output of the transistor decreases the power gain dramatically, and a parallel resistor
connected at the input of the transistor can produce a significant deterioration in the noise
performance of the power amplifier. Therefore, the preferred method is just to connect a
resistor at the device output in parallel as shown in Fig 4.4 (d). However, this method has also
its disadvantages. Firstly, the parallel resistor consumes additional DC power; therefore, the
power added efficiency is greatly decreased. Secondly, to ensure the high frequency
performance of the power amplifier, resistors only with very small dimensions can be applied
in the circuit, for instance, resistors as surface mount device (SMD) should be used. However,
such devices can easily be destroyed by a large current resulting in the instability of the power
amplifier again.
85
load stability circle
source stability circle
Design of the Broadband LDMOS Power Amplifiers
frequency
2140 MHz
mag.(S11)
0.427
mag.(S12)
0.06
P
mag.(S21)
6.872
mag.(S22)
0.979
mag.(S21)
6.037
mag.(S22)
0.762
load stability circle
source stability circle
(a)
frequency
2140 MHz
mag.(S11)
0.45
mag.(S12)
0.053
(b)
Fig. 4.3. The stability improvement with series resistor simulated at 2.14 GHz.
(a) without the series resistor at the output; (b) with the series resistor at the output.
Fig. 4.4. Four methods of resistive loading for the stability improvement.
86
Design of the Broadband LDMOS Power Amplifiers
A modified configuration [70] for the stability improvement is introduced in this work by
adding a series SMD capacitor C to the shunt resistor as shown in Fig 4.5.
frequency
1850 MHz
load stability circle
source stability circle
Fig. 4.5. The advanced method for the stability improvement.
mag.(S11)
1.048
mag.(S12)
0.033
mag.(S21)
3.337
mag.(S22)
1.004
mag.(S21)
2.589
mag.(S22)
0.686
frequency
2140 MHz
load stability circle
source stability circle
(a)
mag.(S11)
1.005
mag.(S12)
0.026
(b)
Fig. 4.6. The stability simulated at 1.85 GHz.
(a) original stable region; (b) improved stability with shunt resistor and series capacitor.
87
Design of the Broadband LDMOS Power Amplifiers
The series capacitor prevents a DC current flowing through the shunt resistor R, and reduces
the total DC power consumption; so that a higher power added efficiency can be guaranteed.
Moreover, the series capacitor protects the shunt resistor against a large current ensuring the
stability improvement obtained by it.
Since the active device MRF21030SR3 is recommended by the manufacturer only for the
power amplifier design used in the UMTS band, it is more important to observe, how stable
this device is in the downlink frequency band of the GSM1800 system. Using ADS2003C, the
source stability circle and the load stability circle of the LDMOS transistor are simulated at
1850 MHz, the center frequency of the GSM1800 system. The simulation results are shown in
Fig. 4.6 (a). According to the rules introduced in section 2.7.2 and the magnitude of the Sparameters listed below, the stable regions are determined to be inside the stability circles.
They are depicted with grey in the Smith charts. Obviously, the stable regions only occupy
small areas in both Smith charts. Therefore, a 50 Ohm shunt resistor with an additional series
capacitor of 47 pF is directly connected at the drain of the transistor, in order to improve the
stability. Fig. 4.6 (b) illustrates the new simulation results, where it is clear to see, that the
stable regions both for the source and for the load are greatly enhanced. The other benefits of
this structure, such like the enhancement of power added efficiency, will be shown later in the
large signal simulation.
4.1.4 Design of the Matching Networks and the S-parameter Simulation
The optimum input and output impedance, namely Zin_opt and Zout_opt, of the power device
MRF21030SR3 measured in the UMTS band, are given in Table 4.1. These values are
determined using the load-pull measurement introduced in section 2.1 and are provided by the
manufacturer Motorola. The 50 Ohm reference impedance from the source and the load
should be transformed to these values, respectively. Obviously, the optimum output
impedance is in the entire frequency band well below 50 Ohm, the reference impedance. The
typical characteristics of the LDMOS transistors is shown here again.
Table 4.1
Optimum input and output impedance of MRF21030SR3
f (MHz)
2110
2140
2170
Zin_opt (Ohm)
15.3 - j9.4
14.6 - j9.4
14.3 - j8.8
Zout_opt (Ohm)
3.7 - j0.78
3.4 - j0.37
3.0 + j0.13
In order to achieve a broadband power amplifier, several different impedance matching
networks are proposed in this work. The first one is carried out with the lumped elements, i.e.
with the discrete inductors and capacitors as introduced in subsection 2.5.1. Since the real part
of Zin_opt and Zout_opt are smaller than 50 Ohm, the L-matching network shown in Fig.
2.30 (a) is used both for the input and for the output matching networks. In the second attempt,
matching networks consisting of an open-circuited stub followed by a series microstrip
transmission line shown in Fig. 2.34 (a) are selected. The third possibility to realize the input
and output matching networks applied in this work is using a single-section transmission line
as described in subsection 2.5.5. The S-parameters of the power amplifier circuits with these
matching networks are simulated, whereas the 3-dB bandwidth can be found out in the S21
curve. The simulation results show that the bandwidth obtained by using these three matching
networks is not large enough to simultaneously cover the in UMTS and GSM1800 systems in
Europe.
88
Design of the Broadband LDMOS Power Amplifiers
Finally, the multi-section transmission lines are used as microstrip matching networks both
for the input matching and for the output matching. There are lots of different possibilities for
the multi-section impedance transformer. For instance, both the input and the output matching
networks use a two-section impedance transformer, respectively, or both of them use a threesection impedance transformer, etc. Also the combinations of two- and three- section
impedance transformer can be adopted. Moreover, for example, only for a simple two-section
impedance transformer design, there are also many different alternatives; since arbitrary interimpedance point can be selected.
To optimize the performance of the power amplifier circuit, lots of matching networks are
attempted in this work, until the satisfactory results are achieved. All the different
transformers can first be designed in LLsmith, in order to obtain the characteristic impedance
of each section transmission line and the length of them in form of percentage of the
wavelength. Furthermore, the length of the transmission lines can be described in form of
millimetre by using equations (2.53) and (2.54). Observed from these equations, the phase
velocity v p is slightly dependent on the width of the transmission lines. Different v p , and
hence different wavelength for each line, can separately be determined using these two
equations. These different matching networks are one by one adopted in the power amplifier
circuit for the S-parameter simulations in ADS2003C. Usually, the calculated design
parameters can not directly provide the best simulation results. To fulfil all the circuit
specifications, optimisations are always necessary. Finally, a combination of matching
networks, which contains a three-section impedance transformer at the input and a twosection impedance transformer at the output, is regarded as the best selection for this work. It
must be emphasised that this final result shown here is obtained considering not only the 3-dB
bandwidth, but also the other specifications, such like the stability, the maximum output
power, the linearity and the power added efficiency. The schematic of this final power
amplifier circuit is demonstrated in Fig. 4.7.
Fig. 4.7. The schematic of the broadband power amplifier using multi-section
impedance transformer for the input and output matching networks.
In Fig. 4.7, T indicates the single transistor MRF21030SR3 used as the power device. The
bias voltages for this single-ended power amplifier are Ugg = 3.8 V and Udd = 26 V. As
introduced in section 2.6, two sections of quarter-wave transmission line have separately been
applied at the gate and at the drain of the transistor as biasing networks, which present open
circuits to the RF signal at the fundamental frequency and simultaneously short the second
harmonic. Both of them have a line-width of only 0.8 mm indicating a high characteristic
impedance of about 80 Ohm on the RO4003 substrate. According to the data sheet of this
substrate, a current of 3.2 A can be sustained by such a line with the width of 0.8 mm, if it has
89
Design of the Broadband LDMOS Power Amplifiers
a conductor-thickness of 35 µm. As shown in Fig. 4.2, the drain current is only about 0.35 A
at the selected operating point. However, it can dramatically be enhanced with an increased
RF input power. Therefore, the quarter-wave transmission line, especially used at the drain
should be sufficiently wide. Moreover, these lines can also not be too narrow due to some
mechanical structures, e.g. the bypass capacitors Cb1 – Cbn must be soldered between these
lines and the ground area. Therefore, these lines must be wide enough for the soldering. In
this work, the bypass capacitors are selected from 1 pF to 100 nF. The parameters Lx and Wx
in Fig. 4.7 denote the length and width of each section of transmission line, where x is an
integer between 1 and 5. The design parameters are listed in Table 4.2. A shunt resistor of 50
Ohm connected with a series capacitor of 47 pF is used at the drain of the transistor, in order
to improve the stability of the circuit.
Table 4.2
Design parameters of the broadband power amplifier
L1
18 mm
W1
3 mm
L2
14 mm
W2
4.5 mm
L3
10 mm
W3
13.6 mm
L4
15 mm
W4
10.2 mm
L5
14 mm
W5
3 mm
Cc1
47 pF
Cc2
47 pF
CS
47 pF
Rp
50 Ohm
The simulation results of the S-parameters for this power amplifier in the frequency band of
1 GHz – 3 GHz are shown in Fig. 4.8. A maximum small-signal gain of about 12.5 dB is
accomplished, while the 3-dB bandwidth reaches 1 GHz. Obviously, a broadband power
amplifier is realized, whose bandwidth covers simultaneously the UMTS band and the
GSM1800 band in Europe. The input matching and the output matching of this amplifier
circuit indicated by the magnitude of S11 and S22 are mostly located between 0 dB and -10 dB.
Fig. 4.8. Simulated S-parameters of the power amplifier with matching networks
realized with multi-section impedance transformer.
The unconditional stability factor µ is first simulated in the frequency range and shown in
Fig. 4.9. The stability curves for the following three cases are presented here:
1. circuit without any resistive loading
2. circuit with a 50 Ω shunt resistor connected at the drain of the device.
3. circuit with a 50 Ω shunt resistor and a 47 pF series capacitor at the drain of the device.
90
Design of the Broadband LDMOS Power Amplifiers
L2
L3
L1
Fig. 4.9. Simulated unconditional stability factor µ versus the frequency.
stable region
indep(S_StabCircle1) (0.000 to 51.000)
load L_StabCircle1
stability circles
source stability circles
Obviously, with a shunt resistor, the stability in the GSM1800 band is greatly improved. The
stability improvement is hardly interrupted in case that a sufficiently large series capacitance
is used. However, the condition that µ > 1 is not achieved in the whole frequency band,
especially in the UMTS band. This circuit is not unconditionally stable. This assessment can
also be confirmed in Fig. 4.10, where the stability circles in the frequency range between
1 GHz and 3 GHz are demonstrated. Simulation shows that the magnitudes of S11 and S22
remain smaller than 1 in the entire frequency range.
stable region
indep(L_StabCircle1) (0.000 to 51.000)
Fig. 4.10. Simulated stability circles versus frequency.
Altogether, the multi-section impedance transformer is the single effective tool to realize
the matching networks for a broadband power amplifier. Using an adequate resistive loading,
especially a shunt resistor at the output of the active device, it is feasible to design a LDMOS
power amplifier being conditional stable, even in a very large frequency band.
4.1.5 Simulation for Large Signal Response of the Broadband Power Amplifier
In this work, the large signal behaviours, such as the maximum output power, the large
signal power gain and the power added efficiency, are simulated. For a broadband power
amplifier, it is not only important to see whether the proposed power amplifier circuit
91
Design of the Broadband LDMOS Power Amplifiers
provides a relatively constant small signal gain in a wide frequency range. It is for instance
also important to observe whether large output power can be accomplished in different
frequency bands. In this subsection, several large signal simulations for the broadband power
amplifier shown in Fig. 4.7 are presented.
Using harmonic balance simulation of ADS2003C, the power transfer functions, which
indicate the relationship between Pin and Pout, are simulated both in the UMTS band and in the
GSM1800 band. The simulation results are shown in Fig. 4.11. A maximum output power of
about 45.5 dBm is obtained at 2140 MHz, with a 1-dB compression point of about 45 dBm.
The 6 dB back-off point is then fixed at the point of Pout = 39 dBm, correlating with the input
power of 27 dBm. The maximum output power achieved at 1850 MHz is about 44.5 dBm,
with a 1-dB compression point of about 43.7 dBm. Obviously, though the maximum output
power and 1-dB compression point at 1850 MHz are a little bit lower than those at 2140 MHz,
reasonable large output power are obtained in both frequency bands. Using these simulation
results, the large signal power gain versus Pin obtained at these two different frequencies is
calculated and presented in Fig. 4.11. They are saturated in the higher input power levels.
Similar to the simulation results shown in Fig. 4.8, the power gain in the GSM1800 band is
slightly lower than that in the UMTS band.
Fig. 4.11. Simulated power transfer function and large signal power gain.
Fig. 4.12. Simulated waveform of the current flowing through the shunt resistor.
92
Design of the Broadband LDMOS Power Amplifiers
As mentioned in subsection 4.1.3, a series capacitor and a shunt resistor are directly
connected at the drain of the LDMOS transistor in order to improve the stability. Fig. 4.12
depicts the simulated waveform of the current IR, which flows through the shunt resistor Rp
with or without the capacitor Cs. It is simulated in case that the power amplifier circuit has an
output power of 40 dBm. Obviously, using the series capacitor Cs the DC current having a
magnitude of about 0.52 A is deleted.
Fig. 4.13. Simulated power added efficiency of the single-ended power amplifier.
The simulated power added efficiency depending on the input power is shown in Fig. 4.13.
Simulation is also done at two different frequencies. A maximum PAE of 41 % is achieved at
2140 MHz, and 35 % at 1850 MHz. To meet the high requirement of linearity, power
amplifiers of CDMA transmitters usually operate 6 dB backed off from the saturation.
Therefore, it is sometimes more interesting to observe the power added efficiency obtained at
the 6 dB back-off point. As analysed above, the input power related 6 dB back-off point is
located at 27 dBm. A PAE of 22 % is obtained at this point.
4.1.6 Experiments and Measurement Results
According to the circuit schematic introduced in Fig. 4.8 and the design parameters given
in Table 4.2, a broadband single-ended class AB LDMOS power amplifier is fabricated using
the Motorola LDMOS transistor MRF21030SR3. As mentioned in the design process, this
power amplifier is built on a 0.81 mm-thick RO4003 substrate, which has a relative
permittivity of 3.38 and a conductor thickness of 35 µm. The photograph of this circuit is
presented in Fig. 4.14.
In this circuit, straight medium adaptors (SMA) are applied as the input port and the output
port, which have a coaxial structure and perform perfect RF closeness. Just the same as the
simulation, the bias voltages used for the measurements are Ugg = 3.8 V and Udd = 26 V.
Obviously, multi-section transmission-lines are used both at the input and at the output of this
circuit, in order to yield a broadband matching. By reason of symmetry, the shunt resistor of
50 Ohm connected with a series capacitor of 47 pF, which is used in the simulation for the
stability-improvement, is replaced by two parallel shunt resistors, each of which is 100 Ohm
and connected with a series capacitor of 47 pF. They are separately soldered on both sides of
the conductor line, which is directly connected to the drain of the LDMOS transistor.
93
Design of the Broadband LDMOS Power Amplifiers
ground
Ugg = 3.8 V
Udd = 26 V
input
output
MRF21030SR3
resistor + capacitor
Fig. 4.14. The photograph of the fabricated single-ended power amplifier.
Using HP 8510B Network Analyzer, the S-parameters of the amplifier circuit are measured.
The measurement results are shown in Fig. 4.15. Obviously, a gain of about 13 dB is achieved
in a large frequency range. This power amplifier circuit has a 3-dB bandwidth of 1 GHz with
the centre frequency of 2.1 GHz. In terms of the bandwidth, there is a good agreement
between the simulated and the measured results. The difference is that the flatness of the
measured S21 curve is not as good as that of the simulated result and all the curves are shifted
to the lower frequency range about 200 MHz. However, just due to this shift, both the UMTS
band and the GSM1800 band are perfectly covered by the bandwidth of this power amplifier.
Other than the simulated results, the measured gain in the GSM1800 band is a little bit larger
than that in the UMTS band. Moreover, it can be seen that the input and the output matching
of this circuit are not as desired lower than -10 dB in the entire frequency range. This is a
typical feature obtained for a single-ended power amplifier, since the optimum input and
output impedance provided by the manufacturer concentrate mainly on the maximum output
power, not on the VSWR.
Fig. 4.15. Measured S-parameters of the single-ended power amplifier.
94
Design of the Broadband LDMOS Power Amplifiers
Using HP 8664A Synthesized Signal Generator and Agilent E4419B Power Meter, the
output power Pout of the power amplifier versus the input power Pin is measured, not only at
1.85 GHz but also at 2.14 GHz. The measurement results are presented in Fig. 4.16.
Obviously, almost the same maximum output power of about 43.5 dBm (22.4W) is
achieved at both frequencies, while the 1-dB compression points are located at 42.7 dBm. The
power gain versus Pin can be calculated and shown in the same figure. A linear gain of about
13 dB is also obtained during this measurement. Also in the large signal measurement, the
power gain obtained in the GSM1800 band is slightly higher than that in the UMTS band.
Pout [dBm]; gain [dB]
40
35
45
Pout at 2.14 GHz
Pout at 1.85 GHz
PAE at 2.14 GHz
PAE at 1.85 GHz
gain at 2.14 GHz
gain at 1.85 GHz
40
35
30
30
25
25
20
20
15
15
10
10
5
5
0
10
15
20
22
Pin [dBm]
30
35
PAE [%]
45
0
Fig. 4.16. Measured output power, power added efficiency and power gain
versus the input power.
The power added efficiency is also measured and shown in Fig. 4.16. The maximum power
added efficiency achieved at the frequency of 1.85 GHz is 30.5 % for the maximum output
power. At the frequency of 2.14 GHz, the power added efficiency is as high as 37.2 % for the
maximum output power. Though the same maximum Pout are obtained at the two frequencies,
the maximum PAE are quite different, since the DC power consumed by the transistor are not
the same at these two different frequencies. In case that a RF signal is fed at the input, the DC
current flowing through the transistor is not equal to that shown in Fig. 4.2, but much larger;
and it doesn’t remain the same if the frequency changes. Furthermore, at the frequency of
2.14 GHz PAE of 18 % is obtained at the 6 dB back-off point from the 1-dB compression
point, where Pout is equal to 36.7 dBm. The measured values of the output power and PAE are
all somewhat lower than those of the simulations, but in a reasonable range.
Using MS 2668C Spectrum Analyser, the third order intermodulation distortion of this
single-ended power amplifier is measured with 1 MHz offset frequency. The two input signals
are generated by using HP 83650B and HP 8664A Synthesized Signal Generator. Due to the
limited output power of these signal generators, the lower and upper IMD3 versus the output
power is only measured up to Pout = 40 dBm as shown in Fig. 4.17. At the frequency of
2140 MHz, IMD3 better than -35 dBc is obtained at the 6 dB back-off point.
Using Anritsu MG3700A vector signal generator and Anritsu MS2781A signal analyzer,
the spectrum of the output signal is measured, whose results are shown in Fig. 4.18. The
measurement was first implemented at 2.14 GHz for a 5 MHz single-carrier W-CDMA-signal
with a peak to average ratio (PAR) larger than 10 dB, while the peak output power is about
95
Design of the Broadband LDMOS Power Amplifiers
IMD3 [dBc]
39 dBm. The average power of - 4.25 dBm shown in the figure below is measured with 33 dB
attenuation at the power amplifier output. Obviously, ACPR of about 45 dBc is obtained at
this power level, with which the 3GPP ACPR requirement is met. There is a rule of thumb
obtained from the practice, namely, at the power level, where the IMD3 is about 30 dBc,
ACPR of 45 dBc can be approximately fulfilled. This rule is here again proven.
Pout [dBm]
Fig. 4.17. Measured third order intermodulation distortion versus the output power.
Fig. 4.18. Measured ACPR at 2.14 GHz and with 5 MHz offset
as well as 39 dBm peak output power.
96
Design of the Broadband LDMOS Power Amplifiers
ACPR [dBc]
Furthermore, the measured ACPR versus the peak output power is given in Fig. 4.19.
Clearly, ACPR performance is degraded with the increased power level. It is also evident that
there is a slight difference between the ACPR lower and ACPR upper.
Pout [dBm]
Fig. 4.19. Measured ACPR versus the output power of the single-ended power amplifier.
Comparisons are done between the power amplifier realized in this work and the other
LDMOS power amplifiers achieved in recent years. Results of the comparisons are
summarized in Table 4.3. Obviously, the power amplifier realized here has the largest
bandwidth.
Table 4.3
Comparisons of LDMOS power amplifiers
Author
Cassan et al. [71]
Bagger et al. [72]
This work
Center
Frequency
[GHz]
3.5
2.1
2.1
Bandwidth
[MHz]
Pout
[dBm]
PAE
[%]
Udd
[V]
550
400
1000
46
43
43.5
36.7
45
37.2
28
28
26
97
Design of the Broadband LDMOS Power Amplifiers
4.2 Design of a Broadband LDMOS Balanced Class AB Power Amplifier
Since the designed power amplifier will be connected with the other components as well as
the antenna in the transmitter, it is demanded that the proposed power amplifier should have
very low voltage standing wave ratio (VSWR) at its input and output, which indicate excellent
cascading ability. Moreover, an even larger output power up to 50 W (47 dBm) is expected.
Therefore, a balanced power amplifier is introduced in this work, which contains two power
devices connected in parallel, providing the possibility for even higher maximum achievable
output power.
In this section, the functional principle of a balanced structure is introduced. Using the
same LDMOS transistors and the same matching networks obtained in the design of the
broadband single-ended power amplifier, a broadband LDMOS balanced class AB power
amplifier is developed. The simulation processes as well as the measurement results are
demonstrated below.
4.2.1 Balanced Structure
The balanced structure, whose configuration is shown in Fig. 4.20, is attractive due to the
very low VSWR and the excellent cascading ability. Two identical single-ended amplifiers T1
and T2 are connected in parallel through two quadrature hybrid couplers, which operate as a
power divider at the input and a power combiner at the output, respectively.
Quadrature hybrid couplers are 3-dB directional couplers with a 90° phase difference in the
outputs of the through and coupled arms [32]. Therefore, at the input of the balanced amplifier,
the two reflected signals from the two individual amplifiers are 180° out of phase. They
compensate each other, so that the balanced amplifier has ideally a VSWR of 1 at its input.
The same operational mode is also valid for the two reflected signals at the output. Therefore,
VSWR of a balanced amplifier depends on the coupler, not on each individual amplifier. The
forward transmitted signals of the two individual amplifiers are again in phase at the output,
due to the same length of their routes.
Fig. 4.20. The balanced structure.
98
Design of the Broadband LDMOS Power Amplifiers
The magnitudes of the S-parameters for a balanced amplifier can be given as follows [34]
S11 = 0.5 ⋅ S11T 1 − S11T 2
(4.1)
S 21 = 0.5 ⋅ S 21T 1 + S21T 2
(4.2)
S12 = 0.5 ⋅ S12T 1 + S12T 2
(4.3)
S 22 = 0.5 ⋅ S 22T 1 − S 22T 2 ,
(4.4)
where S11T1, S11T2 ··· S22T1 and S22T2 indicate the S-parameters of the individual amplifiers T1
and T2. It can be seen that the magnitude of S11 and S22 should be zero, if the amplifiers T1
and T2 are absolutely identical. Excellent stability can therefore also be expected. Moreover,
in case of entire identity of two individual amplifiers, the gain of a balanced power amplifier
remains same to that of a single-ended one, according to equation (4.2). The same is with the
reverse transmission coefficient S12 as shown in equation (4.3). Though the gain of a balanced
PA will not be doubled in spite of the use of two transistors, the maximally accomplishable
output power of a balanced power amplifier is twice that of a single-ended amplifier.
Fig. 4.21. The balanced structure using Wilkinson couplers.
A typical quadrature hybrid coupler can be realized with a branch-line coupler [32].
Because the input signal of a branch-line coupler is equally divided and further transmitted to
the two output ports. There is a 90° phase difference between two output signals. In this work,
however, Wilkinson couplers [32] are used as the power divider and as the power combiner.
The schematic of a balanced structure using Wilkinson couplers is shown in Fig. 4.21. Since
the two output signals of a Wilkinson divider are in phase, it is necessary to shift the phase of
the input signal before one single-ended amplifier (e.g. T1) and the phase of the output signal
after the other single-ended amplifier (e.g. T2) for 90°, respectively. Quarter-wave
transmission-lines can be used for such phase-shift. The 180° out-of-phase of the two
reflected signals at the input and at the output of the balanced amplifier is generated again. The
in-phase signals at the output of the balanced amplifier, which are forward transmitted from
the two individual amplifiers, can also be obtained in this manner.
4.2.2 Simulation of the LDMOS Balanced Power Amplifier
Similarly, using the MET-model of Motorola LDMOS device MRF21030SR3, a broadband
balanced radio frequency power amplifier is simulated in ADS2003C. As mentioned above,
99
Design of the Broadband LDMOS Power Amplifiers
the same biasing networks and the same impedance matching networks as those of the singleended power amplifier presented in Fig. 4.7 are also used in this design. The same operating
points of Ugg = 3.8 V and Udd = 26 V are also selected here for the two individual power
amplifiers. Simulations for the S-parameters and for the large signal behaviours are
implemented. The simulation results are shown below.
The simulated S-parameters are demonstrated in Fig. 4.22. A maximum small-signal gain
of about 12.5 dB is accomplished. Using the multi-section impedance transformers for the
input and the output matching networks, the proposed balanced power amplifier remains to be
broadband. Both the UMTS and the GSM1800 bands in Europe are covered by its bandwidth.
Compared to the single-ended power amplifier, the bandwidth of the balanced power
amplifier is slightly diminished, because the gain in some frequency ranges is a little reduced
due to the additional attenuation on the Wilkinson power couplers. Obviously, the magnitudes
of S11 and S22 are in a large frequency range lower than -10 dB. The largest benefit of the
balanced structure, namely very low VSWR, is clearly proven again in this simulation.
Therefore, this balanced power amplifier has perfect cascading ability and the excellent
stability.
Fig. 4.22. Simulated S-parameters of the broadband balanced power amplifier.
Fig. 4.23. Simulated unconditional stability factor µ of the balanced power amplifier.
100
Design of the Broadband LDMOS Power Amplifiers
The unconditional stability factor µ simulated in the frequency range between 1 GHz and 3
GHz is shown in Fig. 4.23. Obviously, it is in the whole frequency range even larger than 1.5.
This balanced structure is therefore unconditional stable. However, an important point must
be emphasised here. Though the balanced structure is unconditional stable, each individual
single-ended power amplifier used in the balanced structure must also be stable. The methods
for stability improvement introduced in section 4.1.3 are absolutely necessary.
Fig. 4.24. Simulated power transfer function and large signal power gain
of the balanced power amplifier.
Fig. 4.25. Simulated power added efficiency of the balanced power amplifier.
The power transfer function of this proposed balanced power amplifier, which indicates the
output power versus the input power, is simulated at two different frequencies. The simulation
results are shown in Fig. 4.24. The maximum output power of about 48.6 dBm is obtained at
the frequency of 2140 MHz, with a 1-dB compression point of about 48 dBm. The 6 dB backoff point is therefore as high as 42 dBm, as denoted in this figure. The maximum output
power achieved at 1850 MHz is about 47.2 dBm, with a 1-dB compression point of about
46.6 dBm. Obviously, though the maximum output power and 1-dB compression point at
1850 MHz are slightly lower than those at 2140 MHz, reasonable large output power is
101
Design of the Broadband LDMOS Power Amplifiers
obtained in both frequency bands. This balanced power amplifier is proven to be useful both
for the UMTS and for the GSM1800 systems in Europe indeed. Moreover, it is clear to see
that the maximum output power of the balanced power amplifier is just about 3 dB higher
than the simulated values of the single-ended power amplifier at both frequencies, since the
two power devices are connected in parallel.
Applying the simulation results given above, the large signal power gain of this balanced
amplifier can be calculated at the two different frequencies mentioned above. They are also
presented in Fig. 4.24 related to the input power. Note that the gain of a balanced power
amplifier is approximately the same as that of the single-ended one presented in subsection
4.1.6. Similar to the simulation results shown in Fig. 4.22, the large signal power gain in the
GSM1800 band is slightly lower than that in the UMTS band. Both of them are saturated in
the higher power levels.
The simulated power added efficiency versus the input power is shown in Fig. 4.25.
Obviously, the maximum PAE reaches 47 % at 2140 MHz and 38 % at 1850 MHz. A PAE of
21.5 % is obtained at 2140 MHz and at the point of Pin = 30 dBm. This input power correlates
with Pout = 42 dBm, the 6 dB back-off point as presented in Fig. 4.24.
4.2.3 Experiments and Measurement Results
A balanced power amplifier is fabricated using two Motorola LDMOS transistor
MRF21030SR3. Similar to the single-ended amplifier, it is also fabricated on the RO4003
substrate. The photograph of the balance amplifier is shown in Fig. 4.26. The bias voltages are
Ugg = 3.8 V and Udd = 26 V. Obviously, Wilkinson couplers are used as the power divider at
the input and as the power combiner at the output. Two λ/4-lines are used before the upper
amplifier and after the lower amplifier respectively, in order to tune the signal phase as
introduced above.
Ugg = 3.8 V
Udd = 26 V
λ/4 - line
output
input
λ/4 - line
Udd = 26 V
Ugg = 3.8 V
Fig. 4.26. The photograph of the fabricated balanced power amplifier.
Measured S-parameters are shown in Fig. 4.27. A linear gain of about 12 dB is obtained.
This power amplifier has a 3-dB bandwidth of more than 830 MHz with the center frequency
102
Design of the Broadband LDMOS Power Amplifiers
of 2 GHz. Compared to the simulation results, the center frequency is shifted to the lower
frequency range about 200 MHz and the gain is degraded in high frequency range due to the
additional attenuation on the couplers. However, the obtained bandwidth is sufficiently large
to simultaneously cover the UMTS and the GSM1800 down-link bands in Europe.
Magnitudes of S11 and S22 of this power amplifier are in the frequency range of interest
between -10 dB and -30 dB.
Fig. 4.27. Measured S-parameters of the LDMOS balanced power amplifier.
45
Pout [dBm]; gain [dB]
40
35
50
Pout at 2.14 GHz
Pout at 1.85 GHz
PAE at 2.14 GHz
PAE at 1.85 GHz
gain at 2.14 GHz
gain at 1.85 GHz
45
40
35
30
30
25
25
20
20
15
15
10
10
5
5
0
10
15
20
25
Pin [dBm]
30
35
40
PAE [%]
50
0
Fig. 4.28. Measured output power, PAE and power gain of the balanced power amplifier.
Fig. 4.28 presents the input-referred output power Pout, power added efficiency and the
power gain measured at 1.85 GHz and 2.14 GHz, respectively. The maximum output power
of 50 W (47 dBm) is accomplished at both frequencies, while the 1-dB compression points
103
Design of the Broadband LDMOS Power Amplifiers
IMD3 [dBc]
are located at about 46 dBm. The power added efficiency of 35.5 % is achieved at 1.85
GHz for the maximum output power. At 2.14 GHz, the power added efficiency is as high as
42.5 % for the maximum output power. Even with the consideration of 6 dB back off from
the 1-dB compression point, namely at the point of Pout = 40 dBm, a PAE of 20 % is obtained
at this frequency. The measured values of the output power and the PAE are all lower than
those of the simulations. However, all the requirements in terms of output power, the PAE
and the power gain are fully fulfilled.
The third order intermodulation distortion versus the output power is measured with 1 MHz
offset frequency. It is also measured in the UMTS and the GSM1800 bands, respectively. Due
to the limited output power of the two signal generators, the measurements are only
implemented up to Pout = 40 dBm, but this is just the 6 dB back off point in the UMTS band.
The measurement results are shown in Fig. 4.29. Obviously, the third order intermodulation is
degraded with the increased power level. However, IMD3 better than - 42.5 dBc at 1.85 GHz
and than - 39 dBc at 2.14 GHz are obtained when the output power is lower than 40 dBm.
High linearity is yielded for this balanced LDMOS power amplifier.
Pout [dBm]
Fig. 4.29. Measured third order intermodulation distortion versus the output power.
The spectrum of the output signal is measured using a 5 MHz single-carrier W-CDMAsignal, which has a center frequency of 2.14 GHz and a peak to average ratio (PAR) larger
than 10 dB. The measurement results are shown in Fig. 4.30. The measurement is first done in
case that the peak output power is about 45.8 dBm. The average power of 2.87 dBm shown in
the figure above is measured with 33 dB attenuation at the power amplifier output. Obviously,
ACPR of about 45 dBc is obtained at this output power level, with which the 3GPP ACPR
requirement is met.
Furthermore, the measured ACPR in dependence on the peak output power is presented in
Fig. 4.31. It can be seen that this power amplifier performs high linearity in the whole power
range. The difference between the ACPR lower and ACPR upper are as small as negligible.
The symmetry of this balanced amplifier is better than that of the single-ended one presented
in subsection 4.1.6.
104
Design of the Broadband LDMOS Power Amplifiers
ACPR [dBc]
Fig. 4.30. Measured ACPR at 2.14 GHz and with 5 MHz offset
as well as 45.8 dBm peak output power.
Pout [dBm]
Fig. 4.31. Measured ACPR versus the output power of the balanced power amplifier.
Finally, a 50 W broadband balanced power amplifier using LDMOS transistors
MRF21030SR3 is developed, which can simultaneously be adopted in the UMTS and in the
GSM1800 systems in Europe. The bandwidth realized by this balanced power amplifier is
105
Design of the Broadband LDMOS Power Amplifiers
also larger than the bandwidth obtained by the other works listed in table 4.3. High efficiency,
high linearity and outstanding cascading ability prove this design concept to be an ideal
candidate for multi-standard multi-frequency base-station transmitters.
106
Summary
5. Summary
The provision of information and services at any time and any place is supported by the
development of modern mobile communications. Every wireless communications system
includes a transmitter, which mostly requires a power amplifier circuit in its radio frequency
stage. In this work, radio frequency power amplifiers and their driving stages not only for the
base stations but also for the cellular phones are developed. Both the hybrid and the integrated
power amplifier circuits are designed with MOS transistors, which are regarded as the most
cost-efficient devices due to the materials with lower cost and relatively simple process for
the fabrication. Thanks to the development of modern semiconductor technologies, these
transistors are now fast enough for designing the radio frequency circuits operating at several
GHz. However, MOS transistors also perform drawbacks in designing some radio frequency
circuits. For instants, CMOS devices perform exponential or logarithmic transfer functions
only in the subthreshold region. In this region, however, the current is very small and hence
the MOS devices are only suitable for very low power applications. Therefore, it is generally
difficult to realize a logarithmic PGA with high output power in the CMOS technologies.
Moreover, with the decreased size scaling to deep-submicron, the breakdown voltage of the
CMOS transistors becomes lower and lower. Therefore, the ability of these transistors to
sustain a large output voltage decreases and the difficulty of designing power amplifiers using
CMOS technologies increases. In order to enhance the breakdown voltage of the MOS
transistors, additional low doped n-drift region is used at the drain-terminal of the LDMOS
transistors. The breakdown voltage of such transistors is boosted even up to 70 V, so that the
design of power amplifiers for base station applications by using MOS transistors becomes
feasible. But on the other hand, the optimum output impedance of the LDMOS transistors is
usually very low, so that these transistors are principally not suitable for designing the
broadband power amplifiers. To solve the problems mentioned above, modified circuit
topologies are introduced in this work for designing different power amplifier circuits and
their driving stages. The functional principle of these circuit topologies are described in detail.
Simulation and experimental results of these circuits are also presented.
Today, CMOS is the technology of choice for a higher integration level and lower cost
because it is capable of implementing a significant amount of digital signal processing and
because the vast majority of today’s integrated circuits are implemented in this technology. In
this work, efforts are devoted to design the power amplifiers and their driving stages for
cellular phones using standard deep-submicron CMOS technology.
Firstly, an RF CMOS logarithmic programmable gain amplifier is designed using a
0.12-µm CMOS technology. This work presents a novel circuit concept for the PGA design,
where several amplifier cells are connected in parallel which are digitally controlled by a
demutiplexer. These amplifier cells separately employ the transistors with different gate width;
and at any given time, only one amplifier cell is turned on. In this manner, different gain and
adaptive power consumption can be achieved. In order to obtain the high immunity to the
environmental noise, differential operation is adopted in the amplifier cells. The cascode
configuration is also applied in the circuit, which effectively suppresses the Miller effect and
increases the output impedance of the active devices. Instead of active load, an LC-tank is
applied as the common load for all the amplifier cells. It is proven to consume much less
voltage headroom than the active load; hence a higher output power can be accomplished. The
PGA circuit is fabricated and is measured at RF. The gain of the PGA can be varied
between -43 dB and 8 dB with a gain control step of about 3 dB. A large gain control range of
51 dB is realized. This is the largest logarithmic gain control range reported so far for the
CMOS radio frequency PGA. Adaptive power consumption is also achieved by using the
parallel configuration of the amplifier cells. With the largest gain of 8 dB, the maximum
107
Summary
output power reaches 9 dBm and the 1-dB compression point is located at 8 dBm, while the
oIP3 is as high as 22 dBm.
Furthermore, a CMOS power amplifier for the application in a cellular phone is proposed in
this work. To solve the problem of low breakdown voltage, the HiVP structure is employed in
this design. The HiVP structure is a High Voltage and High Power device configuration in
which several transistor devices are connected DC and RF in series, so that the large output
voltage can be divided by all the cascaded devices. However, the number of the transistors
used in the HiVP structure must be restricted under the consideration of equal division of the
supply voltage and the shift of the output characteristic. Since the same current flows through
all the transistors, the different drain voltage can only be obtained with different drain
impedance, which can be adjusted by the shunt capacitance connected at the gate of the upper
transistor. In case that high output power is required, the DC current flowing through the
HiVP circuit can even be larger than 1 A; hence transistors with gate width of several mm are
required. The design approach to build compact layout for the large transistors is described in
this work. Using the staggered layout concept described in Fig. 3.24, the chip area can
effectively be decreased. Additionally, the phase difference along the gate lines of the
numerous amplifier cells can be diminished by using the H-structure. In this work, microwave
HiVP class AB power amplifiers are attempted in the deep-submicron CMOS technologies.
To increase the matching flexibility and avoid excessive power loss of the on-chip inductors,
the matching networks are implemented on the PCB. The fabricated power amplifier circuit is
measured and the final measurement results are summarized and analysed as follows. With a
supply voltage of 3.6 V, the maximum output power of 29.5 dBm is obtained at 900 MHz,
while the maximum power added efficiency reaches 34.5 %. This amplifier circuit belongs to
the very few efforts over the world to attempt microwave power amplifiers in deep-submicron
CMOS technologies. The realized characteristics of this power amplifier are comparable in
comparison to the other works presented in recent years, or even better. Moreover, the design
concept for transistors with adjustable gate width is introduced in this work, where the power
added efficiency achieved on the low power levels is greatly improved.
Using Motorola LDMOS transistor MRF21030SR3, broadband power amplifiers used in
the base stations of the mobile communications systems are also developed in this work. A
single-ended class AB power amplifier is first designed, which can simultaneously be used in
the GSM1800 and in the UMTS base stations of Europe. The stability is one of the most
important issues for such broadband power amplifier design, since almost all the transistors
are potentially unstable within a large bandwidth. A method for the stability improvement is
demonstrated in this work, where a shunt resistor with an additional series capacitor is directly
connected at the drain of the LDMOS transistor. This series capacitor protects the shunt
resistor against a large current; hence the stability improvement obtained by the shunt resistor
is guaranteed. Simulations also show that the series capacitor reduces the total DC power
consumption; hence the power added efficiency of the amplifier circuit is enhanced. In order
to fulfil the specification for the bandwidth of this multi-frequency single-ended power
amplifier, not only discrete but also distributed impedance matching networks are attempted.
The S-parameters of these power amplifier circuits with different matching networks are
simulated. Comparing the simulation results, the matching network consisting of multisection transmission lines is determined to be the best candidate to realize a broadband power
amplifier. Moreover, quarter-wave transmission lines determined at the frequency of 2 GHz is
applied as the biasing networks, which provide the DC path for the biasing voltage and
simultaneously an open circuit for the RF signal at the fundamental frequency. The even
harmonics, which cause significant signal distortions, can be shorted by such biasing
networks. The proposed power amplifier circuit is fabricated on the RO4003 substrate and
measured. With a supply voltage of 26 V, the maximum output power reaches 43.5 dBm both
in the GSM1800 band and in the UMTS downlink band. A linear power gain of about 13 dB
108
Summary
is achieved in a large frequency band. The highlight of this work is the 3-dB bandwidth of
1 GHz with the center frequency of 2.1 GHz. This is the largest bandwidth reported so far in
the LDMOS technology. The maximum power added efficiency larger than 37 % is
accomplished in the UMTS band and than 30 % in the GSM1800 band. High linearity is also
obtained, which is denoted by the adjacent channel power ratio (ACPR) lower than - 40 dBc
within the whole power level.
The voltage standing wave ratio (VSWR) is an essential problem in the design of a singleended power amplifier, since the output matching network is generated according to the
power matching, not according to the conjugate complex matching. In order to solve this
problem, a balanced LDMOS broadband class AB power amplifier is designed. Two identical
single-ended amplifiers are connected in parallel through two quadrature hybrid couplers,
which operate as a power divider at the input and a power combiner at the output, respectively.
The two reflected signals from the two individual amplifiers are 180° out of phase both at the
input port and at the output port of the balanced amplifier. They compensate each other, so
that a VSWR of 1 can theoretically be accomplished at both ports. In this work, the
quadrature hybrid couplers are realized with Wilkinson power dividers and additional quarterwave transmission lines. Using the same active device, the same matching networks and the
same biasing networks obtained for the single-ended one, the balanced power amplifier is
fabricated. Good performances are obtained in the measurements. With a supply voltage of 26
V, the maximum output power reaches 47 dBm (50 W) both in the GSM1800 and in the
UMTS downlink bands. A linear power gain of about 12 dB is achieved in a large frequency
band. It has a 3-dB bandwidth of 830 MHz with the center frequency of 2 GHz. The
magnitudes of S11 and S22 are lower than -10 dB in the entire frequency band. Therefore, the
realized balanced power amplifier has superior cascading ability. The maximum power added
efficiency higher than 42 % is accomplished in the UMTS band and than 35 % in the GSM
band. High linearity is also obtained in the measurement, which is denoted by the ACPR
lower than - 40 dBc within the whole power level. It is proven that this realized LDMOS
balanced power amplifier is suitable for the multi-standard multi-frequency mobile
communication systems.
109
Summary
110
Appendix
Appendix
A1. Logic of the 5-to-18 demultiplexer
Y1 = X 5 ⋅ X 4 ⋅ X 3 ⋅ X 2 ⋅ X 1 = X 5 ⋅ X 3 + X 4 + X 2 ⋅ X 1
Y2 = X 5 ⋅ X 4 ⋅ X 3 ⋅ X 2 ⋅ X1 = X 5 ⋅ X 3 + X 4 + X 2 ⋅ X1
Y3 = X5⋅ X4 ⋅ X3⋅ X 2⋅ X1= X5⋅ X3 + X4 + X 2⋅ X1
Y4 = X5⋅ X4 ⋅ X3⋅ X 2⋅ X1= X5⋅ X3 + X4 + X 2⋅ X1
Y5 = X5⋅ X4 ⋅ X3⋅ X 2⋅ X1= X5⋅ X4 ⋅ X3 + X 2⋅ X1
Y6 = X 5 ⋅ X 4 ⋅ X 3 ⋅ X 2 ⋅ X 1 = X 5 ⋅ X 4 ⋅ X 3 + X 2 ⋅ X 1
Y7 = X 5 ⋅ X 4 ⋅ X 3 ⋅ X 2 ⋅ X 1 = X 5 ⋅ X 4 ⋅ X 3 + X 2 ⋅ X 1
Y8 = X5⋅ X4 ⋅ X3⋅ X 2⋅ X1= X5⋅ X4 ⋅ X3 + X 2⋅ X1
Y9 = X 5⋅ X 4 ⋅ X3⋅ X 2 ⋅ X1= X5 + X 4 + X3 + X 2 ⋅ X1
Y 10 = X 5 ⋅ X 4 ⋅ X 3 ⋅ X 2 ⋅ X 1 = X 5 + X 4 + X 3 + X 2 ⋅ X 1
Y 11 = X 5 ⋅ X 4 ⋅ X 3 ⋅ X 2 ⋅ X 1 = X 5 + X 4 + X 3 + X 2 ⋅ X 1
Y 12 = X 5 ⋅ X 4 ⋅ X 3 ⋅ X 2 ⋅ X 1 = X 5 + X 4 + X 3 + X 2 ⋅ X 1
Y 13 = X 5 ⋅ X 4 ⋅ X 3 ⋅ X 2 ⋅ X 1 = X 5 ⋅ X 4 ⋅ X 3 + X 2 ⋅ X 1
Y 14 = X 5 ⋅ X 4 ⋅ X 3 ⋅ X 2 ⋅ X 1 = X 5 ⋅ X 4 ⋅ X 3 + X 2 ⋅ X 1
Y 15 = X 5 ⋅ X 4 ⋅ X 3 ⋅ X 2 ⋅ X 1 = X 5 ⋅ X 4 ⋅ X 3 + X 2 ⋅ X 1
Y 16 = X 5 ⋅ X 4 ⋅ X 3 ⋅ X 2 ⋅ X 1 = X 5 ⋅ X 4 ⋅ X 3 + X 2 ⋅ X 1
Y 17 = X 5 ⋅ X 4 ⋅ X 3 ⋅ X 2 ⋅ X 1 = X 5 ⋅ X 3 + X 4 + X 2 ⋅ X 1
Y 18 = X 5 ⋅ X 4 ⋅ X 3 ⋅ X 2 ⋅ X 1 = X 5 ⋅ X 3 + X 4 + X 2 ⋅ X 1
111
Appendix
A2. Schematic of the 5-to-18 demultiplexer
X3
X5
>1
&
X1
X2
Y1
>1
Y2
>1
Y3
>1
Y4
>1
Y5
>1
Y6
>1
Y7
>1
Y8
>1
Y9
>1
Y10
>1
Y11
>1
Y12
>1
Y13
>1
Y14
>1
Y15
>1
Y16
>1
Y17
>1
Y18
1
&
X4
>1
1
>1
1
&
1
&
&
&
&
&
112
References
References
[1]
W. C. Jakes, “Microwave mobile communications,” AT&T, 1974, reprinted by IEEE
Press, Piscataway, NJ.
[2]
J. G. Proakis, “Digital communications,” McGraw-Hill, New York, 1989.
[3]
S. C. Cripps, “RF power amplifier for wireless communications,” 1999 Artech House,
Inc.
[4]
D. R. Lohrmann, “Amplifier has 85% efficiency while providing up to 10 Watts power
over a wide frequency band,” Electronic Design, vol. 14, pp. 38-43, March 1966.
[5]
A. D. Artym, “Switching mode of high frequency power amplifiers,” Radiotekhnika, vol.
24, pp. 58-64, 1969.
[6]
V. V. Gruzdev, “Calculation of circuit parameters of single-ended switching-mode
tuned power amplifiers,” Trudy MEI, vol. 2, pp. 124-128, 1969.
[7]
I. A. Popov, “Switching mode of single-ended transistor power amplifier,”
Poluprovodnikovye pribory v tekhnike svyazi, vol. 5, pp. 15-35, 1970.
[8]
V. B. Kozyrev, “Single-ended switching-mode tuned power amplifier with filtering
circuit,” Poluprovodnikovye pribory v tekhnike svyazi, vol. 6, pp. 152-166, 1971.
[9]
H. Kobayashi, J. M. Hinrichs, and P. M. Asbeck, “Current-mode class D power
amplifiers for high-efficiency RF applications,” IEEE Transactions on Microwave
Theory and Techniques, vol. 49, no. 12, Dec. 2001, pp. 2480-2485.
[10] N. O. Socal, and A. D. Socal, “Class E – a new class of high-efficiency tuned singleended switching power amplifiers,” IEEE J. Solid-State Circuits, vol. SC-10, pp. 168176, June 1975.
[11] A. V. Grebennikow, and H. Jaeger, “Class E with parallel circuit – a new challenge for
high-efficiency RF and microwave power amplifiers,” IEEE MTT-Digest, pp. 16271630, 2002.
[12] A. Grebennikov, “Switched-mode tuned high-efficiency power amplifiers: historical
aspect and future prospect,” IEEE Radio Frequency Integrated Circuits Symposium, pp.
49-52, June, 2002.
[13] D. Milosevic, J. Tang, and A. Roermund, “Explicit design equations for Class-E power
amplifiers with small DC-feed inductance,” European Conference on Circuit Theory
and Design, vol. 3, pp. 111-113, August, 2005
[14] V. J. Tyler, “A new high-efficiency high power amplifier,” Marconi Review, vol. 21,
1958, pp. 96-109.
[15] S. Tu, and C. Toumazou, “Highly efficient CMOS class E power amplifier for wireless
communications,” Proceedings of the 1998 IEEE International Symposium on Circuits
and Systems, vol. 3, pp. 530-533, June, 1998.
113
References
[16] F. Fortes and M. Rosario, “A second harmonic class F power amplifier in standard
CMOS technology,” IEEE Transactions on Microwave Theory and Techniques, vol. 49,
no. 6, June. 2001, pp. 1216-1220.
[17] J. E. Lilienfeld, US Patent 1,745,175, 1930.
[18] O. Heil, British Patent 439,457, 1935.
[19] C. T. Sah, “A new semiconductor tetrode – the surface-potential controlled transistor,”
Proc. IRE, vol. 49, 1961, pp. 1623-1634.
[20] A. S. Grove, and D. J. Fitzgerald, “Surface effects on p-n junctions: characteristics of
surface space-charge regions under nonequilibrium conditions,” Solid-State Electron.,
vol. 9, pp. 783-806, 1966.
[21] H. J. M. Veendrick, “MOS ICs,” VCH Verlagsgesellschaft mbH, 1992.
[22] B. Razavi, “Design of analog CMOS integrated circuits,” McGraw-Hill. Inc., 2001.
[23] A. K. Ezzeddine, and H. Huang, "The high voltage/high power FET (HiVP)," IEEE
Radio Frequency Integrated Circuits Symposium, 2003, pp. 215-218.
[24] L. Wu, R. Tao, U. Basaran, J. Luger, I. Dettmann, and M. Berroth, “The integrated 2W
high voltage/high power 0.12-µm RF CMOS power amplifier,” 34th European
Microwave Conference (EuMC 2004), Amsterdam, Netherlands, pp. 451-454, October
12-15, 2004.
[25] S. R. Novis, and L. Pelletier, “IMD parameters describe LDMOS device performance”,
Microw. RF, vol. 37, pp. 69-74, July 1998.
[26] F. Lepine, A. Adahl, and A. Zirath, “L-Band LDMOS power amplifiers based on an
inverse class-F architecture,” IEEE Transactions on Microwave Theory and Techniques,
vol. 53, no. 6, June. 2005, pp. 2007-2012.
[27] F. Jian, L. Zhaoji, and Z. Bo, “Study for safe operating area of high voltage LDMOS,”
in Int. Business of Elec. Product Reliability and Liability Conf., Apr. 2004, pp. 15-18.
[28] T. Lee, “The design of CMOS radio-frequency integrated circuits,” Cambridge
University Press, 1998.
[29] P. R. Gray, and R. G. Meyer, “Analysis and design of analog integrated circuits,” John
Wiley &Sons, Inc, pp. 226, 3rd. Edition, 1992.
[30] P. H. Smith, “Transmission line calculator,” Electronics, vol. 12, no. 1, pp. 29-1,
January 1939.
[31] M. Albulet, “RF power amplifiers,” Noble Publishing Corporation, 2001.
[32] D. M. Pozar, “Microwave engineering,” John Wiley & Sons, Inc, 2nd ed., 1998.
[33] I. J. Bahl, and D. K. Trivedi, “A designer’s guide to microstrip line,” Microwaves, May
1977, pp. 90-96.
114
References
[34] G. Gonzalez, “Microwave transistor amplifiers,” Second edition, Prentice Hall Inc.,
New Jersey, 1997.
[35] L. Young, “Table of cascaded homogeneous quarter-wave transformers,” IEEE Trans.
on Microwave Theory and Techniques, vol. 7, no. 2, April. 1959, pp. 233-237.
[36] W. H. Doherty, “A new high efficiency power amplifier for modulated waves,”
Proceedings of the IRE, vol. 24, no. 9, pp. 1163-1182, 1936.
[37] I. Dettmann, L. Wu, and M. Berroth, “Comparison of A single-ended class-AB, a
balanced and a Doherty power amplifier”, 17th Asia-Pacific Microwave Conference
(APMC 2005), Suzhou, China, vol. 2, pp. 1167-1170, 2005.
[38] Y. S. Noh, “An intelligent power amplifier MMIC using a new adaptive bias control
circuit for W-CDMA Applications”, IEEE Journal of solid-state circuits, vol. 39, no.6,
pp. 967-970, June, 2004.
[39] S. Reed, Y. Wang, F. Huin, and S. Toutain, “HBT power amplifier with dynamic base
biasing for 3G handset applications,” IEEE Microwave and Wireless Components
Letters, vol. 14, no. 8, pp. 380-382, August, 2004.
[40] M. L. Edwards, and J. H. Sinsky, “A new criteria for linear 2-Port stability using a
single geometrically derived parameter,” IEEE Transactions on Microwave Theory and
Techniques, vol. MTT-40, December 1992, pp. 2803-2811.
[41] M. E. Hines, “The virtures of nonlinearity-detection, frequency conversion, parametric
amplification, and harmonic generation,” IEEE Transactions on Microwave Theory and
Techniques, vol. MTT-32, September 1984, pp. 1097-1104.
[42] D. M. Pozar, “Microwave and RF Design of Wireless Systems,” 2000, John Wiley &
Sons, Inc.
[43] R. Harjani, "A variable gain CMOS amplifier with exponential gain control," in Symp.
VLSI Circuits Dig. Tech. Papers, June 2000, pp. 146-149.
[44] W. C. Song, C. J. Oh, G. H. Cho, and H. B. Jung, "High frequency/high dynamic range
CMOS VGA," Electron. Lett., vol. 36, pp. 1096-1098, Jun 2000.
[45] P. Orsatti, F. Piazza, and Q. Huang, "A 71-MHz CMOS IF-baseband strip for GSM,"
IEEE Journal of Solid-State Circuits, vol. 35, no. 1, pp. 104-108, Jan. 2000.
[46] Recommended Minimum Performance Standards for CDMA2000 Spread Spectrum
Mobile Station, 3GPP2 Doc. C.S0011-A
[47] Recommended Minimum Performance Standards for Dual-Mode Wide-band Spread
Spectrum Cellular Mobile Station, IS-98A.
[48] Recommended Minimum Performance Standards for 1.8 to 2.0 GHz Code Division
Multiple Access (CDMA) Personal Stations, ANSI J-Standard 018.
115
References
[49] S. Aggarwal, A. Khosrowbeygi, and A. Daanen, “A single-stage variable-gain amplifier
with 70-dB dynamic range for CDMA 2000 transmit application,” IEEE Journal of
Solid-State Circuits, vol. 38, no. 6, pp. 911-917, 2003.
[50] R. Saito, K. Hosoda, A. Hyogo, and T. Maruyama, H. Komuraki, H. Sato, K. Sekine,
“A 1.8-V, 73-dB dynamic-range CMOS variable gain amplifier,” ESSCIRC 2004-29th
European Solid-State Circuits Conference, pp. 301-304, 2003.
[51] Y. S. Wang, and L. H. Lu, “5.7 GHz low-power variable-gain LNA in 0.18-µm
CMOS,” Electronic Letters, vol. 41, no. 2, pp. 66-68, 2005.
[52] Q. Chaudhry, R. Alidio, G. Sakamoto, and T. Cisco, “A SiGe MMIC variable gain
cascade amplifier,” IEEE Microwave and Wireless Components Letters, vol. 12, no. 11,
pp. 424-425, 2002.
[53] K. R. Nary, and R. L. Van-Tuyl, “An MMIC amplifier for automatic level control
applications,” IEEE Microwave and Millimetre-Wave Monolithic Circuits Symposium,
Digest of Papers, pp. 73-76, 1990.
[54] M. Detratti, J. P. Pascual, M. L. De-La-Fuente, J. Cabo, and J. L. Garcia, “A GaAs
monolithic linear-in-dB wide-dynamic-range variable-gain amplifier with matching
compensation for 1.95-GHz applications,” Microwave and Optical Technology Letters,
vol. 44, no. 3, pp. 251-257, 2005
[55] K. Nishikawa, and T. Tokumitsu, “An MMIC low-distortion variable-gain amplifier
using active feedback,” IEEE Transactions on Microwave Theory and Techniques, vol.
43, no. 12, pt. 2. pp. 2812-2816, 1995.
[56] M. Anowar Masud, and H. Zirath, “A 45 dB variable gain low noise MMIC amplifier,”
35th European Microwave Conference, pp. 669-672, 2005.
[57] L. Wu, U. Basaran, R. Tao, M. Berroth, and Z. Boos, “A 2 GHz CMOS dB-Linear
programmable-gain amplifier with 51 dB dynamic range,” 35th European Microwave
Conference (EuMC 2005), Paris, France, October 3-7, 2005, pp. 617-620.
[58] G. Hau, T. Nishimura, and N. Iwata, "High efficiency, wide dynamic range variable
gain and power amplifier MMICs for wide-band CDMA handsets," IEEE Microwave
and wireless components letters, vol. 11, no. 1, pp. 13-15, Jan. 2001.
[59] C. Hsiao, C. Kuo, and Y. Chan, “Integrated CMOS power amplifier and down-converter
for 2.4 GHz Bluetooth applications,” IEEE Radio and Wireless Conference, pp. 29-32,
August, 2001.
[60] C. Fallesen, and P. Asbeck, “A 1 W CMOS power amplifier for GSM-1800 with 55 %
PAE,” IEEE MTT-S International Microwave Symposium, vol. 2, pp. 911-914, May,
2001.
[61] Y. Ding, and R. Harjani, “A CMOS high efficiency 22 dBm linear power amplifier,”
IEEE Custom Integrated Circuits Conference, pp. 557-560, Oct. 2004.
116
References
[62] T. Sowlati, and D. Leenaerts, “A 2.4-GHz 0.18-µm CMOS self-biased cascade power
amplifier,” IEEE Journal of Solid-State Circuits, vol. 38, no. 8, pp. 1318-1324, Aug.
2003.
[63] P. Reyneart, and M. Steyaert, “A 1.75-GHz polar modulated CMOS RF power amplifier
for GSM-EDGE,” IEEE Journal of Solid-State Circuits, vol. 40, no. 12, pp. 2598-2608,
Dec. 2005.
[64] V. Knopik, B. Martineau, and D. Belot, “A 20 dBm CMOS class AB power amplifier
design for low cost 2GHz-2.45GHz consumer applications in a 0.13-µm technology,”
IEEE International Symp. on Circuits and Systems, vol. 3, pp. 2675-2678, May. 2005.
[65] P. Reynaert, and M. Steyaert, “RF Power Amplifiers for Mobile Communications,”
2006, Springer.
[66] J. A. Hopwood, “Microplasma: physics and applications,” Plasma Science Committee of
the National Academies, Boston, USA, Sep. 27, 2003.
[67] X. Jing, Z. Du, and K. Gong, “A compact multiband planar antenna for mobile
handsets,” Antennas and wireless propagation letters, vol. 5, Issue 1, Dec. 2006, pp.
343-345.
[68] J. Anguera, C. Puente, C. Borja, N. Delbene, and J. Soler, “Dual-frequency broad-band
stacked microstrip patch antenna,” Antennas and wireless propagation letters, vol. 2,
Issue 1, 2003, pp. 36-39.
[69] C. Monzon, “A small dual-frequency transformer in two section,” IEEE Trans. On
microwave theory and techniques, vol. 51, no. 4, pp. 1157-1161, Apr. 2003.
[70] L. Wu. U. Basaran, I. Dettmann, M. Berroth, T. Bitzer, and A. Pascht, “A broadband
high efficiency class-AB LDMOS balanced power amplifier,” 35th European
Microwave Conference (EuMC 2005), Paris, France, October 3-7, 2005, pp. 1079-1082.
[71] C. Cassan, and P. Gola, “A 3.5 GHz 25 W silicon LDMOS RFIC power amplifier for
WiMAX applications,” RFIC Symposium, Issue 3-5, pp. 87-90, June 2007.
[72] R. Bagger, P. Andersson, and C. D. Shih, “20 W LDMOS power amplifier IC for linear
driver application,” IEEE MTT-S International Microwave Symposium, Issue 3-8, pp.
1075-1078, June. 2007.
117
Was this manual useful for you? yes no
Thank you for your participation!

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Download PDF

advertising