Bandwidth considerations of high efficiency microwave power amplifiers

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B

ANDWIDTH

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ONSIDERATIONS OF

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IGH

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FFICIENCY

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ICROWAVE

P

OWER

A

MPLIFIERS

Vorgelegt von

M.Sc. Ahmed Altanany

aus. Palästina

Von der Fakultät IV - Elektrotechnik und Informatik der Technischen Universität Berlin

zur Erlangung des akademischen Grades

Doktor der Ingenieurwissenschaften (Dr.-Ing.)

Genehmigte Dissertation

Promotionsausschuss:

Vorsitzender: : Prof. Dr.-Ing. Sibylle Dieckerhoff - Technische Universität Berlin Berichtender: : Prof. Dr.-Ing. Georg Böck - Technische Universität Berlin

Berichtender: : Prof. Dr.-Ing. Reinhard Knöchel - Christian-Albrechts-Universität zu Kiel

Tag der wissenschaftlichen Aussprache: 10. Dezember 2014

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To my parents

who have given me the opportunity of an education from the best institutions and support throughout my life.

To my lovely wife and daughters

who have always stood by me and dealt with all of my absence from many family occasions with a smile.

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Acknowledgement

First and foremost, it is with immense gratitude that I acknowledge the support and help of my supervisor Prof. Dr.-Ing. Georg Böck. I would like to thank him for encouraging my research and for allowing me to grow as a research scientist in his eminent group. His advice on both research as well as on my career have been invaluable. I could never have imagined a better advisor for my Ph.D study.

I would also like to thank Prof. Dr.-Ing. Reinhard Knöchel who accepted to be a second examiner for this Ph.D. thesis as well as Prof. Dr.-Ing. Sibylle Dieckerhoff being the chairman of the dissertation committee.

It gives me great pleasure in acknowledging the support and help of Dr. Chafik Meliani and Dr. Olof Bengtsson from the Leibniz Institut für innovative Mikroelektronik (IHP) and Leibniz Ferdinand Braun institute (FBH) for their valuable discussions and help. Without their guidance and persistence help this dissertation would not have been perfected.

I owe my deepest gratitude to the Federal ministry of economics and technology in Germany for funding this project. Without their fund this work would never been in completed.

I am indebted to my many colleagues in TU-Berlin who supported me during all the last years. The technical discussions we had have inspired the flow of this work to reach its current status. The perfect atmosphere in and the social activities gave me the energy to put my ideas to the world’s demands. My deep thanks

My completion of this work could not have been accomplished without the support of my friends overseas and specially my cousin Mohammed El-Tanani.

I can not find words to express my gratitude to my family and parents. Their continuous encouragement and motivation have given me a perfect launch to achieve successful results. Their wishes lighten my path towards my goal.

Finally, my deepest gratitude to my wife and daughters for their patient during my study and for giving me a push to start writing.

Thank you all Ahmed Altanany 5th June 2015

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Abstract

The dissipated power of mobile base stations is mainly consumed by the power amplifiers (PAs) and their cooling devices. On-going research and developments in the wireless field leads to new communication standards and operating frequencies. As a result, the bandwidth becomes an important figure in modern wireless base stations. Moreover, the new standards have high peak to average power ratios (PAPR), which require high efficiency at saturation and at back-off power levels as well. Hence, high average efficiency, linearity and bandwidth are the key parameters for the current developments and the optimum trade-off between these parameters is in the focal point of current developments. Switch-mode power amplifiers are strong candidates for highly efficient PAs because of their theoretical drain efficiency of 100 % at saturation.

Investigations on highly efficient power amplifier techniques such as switch mode and har-monically tuned PAs have been the subject of research for many years. However, there have been only a small number of researches that have extended the amplifier bandwidth while keeping high the efficiency. Extending the bandwidth of highly efficient power amplifiers is the scope of this work. Several techniques are presented and limiting factors on the achievable efficiency and bandwidth are analysed. It is shown, that the output capacitor of the transistor is the main limiting factor on efficiency and gain. The GaN HEMT is a promising device technology for the SMPA. This is due to its high breakdown voltage, high power density, high cut-off frequency and low thermal resistance. However, designing high frequency and high output power switch-mode PAs for maximum efficiency remains a challenge. The reason is that the output capacitance increases with the transistor size. Hence, the influence on efficiency enhancement by proper impedance matching at harmonic frequencies drops. Nevertheless, with respect to that issue GaN HEMTS are advantageous over Si-LDMOS.

This work presents four different broadband power amplifiers using GaN HEMTs working at different output power levels and different frequency bands from VHF- over UHF- to L- and S-band. The amplifiers were designed, built up and the simulations were verified by measurements. Techniques for bandwidth extension while keeping up output power level and efficiency are investigated and discussed. These amplifiers achieve outstanding results approaching 88 % of maximum drain efficiency for the PA in UHF band and 85 % of peak drain efficiency for the PA in L-Band. The output powers of the low frequency amplifiers were 50 W and for the high frequency amplifiers 10 W.

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Kurzfassung

Die Verlustleistung mobiler Basisstationen wird hauptsächlich durch den Leistungsverstärker und seine Kühleinrichtungen generiert. Die kontinuierlich fortschreitende Innovation auf dem Gebiet der drahtlosen Kommunikationstechnik führt zu immer neuen Betriebsfrequenzen und Standards, die u.a. auch durch zunehmende CREST-Faktoren gekennzeichnet sind. Dies erfordert Leistungsverstärker mit hoher Effizienz und Bandbreite, nicht nur bei maximaler Ausgangsleis-tung, sondern auch bei reduzierten Leistungspegeln (Back-Off Betrieb). Dem bestmöglichen Kompromiss zwischen Linearität und Effizienz bei gleichzeitig hoher Bandbreite, kommt daher bei modernen Leistungsverstärkern eine herausragende Bedeutung zu. Sogenannte Schaltver-stärker sind besonders geeignete Kandidaten zur Bewältigung dieser Herausforderungen, da ihr theoretischer Wirkungsgrad bei maximaler Ausgangsleistung gegen 100 % geht.

Mikrowellen-Schaltverstärker stehen seit Jahren im Zentrum der Forschung. Allerdings gibt es bislang nur wenige Arbeiten, die einem hohen Wirkungsgrad bei gleichzeitig hoher Bandbreite erreichen. Die simultane Optimierung dieser beiden Performanz-Parameter ist die Zielrichtung dieser Arbeit. Limitierende Faktoren hinsichtlich Effizienz und Bandbreite werden analysiert. Einen in dieser Hinsicht besonders nachteiligen Einfluss übt die Ausgangskapazität des Transistors aus. Der GaN-HEMT Technologie ist wegen ihrer hohen Durchbruchspannung und Leistungsdichte und wegen ihres geringen Wärmewiderstandes eine vielversprechende Tech-nologie für die Realisierung von hocheffizienten Mikrowellen-Leistungsverstärkern. Ihr Entwurf für hohe Frequenzen, Ausgangsleistungen und Bandbreiten bei gleichzeitig hoher Effizienz bleibt dennoch eine Herausforderung. Der hauptsächliche Grund dafür ist die mit zunehmender Transistorgröße und Frequenz ansteigende Ausgangskapazität, die wegen zunehmendem Kurz-schluss der harmonischen Frequenzanteile eine Optimierung der Kurvenform von Strom und Spannung im intrinsischen Transistor weitgehend verhindert. Diese Gegebenheit führt zu einer stetigen Abnahme des Wirkungsgrades mit zunehmender Betriebsfrequenz. Wegen der höheren Kapazitäten von Si-LDMOS Transistoren gegenüber GaN HEMTs, besitzen Letztere mit zun-ehmender Frequenz grundsätzlich Vorteile. Aufgrund dessen wird hier ausschließlich auf die GaN-HEMT Technologie zurückgegriffen.

Diese Arbeit beschäftigt sich mit dem Entwurf von vier Breitband-Leistungsverstärkern für das VHF-, UHF-, L und S-Band. Die entworfenen Verstärker wurden realisiert und charakterisiert. Die Verstärker zeigen mit nahezu 88 % maximaler Drain-Effizienz im UHF-Band und 85 % im L-Band ein hervorragendes Verhalten. Die Ausgangsleistung der beiden niederfrequenten Verstärker betrug 50 W, die der hochfrequenten 10 W.

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List of Figures

1.1 Spectrum allocation for the most common wireless standards. . . 2

1.2 Base-station model showing the consumed power in different blocks. . . 3

1.3 a) Cross section view of the GaN HEMT transistor, and b) band-gap structure of the HEMT transistor. . . 6

1.4 Typical large signal GaN HEMT model. . . 7

2.1 Energy conservation in power amplifier operation. . . 13

2.2 Two-port network with power definitions. . . 14

2.3 Typical performance for a power amplifier versus input power. . . 16

2.4 Different types of linearity measurements. . . 16

2.5 Voltage gain compression as in (2.13). . . 17

2.6 Single tone output power for the fundamental, second harmonic and third harmonic. 18 2.7 Typical AM-AM/AM-PM curves for power amplifiers. . . 18

2.8 Output frequency component of an amplifier excited by a two tone signal. . . . 20

2.9 Third order intercept point example. . . 21

2.10 Typical spectrum for a UMTS signal for PA. . . 21

2.11 Different stabilization techniques are used in this work. . . 23

3.1 Simple FET model. . . 25

3.2 Characteristic I-V curve for ideal FET operation. . . 26

3.3 Class-A power amplifier waveforms . . . 26

3.4 Typical load pull simulation showing output power (filled circle), PAE (cross symbol) and IMD3(solid) for, a) fundamental load impedance, and b) second harmonic load impedance. . . 27

3.5 Classification of power amplifier . . . 28

3.6 Classical PA classes waveforms, bias points, load lines and drive signals. . . 29

3.7 Typical schematic for classical classes. . . 29

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xvi LIST OF FIGURES

3.9 Drain current DC and harmonic component for the DC, fundamental and the harmonics up to the fifth components. . . 30 3.10 Drain efficiency η and output power Pout for general conduction angle. . . 31 3.11 Typical circuit of class-E PA. . . 32 3.12 Drain current isw(t), Drain Voltage vsw(t) and output capacitance current iCds(t)

of Class-E power amplifier. . . 33 3.13 Typical voltage mode Class-D power amplifier circuit. . . 35 3.14 Ideal current and voltage waveforms for Class-D family power amplifiers. . . . 35 3.15 Schematic diagram for Current mode Class-D power amplifier. . . 37 3.16 Typical circuit diagram for A Class F-Power amplifier. . . 37 3.17 Typical circuit diagram for an inverse Class-F-Power amplifier. . . 38 3.18 Ideal current and voltage waveforms for inverse Class-F powers amplifier, for up

to two/three controlled harmonics for even/odd components (dotted) and for up to four/five controlled harmonics for even/odd components (solid). . . 38 3.19 Efficiency and output power capability for maximum flat Class-F power amplifier

with different odd and even components combination . . . 39 3.20 Output power and efficiency of different combinations of harmonically tuned

power amplifier. . . 41 3.21 Typical I-V curve with knee effect . . . 42 3.22 Circuit model for FET with major parasitic capacitances . . . 43 3.23 Calculated gain from (3.75) over the frequency with a) Cgsof a range between

2 pF and 10 pF in 0.2 pF steps, b) C_gd of a range between 0.1 pF and 1.3 pF in 0.3 pF steps, and c) a) Cdsof a range between 1 pF and 10 pF in 2 pF steps; g_m= 0.525 S, RL= 1 Ω and LL = 2.696 nH. . . 45 3.24 fmax for different parasitic values obtained from each diagram in Fig. 3.23

crossing the unity power gain (zero in dB). For each graph in the diagram, the other capacitance values are kept similar to Fig. 3.23. . . 46 3.25 Calculated efficiency factor from (3.102) over the frequency with a) Cgd of a

range between 0.1 pF and 1.3 pF in 0.3 pF steps, and b) Cdsof a range between 1 pF and 10 pF in 2 pF steps; gm= 0.525 S, RL = 1 Ω and LL= 2.696 nH. . . . 50

4.1 Designed Resonant Circuit utilizing the DC-feed as parallel inductor. . . 52 4.2 a) Ideal Parallel LC resonant circuit presented to ideal CMCD PA, and b)

Imped-ance resulted from the designed resonator (red) and from the ideal parallel LC circuit (blue). The small circles represent the the operating frequency (2.14 GHz) 52 4.3 Designed single stub output matching network for CMCD PA. . . 53 4.4 Photo of the fabricated CMCD power amplifier using 30 W GaN HEMT from

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LIST OF FIGURES xvii

4.5 Simulation results of time domain voltage and current waveforms for the designed CMCD PA taken without de-embedding output die parasitics. . . 54 4.6 Simulation (solid) and Measured (symbol) for the a) insertion loss and b) small

signal gain of the designed PA . . . 54 4.7 Large signal measurement setup used in to measure the designed PA in this thesis. 55 4.8 Simulation (solid) and Measured (symbol) for the a) output power and power gain,

and b) efficiency (drain and PAE) of the designed PA at the designed frequency, i.e.; 2.14 GHz . . . 55 4.9 Efficiency performance versus output power showing more than 50 % PAE at

3 dB OPBO at the designed frequency, i.e.; 2.14 GHz. . . 56 4.10 Typical voltage mode Class-D power amplifier circuit. . . 57 4.11 Load impedance of the output matching network integrated with resonator for

the designed Class-F−1 power amplifier shown in Fig. 4.10. . . 57 4.12 Measured (symbol) result for the output power, power gain and efficiency versus

a) frequency and b) input power for the designed Class-F−1 PA. . . 58 4.13 output power, power gain and efficiency over the drain supply voltage for designed

Class-F−1PA at 2.35 GHz operating frequency. . . 59 4.14 Fundamental and harmonic spectral density for an arbitrary signal with a certain

bandwidth. . . 59

5.1 Circuit diagrams of broadband matching problems for a) resistive matching, b)single matching, c) double matching. . . 62 5.2 Different load problem for Bode-Fano limit with passive lossless matching

net-work (MN) and a) resistive load and shunt capacitor, b) resistive load and shunt capacitor series inductor. . . 62 5.3 Bode-Fano limit criterion for a constant reflection coefficient. . . 63 5.4 Fractional bandwidth limit according to Bode-Fano limit with different reflection

coefficient and different quality factor assuming constant Γm. . . 63 5.5 Reflection coefficient definition for resistive load network with shunt capacitor

and series inductor including a passive lossless matching network. . . 64 5.6 Evaluation of Bode-Fano limit for the circuit in Fig. 5.5 with XCas a parameter

and XL= 2 showing a) reflection coefficient and b) return loss from the reflection coefficient; the dashed line shows the case where the inductor is not present. . 65 5.7 Evaluation of Bode-Fano limit for the circuit in Fig. 5.5 with XL as a parameter

and XC= 2 showing a) reflection coefficient and b) return loss from the reflection coefficient; the dashed line shows the case where the inductor is not present. . . 65

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xviii LIST OF FIGURES

5.8 Different matching component behaviour in a matching network, the black dot is the default load impedance and the arrow present the increasing value/length of the component and transmission line TL. . . 66 5.9 Design algorithm for the matching network to design a broadband highly efficient

PA. . . 68 5.10 Load-pull contours for the output power (red) with step 0.5 dB, drain efficiency

(green) with 2 % step and DC current (blue) with 0.6 mA step for a) 225 MHz, b) 312 MHz and c) 400 MHz. the black dot is the realised load impedance. . . 70 5.11 Ideal optimum a) source impedances and b) load impedances over the entire band

according to the load/source-pull simulation. . . 71 5.12 Ideal performance for the transistor with ideal load/source-pull impedances;

out-put power (red), gain (blue), drain efficiency (green) and power added efficiency (black). . . 71 5.13 Proposed circuit diagram topology consists of output matching network (OMN)

and band-pass filter (BPF). . . 72 5.14 Load matching network synthesize showing a) circuit impedance network and b)

Load impedances for each element in the matching network. . . 72 5.15 Butterworth bandpass filter used in the matching network of the designed PA. . 73 5.16 Matching network design to include the first series capacitor of the band-pass filter. 74 5.17 Drain and gate DC-feed network used in the PA design including the bypass

capacitors, the dots here represent a multi section of the same DC-feed network. 74 5.18 The designed PA circuit with the stability circuits. . . 75 5.19 Simulation without stability network (solid) and with stability network (dashed)

for a) K-factor and b) maximum gain. . . 76 5.20 Photo of the fabricated VHF broad-band Class-E power amplifier using 45 W

GaN HEMT from Eudyna. . . 77 5.21 Simulated (solid) and measured (symbol) of the measured small signal gain using

-20 dBm, the dots showing the second harmonic small signal gain. . . 77 5.22 Simulated (solid) and measured (symbol) for a) output power (red) and Gain

(blue), and b) drain efficiency (green) and power added efficiency (black), versus input power with Idq= 115 mA, Vgg= −1.35 V, Vdd = 50 V. . . 78 5.23 Simulated (solid) and measured (symbol) for output power (red) and Gain (blue),

drain efficiency (green) and power added efficiency (black), versus input power with Idq= 115 mA, Vgg= −1.35 V, Vdd = 50 V. . . 79 5.24 Measured fundamental output power (red), second harmonic power (blue) and

third harmonic (green). . . 79 5.25 Linearity measurement for the amplifier showing a) IMD3and b) OIP3. . . 80

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LIST OF FIGURES xix

5.26 Output power (red) and drain efficiency (green) with different biasing voltage values and input power for a) 225 MHz b) 312 MHz and c) 400 MHz. . . 81 5.27 Measurement set-up for the PA reliability showing the tuner (VSWR), phase

shifter (Φ) and the de-embedded reference plane. . . 82 5.28 Simulated (solid) and measured (dashed) for the Output power with different

VSWR and phase values for a) 225 MHz b) 312 MHz and c) 400 MHz. . . 83 5.29 Simulated (solid) and measured (dashed) for the drain efficiency with different

VSWR and phase values for a) 225 MHz b) 312 MHz and c) 400 MHz. . . 84 5.30 De-embedded impedance contour for sweeping VSWR value and phase (star

black) imposed on the ideal output power contours (red) with 0.5 dB step, drain efficiency contours (green) with 2 % step and DC current contours (blue) with 0.6 mA step, The black line is the designed load impedances for a) 225 MHz b) 312 MHz and c) 400 MHz. . . 85 5.31 Ideal load/source-pull a) load impedance magnitude (blue) and phase (red), and

b) ideal performances for output power (red), gain (blue), drain efficiency (green) and power added efficiency (black). . . 86 5.32 a) Filter topology used in output matching network showing the capacitor dashed

box that will be replaced, and b) the filter transmission loss over the targeted band and the harmonic. . . 87 5.33 Full output matching network including the filter used in the ideal design step. . 88 5.34 Photo of the fabricated UHF broad-band Class-E power amplifier using 30 W

GaN HEMT from Eudyna. . . 89 5.35 Simulation of final stage for the current (red) and voltage (blue) waveforms. The

dashed lines shows the zero level for the current, where below the dashed line is the time for the output capacitor Cds discharging and above the line is the charging period of the output capacitor Cds. . . 89 5.36 Measured small signal gain across the bandwidth with -30 dBm showing the gain

for the second harmonic of the lowest frequency. . . 90 5.37 Measured output power (red), gain (blue) drain efficiency (green) and PAE (black)

over the stimulated input power for the centre frequency, i.e., 800 MHz, of the designed power with Vd= 50 V, Idq= 150 mA . . . 90 5.38 Measured output power (red), gain (blue) drain efficiency (green) and PAE (black)

across the bandwidth for the maximum output power (Pin= 34 dBm) frequency, i.e., 800 MHz, of the designed power with Vd = 50 V, Idq= 150 mA. . . 91 5.39 Circuit diagram of the PA showing the de-embedded load impedance and drain

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xx LIST OF FIGURES

5.40 Simulated current (red) and voltage (blue) waveforms for a) 600 MHz, b) 800 MHz and c) 1000 MHz. The dashed lines shows the zero level for the current, where below the dashed line is the time for the output capacitor Cds discharging and above the line is the charging period of the output capacitor Cds. 93 5.41 Calculated load impedances from the simulation for a) 600 MHz, b) 800 MHz

and c) 1000 MHz. . . 94

6.1 Output power and PAE contours for 10W PA design at a) 1.7 GHZ, b) 2.2 GHz, and, c) 2.7 GHz. The input power was 29 dBm, Vdd = 28 V and Id= 20 mA. . 98 6.2 Optimum load impedances, i.e., magnitude and phase, for the fundamental

frequency, second and third harmonic. The input power was 29 dBm, V_dd= 28 V and Id= 20 mA. . . 99 6.3 Optimum output power and PAE obtained from the optimum load impedances.

The input power was 29 dBm, Vdd = 28 V and Id= 20 mA. . . 99 6.4 Output power and PAE for three different frequencies versus (a) the magnitude of

the fundamental frequency load impedance and (b) the phase of the fundamental frequency load impedance. The input power was 29 dBm, Vdd= 28 V and Id= 20 mA. . . 100 6.5 Output power and PAE for three different frequencies versus (a) the magnitude of

the second harmonic load impedance and (b) the phase of the second harmonic load impedance. The input power was 29 dBm, Vdd = 28 V and Id= 20 mA. . . 101 6.6 Output power contours with 0.3 dB step (solid green) and PAE (symbol red)

with 5 % step performances versus the second harmonic load impedances for; a) 1.7 GHz, a) 2.2 GHz, and, a) 2.7 GHz. The input power was 29 dBm, Vdd= 28 V and Id= 20 mA. . . 102 6.7 PAE performance with full second harmonic reflection coefficient and different

phase values for three different frequencies. The input power was 29 dBm, V_dd= 28 V and Id= 20 mA. . . 103 6.8 Method for obtaining the safe-zone of load impedances by finding the intersection

of optimum impedance for a) fundamental frequency and b) second harmonic. . 103 6.9 Safe zone region definition. . . 104 6.10 a) Ideal single section matching network for 10 W power amplifier design, b) load

impedances for the first three harmonics at three different frequencies obtained at each section from the matching network. . . 104 6.11 Realised load impedance from two section matching network for the fundamental

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LIST OF FIGURES xxi

6.12 comparison between realised simulated results (symbol) and optimum simulated results (solid) for the output power and PAE. The input power was 29 dBm, V_dd = 28 V and Id = 20 mA. . . 106 6.13 Photo of the fabricated broad-band harmonically tuned power amplifier using

10 W GaN HEMT from Cree Inc. . . 106 6.14 Measured output power, power gain and PAE for the designed power amplifier

across the bandwidth for the 1 dB compression point (hollow symbol) and 3 dB compression point (filled symbol). The input power was 30 − 32 dBm, Vdd= 28 V and Id= 20 mA. . . 107 6.15 Measured power amplifier performances across the input power at the centre

frequency (2.125 GHz). Vdd = 28 V and Id = 20 mA. . . 107 6.16 ACPR and average output power and drain efficiency versus the supply drain

voltage and gate bias voltage at 35 dBm. . . 108 6.17 a) Typical transistor package model and b) small signal load impedances seen

from the lead reference plane of a 100W Cree transistor. The input power was 40 dBm, Vdd = 28 V and Id= 400 mA. . . 108 6.18 Output power contours with 0.5 dB step and PAE contours with 5 % step for

100 W power amplifier at the edge frequencies. . . 110 6.19 Fundamental (red) second harmonic (green) and third harmonic (blue) load

im-pedances for a) optimum case with Smith chart centred at 50 Ω, and b) optimum (dotted), realised from ideal lumped OMN (crossed) and realised from microstrip OMN (solid). The input power was 40 dBm, Vdd = 28 V and Id= 400 mA. . . 111 6.20 PAE performance with full second harmonic reflection coefficient and different

phase values for two different frequencies. The input power was 40 dBm, V_dd = 28 V and Id= 400 mA. . . 111 6.21 Stability factor for the designed power amplifier. The input power was 40 dBm,

V_dd = 28 V and Id = 400 mA. . . 112 6.22 Ideal lumped component matching network for the designed amplifier. The input

power was 40 dBm, Vdd = 28 V and Id= 400 mA. . . 113 6.23 Ideal (hollow symbol) and realies from ideal lumped OMN (filled symbol) for

a) output power and b) PAE. The input power was 40 dBm, Vdd = 28 V and I_d = 400 mA. . . 113 6.24 Simulated output power and PAE performances for different case temperature

(i.e., 25◦C, 50◦C and 85◦C). The input power was 40 dBm, Vdd = 28 V and I_d = 400 mA. . . 114 6.25 Photo of the fabricated broad-band harmonically tuned power amplifier using

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xxii LIST OF FIGURES

6.26 Measured output power and PAE performances of the designed PA for different frequency vs.(a) gate bias voltage (b) drain supply voltage. . . 115 6.27 Simulated (solid) and measured (symbol) Small signal gain. The input power

was −20 dBm, Vdd= 28 V and Id= 650 mA. . . 115 6.28 Simulated (solid) and measured (symbol) performances at 28 V drain supply

voltage and Id= 650 mA for CW signal at frequency of 1.95 GHz. . . 116 6.29 performance over the frequency for different input power i.e.; 22, 27, 32, 37 and

40 dBm for (a) output power (black) and power gain (blue) , (b) drain efficiency (green) and power added efficiency (brown). The supply voltage is Vdd = 28 V and Id= 650 mA. . . 116 6.30 Performance over the frequency for the post-tuned power amplifier with different

output power levels i.e.; Pout_sat, Pout_3dB and Pout_1dB. The supply voltage is V_dd= 28 V and I_d= 650 mA. . . 117 6.31 Measured upper (red) and lower (black) ACLR without memory DPD (hollow

symbol) and with memory DPD (filled symbol) vs. average output power at 2.15 GHz operating frequency. The supply voltage is V_dd = 28 V and I_d= 650 mA.117

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List of Tables

1.1 Important parameters for the most common materials used in semiconductor devices, adapted from [5, 6]. . . 4 1.2 An important parameters for the most common substrates used in semiconductor

devices, adapted from [7]. . . 6 1.3 State of the art for broadband power amplifier with more than 50 % drain

effi-ciency published in the last five years Based on GaN HEMT technology. . . 10

3.1 Design Parameters for Class-AB, Class-C and Class-B PAs with Class-A PA Parameters. . . 32 3.2 Optimum voltage harmonic gain and design factor for Harmonically Tuned power

amplifiers . . . 40

4.1 Results of Harmonic Impedances Obtained from the Proposed Topology in Fig.4.10. The symbols are defined in Fig. 4.11 . . . 58 4.2 Frequency Parameters for Class-F/F−1 and Class-E PA for minimal Broadband

condition value design. . . 60

5.1 Ideal lumped element values for the output matching network used to design broadband VHF PA. . . 72 5.2 Measured IMD3for three different frequencies with four output power levels . 80 5.3 Extreme output power degradation for three different frequency points with

different VSWR values. . . 82 5.4 Ideal lumped elements values used in the matching network shown in Fig. 5.33. 88 5.5 Measured PA performances across the bandwidth with 100 MHz step. . . 91

6.1 Optimum Load Impedances for the First Three Harmonic at Three Different Frequencies . . . 100

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Acronyms

2-DEG Two-dimensional electron gas

AC Alternating current

ACLR Adjacent channel leakage Ratio

ACPR Adjacent channel power ratio

AlGaN Aluminium gallium nitride

AlN Aluminium nitride

CMCD Current mode Class-D

DC Direct current

FET Field effect transistor

GaN Gallium nitride

GSM Global System for Mobile Communications, originally Groupe Spécial Mobile

HD Harmonic distortion

HTPA Harmonically tuned PA

IIP Input intercept point

IMD Intermodulation distortion

LTE Long-Term Evolution

OIP Output intercept point

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xxvi Acronyms

PAE Power added efficiency

RF Radio frequency

SiC Silicon carbide

SNR Signal-to-noise ratio

SRF Self resonant frequency

UMTS Universal Mobile Telecommunications System

VMCD Voltage mode Class-D

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List of Symbols and units

A Ampere

C Capacitor

cm Centimetre

dB Decibel

dBc Decibel referenced to the carrier

dBm Decibel referenced to the mW

eV Electron volt G Gain GHz Gigahertz K Stability factor k kelvin L Inductor mA milliampere MHz Megahertz mW milliwatt

PAE Power added efficiency

R Resistor

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xxviii Symbols and Units

t Time

V Voltage

W Watt

E_br Break down field

E_g Band gap

f Frequency

f₀ Fundamental frequency

gm,max Maximum transconductance

g_m Transconductance

I Current

I0 DC-component current

I1 Fundamental-component voltage

I_d Channel drain current

IDS Drain-source current

i_ds(t) Compound (different frequency component) drain–source current

I_max Maximum current

P Power

P_1dB One decibel compression power

P_avg Average power

P_{DC,T L} DC power for tuned load PA

P_DC DC supply power

P_DCA DC power for Class-A PA

P_diss dissipated power

P_in RF input power

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Symbols and Units xxix

P_out Output power

P_{Pmax, f 0} Maximum power at the center frequency

P_sat Saturated power

Q Quality factor

RL,opt Optimum load resistance

RL,T L Optimum load resistance for tuned load PA

R_LA Optimum load resistor for Class-A PA

R_opt Optimum loadline impedance

R_L Load resistance

S Scattering parameter

S11 Input reflection coefficient

S21 Transmission coefficient

S22 Output reflection coefficient

V0 DC-component voltage

V1 Fundamental-component voltage

V_DS Drain-source voltage

v_ds(t) Compound (different frequency component) drain–source voltage

V_dsi Intrinsic drain-source voltage

V_GS Gate-source voltage

V_gsi Intrinsic gate-source voltage

V_in Input RF voltage

V_knee Knee voltage for FET

V_max Maximum voltage

v_o(t) Compound (different frequency component) output voltage

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xxx Symbols and Units

Z Impedance

Z_out Output impedance

β The gain of output current to the gate-source voltage

∆ scattering matrix determinant

∆ f Frequency spacing

εr Dielectric constant

η Drain efficiency

ηT L Drain efficiency for tuned load PA

Γ Reflection coefficient

γ The gain of input current to the gate-source voltage

κ Thermal conductivity

λ Wavelength

µ Input stability parameter

µ′ Output stability parameter

µ_n Electron mobility

Ω Ohm

ω Angular frequency

φ Phase

ρ Resistivity

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1 |

Introduction

1.1 Wireless Communication Networks

Since the early invention of wireless technology, there has been growing interest on its implemen-tations and developments, and it has been used to serve human beings in all aspects. Radio, television and cellular phones are some of the most influential wireless inventions of human beings. Each of these inventions is developed by introducing new standards. GSM, UMTS and LTE are different standards for mobile phone systems. The integration of these standards is a major issue in the base station transceivers.

In an RF transceiver chain, a power amplifier (PA) is one of the most influential RF blocks in the transceiver chain. It is an essential block in an RF transceiver to send a considerable amount of information to a remote destination in clear data transmissions and with minimum consumed power. The bold words in the last sentence describe the most important characteristics of the power amplifier operation. A considerable amount of information means high bandwidth and capacity. Remote destination describes the output power of the amplifier. Clear data transmission explains the linearity characteristics of a power amplifier. Finally, minimum consumed power is a measure of the power amplifier efficiency.

Achieving good values of these characteristics is a goal for power amplifier designers over the years. However, linearity and efficiency can not be achieved simultaneously from simple power amplifier architecture [1] [2]. In principle, power amplifier linearity is achieved when the signal is not clipped because it has zero harmonic contents. Nevertheless, the efficiency is only maximum if the signal is clipped that results in minimum current and voltage overlapping. The following subsection gives answers to the next three statements:

• The importance of the bandwidth in PA.

• Why the efficiency is significant for a power amplifier.

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2 1. Introduction

1.2 Motivation

The goal of this thesis is to design broadband power amplifiers in high-efficiency operations with high-output power. Usually, high-output power is defined based on wireless standard, size and capacity of a typical cellular cell. High-output power for a base station gives a high signal to noise ratio (SNR), which permits the use of high modulation rate near the base station. On the other hand, high power extends the range of the signal reception and reduces the total cost of wireless infrastructure.

1.2.1 Broadband Power Amplifier

Increasing the capacity of wireless communication requires high data rate transmissions. As a result, new standards are used to accommodate the need of high data rates. Fig. 1.1 represents the most common wireless standards used for data transmission. It is shown that these standards are allocated, mostly, around two frequencies: 0.8 GHz and 2.0 GHz. For a base station, it is convenient to integrate these standards together in one base station. This reduces the cost of the base station and makes it easier for upgrading new standards on one base station.

1.2.2 Efficient Power Amplifier

According to [3], information and communication technology (ICT) consumes, approximately, 3 % (600 TWh) of worldwide electrical energy. Wireless mobile base stations consume almost half of this energy [3]. Over 4 billion subscribers of mobile phones over the entire world demand an increasing number of base stations, which comes at the cost of consumed energy. Minimizing the dissipated power in base stations reduces the cost of the operation. Additionally, low energy consumptions reduce the environmental impact from CO2emissions.

The largest power consumption in a mobile base station is from the power amplifier, which consumes 65 % of the total energy. Digital Signal processing and baseband operations are consuming about 10 %, and AC/DC conversion components consume more than 7.5 %. The rest of the energy (17.5 %) is consumed by the air conditioning and cooling devices of a base station [4]. The lost energy in the latter part is the second largest consumption in a base station.

0.1 0.5 1.0 1.5 2.0 2.5 3.0 freq. [GHz] DVB-T DVB-T GSM-450 GSM-900 LTE UMTS LTE GSM-1800 GSM-1900 UMTS WLAN 802.11 b/g/n LTE

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1.2 Motivation 3 Cooling 17.5% AC/DC Converter 7.5% DSP/Baseband 10% RF component/PA 65% 1800 W 120 W Power Amplifier 65% Cooling 17.5% DSP/Baseband 10% AC/DC Converter 7.5%

Figure 1.2: Base-station model showing the consumed power in different blocks.

Most of the cooling system is dedicated to the heat produced from the power amplifier. Therefore, making an efficient power amplifier minimizes, in addition to the cost of the power amplifier energy, the cost of the cooling energy required for the base station. Fig. 1.2 presents the power loss distribution on different base-station's components. Typical base station requires 1800 W as an input signal, where the radiated power is about 120 W. This makes an overall base station's efficiency 6.7 %; in other word, base stations have a 1680 W loss in the energy.

In addition, an efficient power amplifier reduces the thermal problem of an RF transistor. It prolongs the transistor's life and gives a better linearity performance. It prevents the reduction of the output power over the time. Achieving a better power amplifier in terms of efficiency and output power, in addition to the bandwidth and the linearity, requires a good choice of RF power transistors.

1.2.3 RF Power Transistor

Since the early invention of the transistor, Silicon (Si) based BJT devices were the most preferable RF transistors for power amplifiers. However, many researches are carried to find different transistor technologies and different materials to increase RF performances. Semiconductor properties have different influences on different power amplifier characteristics. Table 1.1 presents the major semiconductor properties to the most-used materials. The shown properties have different impacts on the RF performance of power amplifier applications. In this table, the diamond is presented to show its out-performance and will not be considered in the following analysis.

Bandgap energy: Higher value of this parameter results in a higher operating temperature. This allows smaller devices to be fabricated compared to smaller bandgap materials. Higher operating temperatures permit cheaper packages to be used for the device. Smaller device

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4 1. Introduction

sizes increase the output impedance and, hence, make it easier to design a broadband power amplifier.

Thermal conductivity: It measures the ability of conducting heat to the external environment. Reducing this parameter will degrade the performance of the device over the time. Ad-ditionally, low thermal conductivity reduces electron mobility and the saturated electron velocity, which results in a degraded efficiency. GaN and SiC have 1.70 and 4.90 eV, respectively, which make them the best candidates for a high-power RF amplifier, and make them good for cheaper packaging.

Dielectric constant: The physical structure of any transistor can be modelled with different capacitors, inductors, resistors and a current source. These capacitors'values are influenced, mainly, from the dimension of the transistor and the dielectric constant. Decreasing this property reduces the associated capacitance and, hence, increases the load impedance. This leads to increasing the dimensions of the transistor to increase the output power. GaN has a relative dielectric constant of 8.90. It is the best candidate for a high bandwidth and efficiency operation.

Breakdown voltage: This indicates the maximum applied electric field without destroying the device. This increases the RF power swing and boosts the device power density. High breakdown voltage is suitable to increase the doping concentration and reduces the device dimension. As a result, high transconductance, high gain, maximum frequency and low parasitics are obtained in the device. Low parasitics increase the efficiency of the power amplifier. The highest breakdown voltage shown in Table 1.1 is obtained for GaN then SiC. This is the reason for choosing these materials for a high-performance power amplifier.

Saturation velocity: Higher saturation velocity of the electron leads to the reduction of the required time for the electrons to be transported through a channel which, in turn, increases the operating frequency. On the other hand, the current increases with increasing the

Table 1.1: Important parameters for the most common materials used in semi-conductor devices, adapted from [5, 6].

Material Si 4H-SiC InP GaAs GaN Diamond Bandgap Eg[eV] 1.11 3.20 1.34 1.43 3.40 5.45

Thermal Conductivity κ [W/cm·◦K] 1.50 4.90 0.68 0.46 1.70 20 Dielectric constant εr 11.70 9.70 14.00 12.90 8.90 5.70

Breakdown voltage Ebr[V/cm] 300 2000 500 400 5000 5000

Saturation velocity υsat[cm/s] 9 × 106 2 × 107 1.9 × 107 1.3 × 107 2.3 × 107 2.7 × 107

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1.2 Motivation 5

velocity of the electron. The corresponding saturated electrical field indicates how fast the electrons can be accelerated to reach their saturated velocity. GaN and SiC are the best materials for this parameter compared to GaAs and Si devices.

Electron mobility: Increasing electron mobility will increase the velocity of the electron and, hence, the current density increases. Moreover, a low value of mobility requires a larger electric field to reach the saturation velocity and, in turn, the maximum current. This results in increasing the knee effect of the transistor. The on-resistance becomes higher for lower mobility values, which increases the losses and reduces the efficiency. The electron mobility of GaN and SiC is the lowest among other materials shown in Table 1.1. However, GaN HEMT has a higher electron mobility, reaching more than 1000 cm2/V·s. This results from the 2DEG layer produced from the discontinuity in the energy bandgap between AlGaN and GaN. It is worth noting that it is very difficult to manufacture p−type transistors from wideband gap materials due to their low hole mobility. Additionally, there is no saturated hole velocity for these materials.

1.2.3.1 GaN HEMT Technology

High electron mobility transistor (HEMT) is a heterojunction field effect transistor (HFET). Another name for this transistor is modulation doped field effect transistor (MODFET). Fig. 1.3.a presents the basic structure of a HEMT transistor.

One of the important layers in manufacturing GaN HEMT is the substrate used in the transistor. The most important properties for the substrate are good thermal conductivity, high resistivity and low lattice mismatch with GaN. Table 1.2 shows that SiC is a very good substrate material choice. However, it is expensive and not produced in large wafer size, which makes a transistor made from this substrate very expensive compared to other high RF power transistors. After the substrate, a nucleation layer from GaN, AlGaN or AlN is used to increase the growth quality of other layers by optimizing the polarity of GaN crystal [7]

A modulated doped AlGaN, which is a wideband semiconductor, is grown over undoped GaN layer, i.e., narrow-bandgap semiconductor. Modulated doped layer refers to a layer of a certain semiconductor material doped for a certain thickness, i.e., close to the gate side, and undoped for smaller thickness near the undoped GaN. Fig. 1.3.b shows the energy band structure of this configuration. Due to the big bandgap difference of these semiconductor materials, there is a bend in the bandgap at the interface of the AlGaN/GaN which attracts the electrons from the AlGaN material and performs a two-dimensional electron gas (2DEG) layer. The reason for this name is that the electron confined in this layer is moving at a very high speed, nearly with saturation velocity, in y-direction, i.e., from source to drain, and in z-direction. The concentration of electrons in this layer is particularly very high, which increases the current density of this transistor. Furthermore, the mobility of these electrons is very high. This layer overcomes the

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6 1. Introduction

Table 1.2: An important parameters for the most common substrates used in semiconductor devices, adapted from [7].

Material Si 4H-SiC Sapphire

Thermal Conductivity κ [W/cm·◦K] 1.50 4.90 0.42 Resistivity ρ [Ω· cm] ≤ 104 ₁₀5_{− 10}8 _{> 10}6

lattice mismatch with GaN [%] −17 +3.5 −16

Wafer size [cm] 30.5 3.7 15

Cost low high low

drawback of the wideband semiconductor in their low mobility [8]. This thickness of the 2DEG layer can be controlled by the undoped layer of AlGaN, where a thick layer of this makes the 2DEG layer far from the ionized donor, i.e., doped AlGaN layer, thus electron mobility increases. However, electron charge density decreases if the undoped AlGaN layer thickness increases because it becomes hard for the electron to diffuse to the 2DEG layer [9].

1.2.3.2 GaN HEMT modelling

Transistor modelling is an important aspect for a RF-designer. It is beyond the thesis scope. However, it must be briefly mentioned here. Usually transistor modelling can be classified into three categories. First, the physical/electromagnetic model where the physical dimensions and boundary condition for solving the current and voltage across the device are used to describe the transistor. Usually, this model is very accurate, but it is hard to be simulated and requires fast computers to solve its equation. Second, the empirical model which is based on an equivalent circuit model. The basic elements in this model are curved fitted from different measurement parameters. Third, the table based model where the transistor is described as a two port black box

Substrate: Sapphire/SiC/Si Nucleation layer: GaN/AlGaN/AlN

Undoped GaN Undoped AlGaN Doped AlGaN Gate Source Drain 2DEG x y z (a) Schottky gate

n AlGaN Undoped GaN Undoped AlGaN

2DEG x

(b) Figure 1.3: a) Cross section view of the GaN HEMT transistor, and b) band-gap structure of the HEMT transistor.

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1.2 Motivation 7

with its response based on the applied current/voltage for each port. Most of the GaN HEMT models are based on an empirical model because of its extrapolation property.

A compact model describing GaN HEMT behaviour is shown in Fig. 1.4 adopted from [10]. The model consists of three parts; intrinsic, extrinsic and a thermal part. The intrinsic part contains a current source describing the drain source channel current. It also contains two other current sources which describe the leakage current from the gate to the drain and to the source. Moreover, two non-linear capacitors between the gate and drain, and gate and source terminals, i.e., (Cgd) and (Cgs). It also contains small resistances describing the losses between these terminals.

The extrinsic part contains, mainly, models of the terminal pads. Each of these pads is modelled as an inductance, resistance and capacitance between the pads. Additionally, a drain source capacitance is used to model the channel capacitance (Cds). It is worth noting that this capacitance is constant over all the voltage terminals. It is one of the advantages of a HEMT transistor compared to other high-power RF transistors, e.g., LDMOS. This capacitor is considered, with (Cgd), as main non-linear capacitance seen at the output of the transistor. Hence,

Lg Rg

+

Vgsi

−

Igs Cgs Rgs Igd Cgd Rgd

+

Vdsi

−

Ids Rd Ld RS LS Cds Cpds

+

Vds

−

Cpgs

+

Vgs

−

Cpgd Gate Drain Source Intrinsic

+

Vth

−

Ith Rth Cth

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8 1. Introduction

a linear output capacitance behaviour will enhance the switching performances of the transistor which makes GaN HEMT a good candidate for switch mode high efficiency power amplifier. The reason of this linear behaviour could be the high speed of the 2DEG layer which is not affected by the external applied field.

Finally, the thermal part contains a current source (Ith) calculated from the dissipated power. Thermal resistance (Rth) describes the losses, and the thermal capacitance (Cth) represents the thermal delay.

The drain channel current is a voltage controlled parameter described by [10]:

I_ds(V_gsi,V_dsi) = f1(Vgsi) · f2(Vdsi,Vgsi) · f3(Vdsi) · f4(∆T ) (1.1)

where f1(Vgsi) is the transfer function of the transistor and given by:

f1(Vgsi) = CDvc· [1 + tanh(β(Vgsi−Vc) + γ(Vgsi−Vc)3)] + CD_vsb· [1 + tanh(δ(Vgsi−Vsb))]

(1.2)

The parameter CDvcis the drain-source current at Vcgate voltage, where the transconductance is maximum (gm,max). Parameter β is calculated by gm,max/CDvc. The second term parameters are used to fine-tune the model at high gate voltages.

The f2(Vdsi,Vgsi) describes the output conductance of the transistor and is given by:

f₂(Vdsi,Vgsi) = 1 + λ 1 + ∆_λ(Vgsi−Vto)2 V_dsi, where Vto= Vc− 2 β (1.3)

The parameter λ models the drain current in the saturation region. ∆_λ is a parameter used to fine-tune the drain-source current in the sub-threshold region defined by Vto.

The f3(Vdsi,Vgsi) describe the triode region of the transistor and is given by:

f₃(Vdsi) = tanh(αVdsi), where α = α0 1 + KVgs

(1.4)

The slope of the drain-source current in the linear transistor region is controlled by the parameter α0. However, K is introduced here to add the dependence of the linear region on the gate source region.

Finally, f4(∆) models the behaviour of the drain-source current with respect of the temperature. It is given by:

f3(Vdsi) = 1 + κ ∆T

T₀ , where ∆T = RthIth (1.5)

The thermal current is equal to the total power passed through the channel, i.e., Ith = IdsVds.

However, it is worth to note that there are different models for GaN HEMT transistors, but more or less they have the basic principle of the already described model.

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1.3 State of the Art 9

1.3 State of the Art

Broadband power amplifier with high-efficiency operation has been under the research spot for the last decade. Most of these designed amplifiers were based on GaN HEMT technology. Table 1.3 represents the state of the art of highly efficient power amplifiers designed recently based on

GaN HEMT.

The designed amplifier in [11] uses Class-E PA concept. The resonator of the matching network uses spiral inductors based on a two layer substrate. The parasitic of the designed output resonator were used for the matching network. Without second harmonic trapping at the input matching network, the relative bandwidth was 22.22 %. The authors had shown that using the second harmonic trapping at the input side increases the relative bandwidth. However, this reduces the peak efficiency.

In [12], the author used the Class-J concept for designing linear high-efficiency PA. The output impedances, which gave optimum waveforms for the class, were acquired from the load-pull measurement system. The amplifier delivered a constant 10 W output power with drain efficiency ranges from 55 % to 65 %.

In [13], An octave bandwidth PA was designed using low pass matching network techniques, based on ideal lumped elements. From a source/load-pull simulation, optimum source/load impedances were extracted. The ideal matching network was converted step-by-step to be realised using microstrip lines. The achieved output power was from 10 W to 15 W with drain efficiency over the range of 57 − 72 %.

The amplifiers presented on [14], [18] and [19] were implemented based on a push-pull operation where they first delivered 100 W output power using 4-cell PA each of which has 30 W minimum output power. The latter two amplifiers used 2-cell of a power amplifier based on 45 W PA in two different bands and two different relative bandwidths.

In [15], the authors presented 1 GHz power amplifier based on simplified real frequency technique (SRFT). The amplifier operated with nearly 42 % bandwidth. The output power is 45 W, and the average drain efficiency is 63 %.

The concept of realizing the amplifier in [16] is by implementing distributed second harmonic impedance. The output matching network is composed of two blocks; the first was the funda-mental matching network, and the second was the second harmonic termination. About 25 % relative bandwidth was achieved with an average output power 45 W, and average drain efficiency of 66 % was achieved.

In [17], the authors implemented the novel concept of a continuous mode of operation for the power amplifier. This concept introduces a new dimension for a range of impedances, which are in favour of broadband operations. It used an output termination for the first three harmonic impedances. The average drain efficiency achieved was 74 % with output power of 10 W. The achieved operating bandwidth was more than 66 %.

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10 1. Introduction

Table 1.3: State of the art for broadband power amplifier with more than 50 % drain efficiency published in the last five years Based on GaN HEMT technology.

Year/Ref. Bandwidth [GHz] BW [%] Pout [W] Gain [dB] η [%]

2009 [11] 2.00 − 2.50 22.22 7.10 − 12.80 10.73 − 13.29 74.00 − 77.00 2.10 − 2.70 25.00 9.30 − 12.70 10.90 − 13.26 55.00 − 66.00 2009 [12] 1.40 − 2.60 60.00 10.00 10.20 − 12.20 55.00 − 65.00 2009 [Paper A] 0.60 − 1.00 50.00 36.00 − 52.00 10.20 − 12.20 66.00 − 87.00 2010 [13] 1.90 − 4.30 77.42 10.00 − 15.00 9.00 − 11.00 57.00 − 72.00 2010 [14] 0.10 − 1.00 163.64 104.00 − 121.00 15.50 − 18.60 61.40 − 76.60 2010 [15] 1.90 − 2.90 41.67 45.00 − 47.00 10.00 − 11.80 60.00 − 65.00 2010 [16] 1.80 − 2.30 24.39 45.00 − 48.00 11.50 − 14.00 60.00 − 76.00 2010 [Paper B] 1.55 − 2.75 50.00 9.80 − 15.50 10.20 − 12.20 71.00 − 87.00 2011 [17] 0.55 − 1.10 66.67 8.50 − 13.20 9.50 − 12.00 65.00 − 80.00 2011 [18] 0.9 − 2.20 83.87 10.00 − 20.00 10.00 − 13.00 63.00 − 89.00 2011 [19] 0.10 − 1.00 163.64 82.20 − 107.50 15.20 − 16.30 51.90 − 73.80 2011 [20] 2.15 − 2.65 20.83 11.40 − 15.00 11.00 − 12.50 65.00 − 76.00 2011 [Paper C] 1.55 − 2.53 41.10 89.00 − 110.00 8.90 − 11.00 61.00 − 79.00

Finally, in [20], the broadband concept of continuous mode of PA operation was used to find the load impedances up to third harmonic load impedance. SRFT was used to synthesize the output matching network. The achieved operating bandwidth was 21 % with more than 10 W output power and more than 65 % drain efficiency.

Comparing these results to the already published work by the authors, it is easily seen that the designed amplifiers in this work are among the top listed broadband state of the art power amplifiers. Additionally, the designed broadband power amplifiers cover all the wireless standards from VHF to S-Bands and have different ranges of output power, i.e., from 10 W passing through 50 W to 100 W.

1.4 Thesis Outline

To achieve the thesis goals, this work is divided into two parts: theory and implementation. The second chapter presents the most important figure of merit's definitions for power amplifier. Most of the definitions are used in this work and the rest are mentioned to give a better overview of the concept. The last section of this chapter talks about the stability criteria of power amplifier designs. Finally, some techniques that suppress the oscillation problem are presented.

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1.4 Thesis Outline 11

the load-pull technique and the load line theory. Followed by the power amplifier classes, which are divided into classical classes and the highly efficient classes. This is supported with design equations. The last section analyses the efficiency, gain and power limitations of the power amplifier from a typical parasitic of simple FET model. This chapter ends the discussion in the theory section of this dissertation.

Chapter four presents first step of designing broadband efficient power amplifiers. It discusses two published papers of the authors, [Paper D] and [Paper E]. It describes the design of single band power amplifiers using the two modes of operation; CMCD PA and Class-F−1PA. Their design approach and their measurements are shown for each of them.

Chapter five is the core of the thesis. The theory of the broadband matching technique is analysed. The implementation of a matching network, which is used throughout the thesis, is presented. Design procedure of a broadband power amplifier is also shown. This is followed by a design of two broadband power amplifiers for VHF and UHF applications. Extensive study and analysis of measured data is given. It also discusses the behaviour of the broadband amplifier over an entire band and gives a description to the power amplifier class of operation for every single frequency over the band, which gives a continous mode of operation. This section is based on [Paper A], [Paper F] and [Paper G].

In Chapter six, full broadband design concepts for L-band power amplifiers with two different output powers are presented. This is based on the continuity behaviour found in the previous chapter. A load pull simulation is shown to implement what is called the "safe-zone" on the Smith chart is analysed. Design and consideration of a high-output power amplifier is given. Evaluation from simulation as well as measurement results are presented. These two amplifiers were published in [Paper B] and [Paper C].

Chapter 7 concludes the overall work and gives key results of the broad band highly efficient power amplifier based on this contribution.

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2 |

Power Amplifier Characteristics

2.1 Power Amplifier Definitions

A RF power amplifier is an electronic device which converts DC-power to an RF power with the same RF input behaviour. From this definition, there are different characteristics for RF power amplifiers. The output power, from Fig. 2.1, can be defined as:

P_out = P_DC− P_diss (2.1)

where: Pout is the output power, PDCis the input DC power and Pdissis the dissipated power. The dissipated power includes ohmic losses, switching losses and losses in matching networks.

2.1.1 Basic Definitions

RF output power is the converted power to the load, mostly 50 Ω, from the DC-power within a finite bandwidth. This power is represented as a thermal power in the load, which is expressed as:

P_out= 1

2Re{Vout· I ∗

out} (2.2)

RF input power is the available input power that contains the signal information in the finite

PA

P_DC

P_diss

P_in P_out

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14 2. Power Amplifier Characteristics

bandwidth, which is expressed as:

P_in= 1

2Re{Vin· I ∗

in} (2.3)

DC input power is the injected power at DC, which is the main source of the power amplific-ation:

P_DC= V_DC· I_DC (2.4)

In an ideal FET operation the DC voltage and current in Eq. (2.4) are replaced with their respective drain components.

2.1.2 Gain Definitions

Gain definition depend on the reference plane and matching network. Fig. 2.2 shows four basic definitions for the power which will help for defining the gain.

• Pinis the input power stimulating the transistor.

• Pav,S is the power available from the source. It is equal to the Pin if the input matching network is conjugate match at the source side, otherwise it is larger than Pin.

• PLis the delivered power to the load.

• Pav,L is the device output power which is equal to the PL if the output matching network is a conjugate match, otherwise it is larger than PL.

Power gain is the ratio of an output power to an input power, i.e.;

GP= P_L

P_in (2.5)

It depends on the output impedance seen from the DUT but never on the source impedance.

⎡ ⎢ ⎢ ⎣ Z₁₁ Z₁₂ Z₂₁ Z₂₂ ⎤ ⎥ ⎥ ⎦ Zs + Vs − ZL Pin Pav,S PL Pav,L

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2.1 Power Amplifier Definitions 15

Available gain is the ratio of the power available from the DUT to the power available to the DUT. It depends on the source impedance.

G_A= Pav,L

P_av,S (2.6)

Transducer gain is the ratio of the power delivered to the load to the available power from source. In this definition, both source and load impedance influencing this gain:

GT = P_L P_av,S

(2.7)

It is worth noting that GP≥ GT ≤ GA. These gain definitions are used with different applications and with different circuits. However, the transducer gain is the measured gain which will be used in this work unless it is specified.

One of the important figures of merit of the RFPA is the 1-dB compression point. This point is found when the gain is one dB less than the small signal gain. This phenomena is a natural behaviour for the nonlinear operation of the active devices. The corresponding output power and input power is represented by; Pout,1−dBand Pin,1−dB, respectively. Fig. 2.3 clarifies the 1-dB compression point concept.

2.1.3 Efficiency Definitions

For any power conversion, a measure for this conversion is usually named as efficiency. In FET-RFPA, it is called as drain efficiency and its mathematical definition is:

η = P_out

P_DC (2.8)

The drain efficiency increases exponentially with the input power (in Logarithmic). However, for higher input power, near 1-dB point occurs, the efficiency reaches its maximum and the gain reduces further. Additionally, the output power is directly proportional to the input power. Hence, the influence of the input power must be included leading to the power added efficiency (PAE) definition: PAE = Pout− Pin PDC = Pout· (1 − 1 G) PDC (2.9)

Another reason for this new definition is that drain efficiency increases as the operating conduction angle decreases, where the required input power increases beyond this point and reaches the 1-dB compression point, Fig 2.3.

Additionally, there are further different definitions for the efficiency. However, these are the most common used in RFPA.

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16 2. Power Amplifier Characteristics Pou t [dBm], Gain [dB] 0 10 20 30 40 η , P AE [%] 0 20 40 60 80 Pin[dBm] 0 5 10 15 20 25 Gain Pout PAE η Pout,1dB Pin,1dB

Figure 2.3: Typical performance for a power amplifier versus input power.

2.2 Linearity and Distortion

Linearity, as a term, is a measure of the output current and voltage waveforms’ clarity compared to the input waveforms. The distortion reduces, further, the signal quality and, consequently, the receiver can not recover the transmitted information completely. Modern communication standards such as WCDMA signals, demand strict requirements regarding the linearity. The nonlinear effects in power amplifiers are usually expressed in the form of a third-order power series expansion:

v_o= α1vi+ α2v2i + α3v33 (2.10)

where vo is the output voltage, vi is the input voltage and αiare the voltage coefficients. This equation is the simplest expression that represents the nonlinear effect. However, more efficient expression (Volterra series) which includes time as a dependent variable, is used for advanced linearity analysis. Fig. 2.4 represents the most common linearity measurements categorized based on the input signal. The next few subsections discuss these phenomena.

Linearity Single Tone 1-dB Compression point AM-AM/AM-PM Harmonic distorsion Dynamic Signal ACPR/ACLR Multi Tone Intermodulation distortion Intercept point

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2.2 Linearity and Distortion 17

2.2.1 Single Tone

Single-tone measurements are the basic method of the RF power amplifier to quantify linearity performance. If the input signal for a PA is expressed as:

vi= γ cos(ωt) (2.11)

where γ is the amplitude of the input signal and ω is the radial operating frequency. The output power can be obtained from (2.10) as:

v_o= α2γ 2 2 + (α1γ + 3 4α3γ 3_{) cos(ωt) +}α2γ2 2 cos(2ωt) + α3γ3 4 cos(3ωt) (2.12) As it can be observed from (2.12), the output voltage contains harmonic components in addition to the fundamental and DC components. The voltage gain for the fundamental component is expressed as: v_o v_i = (α1+ 3 4α3γ 3₎ _(2.13)

It is evident from (2.13) that the gain is proportional to the cubic input voltage amplitude (γ). This gain compresses if and only if the α3is negative; otherwise it will expand, which is not a nature of the nonlinear devices. This gain shows the compression discussed before, which is usually referred to as the maximum input that can be applied to a RFPA without distorting the signal, in Fig. 2.5. For the other harmonic component in (2.12), it can be easily seen that the output harmonic power (P = v

2

2R) increases twice as fast as in the fundamental power for the second harmonic and three times as fast as in the fundamental power for the third harmonic, Fig. 2.6.

2.2.1.1 AM-AM/AM-PM

AM-AM is a measure of the compression between the output and the input waveforms and can simply be expressed by the gain expression. AM-PM is a measure of the change in the output

V oltage Gain [dB] 0 5 10 15 vi[dB] 0 5 10 15 Gv,1dB Vi,1dB

(48)

18 2. Power Amplifier Characteristics Pou t [d Bm ] -10 0 10 20 30 40 P_in[dBm] 0 5 10 15 20 25 Pout,sec 2 3 Pout,third Pout, f und 1

Figure 2.6: Single tone output power for the fundamental, second harmonic and third harmonic.

phase that depends on the input amplitude, expressed as:

AM− PM = ϕo(vi) (2.14)

where ϕoand viare the output phase and the input amplitude components, respectively. Usually, these parameters are plotted versus the input power, Fig. 2.7.

2.2.1.2 Total harmonic distortion

The harmonic distortion due to n-order of harmonic is defined by:

HD_n= Pout,n

P_{out, f und} (2.15)

An ideal operation for a PA requires zero harmonic distortion (HDn). Higher value of this parameter reduces the efficiency of the power amplifier and increases the nonlinearity.

AM-AM [dBm], AM-PM [de g.] -10 0 10 20 30 Pin[dBm] 0 5 10 15 20 25 AM-PM AM-AM

(49)

2.2 Linearity and Distortion 19

In a straightforward manner, the total harmonic distortion is defined by:

T HD=

_∑

n≥2

P_out,nth Pout, f und

(2.16)

The above expressions are usually expressed on a logarithmic scale with reference to the funda-mental (dBc). This describes how far the harmonic powers are from the fundafunda-mental power.

2.2.2 Multi Tone

Single tone measurements and analysis give limited information regarding the linearity perform-ance. In reality, the input signal for a PA is not a single tone signal. Hence, a multi tone test gives a better picture of the distortion that might appear on the output signal of a PA. In this section, analysis for a two-tone signal is presented and discussed. Nevertheless, the same analysis applies for higher-order tones.

2.2.2.1 Intermodulation distortion

In reality, the input signal of a PA consists of two closely spaced frequencies f1and f2( f1< f2). For simplicity, in this analysis both signals will be assumed to have an equal amplitude:

v_i= γ cos(ω1t) + γ cos(ω2t) (2.17)

Applying (2.17) in (2.10) and making some mathematical simplifications, the output signal is given by: v_o= α2γ2 + [α1γ +9 4α3γ 3_][cos(ω 1t) + cos(ω2t)] + α2γ 2 2 [cos(2ω1t) + cos(2ω2t)] + α3γ 3 4 [cos(3ω1t) + cos(3ω2t)] (2.18) + α2γ2[cos(ω1t+ ω2t) + cos(ω1t− ω2t)] + 3α3γ 3

4 [cos(ω1t+ 2ω2t) + cos(ω1t− 2ω2t) + cos(2ω1t+ ω2t) + cos(2ω1t− ω2t)] The output voltage from the two-tone input signal contains an infinite number of a combination

Bandwidth considerations of high efficiency microwave power amplifiers

B

ANDWIDTH

C

ONSIDERATIONS OF

H

IGH

E

FFICIENCY

M

ICROWAVE

P

OWER

A

MPLIFIERS

M.Sc. Ahmed Altanany

Acknowledgement

Abstract

Kurzfassung

Contents

List of Figures

List of Tables

Acronyms

List of Symbols and units

1 |

Introduction

1.1

Wireless Communication Networks

1.2

Motivation

1.2.1

Broadband Power Amplifier

1.2.2

Efficient Power Amplifier

1.2.3

RF Power Transistor

+

−

+

−

+

−

+

−

+

−

1.3

State of the Art

1.4

Thesis Outline

2 |

Power Amplifier Characteristics

2.1

Power Amplifier Definitions

2.1.1

Basic Definitions

PA

2.1.2

Gain Definitions

2.1.3

Efficiency Definitions

2.2

Linearity and Distortion

2.2.1

Single Tone

∑

2.2.2

Multi Tone

_∑