Universidade de Aveiro Departamento deElectr´onica, Telecomunica¸c˜oes e Inform´atica 2019
Micael Moreira
Monteiro
Amplificador de 500W de Banda Larga para UHF
Wideband 500W Power Amplifier for UHF
Universidade de Aveiro Departamento deElectr´onica, Telecomunica¸c˜oes e Inform´atica 2019
Micael Moreira
Monteiro
Amplificador de 500W de Banda Larga para UHF
Wideband 500W Power Amplifier for UHF
Disserta¸c˜ao apresentada `a Universidade de Aveiro para cumprimento dos re-quesitos necess´arios `a obten¸c˜ao do grau de Mestre em Engenharia Eletr´onica e de Telecomunica¸c˜oes, realizada sob a orienta¸c˜ao cient´ıfica do Doutor Ant´onio Navarro, Professor Auxiliar do Departamento de Eletr´onica, Tele-comunica¸c˜oes e Inform´atica da Universidade de Aveiro e co-orienta¸c˜ao cient´ıfica do professor Nuno Borges de Carvalho, Professor Catedr´atico do Departamento de Eletr´onica, Telecomunica¸c˜oes e Inform´atica da Universi-dade de Aveiro .
o j´uri / the jury
presidente / president Professor Doutor Armando Carlos Domingues da Rocha
Professor Auxiliar da Universidade de Aveiro
vogais / examiners committee Professor Doutor Mois´es Sim˜oes Piedade
Professor Jubilado, Instituto Superior T´ecnico - Universidade de Lisboa
Professor Doutor Ant´onio Jos´e Nunes Navarro Rodrigues
Agradecimentos A realiza¸c˜ao deste trabalho de um ano foi d´ıficil n˜ao s´o para mim, mas tamb´em para os que me s˜ao pr´oximos. Gostaria de agradecer a todos pela paciˆencia e ajuda fornecida.
Em primeiro lugar, gostaria de agradecer ao meu orientador, o professor Ant´onio Navarro pela sua ajuda ao longo deste percurso. Um muito obri-gado pelo tempo dispendido para me guiar ao longo da realiza¸c˜ao deste trabalho e por ter contribu´ıdo para o meu enriquecimento acad´emico e pes-soal.
Naturalmente, gostaria de agradecer aos meus pais pelo apoio e valores transmitidos. Sei o que custou e agrade¸co os sacrif´ıcios feitos. Um muito obrigado.
Gostaria tamb´em de agradecer a todos os meus amigos e colegas, em es-pecial, Bruno Brand˜ao, Diogo Alves e Guilherme Pinho pelas discuss˜oes ao longo da realiza¸c˜ao da tese. Ajudaram-me bastante e por isso agrade¸co. Obrigado ao IT por me ter acolhido e proporcionado meios para a realiza¸c˜ao deste trabalho.
Por ´ultimo mas n˜ao menos importante, um agradecimento especial para a Tˆania Martins pelo carinho e for¸ca transmitidas. Obrigado por n˜ao me teres deixado desistir e por estares sempre ao meu lado.
Palavras Chave Amplificador de Banda Larga, Amplificador de Potˆencia, Dispositivo UHF, TV broadcasting.
Resumo At´e aos dias de hoje nunca houve uma necessidade t˜ao grande de estar constantemente ligado `as redes de informa¸c˜ao. Esta necessidade ´e a for¸ca por tr´as do desenvolvimento de novas tecnologias sem-fios capazes de aco-modar as necessidades da sociedade. Consequentemente, existem diversos sistemas de telecomunica¸c˜oes que cobrem m´ultiplas bandas de frequˆencia o que leva a que o design de circuitos front-end para sistemas r´adio seja cada vez mais exigente tanto em termos de desempenho como de custo.
Sendo os amplificadores um dos elementos mais dispendiosos, procura-se, especialmente em emissores de alta potˆencia, implementar dispositivos mais eficientes e que sejam capazes de cobrir o maior n´umero de bandas de frequˆencia poss´ıvel. Dispositivos mais eficientes levam a menor energia dissipada e, portanto, menor necessidade de arrefecimento o que conduz a um menor custo do emissor. Amplificadores de banda larga permitem cobrir um maior n´umero de bandas de frequˆencia, levando a um menor n´umero de dispositivos e por conseguinte a menores custos de manuten¸c˜ao.
No ˆambito deste trabalho foi realizado o projeto de um amplificador de banda larga, mais especificamente, um classe AB com baluns constru´ıdos com cabos coaxiais de λ/4 recorrendo ao software ADS (Advanced De-sign System). Foram abordadas duas topologias de malhas de adapta¸c˜ao e portanto foram estudadas duas vers˜oes. Uma vers˜ao em que a malha de adapta¸c˜ao da sa´ıda consiste em m´ultiplas se¸c˜oes de transformadores de λ/4 e outra em que essa malha de adapta¸c˜ao da sa´ıda foi implementada com linhas e condensadores em paralelo.
Para ambos os casos, as simula¸c˜oes efetuadas revelam que o ganho ´e igual ou superior a 20 dB tendo menos do que 1-dB de ripple para a banda de frequˆencia dos 470-740 MHz em que a eficiˆencia assume valores entre os 30-61% para valores de potˆencia de entrada na ordem dos 30-39 dBm. Relativamente `a potˆencia de sa´ıda no ponto de compress˜ao de 1-dB, para a banda de frequˆencia dos 470-740 MHz, esta varia entre os 57.5 dBm e os 58.8 dBm no caso em que a malha de adapta¸c˜ao da sa´ıda consiste em transformadores de λ/4. Para a variante em que a malha de adapta¸c˜ao da sa´ıda consiste em linhas e condensadores, o ponto de compress˜ao de 1-dB varia entre os 57 dBm e 58.5 dBm para a mesma banda de frequˆencia. Ap´os avaliar o desempenho e custo de ambas as alternativas, optou-se por implementar a vers˜ao com linhas e condensadores e foram feitas simula¸c˜oes utilizando um sinal de duas portadoras com um espa¸camento de 1kHz em que a distor¸c˜ao de intermodula¸c˜ao de -30 dBc corresponde a uma potˆencia de 52.5 dBm por portadora. Por fim, realizou-se o layout e foi gerado um modelo eletromagn´etico que permitiu a realiza¸c˜ao das mesmas simula¸c˜oes, obtendo-se valores muito pr´oximos dos obtidos previamente por simula¸c˜ao. Implementou-se o amplificador e obteve-se um ganho igual ou superior a 20 dB para a banda de frequˆencia 400-550MHz. Para a banda dos 550-630
Keywords Broadband amplifiers, High power amplifiers, TV broadcasting, UHF de-vices.
Abstract Until nowadays there never was a necessity of being constantly connected in the history of mankind. This necessity is the moving force behind the development of new wireless technologies capable of accommodating soci-ety’s necessities. Consequently, telecommunications systems which operate in different frequency bands exist and lead to increasing demands in terms of performance and cost.
Power amplifiers are one of the most costly components in a RF front-end, specially in high power transmitters, telecommunications operators are con-tinuously searching to implement devices which operate more efficiently and capable of operating in multiple frequency bands. Efficient amplifiers con-sume less energy and, therefore, less cooling equipment is required. Thus, the overall cost of the transmistter will be lowered. Wideband amplifiers handle multiple bands; this leads to less devices and lower maintenance costs.
In the scope of work, a wideband class AB amplifier was implemented by using λ/4 coaxial cables baluns as power splitters/combiners in ADS (Ad-vanced Design System). Two topologies of matching networks were studied and simulated. The first topology consists in multi-section quarter wave transformers. The second topology studied is made of lines and shunt ca-pacitors. For both versions, the simulations show the gain is equal or greater to 20 dB and has less than a 1 dB of ripple for 470-740 MHz frequency band. The efficiency values assume to be in the order of 30-61% for input power in range of 30-39 dBm. Considering the 1-dB compression point, it varies between 57.5 dBm and 58.8 dBm for 470-740 MHz frequency band in the case where multi-section quarter wave lines were used as output match-ing networks. For the case where the output matchmatch-ing networks consist in lines with shunt capacitors, the 1-dB compression point varies between 57 dBm and 58.5 dBm for the same frequency band. After evaluating the per-formance and cost, the version which uses capacitors and lines was chosen. Thus, a two-tone signal with a spacing of 1kHz between carriers was fed to the amplifier and for a inter-modulation to carrier ratio of -30 dBc a power of 52.5 dBm per tone was obtained. Lastly, the layout was implemented and Eletromagnetic simulations were carried out for a more accurate model. The same simulations were repeated and the noted values are comparable to previously obtained results. After the amplifiers implementation, the gain was measured in a network analyzer and it showed that the gain is equal or greater than 20 dB for the 400-550 MHz frequency band. For the 550-630 MHz frequency band the amplifier has a gain that varies between 20 dB and 5 dB.
Contents
Contents i List of Figures v List of Tables ix List of Acronyms xi 1 Introduction 11.1 Motivation and Context . . . 1
1.2 Thesis Goals . . . 3
1.3 Thesis Layout . . . 4
2 RFPA: Fundamental Theory 5 2.1 Overview . . . 5
2.2 Linearity . . . 6
2.2.1 Linearity in Power Amplifiers . . . 6
2.2.2 1-dB Compression Point . . . 7
2.2.3 Third Order Interception Point . . . 8
2.2.4 Adjacent Channel Power Ratio . . . 10
2.2.5 Error Vector Magnitude . . . 11
2.3 S-Parameters . . . 12
2.4 Power Gain . . . 13
2.4.1 Power Gain . . . 14
2.4.2 Available Power Gain . . . 14
2.4.3 Transducer Power Gain . . . 14
2.4.4 Constant Gain Circles . . . 14
2.5 Stability . . . 16
2.5.1 Stability Circles . . . 16
2.5.2 Simpler Tests for Stability Analysis . . . 18
2.6 Efficiency . . . 19
2.6.1 Drain Efficiency . . . 19
2.6.2 Power Added Efficiency . . . 19
2.7 Amplifier Types and Classes of Operation . . . 19
2.7.1 Transconductance PAs . . . 19
Class A . . . 20
Class AB . . . 21
Class C . . . 22
2.7.2 Switch Mode PAs . . . 22
Class D . . . 23
Class E . . . 24
Class F . . . 25
2.8 Efficiency Enhancement Architectures . . . 26
2.8.1 Doherty Amplifier . . . 26
2.8.2 Principle of Operation . . . 26
2.8.3 Doherty Amplifier Limitations . . . 29
3 An overview of Power Amplifier Design Approaches 31 3.1 Bode-Fano Criterion . . . 31
3.2 Wideband Matching Networks . . . 33
3.2.1 Matching Using Lumped Elements . . . 34
L-Network . . . 35
π-Network . . . 35
T-Network . . . 37
Multi-Section LC Networks . . . 39
Equal-Q Approach for Matching Networks Design . . . 39
3.2.2 Matching Using Distributed Elements . . . 40
Matching Networks Using Stubs . . . 40
Multi-Section Quarter Wave Transformer . . . 41
Tapered Lines . . . 44
3.2.3 Matching Using Lumped Elements and Distributed Elements . . . 45
3.3 Typical Amplifier Architectures . . . 45
3.3.1 Architectures Based on Lossy Matching Networks . . . 45
3.3.2 Amplifiers Based on Negative Feedback . . . 46
3.3.3 Balanced Amplifiers . . . 47
3.4 Power Divider Architectures . . . 48
3.4.1 Wilkinson Power Divider . . . 49
3.4.2 Quadrature Hybrid - 90o. . . 50
3.4.3 The 180o hybrid . . . 53
3.4.4 Lange Coupler . . . 54
Quarter Wavelength Coaxial Balun . . . 56
4 Designing a Wideband UHF Power Amplifier 59 4.1 Active Device . . . 59
4.2 DC Analysis . . . 60
4.2.1 Bias Point . . . 60
4.2.2 Bias Network . . . 60
Output Bias Network . . . 61
Input Bias Network . . . 63
4.3 Load-Pull . . . 64
4.4 Impedance Matching Networks . . . 66
4.4.1 Input Matching Network (IMN) . . . 66
4.5 Stability Analysis . . . 71
4.6 Simulation Results . . . 72
4.6.1 One Tone Measurements . . . 72
Multi-Section Quarter Wave Matching Network. . . 73
Hybrid Matching Network. . . 75
4.6.2 Two Tone Measurements . . . 77
4.7 Layout and EM Simulation Results. . . 79
4.7.1 Stability . . . 81
4.7.2 One Tone Measurements . . . 81
4.7.3 Two Tone Measurements . . . 84
5 Layout (PCB) Practical Results 85 5.1 Initial Tests . . . 85
6 Final Remarks and Future Work 89 6.1 Conclusions . . . 89
6.2 Future Work . . . 90
Bibliography 93
A Schematic - Hybrid Output Matching Network 97
B Schematic - Multi-Section λ/4 Output Matching Network 99
C Schematic - PCB Layout and Aluminum Base 101
List of Figures
1.1 Ideal vs Real PA behaviour. . . 2
1.2 Lossless matching network for a arbitrary load impedance. . . 3
2.1 Ilustration of the power flow in a PA. . . 5
2.2 Illustration of output power in function of input power and 1-dB compression point. . . 8
2.3 Output considering the two-order and third-order intermodulation products (ω1 < ω2). . . 9
2.4 Third order interception illustration. . . 10
2.5 Input and output power spectral densities to better illustrate the ACPR bands of interest. . . 11
2.6 Error vector magnitude and respective quantities. . . 11
2.7 Diagram of S-parameter two-port network. . . 12
2.8 Two-port network connected to a source and load impedance. . . 13
2.9 Example of what power circles would look like in a Smith chart. . . 16
2.10 Output stability circles for a conditionally stable device . . . 18
2.11 Class A operation principle. . . 20
2.12 Class B operation principle. . . 21
2.13 Class AB operation principle. . . 21
2.14 Class C operation principle. . . 22
2.15 Output power and efficiency as a function of conduction angle . . . 23
2.16 Complementar voltage-switching configuration. . . 24
2.17 Example of a class E PA. . . 25
2.18 Example of a class F PA. . . 26
2.19 Doherty amplifier basic architecture. . . 27
2.20 Efficiency in function of input power. . . 28
3.1 Bode-Fano limits for RC and RL loads to match using lossless matching networks 32 3.2 Compromise between bandwidth and reflection coefficient . . . 33
3.3 Realizable and not realizable reflection coefficient responses . . . 33
3.4 Ideal Transformer. . . 33
3.5 Matching networks using lumped components topologies. . . 34
3.6 L-network with Source and load impedances attached. . . 35
3.7 Different arrangements of components for a π-network. . . 36
3.8 Different arrangements of components for a T-network. . . 37
3.10 Equal-Q approach for multi-section LC networks design . . . 40
3.11 Inductors and capactiors implementation using stubs. . . 41
3.12 Multi-section quarter wave transformer with N sections. . . 42
3.13 Binomial multi-section quarter wave transformers. . . 43
3.14 Chebyshev multi-section quarter wave transformers . . . 44
3.15 Multiple LC matching network using lines and capacitors. . . 45
3.16 Two topologies of lossy matching networks. . . 46
3.17 Possible topologies of negative feedback. . . 47
3.18 Balanced Architecture. . . 48
3.19 Wilkinson power divider as a microstrip implementation (left) and equivalent form using transmission lines (right) . . . 49
3.20 One section Wilkinson Power Divider. . . 50
3.21 Branch line coupler . . . 50
3.22 Quadrature hybrid coupler working principle. . . 52
3.23 Quadrature hybrid phase and return/transmission loss behavior. . . 53
3.24 180o ring coupler . . . 54
3.25 Example of a Lange coupler implemented using microstrip technology . . . . 54
3.26 Lange coupler behavior. . . 56
3.27 Quarter wavelength coaxial balun. . . 57
3.28 Quarter wave coaxial balun behavior. . . 58
4.1 Power handling ability for different technologies and selected device’s package. 59 4.2 I-V characteristic curves. . . 60
4.3 Output bias network schematic. . . 61
4.4 Output bias network response. . . 61
4.5 ADS optimizer interface. . . 62
4.6 Final output bias network schematic. . . 62
4.7 Final output bias network response. . . 63
4.8 Input bias network schematic. . . 63
4.9 Input bias network response. . . 64
4.10 Power delivered and PAE contours. . . 65
4.11 Matching networks to be designed using the load pull values. . . 65
4.12 Matching network with only stubs schematic. . . 66
4.13 S-parameters from the input matching network with only stubs. . . 66
4.14 S-parameters from the hybrid matching network. . . 67
4.15 Final input matching network. . . 67
4.16 Two section quarter wave matching network. . . 68
4.17 Two section quarter wave matching network S-parameters. . . 68
4.18 Three section hybrid matching network. . . 69
4.19 Three section vs five section hybrid matching network. . . 69
4.20 Tolerance influence on the matching quality. . . 70
4.21 Final output matching network. . . 71
4.22 Stability factor and measure over the operating range. . . 71
4.23 Gain in function of the input power using the hybrid matching networks. . . 72
4.24 Output power at the 1-dB compression point. . . 73
4.25 Gain in function of input/output power. . . 73
4.27 Drain Efficiency in function of the input/output power. . . 74
4.28 Gain in function of frequency for an input power of 33 dBm. . . 75
4.29 Gain in function of output power and output power at the 1-dB comp. point. 75 4.30 PAE in function of the input/output power. . . 76
4.31 Drain Efficiency in function of the input/output power. . . 76
4.32 Gain in function of frequency for an input power of 33 dBm. . . 77
4.33 Carrier to intermodulation distortion in function of input power. . . 78
4.34 Layout of the PCB of the device. . . 79
4.35 Stability factor and measurement using the EM model. . . 81
4.36 Gain in function of the input/output power using the EM model. . . 81
4.37 PAE in function of the input/output power using the EM model. . . 82
4.38 Drain Efficiency in function of the input/output power using the EM model. . 82
4.39 Gain for constant input power and output power at 1-dB compression point. 83 4.40 Carrier to intermodulation distortion in function of input power using the EM model. . . 84
5.1 Physical implementation of the PA. . . 85
5.2 Setup of the initial test. . . 86
5.3 Transmission loss (gain) of the amplifier for the 400-900 MHz frequency band. 86 5.4 Transmission loss (gain) of the amplifier for the 300-900 MHz frequency band. 87 6.1 New matching network to be implemented to solve the frequency shift. . . 90
List of Tables
1.1 RFPA specifications . . . 3 2.1 Theoretical efficiency and conduction angle for classes A, B, AB, and C. . . . 22 3.1 Impedance transformation ratios for 2 and 3 sections of a Binomial transformer 42 3.2 Impedance transformation ratios based on fractional bandwidth for a
Cheby-shev transformer . . . 43 3.3 Substrate characteristics. . . 55 3.4 EZ-90-25 characteristics. . . 57 4.1 Impedance values for maximum efficiency and power delivered to the load. . . 65 4.2 IMD, per tone power and PEP in function of input power at 650 MHz. . . 78 4.3 Components. . . 80 4.4 IMD, per tone power and PEP in function of input power for 650 MHz using
List of Acronyms
ACPR Adjacent Channel Power Ratio ADS Advanced Design System
AM/AM Amplitude to Amplitude conversion AM/PM Amplitude to Phase conversion CAD Computer Assisted Design
CW Continuous Wave DC Direct Current
DVB-T Digital Video Broadcasting - Terrestrial DSP Digital Signal Processing
EM Eletromagnetic
EVM Error Vector Magnitude FET Field Effect Transistor GaN Gallium Nitrate
HEMT High Electron Mobility Transistor IMN Input Matching Network
IMD Intermodulation Distortion
LDMOS Laterally Diffused Metal Oxide Silicon LSB Lower Side Band
OFDM Orthogonal Frequency Division Multiplexing OMN Output Matching Network
PAE Power Added Efficiency
PAPR Peak to Average Power Ratio PCB Printed Circuit Board
PEP Peak Envelope Power
QAM Quadrature Amplitude Modulation RF Radio Frequency
RFPA Radio Frequency Power Amplifier UHF Ultra High Frequency
USB Upper Side Band UWB Ultra Wide Band
Chapter 1
Introduction
1.1
Motivation and Context
There is no denying that nowadays humanity is highly dependent on technology. This necessity of being always connected keeps leading to a massive development of wireless com-munications and to an unprecedented growth in the number of existent devices. To address this, there is a need to continuously improve and develop new technologies capable of work-ing with high data rates, uswork-ing the frequency spectrum in the best way possible, i.e, without generating energy at other frequencies than the frequency of interest and being energetically efficient. To accomplish this, and being power amplifiers (PAs) one of the most costly and important components in microwave transmitters, novel PAs have to be designed.
Power amplifiers, as the name suggests, are responsible for amplifying the signal. They are active devices responsible for getting the signal up to the necessary level of energy so that the signal can be properly transmitted at enough power. There are multiple factors to take into consideration when designing PAs depending on the scenario. One of the main focus when developing new devices is to decrease development and operation costs so that base stations and radio link equipment can be developed and operated with low complexity. There are multiple variables to take into account to accomplish it. One of the key aspects is power consumption. Power consumption is a big concern, because under maximum load, power dissipation is more than half of the total direct (DC) power supplied [1] and it often leads to a more complex system since it is needed to install bulky and complex cooling equipment to keep the temperature low. Then reducing the power consumption (increasing efficiency) is very important since it leads to power saving and, consequently, to reduction of consumer costs and system’s complexity.
Output power is another issue to take into consideration when designing a PA. There are applications where the output power must be prioritized in relation to power efficiency. For example, if the system in cause is a system whose goal is to transmit a signal over a long distance in a noisy environment, it is preferable to design a PA capable of providing a high output power instead of maximum power efficiency.
Another concern when projecting a PA is the strict linearity specifications. As stated previously, there are a massive number of devices and the spectrum is pretty saturated, i.e,
there are multiple communications systems with multiple designated channels that require a share of the spectrum. Therefore, a PA has to work in a linear zone in order to not leak to the adjacent bands and, consequently, cause interference in other wireless systems. Apart from that, in order to function properly with higher data rates and taking into account the spectrum fragmentation as well, the bandwidth is another concern. The concept is easy to grasp. If there is a desire to keep development and maintenance costs low in microwave trans-mitters, then instead of using multiple narrow PAs for each band, a wide-band PA with a flat gain across the desired band coverage is a cheaper approach, because it leads to the removal of further circuitry. Therefore wide-band amplifiers are of great interest in actual and future wireless communication systems.
Ideally PAs should be designed to be as efficient, as linear and to have a bandwidth as high as possible. However, reaching a PA with all this perks is very difficult. Modern wireless communication systems, like DVB-T use complex modulation schemes like Orthogonal Fre-quency Division Multiplexing (OFDM) in order to maximize spectral efficiency and to reduce multipath interference[2]. It comes with a cost, because this modulation techniques result in signals with large amplitude variations and Peak-to-Average Power Ratio (PAPR) in the range of 6-12 dB [3]. Thus, this signals have a high PAPR, defined by the expression below (Equation 1.1). P AP R(dB) = 10 log10 Ppeak Paverage (1.1) Thus, in order to prevent the signal peaks clipping, in other words, to avoid the removal of some frequency components from the signal (distortion), these type of signals require the PA to operate in a level of output power (back-off power level) below the corresponding power in saturation region, where the efficiency is at it is maximum [2]. One may conclude then that efficiency and linearity don’t go around ”holding hands” (see figure 1.1).
Figure 1.1: Ideal vs Real PA behaviour.
Beyond defining appropriate linearity, efficiency and bandwidth, the choice of the technol-ogy used to manufacture the device must also be taken into consideration. Firstly introduced
by H.Bode [4] and posteriorly studied in depth by R.Fano [5] is the idea that the impedance seen when looking at the output of a device is, normally, a complex impedance (Z) and can be represented by a ”resistance R shunted by a capacitance C”[5], i.e, a shunt RC circuit (see Figure 1.2). It has been demonstrated that the bandwidth which a good match of a complex load can be obtained for is limited by the RC product. If the impedance at the interface of the transistor (die) is very low, then the transformation, between the low impedance at the transistor die to the load impedance (typically a 50Ω load), is harder to accomplish.
Figure 1.2: Lossless matching network for a arbitrary load impedance.
Hence, it is possible to conclude that limitations in projecting efficient and broadband PAs are also imposed by the device, or more specifically, the technology used to manufacture the device and the commitments done to obtain the specifications imposed.
1.2
Thesis Goals
The aim of this dissertation is to design, implement and test a wide-band radio frequency power amplifier (RFPA) for UHF, more specifically, for the DVB-T, operating in the 470-860 MHz band. The amplifier must be capable of amplifying OFDM signals with a bandwidth of 8MHz and with a spacing of 1kHz between carriers. The specifications are listed in the following table 1.1, below.
Table 1.1: RFPA specifications
Bandwidth 250 MHz
Gain ≥ 20 dB
Gain Ripple ≤ 1 dB
Output Power for 1-dB compression point >53 dBm Efficiency As high as possible
In order to accomplish the main goals, it was used a ”divide to conquer” approach where the main objective was divided into multiple and less complex goals. Those include the acquisition of theoretical knowledge about RFPAs like classes of operation, linearity metrics, transistor technologies, bias networks, matching networks, among others.
Furthermore, another objective was to gain expertise on design techniques and simulation techniques resorting to Advanced Design System (ADS) software from Keysight technologies. Finally, one last objective was to learn and gain hands-on experience on testing method-ologies and how to appropriately deal with the available RF instruments and use them to measure several parameters and metrics when designing a broadband PA.
1.3
Thesis Layout
In this section, we describe the thesis structure.
• Chapter 1, Introduction presents the motivation behind the work covered in this dissertation and raises the main concerns to take into consideration when designing a PA. It also includes the main goals and thesis structure.
• Chapter 2, RF Power Amplifier: Fundamental Theory contains all the fun-damental theory necessary to understand the metrics associated with PA design, like linearity, S - Parameters, efficiency, gain, stability and classes of operation. Transistor technologies are presented as well and a comparison between them is introduced. • Chapter 3, An overview of the Power Amplifier Design Approaches focus
in providing knowledge about the different existent architectures and limitations. Here we also cover the possible ways one can use to realize the matching of a specific device focusing in bandwidth.
• Chapter 4, Designing a Wideband UHF Power Amplifier presents the process of design of a wide-band UHF PA. This chapter includes the active device selected, the choice of the bias voltage, bias networks, load - pull simulation to find the best load value to provide maximum efficiency and output power, broadband impedance matching networks and stability analysis. This chapter ends by displaying the layout to be printed out.
• Chapter 5, Tests and results covers the methods followed to test and measure the PA implemented and the respective measurements results.
• Chapter 6, Final Remarks and Future Work presents the conclusions about the work done in the scope of this dissertation and the final remarks. Hence, it is done as retrospective about the work done and it is pointed out the difficulties faced and what could be done differently to avoid those difficulties. It is suggested what work could be done in the future as well.
Chapter 2
RFPA: Fundamental Theory
2.1
Overview
Signal amplification is one of the most simple and yet, important circuit ability in modern RF and microwave systems [6]. Therefore, PAs are of vital importance since they are the devices responsible for performing signal amplification. The process of amplification consists of taking a signal and give it more power. According to the principle of energy conservation, energy cannot be created from nothing. Hence, it is necessary to have an external power supply capable of providing the power needed to amplify the electrical signal to the desired power level. Thus, a PA can be seen as a transducer, i.e, a device that converts one form of energy to another form, in this particular case DC power into RF power (see Figure 2.1).
Figure 2.1: Ilustration of the power flow in a PA.
This conversion cannot be done in a randomly manner, because as stated in Chapter 1, nowadays there are multiple communication systems among which telecommunications,
radar, electronic warfare, heating and microwave imaging [3]. Each communication system demands specific characteristics and consequently there are multiple design considerations to take into account. The most important considerations in a microwave amplifier are linearity, power gain, stability, bandwidth, noise and DC requirements [7].
2.2
Linearity
2.2.1 Linearity in Power Amplifiers
Since an early age we are taught how to solve linear equations as representations of the behavior of linear systems. A linear system is a system where the output corresponding to any linear combination of elementary input stimulus can be given by the sum of outputs corresponding to each of the input stimulus. This condition is equivalent to the properties of additivity and homogeneity. These can be represented mathematically by,
x1(t) = y1(t) ∧ x2(t) = y2(t) 7→ x1(t) + x2(t) = y1(t) + y2(t) ∀x1(t), x2(t) (2.1)
x1(t) = y1(t) 7→ a × x1(t) = a × y1(t) ∀a, x1(t) (2.2)
Equations (2.1) and (2.2) corresponds to the additivity and homogeneity properties, re-spectively. This condition can also be referred as the superposition principle. If a system obeys to this principle, then it is a linear system. If not, then, it is a nonlinear system. That is the case of active devices like diodes and transistors.
This nonlinear behavior results always from the fact that all real components introduce losses, it might even be a small loss, but there is always a loss. Hence, the ideal linear component does not exist. At low signal levels all devices have nonlinear behavior due to noise effects. At high power levels, this behavior is also common and is due to effects like gain compression or inter-modulation distortion (IMD) where spurious frequency components are generated [6]. These effects are responsible for setting the minimum and maximum power range, i.e, dynamic range, over which the device has an approximately linear behavior.
To better understand the nonlinear phenomena and its origins, lets us look at Figure 2.1. Being PDC the power supplied by the external power supply, PDISS the power dissipated by
the active device, PIN the input signal power and PL the power delivered to the load, then
we can express the following equations (Equations 2.60, 2.61 and 2.5),
PDC+ PIN = PL+ PDISS (2.3)
Defining power gain as,
G = PL PIN
(2.4) It can be expressed as,
G = 1 + PDC− PDISS PIN
Therefore, one can conclude from Equation 2.5 that if PDISS is always positive (including
zero) and the power supplied by the source, i.e, PDC is finite, thus the gain simply cannot keep
constant for a range of input power [8]. Consequently, there is a point for a certain input power where the gain will start to compress and the device will start to behave in a nonlinear fashion. So active devices have a nonlinear behavior. Is that really a problem? Yes, it it can be a problem. As stated above, gain compression and spurious frequency components will occur leading to losses, signal distortion and a possible interference with other communication systems. Some possible effects of non-linearity in RF are expressed below [9],
• Harmonic Generation (multiples of the fundamental signal). • Saturation.
• IMD (products of two tone input signal).
• AM-PM conversion (amplitude variation causes phase shift).
• Spectral regrowth (inter-modulation with many closely spaced signals).
Thus, it is necessary to evaluate the non-linearity of a device. It can be characterized by the AM-AM (gain of the device for different power levels) and AM-PM (phase of the output signal for different power levels) distortion. It can be evaluated through the measurement of the 1-dB compression power (P1dB) for a single-carrier system. Measurements related to
two-tone (two sinusoidal signals) provide data about the third order inter-modulation distortion, i.e, about the third order interception point (IP3). Usually for more complex signals which
use complex modulation schemes, like QAM, adjacent channel power ratio (ACPR) or error vector magnitude (EVM) are used [10].
2.2.2 1-dB Compression Point
The 1-dB compression point is one of the most simple metrics to evaluate the linearity of a PA and represents the AM-AM response of a PA. Through this point one can identify until when a PA has an approximate linear behavior and from where it starts to behave as a nonlinear component. At low power levels the PA has a small signal gain. Therefore, plotting the output power in function of the input power would get us a straight line with a unity slope and, consequently, the gain would be simply the ratio between the output power and input power.
Now, if we steadily increase the input power there is a point where the output will start to saturate. This is due to the fact that the output voltage of an amplifier is limited by the power supply used to bias the device. This effect is called of saturation or gain compression. To quantify the linear behavior, the 1-dB compression point is defined. The 1-dB compression point is the point where the output power deviates 1 dB from the ideal linear PA response, as can be observed in Figure 2.2 [6, 8].
Figure 2.2: Illustration of output power in function of input power and 1-dB compression point.
This point can be represented in terms of input power (IP1dB) or output power (OP1dB)
being given typically by the largest of these two values. Normally for amplifiers, the 1 dB compression point is given by (OP1dB). Mathematically the relation can be expressed as
(Equation 2.6),
OP1dB = IP1dB+ G − 1dB (2.6)
2.2.3 Third Order Interception Point
Another figure of merit normally used to evaluate linearity is the third order intercept point. One can represent the output (vo) of a nonlinear device in form of a power series in
terms of input signal (vi) (Equation 2.7):
vo = a0+ a1vi+ a2vi2+ a3v3i + ... (2.7)
For an one-tone signal, it can be shown that the output will have mostly components at integer multiples of the fundamental frequency, i.e, harmonics of the form nω0 for n = 0, 1,
2, ... . Usually, this components are not of big concern because they lay out of the bounds imposed by the passband of the amplifier. Another situation that normally requires more attention is when vi consists of two closely spaced frequencies, i.e, a dual-tone signal. Let’s
consider an input signal consisted of 2 sinusoidal waves at frequencies ω1 and ω2 (Equation
2.8).
vi = Vo(cosω1t + cosω2t) (2.8)
Then, vo can be expressed as (Equation 2.9),
and rearranging it, we obtain [6], v0= a0+ a1Vocos ω1t + a1Vocos ω2t + 1 2a2V 2 o(1 + cos 2ω1t) + 1 2a2V 2 o(1 + cos 2ω2t) + a2Vo2cos(ω1t − ω2t) + a2Vo2cos(ω1t + ω2t) + a3Vo3( 3 4cos ω1t + 1 4cos 3ω1t) + a3V 3 o( 3 4cos ω2t + 1 4cos 3ω2t) + a3Vo3( 3 2cos ω2t + 3 4cos(2ω1− ω2) + 3 4cos(2ω1+ ω2)) + a3Vo3( 3 2cos ω1t + 3 4cos(2ω2− ω1) + 3 4cos(2ω2+ ω1)) (2.10)
From Equation 2.10 we can see that the output consists of parcels in the form of mω1+nω2
with |m|, |n| = 0, 1, 2, 3 ... . These are called intermodulation products and its order is given by the sum m + n.
Figure 2.3: Output considering the two-order and third-order intermodulation products (ω1<
ω2).
From the cubed term of Equation 2.10 and Figure 2.3, it is possible to notice the existence of six third-order intermodulation products: 3ω1 , 3ω2 , 2ω2+ ω1, 2ω1 + ω2, 2ω2 − ω1 and
2ω1 − ω2. The first four do not represent an obstacle since they fall out of the amplifier
passband. The others fall near the fundamental frequencies of the input signal and are hard to remove. These third-order intermodulation products grow at a rate of Vo3 while the input voltage Vo increases. Thus, the power curves of the fundamental and third order component
are bound to intercept at some point. This point is called the third-order interception point (IP3)(Figure 2.4).
The third-order intercept point can be expressed as input power level (IIP3) or output
power level (OIP3) similarly to 1-dB compression point. IP3 normally has a higher power
level relatively to P1dB and it can be shown that (Equation 2.11) [3],
Figure 2.4: Third order interception illustration.
2.2.4 Adjacent Channel Power Ratio
As aforementioned, more complex signals based on modern modulation schemes require different methods to evaluate the linearity of a PA. This is because it is needed to account bandwidth occupation and spectral regrowth [3]. One metric is the adjacent channel power ratio (ACPR) which consists of the ratio between the output power present in the bandwidth of the signal and the output power in the adjacent channels. It can be expressed as a total value or can be expressed in function of the lower side band (LSB), upper side band (USB) and a specific band of interest (spot) (Figure 2.5). The total value can be calculated with Equation 2.12, ACP RT OT AL ≈ R B POU T(f ) df R LSB POU T(f ) df + R U SB POU T(f ) df . (2.12)
Relatively to the LSB and USB and to a specific band they can be expressed as (Equations 2.13, 2.14 and 2.15, respectively), ACP RLSB≈ R B POU T(f ) df R LSB POU T(f ) df (2.13) ACP RU SB ≈ R B POU T(f ) df R U SB POU T(f ) df (2.14) ACP RSP OT ≈ R B POU T(f ) df R BX POU T(f ) df . (2.15)
Figure 2.5: Input and output power spectral densities to better illustrate the ACPR bands of interest.
2.2.5 Error Vector Magnitude
There is another method to measure the distortion generated by the PA. Basically, it is a metric that evaluates the accuracy of a transmitted modulated digital signal. It is possible to get the information relative to this metric from the constellation of a modulated signal. It provides information about the magnitude of distortion of a digital signal introduced by the transmission channel. It can be expressed as the difference between an ideal reference signal and the signal received as the following illustration shows (see Figure 2.6).
2.3
S-Parameters
One approach widely used to evaluate the behavior of a passive or active device is to represent the device as a black-box where the only things that can be ”dealt” with are the input and output ports. Since only two ports are available, this approach is called the two-port network approach [6]. With a two-two-port model, a device can be characterized by the voltage and currents ratios present at the input/output (Y,Z,h, or ABCD - parameters). Problems arise when we are dealing with high frequencies, because the parameters need the device being terminated with an open-circuit, closed circuit or both. These are hard to attain as the frequency range increases [11].
To allow device characterization at microwave frequencies, scattering parameters (S-parameters) were introduced. These are based on incident and reflected wave ratios. To measure this parameters, the device must be terminated in the characteristic impedance of the transmission line, thus solving the problem of the open and short-circuit terminations (see Figure 2.7).
Figure 2.7: Diagram of S-parameter two-port network.
S-parameters are represented in a matrix form called the scattering matrix (Equation 2.16) [7]:
[S] =s11 s12 s21 s22
(2.16) The coefficients s11 through s22 are given by Equation 2.17 through Equation 2.20 :
s11= b1 a1 a2=0 (2.17) (input reflection coefficient with output matched)
s12= b1 a2 a1=0 (2.18) (reverse transmission coefficient with input matched)
s21= b2 a1 a2=0 (2.19) (forward transmission coefficient with output matched)
s22= b2 a2 a1=0 (2.20) (output reflection coefficient with input matched)
The coefficients used above to express the s-parameters, i.e, ai and bi are named power
waves. These are given by Equations 2.21, 2.22, 2.23 and 2.24 a1 = V1+ ZSI1 2pRe|ZS| (2.21) a2 = V2+ ZLI2 2pRe|ZL| (2.22) b1 = V1− ZS∗I1 2pRe|ZS| (2.23) b2 = V2− ZL∗I2 2pRe|ZL| (2.24) The S-parameters are commonly used to characterize a transistor which has to be biased in a particular bias point. Thus, S-parameters are dependent on the bias point and only describe in a proper manner the behavior of a nonlinear device when small signals are fed to it since only in this situation the response can be considered linear around the respective DC point [12].
2.4
Power Gain
An active device can be represented as a two-port network and there are multiple ex-pressions which represent the power gain of a two-port network. A two-port network can be characterized by its S-parameters. The expressions also consider that the device is connected to two impedances, a source and a load impedance as shown in Figure 2.8.
Figure 2.8: Two-port network connected to a source and load impedance.
The equations can be expressed in terms of S-parameters and the source and load reflection coefficients, ΓSand ΓL, where the source and load reflection coefficients are given by Equations
2.25 and 2.26, ΓS= ZS− Z0 ZS+ Z0 (2.25) ΓL= ZL− Z0 ZL+ Z0 , (2.26)
2.4.1 Power Gain
The power gain can be interpreted as the ratio between the power delivered to the load and the power supplied to the input of the device. Therefore, it is independent of the source impedance ZS (Equation 2.27) [7]. G = PL PIN = |S21| 2(1 − |Γ L|2) (1 − |ΓIN|2)|1 − S22ΓL|2 (2.27)
2.4.2 Available Power Gain
Is expressed by the ratio between the power available from the output of the device and power available from the supply source. It is dependent of ZS and independent of ZL and
in this case is assumed that the device is conjugately matched, i.e, matched for maximum transfer of power (Equation 2.28).
GA= PAV N PAV S = |S21| 2(1 − |Γ S|2) (1 − |ΓOU T|2)|1 − S11ΓS|2 (2.28)
2.4.3 Transducer Power Gain
The transducer power gain is normally the metric used because it takes in consideration the device and the matching networks, i.e, it is dependent of the source and load impedances and therefore considers source and load mismatch. It is expressed as the ratio between the power delivered to the load and and the power available from the source (Equation 2.29) [7].
GT = PL PAV S = |S21| 2(1 − |Γ S|2)(1 − |ΓL|2) |1 − ΓINΓS|2|1 − S22ΓL|2 (2.29) There are two special cases to take into consideration. The first case is when the device is fully matched. Then ΓL= ΓS = 0 and the transducer power gain can be simply expressed
as Equation 2.30,
GT = |S21|2 (2.30)
The second case is when the device is an unilateral device. In that case, S12 = 0 and
consequently the transducer power gain is given by Equation 2.31 [7], GT =
|S21|2(1 − |ΓS|2)(1 − |ΓL|2)
|1 − S11ΓS|2|1 − S22ΓL|2
(2.31)
2.4.4 Constant Gain Circles
In certain cases specifically, when we want to design a broadband amplifier, it is preferable to match the device for a specific gain and not the maximum gain by conjugate matching. As gain and bandwidth are opposites, i.e, the bigger the gain the less bandwidth we will have. Therefore, a tool must be used to do so. Constant gain circles are circles plotted in the Smith chart where the gain has a constant value all over the circumference. Using this tool, one can project the input and output matching networks for a specific ”gain” where mismatch is purposely introduced to obtain the desired ”gain” [6, 7].
For a unilateral device, the input and output matching networks gain, ΓS and ΓL
respec-tively, can be calculated using the following expressions (Equations 2.32 and 2.33),
GS= 1 − |ΓS|2 |1 − S11ΓS|2 (2.32) GL= 1 − |ΓL|2 |1 − S22ΓL|2 (2.33) The maximum gains in each case are obtained by the conjugate matching and are given by Equations 2.34 and 2.35, GSmax= 1 1 − |S11|2 (2.34) GLmax= 1 1 − |S22|2 (2.35) Normalized gain factors can be expressed such as (Equations 2.36 and 2.37),
gs= GS GSmax = 1 − |ΓS| 2 |1 − S11ΓS|2 (1 − |S11|2) (2.36) gL= GL GLmax = 1 − |ΓS| 2 |1 − S22ΓS|2 (1 − |S22|2) (2.37)
Thus, analyzing the expressions, it is possible to verify that 0 ≤ gs≤ 1 and 0 ≤ gl≤ 1.
Knowing the desired gains (GS and/or GL), one must draw the circles correspondent to
the input and/or output matching network on the Smith chart (see Figure 2.9). To draw a circle it is needed to know the center (C) and the radius (R). For the input matching network (Equations 2.38 and 2.39), CS = gSS11∗ 1 − (1 − gS)|S11|2 (2.38) RS = √ 1 − gS(1 − |S11|2) 1 − (1 − gS)|S11|2 . (2.39)
For the output matching network (Equations 2.40 and 2.41), CL= gLS22∗ 1 − (1 − gL)|S22|2 (2.40) RL= √ 1 − gL(1 − |S22|2) 1 − (1 − gL)|S22|2 . (2.41)
It might be a little complicated to calculate manually the values for each circle, but fortunately computer assisted design (CAD) software like Advanced Design Systems (ADS) has built-in tools capable of doing it.
Figure 2.9: Example of what power circles would look like in a Smith chart.
2.5
Stability
One of main concerns when designing a PA is the device stability. This condition is imperative and must be always fulfilled. If the device is unstable, there will be oscillations and consequently distortion of the output signal [13].
Oscillations can only happen if the real part of the port impedance has a negative value. In other words if |ΓIN|> 1 or |ΓOU T|> 1. Since ΓIN and ΓOU T depend on the input and
output matching networks, then the device stability will depend on the matching networks [6].
There are two types of stability:
• Unconditional stability: When the input and output reflection coefficients are less than 1 (|ΓIN|< 1 and |ΓOU T|< 1) for any passive load. In other words, when |ΓS|< 1 and
|ΓL|< 1.
• Conditional stability/Potentially unstable: When there are values of passive source or load impedance where the rule above does not apply.
One particular note is that since the matching networks are frequency dependent, then it is possible to have a device stable at the design frequency but unstable at other frequency. Therefore, it is required the guarantee of stability of the device in the desired frequency range. There are some ways of verifying the device stability. Some of them will be referred in the next sections.
2.5.1 Stability Circles
Taking into account, the following conditions (see Equations 2.42 and 2.43 ) for uncondi-tional stability [6], it is possible to infer that if the device is an unilateral device then |s11|< 1
and |s22|< 1 are enough to obtain unconditional stability. |ΓIN|= |s11+ s12s21ΓL 1 − s22ΓL |< 1 (2.42) |ΓOU T|= |s22+ s12s21ΓS 1 − s11ΓS |< 1 (2.43)
One can note as well that Equations 2.42 and 2.43 establish an interval of values where the amplifier will be stable or unstable and the corresponding boundary. To better visualize the range of values where the PA is stable, stability circles are drawn on the Smith chart.
To draw the stability circles we start with the bondary condition, |ΓIN|= 1. It can be
expressed as (Equation 2.44):
|s11(1 − s22ΓL) + s12s21ΓL|= |1 − s22ΓL|. (2.44)
And simplified to,
|s11− ∆ΓL|= |1 − s22ΓL|, (2.45)
where,
∆ = s11s22− s21s12. (2.46)
Squaring and simplifying both sides of Equation 2.45, it is possible to arrive at an equation in the form of |Γ − C|= R which represents a circle with center in C and radius R in the complex plane [6]. This equation represents the output stability circle with center CL and
radius RL (Equations 2.47 and 2.48),
CL= (s22− ∆s∗11)∗ |s22|2−|∆|2 (2.47) RL= | s12s21 |s22|2−|∆|2 |. (2.48)
For the input stability circle all it is needed is to swap s11 for s22 (Equations 2.49 and
2.50), CS = (s11− ∆s∗22)∗ |s11|2−|∆|2 (2.49) RS = | s12s21 |s11|2−|∆|2 |. (2.50)
As an example, let us consider the stability circles only for the output. If we consider that ZL= Z0, thus ΓL= 0 and by manipulating Equation 2.42 then |ΓIN|= |s11|. There are two
possibilities, either |s11|< 1 or either |s11|> 1. If |s11|< 1 then |ΓIN|< 1 and consequently,
ΓL= 0 (center of the Smith chart) is on the stable region. Therefore, all of the Smith chart
area that does not belong to the stability circle defines the range of stable impedances (see Figure 2.10a). If |s11|> 1 the center of the Smith chart is on the unstable area, because
|ΓIN|< 1 for ΓL= 0. Then the range of impedances where the device is stable is the region that belongs to the stability circle and intersects the Smith chart (see Figure 2.10b) [6].
(a) |ΓIN|< 1 (b) |ΓIN|> 1
Figure 2.10: Output stability circles for a conditionally stable device [6].
Thus, having a set of the device S-parameters, we can evaluate the device stability in any frequency range. If the device is unconditionally stable then the stability circle will be completely outside the Smith chart.
2.5.2 Simpler Tests for Stability Analysis
There are simpler and low time consuming metrics that can be used to evaluate the stability of any device. These metrics consist of necessary and sufficient conditions and when met guarantee unconditional stability [7]. One test consists of analyzing the Rollet’s stability factor (K) (Equation 2.51), K = 1 − |s11| 2−|s 22|2+|∆|2 2|s21s12| > 1 (2.51)
Along with this condition, if
|∆|< 1, (2.52)
then the device is unconditionally stable. If both these conditions are not met, then stability circles will have to be drawn to check the zone where the device is conditionally stable.
Another method which consists in checking only one variable µ which can be defined in terms of source or load (Equations 2.53 and 2.54),
µsource= 1 − |s11|2 |s22− ∆s∗11|+|s21s12| (2.53) µload = 1 − |s22|2 |s11− ∆s∗ 22|+|s21s12| (2.54) Says that if either µload ≥ 1 or µsource ≥ 1 then the amplifier is unconditionally stable
2.6
Efficiency
Efficiency is one of the most important metrics used when evaluating a PA performance. From an energetic perspective, a PA can be considered a transducer, i.e, a system that converts one form of energy into another. In this case, it converts DC power into RF power that will be delivered to the load. The process is illustrated in Figure 2.1. Efficiency is a measure that indicates how effective is this conversion and it can be expressed in multiple ways. The most common are η (drain efficiency or collector efficiency if we are considering a bipolar junction transistor) and power added efficiency (PAE).
2.6.1 Drain Efficiency
Drain efficiency (η) is expressed by the ratio between the output power (Pout) and the
power supplied by the external voltage source (PDC) (Equation 2.55).
η = Pout PDC
(2.55)
2.6.2 Power Added Efficiency
This metric is similar to drain efficiency except it takes into account the input power. It is defined then as the ratio between the difference of output power/input power and DC power supplied (Equation 2.56).
P AE = Pout− Pin PDC
(2.56) Considering that Pout= PinGp,
P AE = Pout− Pin PDC
= η(1 − 1 Gp
) (2.57)
Therefore, as the gain increases it loses importance as an evaluation metric and PAE = η [8]. After discussed the power efficiency metrics to be applied in our design, we will discuss different classes of operation in the following section.
2.7
Amplifier Types and Classes of Operation
Typically any PA falls into one of two families, we will discuss both types in the following sub-sections.
2.7.1 Transconductance PAs
Transconductance amplifiers act as a dependent current source and they are classified according to the conduction angle of the current at the Field Effect Transistor (FET) drain. The conduction angle can be defined as the portion of the input waveform during which the transistor is conducting. Defining the conduction angle requires that the designer reaches a compromise between efficiency and linearity. Depending on the performance that the designer wants from the PA he chooses a conduction angle. The conduction angle is chosen through proper selection of the operational point (or bias point). Different bias points lead to different classes of operation.
Class A
Amplifiers that fall into the class A category are very common in audio amplifiers. This is due to the fact that they are the most linear class since they work between the cut-off and saturation. Typically the bias point is set at the midpoint between cut-off and saturation. Therefore, this results in a linear operation and consequently the amplifier will not be driven into a nonlinear zone where content at harmonic and intermodulation frequencies are gener-ated [2]. This perfectly linear behavior comes at a price of inefficiency. This class is known to have the poorest efficiency since it consumes power even when there is no signal at the input of the device. The conduction angle of a class A amplifier is 2π and it has maximum theoretical efficiency of 50% [2] (see Figures 2.11a and 2.11b ).
(a) Class A bias point (Q) and input/output waveform
(b) Output current waveform
Figure 2.11: Class A operation principle.
Class B
B class fills the lack of efficiency of class A. This is possible, because the conduction angle is lower (π). The reason behind that is because the bias point is set at the threshold voltage of the device meaning that it only conducts half the cycle of the input signal resulting in a maximum theoretical efficiency of 78.5% (see Figures 2.12a and 2.12b). This increment in efficiency is obtained in exchange of linearity and small signal gain, since spectral efficiency and power efficiency are ”conflicting requirements” [2][16].
Despite that, theoretically very good linearity can still be achieved, although it is more difficult to obtain than in a class A. Typically, class B power amplifiers are projected in a push-pull configuration with two transistors in parallel. In this way, each one of the transistors will conduct alternately. In this configuration, even harmonics are canceled (ideally) [13].
(a) Class B bias point (Q) and input/output waveform (b) Output current waveform
Figure 2.12: Class B operation principle. Class AB
As the name indicates, class AB amplifier is a compromise between class A and class B. The bias point is set somewhere between the threshold voltage of the device and the mid-point between the cut-off and saturation region (see Figures 2.13a and 2.13b). The designer is completely free to choose the bias point location according to the design requirements (trade-off between linearity and efficiency). The conduction angle assumes values between π and 2π. Therefore, efficiency will be greater than a class A but will never reach the 78.5% of a class B. This type of amplifiers can be implemented using a push-pull configuration as well.
(a) Class AB bias point (Q) and in-put/output waveform
(b) Output current waveform
Class C
Class C amplifiers are less linear than all classes presented above, but at the same time, are the most efficient ones since the conduction angle is really low. Another characteristic is that since the conduction angle is so low, the output power will be low as well. The conduction angle varies from π to 0 and efficiency can go from 78.5% to 100% in theory. The bias point is set below the threshold voltage (see Figures 2.14a and 2.14b).
Due to this disadvantages, class C amplifiers are not used to a great extent. They are used when linearity required is not high or combined with linearization techniques. Nevertheless, it is used in a very particular configuration called Doherty [17] as we will discuss in section 2.8.1.
As shown in Figure 2.15, the lower the conduction angle is, the lower the linearity and output power are. On other hand, efficiency will be bigger. It is possible to see that class AB yields higher output power. On other hand, class C is the class that delivers fewer power to the load.
To clarify the specific characteristics of each class, Table 2.1 shows the values of the conduction angle and maximum efficiency for class A, B, AB and C.
(a) Class C bias point (Q) and input/output waveform (b) Output current waveform
Figure 2.14: Class C operation principle.
Table 2.1: Theoretical efficiency and conduction angle for classes A, B, AB, and C. Class Conduction Angle (2θ)(Radians) Efficiency(%)
A 2π 50 %
B π 78.5 %
AB π < 2θ < 2π 50% < η < 78.5% C 0 < 2θ < π 78.5% < η < 100%
2.7.2 Switch Mode PAs
Switch Mode PAs rely on transistors that are continuously alternating between saturation and cut-off, in other words, working as a switch. This allows to reach greater efficiencies. When the transistor is driven into saturation by a large input signal, the current flowing
Figure 2.15: Output power and efficiency as a function of conduction angle [2].
through the drain is very high and the voltage very low. If there is no signal being applied to the input of the device the transistor will be off, meaning that the voltage across the transistor is high and the current very low.
Therefore, the overlap between voltage and current is minimized and that leads to higher power efficiencies [18]. Naturally, since they are driven into saturation there is a lot of content generated at harmonic and intermodulation frequencies. Thus, this type of amplifiers are not used when there is a high need of linearity.
Since this thesis aims to provide a amplifier with high linearity, some of the switch mode classes will be briefly introduced.
Class D
The class D concept was introduced in 1958 and there are multiple configurations [19]. The resistive load terminated configurations, current-switching and voltage switching config-urations are a few examples. Independently of the configconfig-urations a class D amplifier consists in a pair of transistors and these are driven, typically, by a square signal [18]. There are many examples that could be given, but to keep our explanation short only one will be presented. Figure 2.16 illustrates a complementary voltage-switching configuration. From this image it is possible to identify:
• An input transformer which introduces a 180o out-of-phase between the currents being
provided to the input of the transistors. This feat is accomplished by reversing the way of one of the windings.
• A pair of transistors which act as a switch and define the output waveform.
• A tuned output circuit, i.e, a filter resonant at the switching frequency. This way, the signal delivered to the load only has the fundamental frequency component and all the harmonics are ideally removed meaning there are no power losses at harmonic frequencies.
Class D amplifiers are not used frequently because there are parasitic effects at high frequen-cies. Therefore, they are occasionally used at low frequencies such as short-wave broadcast transmitters [20].
Figure 2.16: Complementar voltage-switching configuration.
Class E
Another type of switched-mode amplification method was introduced by Sokal in 1975 with many applications and with a simpler approach than class D [21]. There are different configurations which rely on different load network implementations. The load network is es-sentially constituted by a shunt capacitance, series inductance and a filter to remove harmonic components.
In Figure 2.17 is possible to observe the architecture of a class E amplifier. From this illustration it is possible to identify:
• One and only one active device responsible for the amplification.
• One Radio Frequency Choke (RFC).
• Load network.
When the switch is closed (on state), the inductor charges, VDS is 0 and the drain current
is equal IDC. When the switch is open the inductor discharges into the load network meaning
that there is voltage pulse. Then, overlap between current and voltage is hopefully nonexistent meaning that there is no dissipated power. The main issue is that a class E PA is strongly nonlinear [20].
Figure 2.17: Example of a class E PA.
Class F
Class F was firstly introduced in 1958 by V.J. Tyler [22]. This type of PAs are based on on biharmonic or polyharmonic concept. This means that a class F amplifier relies on single or multi-resonant circuits at harmonic frequencies to allow a square voltage waveform as well as a half sinusoidal current waveform at the output. One of the basic principles of telecommunications is the Fourier theorem, where any signal can be constructed as a sum of sinusoidal waves since this type of wave is considered to be ”pure” (only one component at the frequency domain). Thus, a square wave is known to be expressed as a sum of sine waves at the fundamental and odd harmonic frequencies. The load network must present (see Figure 2.18):
• Short circuit at even harmonics. • Open circuit at odd harmonics
• Optimum impedance for high power transfer or efficiency.
The main drawback is that in practice the output voltage waveform is not squared since it is impossible to accommodate enough resonant circuits to provide the proper harmonic termination. Also, the device might not produce enough high order harmonics.
All classes previously mentioned are capable of providing efficient/linear operation as-suming that the input signal is a continuous wave (CW) at maximum power. As stated in Chapter 1.1, the signals used in modern telecommunications systems use complex modulation schemes which require high bandwidth and the average value is really low since the modula-tion techniques present a high PAPR. Therefore, the PA is mainly operated in low a power zone meaning that efficiency will be lower. Thus, since there is a big concern in keeping efficiency as high as possible, nowadays more complex architectures are employed. Some of these techniques are explained in the next section.
Figure 2.18: Example of a class F PA.
2.8
Efficiency Enhancement Architectures
2.8.1 Doherty Amplifier
The Doherty amplifier was firstly introduced by Sir William Doherty in 1936 and it was the fruit of many years of work to improve the efficiency of high-power radio transmitters for transoceanic broadcasting which relied in vacuum tubes at that time [17]. This was a huge success, because it surpassed the most efficient and conventional techniques, like the Chireix outphasing concept introduced in 1935 [23]. For many years this architecture was largely adopted, until solid state devices came around. Suddenly, a technique that has been used for decades stopped working. This is because solid state devices are highly non-linear devices and are far from the ideal current source. To solve the problem, linearization techniques would have to be used which was really difficult at the time since the solution was in the analog domain.
Years came and went and the Doherty amplifier fell in disuse... until something that Sir Doherty could not predict came out, the rise of digital electronics. The digital world came and with it telecommunications changed drastically. As stated in Chapter 1.1, to support the high data rates of the modern world, complex modulation schemes are used, like OFDM and QAM. These are modulations characterized by high PAPR which require the PAs to operate in output back-off (OBO) levels where efficiency is typically low. This lead to revive this architecture since one of its characteristics is the high efficiency at OBO levels. Problem solved, right? Not exactly. The old compromise between efficiency and linearity is still valid. This means that the Doherty amplifier introduces a lot of distortion. Fortunately, nowadays it is possible to use Digital Signal Processing (DSP) techniques to improve the linearity, like Pre-distortion algorithms where Pre-distortion is purposely introduced to compensate the Pre-distortion introduced by the transmission chain [24].
2.8.2 Principle of Operation
The Doherty amplifier consists in a combination of at least 2 PAs as shown in Figure 2.19. This two amplifiers are called the carrier amplifier and the peaking amplifier. The carrier
amplifier is typically biased as a class AB or B, while the peaking amplifier is biased as a class C. To improve the performance of the global amplifier, the peaking amplifier only starts to conduct when the carrier amplifier reaches saturation. From that point, both amplifiers are conducting and the load seen by each one changes. This phenomenon is referred as load modulation. This is possible since their outputs are combined by a impedance inverter, which typically consists of a quarter-wave transmission line and therefore introduces a phase shift of 90o. This means that the impedance seen at the output of the carrier amplifier will rise as the peaking amplifier starts to conduct.
Naturally, since this impedance inverter introduces a phase shift of 90o, the two signals cannot be combined since they are out of phase by 90o. Therefore, it is needed to introduce a quarter wave line at the input of the peaking amplifier. In this way, the signals at the output of each PA will have the same phase and can be combined [24].
Apart from the amplifiers and the impedance inverting network, this architecture needs a input power divider, like a Wilkinson power divider to divide the power equally for the two branches and another quarter wave line of characteristic impedance of Z1 = 35Ω to convert
the impedance to the typical 50Ω. To better understand the need of this elements lets look at Figure 2.19, where R1, R2, R3 are the impedance seen at the output of the carrier amplifier,
impedance seen at the output of the peaking amplifier and impedance seen at the end of Z2,
respectively.
Figure 2.19: Doherty amplifier basic architecture. From transmission line theory I3 can be written as (Equation 2.58),
I3 = I1
r R1
R3
. (2.58)
Defining the current division ratio β as (Equation 2.59), β = I3
I2+ I3
. (2.59)
And since the output power is the combination of the output power from the carrier amplifier (P1) and the output power from the peaking amplifier (P2) given by (Equations
2.60 and 2.61),
P1= βPOU T. (2.60)
Then, it is possible to express the impedance seen at the output of the impedance inverter (R3) and the impedance seen at the output of the peaking amplifier (R2) with the following
expressions (Equations 2.62 and 2.63),
R3= Z12 βZL . (2.62) R2 = Z12 (1 − β)ZL . (2.63)
Now if the input power is divided equally both amplifiers produce equal output power, then β = 0.5 and consequently the load impedances are (Equation 2.64),
R3 = R1 = R2= R3 = Z2 =
2Z12 ZL
. (2.64)
If we do the math, it is possible to see that if Z1 = 35Ω then R3= R1 = R2 = R3= Z2=
ZL= 50Ω. At low power levels, the carrier amplifier is conducting and the peaking amplifier
can be seen as a open circuit. Then the load impedance seen by the carrier amplifier starts at 0 until it gets to (Equation 2.65),
R1= (
Z2
Z1
)2ZL= 2ZL= 100Ω (2.65)
At this moment, the carrier amplifier is saturated and since the power is four times less than the peak power which corresponds to -6 dB then the amplifier reaches saturation at -6 dB of OPBO. Reaching that point, assuming that the transistor is biased as class B, the efficiency will be of 78.5%. When the input signal reaches medium power levels the peaking amplifier starts to conduct. Therefore, the load impedance seen by the carrier amplifier (R1) will start
to decrease. Since this amplifier is saturated, the voltage and current will be constant. At the moment the peaking amplifier starts to conduct the efficiency will decrease a little bit because of the consumption of DC power. After a brief moment, the efficiency will start to increase reaching it maximum value of 78.5% at maximum amplitude [24] (see Figure 2.20).
2.8.3 Doherty Amplifier Limitations
In terms of limitations, the basic architecture explained above is not recommended when it is required a lot of operational bandwidth. The reason is because of the quarter wave lines of the combiner which are always projected for a specific frequency. Therefore, its behavior for multiple bands is not the best. This is a problem since nowadays telecommunications operators want to reduce the costs as much as possible and wideband operation is a must as well as high efficiency. The aforementioned architecture can only address the efficiency part because of the high efficiency at OPBO power levels.
At the end of the day, even if great efficiency is attained, we still have the same old problem to solve. Efficiency is obtained in exchange of linearity. In this case, the peaking amplifier, biased as a C class, introduces an incredible amount of distortion. To solve that, typically pre-distortion systems are implemented.
In the next section, we present the design approaches one can make in order to design wideband power amplifiers, specifically wideband matching networks.
