Analysis and design of quadrature oscillators

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Analysis and design of quadrature oscillators

  1. 1. ANALYSIS AND DESIGN OF QUADRATURE OSCILLATORS
  2. 2. ANALOG CIRCUITS AND SIGNAL PROCESSING SERIES Consulting Editor: Mohammed Ismail. Ohio State UniversityTitles in Series:SUBSTRATE NOISE COUPLING IN RFICs Helmy, Ahmed, Ismail, Mohammed ISBN: 978-1-4020-8165-1BROADBAND OPTO-ELECTRICAL RECEIVERS IN STANDARD CMOS Hermans, Carolien, Steyaert, Michiel ISBN: 978-1-4020-6221-6ULTRA LOW POWER CAPACITIVE SENSOR INTERFACES Bracke, Wouter, Puers, Robert, Van Hoof, Chris ISBN: 978-1-4020-6231-5LOW-FREQUENCY NOISE IN ADVANCED MOS DEVICES ¨ Haartman, Martin v., Ostling, Mikael ISBN-10: 1-4020-5909-4CMOS SINGLE CHIP FAST FREQUENCY HOPPING SYNTHESIZERS FOR WIRELESSMULTI-GIGAHERTZ APPLICATIONS Bourdi, Taoufik, Kale, Izzet ISBN: 978-14020-5927-8ANALOG CIRCUIT DESIGN TECHNIQUES AT 0.5V Chatterjee, S., Kinget, P., Tsividis, Y., Pun, K.P. ISBN-10: 0-387-69953-8IQ CALIBRATION TECHNIQUES FOR CMOS RADIO TRANCEIVERS Chen, Sao-Jie, Hsieh, Yong-Hsiang ISBN-10: 1-4020-5082-8FULL-CHIP NANOMETER ROUTING TECHNIQUES Ho, Tsung-Yi, Chang, Yao-Wen, Chen, Sao-Jie ISBN: 978-1-4020-6194-3THE GM/ID DESIGN METHODOLOGY FOR CMOS ANALOG LOW POWERINTEGRATED CIRCUITS Jespers, Paul G.A. ISBN-10: 0-387-47100-6PRECISION TEMPERATURE SENSORS IN CMOS TECHNOLOGY Pertijs, Michiel A.P., Huijsing, Johan H. ISBN-10: 1-4020-5257-XCMOS CURRENT-MODE CIRCUITS FOR DATA COMMUNICATIONS Yuan, Fei ISBN: 0-387-29758-8RF POWER AMPLIFIERS FOR MOBILE COMMUNICATIONS Reynaert, Patrick, Steyaert, Michiel ISBN: 1-4020-5116-6ADVANCED DESIGN TECHNIQUES FOR RF POWER AMPLIFIERS Rudiakova, A.N., Krizhanovski, V. ISBN 1-4020-4638-3CMOS CASCADE SIGMA-DELTA MODULATORS FOR SENSORS AND TELECOM del R´o, R., Medeiro, F., P´ rez-Verd´ , B., de la Rosa, J.M., Rodr´guez-V´ zquez, A. ı e u ı a ISBN 1-4020-4775-4SIGMA DELTA A/D CONVERSION FOR SIGNAL CONDITIONING Philips, K., van Roermund, A.H.M. Vol. 874, ISBN 1-4020-4679-0CALIBRATION TECHNIQUES IN NYQUIST AD CONVERTERS van der Ploeg, H., Nauta, B. Vol. 873, ISBN 1-4020-4634-0ADAPTIVE TECHNIQUES FOR MIXED SIGNAL SYSTEM ON CHIP Fayed, A., Ismail, M. Vol. 872, ISBN 0-387-32154-3WIDE-BANDWIDTH HIGH-DYNAMIC RANGE D/A CONVERTERS Doris, Konstantinos, van Roermund, Arthur, Leenaerts, Domine Vol. 871 ISBN: 0-387-30415-0
  3. 3. Analysis and Design of QuadratureOscillatorsbyLuis B. OliveiraUniversidade Nova de Lisboa and INESC-ID, Lisbon, PortugalJorge R. FernandesTechnical University of Lisbon and INESC-ID, Lisbon, PortugalIgor M. FilanovskyUniversity of Alberta, CanadaChris J.M. VerhoevenTechnical University of Delft, The NetherlandsandManuel M. SilvaTechnical University of Lisbon and INESC-ID, Lisbon, Portugal123
  4. 4. Dr. Luis B. Oliveira Dr. Chris J.M. VerhoevenINESC-ID Delft University of TechnologyRua Alves Redol 9 Mekelweg 41000-029 Lisbon 2628 CD DelftPortugal Netherlandsluis.b.oliveira@inesc-id.pt c.j.m.verhoeven@et.tudelft.nlDr. Jorge R. Fernandes Dr. Manuel M. SilvaINESC-ID INESC-IDRua Alves Redol 9 Rua Alves Redol 91000-029 Lisbon 1000-029 LisbonPortugal Portugaljorge.fernandes@inesc-id.pt manuel.silva@inesc-id.ptDr. Igor M. FilanovskyUniversity of AlbertaDept. Electrical &Computer Engineering87 Avenue & 114 StreetEdmonton AB T6G 2V42nd Floor ECERFCanadaigor@ece.ualberta.caISBN: 978-1-4020-8515-4 e-ISBN: 978-1-4020-8516-1Library of Congress Control Number: 2008928025 c 2008 Springer Science+Business Media B.V.No part of this work may be reproduced, stored in a retrieval system, or transmittedin any form or by any means, electronic, mechanical, photocopying, microfilming, recordingor otherwise, without written permission from the Publisher, with the exceptionof any material supplied specifically for the purpose of being enteredand executed on a computer system, for exclusive use by the purchaser of the work.Printed on acid-free paper9 8 7 6 5 4 3 2 1springer.com
  5. 5. To the authors’ families
  6. 6. PrefaceModern RF receivers and transmitters require quadrature oscillators with accuratequadrature and low phase-noise. Existing literature is dedicated mainly to singleoscillators, and is strongly biased towards LC oscillators. This book is devoted toquadrature oscillators and presents a detailed comparative study of LC and RC oscil-lators, both at architectural and at circuit levels. It is shown that in cross-coupled RCoscillators both the quadrature error and phase-noise are reduced, whereas in LC os-cillators the coupling decreases the quadrature error, but increases the phase-noise.Thus, quadrature RC oscillators can be a practical alternative to LC oscillators, es-pecially when area and cost are to be minimized. The main topics of the book are: cross-coupled LC quasi-sinusoidal oscillators,cross-coupled RC relaxation oscillators, a quadrature RC oscillator-mixer, and two-integrator oscillators. The effect of mismatches on the phase-error and the phase-noise are thoroughly investigated. The book includes many experimental results,obtained from different integrated circuit prototypes, in the GHz range. A structured design approach is followed: a technology independent study, withideal blocks, is performed initially, and then the circuit level design is addressed. This book can be used in advanced courses on RF circuit design. In addition topost-graduate students and lecturers, this book will be of interest to design engineersand researchers in this area. The book originated from the PhD work of the first author. This work was thecontinuation of previous research work by the authors from TUDelft and Universityof Alberta, and involved the collaboration of 5 persons in three different institutions.The work was done mainly at INESC-ID (a research institute associated with Tech-nical University of Lisbon), but part of the PhD work was done at TUDelft and at theUniversity of Alberta. This has influenced the work, by combining different viewsand backgrounds. This book includes many original research results that have been presented atinternational conferences (ISCAS 2003, 2004, 2005, 2006, 2007 among others) andpublished in the IEEE Transactions on Circuits and Systems. vii
  7. 7. viii PrefaceLisbon, Portugal Luis B. OliveiraLisbon, Portugal Jorge R.FernandesCanada Igor M. FilanovskyThe Netherlands Chris J.M. VerhoevenLisbon, Portugal Manuel M. Silva
  8. 8. AcknowledgementsThe work reported in this book benefited from contributions from many personsand was supported by different institutions. The authors would like to thank allcolleagues at INESC-ID Lisboa, Delft University of Technology, and Universityof Alberta, particularly Chris van den Bos and Ahmed Allam, for their contribu-tions to the work presented in this book and for their friendly and always helpfulcooperation. The authors acknowledge the support given by the following institutions:r ¸˜ Fundacao para a Ciˆ ncia e Tecnologia of Minist´ rio da Ciˆ ncia, Tecnologia e e e e Ensino Superior, Portugal, for granting the Ph.D. scholarship BD 10539/2002, for funding projects OSMIX (POCTI/38533/ESSE/2001), SECA (POCT1/ESE/47061/2002), LEADER (PTDC/EEA-ELC/69791/2006), SPEED (PTDC/EEA-ELC/66857/2006),and for financial support to the participation in a number of conferences.r INESC-ID Lisboa (Instituto de Engenharia de Sistemas e Computadores – ¸˜ Investigacao e Desenvolvimento em Lisboa), Delft University of Technology, and University of Alberta, for providing access to their integrated circuit design and laboratory facilities.r European Union, through project CHAMELEON-RF (FP6/2004/IST/4-027378).r NSERC Canada for continuous grant support.r CMC Canada for arranging integrated circuits manufacturing. ix
  9. 9. Contents1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Background and Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Organization of the Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Main Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 Transceiver Architectures and RF Blocks . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 Receiver Architectures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2.1 Heterodyne or IF Receivers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2.2 Homodyne or Zero-IF Receivers . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2.3 Low-IF Receivers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.3 Transmitter Architectures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.3.1 Heterodyne Transmitters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.3.2 Direct Upconversion Transmitters . . . . . . . . . . . . . . . . . . . . . . . 16 2.4 Oscillators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.4.1 Barkhausen Criterion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.4.2 Phase-Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.4.3 Examples of Oscillators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.5 Mixers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.5.1 Performance Parameters of Mixers . . . . . . . . . . . . . . . . . . . . . . 27 2.5.2 Different Types of Mixers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.6 Quadrature Signal Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.6.1 RC-CR Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.6.2 Frequency Division . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.6.3 Havens’ Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343 Quadrature Relaxation Oscillator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.2 Relaxation Oscillator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.2.1 High Level Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.2.2 Circuit Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.3 Quadrature Relaxation Oscillator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 3.3.1 High Level Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 xi
  10. 10. xii Contents 3.3.2 Quadrature Relaxation Oscillator without Mismatches . . . . . . 42 3.3.3 Quadrature Relaxation Oscillator with Mismatches . . . . . . . . . 46 3.3.4 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 3.4 Phase-Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 3.4.1 Phase-noise in a Single Relaxation Oscillator . . . . . . . . . . . . . 56 3.4.2 Phase-noise in Quadrature Relaxation Oscillators . . . . . . . . . . 60 3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614 Quadrature Oscillator-Mixer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 4.2 High Level Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 4.2.1 Ideal Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 4.2.2 Effect of Mismatches and Delay . . . . . . . . . . . . . . . . . . . . . . . . 67 4.3 Circuit Level Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 4.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 795 Quadrature LC-Oscillator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 5.2 Single LC Oscillator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 5.3 Quadrature LC Oscillator Without Mismatches . . . . . . . . . . . . . . . . . . 85 5.4 Quadrature LC Oscillator with Mismatches . . . . . . . . . . . . . . . . . . . . . . 89 5.5 Q and Phase-Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 5.6 Quadrature LC Oscillator-Mixer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 5.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 986 Two-Integrator Oscillator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 6.2 High Level Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 6.2.1 Non-Linear Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 6.2.2 Quasi-Linear Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 6.3 Circuit Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 6.4 Phase-Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 6.5 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 6.6 Two-Integrator Oscillator-Mixer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 6.6.1 High Level Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 6.6.2 Circuit Implementation and Simulations . . . . . . . . . . . . . . . . . . 114 6.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1177 Measurement Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 7.2 Quadrature Relaxation Oscillator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 7.2.1 Circuit Schematic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 7.2.2 Measurement Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 7.3 Quadrature LC Oscillator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 7.3.1 Circuit Schematic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
  11. 11. Contents xiii 7.3.2 Measurement Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 7.4 Quadrature Oscillator-Mixer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 7.4.1 Circuit Schematic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 7.4.2 Measurement Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 7.5 Comparison of Quadrature LC and RC Oscillators . . . . . . . . . . . . . . . . 132 7.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 8 Conclusions and Future Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 8.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 8.2 Future Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139A Test-Circuits and Measurement Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 A.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 A.2 Quadrature RC and LC Oscillators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 A.2.1 Test Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 A.2.2 Measurement Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 A.3 Quadrature Relaxation Oscillator-Mixer . . . . . . . . . . . . . . . . . . . . . . . . 144 A.3.1 Test Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 A.3.2 Measurement Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
  12. 12. Chapter 1IntroductionContents1.1 Background and Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Organization of the Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.3 Main Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.1 Background and MotivationThe huge demand for wireless communications has led to new requirements forwireless transmitters and receivers. Compact circuits, with minimum area, are re-quired to reduce the equipment size and cost. Thus, we need a very high degree ofintegration, if possible a transceiver on one chip, either without or with a reducednumber of external components. In addition to area and cost, it is very important toreduce the voltage supply and the power consumption [1, 2]. Digital signal processing techniques have a deep impact on wireless applications.Digital signal processing together with digital data transmission allows the use ofhighly sophisticated modulation techniques, complex demodulation algorithms, er-ror detection and correction, and data encryption, leading to a large improvementin the communication quality. Since digital signals are easier to process than ana-logue signals, a strong effort is being made to minimize the analogue part of thetransceivers by moving as many blocks as possible to the digital domain. The analogue front-end of a modern wireless communication system is respon-sible for the interface between the antenna and the digital part. The analogue front-end of a receiver is critical, the specifications of its blocks being more stringentthan those of the transmitter. There are two basic receiver front-end architectures:heterodyne, with one intermediate frequency (IF), or more than one; homodyne,without intermediate frequency. So far, the heterodyne approach is dominant, butthe homodyne approach, after remaining a long time in the research domain, isbecoming a viable alternative [1, 2]. The main drawback of heterodyne receivers is that both the wanted signal and thedisturbances in the image frequency band are downconverted to the IF. Heterodynereceivers have better performance than homodyne receivers when high quality RFL.B. Oliveira et al., Analysis and Design of Quadrature Oscillators, 1C Springer Science+Business Media B.V. 2008
  13. 13. 2 1 Introduction(radio frequency) image-reject and IF channel filters can be used. However, suchfilters can only be implemented off chip (so far), and they are expensive. A highIF is required because, with a low-IF, the image frequency band is so close to thedesired frequency that an image-reject RF filter is not feasible. Homodyne receivers do not suffer from the image problem, because the RFsignal is directly translated to the baseband (BB), without any IF. Thus, the maindrawbacks of the heterodyne approach (image interference and the use of externalfilters) are overcome, allowing a highly integrated, low area, low power, and lowcost receiver. However, homodyne receivers are very sensitive to parasitic basebanddisturbances and to 1/f noise. Quadrature errors introduce cross-talk between the I(in-phase) and Q (quadrature) components of the received signal, which in combi-nation with additive noise increases the bit error rate (BER). A very interesting receiver approach, which combines the best features of thehomodyne and of the heterodyne receivers, is the low IF receiver [3–7]. This isbasically a heterodyne receiver using special mixing circuits that cancel the imagefrequency. Since image reject filters are not required, there is the possibility of usinga low IF, allowing the integration of the whole system on a single chip [4]. Thelow-IF receiver relaxes the IF channel select filter specifications, because it worksat a relatively low frequency and can be integrated on-chip, sometimes digitally. Theimage rejection is dependent on the quality of image-reject mixing, which dependson component matching and LO (local oscillator) quadrature accuracy. Thus, veryaccurate quadrature oscillators are essential for low-IF receivers. Conventional heterodyne structures, with high IF, make the analogue to digitalconverter (A/D) specifications very difficult to fulfil with reasonable power con-sumption; therefore, the conversion to baseband has to be done in the analoguedomain. In the low-IF architecture, the two down converted signals are digitizedand mixed digitally to obtain the baseband as shown in Fig. 1.1. Analogue Digital BBI LPF A/D LNA BBQ LPF A/D I Q I Q LO1 LO2 LNA - Low noise amplifier LPF - Low pass filterFig. 1.1 Low-IF receiver (simplified block diagram)
  14. 14. 1.1 Background and Motivation 3 The LO is a key element in the design of RF frontends. The oscillator should befully integrated, tunable, and able to provide two quadrature output signals [8–11],I and Q. In addition to frequency and phase stability, quadrature accuracy is a veryimportant requirement of quadrature oscillators. The most often used circuits to obtain two signals in quadrature have open-loopstructures, in which the errors are propagated directly to the output. Examples ofsuch structures are [1]:1. Passive circuits to produce the phase-shift (RC-CR network), in which the phase difference and gain are frequency dependent.2. Oscillators working at double of the required frequency, followed by a divider by two; this method leads to high power consumption, and reduces the maximum achievable frequency.3. An integrator with the in-phase signal at the input, followed by a comparator to obtain the signal in quadrature (aligned with the zero crossings of the integrator output); this has the disadvantage that the two signal paths are different.In recent years, significant effort has been invested in the study of oscillators withaccurate quadrature outputs [9–11]. Relaxation and LC oscillators, when cross-coupled (using feedback structures), are able to provide quadrature outputs. In thisbook these oscillators are studied in depth, in order to understand their key parame-ters, such as phase-noise and quadrature error. The relaxation oscillator has been somewhat neglected with respect to the LCoscillator, as it is widely considered as a lower performance oscillator in terms ofphase-noise. Although this is true for a single oscillator, it is not for cross-coupledoscillators. In this work we consider alternatives to the LC oscillator and investigate theiradvantages and limitations. We study in detail the quadrature relaxation oscillatorsin terms of their key parameters, showing that due to the cross-coupling it is possibleto reduce the oscillator phase-noise and make the effect of mismatches a secondorder effect, thus improving the accuracy of the quadrature relationship. We showthat, although stand-alone LC oscillators have a very good phase-noise performance,this is degraded when there is cross coupling. In addition to these two types of quadrature oscillators, we investigate a thirdtype of oscillator: the two-integrator oscillator. While in the previous cases we hadtwo oscillators with coupling to provide quadrature outputs, this oscillator is ableto provide inherent quadrature outputs, with phase-noise comparable to that of arelaxation oscillator. The main advantage of this oscillator is its wide tuning range,which in a practical implementation (in the GHz range) can be about one decade. Mixers are responsible for frequency translation, upconversion and downconver-sion, with a direct influence on the global performance of the transceiver [1,2]. Theyhave been realized as independent circuits from the oscillators, either in heterodyneor homodyne structures. The evolution of mixer circuits has been, so far, essen-tially due to technological advancements in the semiconductor industry. Here, weshow that it is possible to integrate the mixing function with the quadrature oscilla-tors. This approach has the advantage of saving area and power, leading to a more
  15. 15. 4 1 Introductionaccurate output quadrature than that obtained with separate quadrature oscillatorsand mixers. We study the influence of the mixing function on the oscillator perfor-mance, and we confirm by measurement the oscillator-mixer concept. However, themain emphasis of this book is on the oscillators: the inclusion of the mixing functionstill requires further study. In this work we study in detail the three types of quadrature oscillators referredabove, and we evaluate their relative advantages and disadvantages. Simulation andexperimental results are provided which confirm the theoretical analysis.1.2 Organization of the BookThis book is organized in 8 Chapters. Following this introduction, we present asurvey, in Chapter 2, of RF front-ends and their main blocks: we describe the basicreceiver and transmitter architectures, then we focus on basic aspects of oscillatorsand mixers, and, finally, we review conventional techniques to generate quadraturesignals. In Chapter 3 we present a study of the quadrature relaxation oscillator, in whichwe consider their key parameters: oscillation frequency, signal amplitude, quadra-ture relationship, and phase-noise. We use a structured approach, starting by con-sidering the oscillator at a high level, using ideal blocks, and then we proceed tothe analysis at circuit level. We present simulation results to confirm the theoreticalanalysis. In Chapter 4 we analyse the quadrature relaxation oscillator-mixer. We first eval-uate the circuit at a high level (structured approach), deriving equations for the os-cillation frequency and quadrature error of the oscillator-mixer. We show that wecan inject the modulating signal in the circuit feedback loop, and we explain whereand how the RF signal should be injected, to preserve the quadrature relationship.Simulation results are provided to validate theoretical results. In Chapter 5 the quadrature LC oscillator is studied in terms of the oscillationfrequency, signal amplitude, Q, and phase-noise. We investigate the possibility ofinjecting a signal to perform the mixing function. In Chapter 6 we study the two-integrator oscillator. We proceed from a high leveldescription to the circuit implementation, and we present simulation results. We alsoshow the possibility of performing the mixing function in this oscillator. In Chapter 7 we present several circuit implementations to provide experimentalconfirmation of the theoretical results:– a 2.4 GHz quadrature relaxation oscillator and a 1 GHz quadrature LC oscillator;– two 5 GHz quadrature oscillators, one RC and the other LC, designed to be suit- able for a comparative study;– a 5 GHz RC oscillator-mixer (to demonstrate the study in chapter 4).In Chapter 8 we present the conclusions and suggest future research directions. In the appendix we describe the measurement setup for the above mentionedprototypes.
  16. 16. 1.3 Main Contributions 51.3 Main ContributionsThe work that we present in this book has led to several papers in internationalconferences and journals. It is believed that the main original contributions of thework are: (i) A study (in Chapter 3) of cross-coupled relaxation oscillators using a structured design approach: first with ideal blocks, and then at circuit level. Equations are derived for the oscillation frequency, amplitude, phase-noise, and quadrature relationship [12–15]. A prototype at 2.4 GHz was designed to confirm the main theoretical results (quadrature relationship and phase-noise). (ii) A study of a cross-coupled relaxation oscillator-mixer at high level (in chap- ter 4) [12, 16–18] and investigation of the influence of the mixing function on the oscillator performance. A 5 GHz prototype was designed to validate the oscillator-mixer concept [19].(iii) A study of cross-coupled LC oscillators concerning Q and phase-noise (in Chapter 5) [20,21]. A comparative study of phase-noise in cross-coupled oscil- lators, which shows that coupled relaxation oscillators can be a good alternative to coupled LC oscillators [14]. A 1 GHz prototype confirms the increase of phase-noise in LC oscillators due to coupling [21], and two circuit prototypes at 5 GHz (RC and LC) confirm that quadrature RC oscillators might be a good alternative to quadrature LC oscillators.A minor contribution is the study of the two-integrator oscillator at high level and atcircuit level (in Chapter 6), in which we show that this circuit has the advantage ofa large tuning range when compared with the previous ones [22]. The work reported in this book has led to further results on quadrature oscillators,with other coupling techniques [23–25]. A pulse generator for UWB-IR based ona relaxation oscillator has been proposed recently [26]. These results, however, areoutside of the scope of this book.
  17. 17. Chapter 2Transceiver Architectures and RF BlocksContents2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2 Receiver Architectures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2.1 Heterodyne or IF Receivers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2.2 Homodyne or Zero-IF Receivers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2.3 Low-IF Receivers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.3 Transmitter Architectures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.3.1 Heterodyne Transmitters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.3.2 Direct Upconversion Transmitters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.4 Oscillators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.4.1 Barkhausen Criterion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.4.2 Phase-Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.4.3 Examples of Oscillators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.5 Mixers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.5.1 Performance Parameters of Mixers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.5.2 Different Types of Mixers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292.6 Quadrature Signal Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.6.1 RC-CR Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.6.2 Frequency Division . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.6.3 Havens’ Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342.1 IntroductionIn this chapter we review the basic transceiver (transmitter and receiver) architec-tures, and some important front-end blocks, namely oscillators and mixers. We givespecial attention to the conventional methods to generate quadrature signals. We start by describing the advantages and disadvantages of several receiver andtransmitter architectures. Receivers are used to perform low-noise amplification,downconversion, and demodulation, while transmitters perform modulation, up-conversion, and power amplification. Receiver and transmitter architectures can bedivided into two types: heterodyne, which uses one or more IFs (intermediate fre-quencies), and homodyne, without IF. Nowadays research is more active concerningthe receiver path, since requirements such as integrability, interference rejection, andL.B. Oliveira et al., Analysis and Design of Quadrature Oscillators, 7C Springer Science+Business Media B.V. 2008
  18. 18. 8 2 Transceiver Architectures and RF Blocksband selectivity are more demanding in receivers than in transmitters. The impor-tance of accurate quadrature signals to realize integrated receivers is emphasized inthis chapter. At block level, the basic aspects of oscillators are reviewed, with special em-phasis on the phase-noise and its importance in telecommunication systems. Theoscillators can be divided into two main groups, according to whether they havestrong non-linear or quasi-linear behaviour. We present an example of each: the RCrelaxation oscillator (non-linear) and the LC oscillator (linear). We survey the main characteristics of mixers, which, being responsible for fre-quency translation (upconversion or downconversion), are essential blocks of RFtransceivers. This chapter ends by discussing the conventional methods to generate quadra-ture outputs, all of which employ open-loop structures. We describe in detail themost widely known method, the RC-CR network, and we also discuss two otherapproaches to generate quadrature outputs: frequency division and the Havens’technique.2.2 Receiver ArchitecturesReceivers can be divided into three main groups:– Conventional heterodyne or IF receivers – that use one intermediate frequency (IF) or more than one intermediate frequency (multi-stage IF);– Homodyne or zero-IF receivers – that convert directly the signal to the baseband.– Low-IF receiver – this is a special case of heterodyne receiver that has become important in recent years [4], since it combines some of the advantages of the homodyne and conventional IF architectures.2.2.1 Heterodyne or IF ReceiversThe heterodyne receiver was called by Armstrong as superheterodyne (patented in1917), because the designation heterodyne had already been applied in a differentcontext (in the area of rotating machines) [2]. This is the reason why the designationsuperheterodyne, instead of heterodyne, became prevalent until recently. The heterodyne receiver has been, for a long time (more than 70 years), the mostcommonly used receiver topology. In this approach the desired signal is downcon-verted from its carrier frequency to an intermediate frequency (single IF); in somecases, it is further downconverted (multi IF). The schematic of a modern IF re-ceiver for quadrature IQ (in-phase and quadrature) signals is represented in Fig. 2.1.This receiver can be built with different technologies, GaAs, bipolar, or CMOS, anduses several discrete component filters. These filters must be implemented off-chip,with discrete components, to achieve high Q, which is difficult or impossible toobtain with integrated components. Using these high Q components, the heterodyne
  19. 19. 2.2 Receiver Architectures 9 LPF A/D Image Channel Reject Select RF IR CS LO2 LNA IF DSP BPF BPF BPF –90º LPF A/D LO1Fig. 2.1 Heterodyne receiverreceiver achieves high performance with respect to selectivity and sensitivity, whencompared with other receiver approaches [1, 4]. This receiver can handle modernmodulation schemes, which require the separation of I and Q signals to fully recoverthe information (for example, quadrature amplitude modulation); accurate quadra-ture outputs are necessary (for conversion to the baseband). The main drawback of this receiver is that two input frequencies can produce thesame IF. For example, let us consider that the IF is 50 MHz and we want to down-convert a signal at 850 MHz. If we consider a local oscillator with 900 MHz, a signalat 950 MHz will be also downconverted by the mixer to the IF. This unwanted signalis called image. To overcome this problem in conventional heterodyne receivers animage reject filter is placed before the mixer as illustrated in Fig. 2.2. An important issue in heterodyne receivers is the choice of IF. With a high IF it iseasier to design the image reject filter and suppress the image. However, in additionto the image, we also need to take into account interferers. At the IF frequency wemust remove interferers (which are also downconverted to the IF) using a channelselect filter (Fig. 2.1). Using a low IF reduces the demand on the channel selectfilter. Furthermore, a low IF relaxes the requirements on IF amplifiers, and makesthe A/D specifications easier to fulfil. Thus, there is a trade-off in the heterodynereceiver: with high IF image rejection is easier, whereas with low IF the suppressionof interferers is easier. The heterodyne architecture described above requires the use of external com-ponents. It is not a good solution for low-cost, low area, and ultra compact modernapplications. The challenge nowadays is to obtain a fully integrated receiver, on a Image Reject BPF Channel Channel Image Image (rejected by filter) ω1 ωLO ωIM ω 0 ωIF ω ωIFFig. 2.2 Image rejection
  20. 20. 10 2 Transceiver Architectures and RF Blockssingle chip. This requires either direct conversion to the baseband, or the develop-ment of new techniques to reject the image without the use of external filters. Thesetwo possible approaches will be described next.2.2.2 Homodyne or Zero-IF ReceiversIn homodyne receivers the RF spectrum is translated to the baseband in a singledownconversion (the IF is zero). These receivers, also called “direct-conversion”or “zero-IF”, are the most natural solution to detect information associated with acarrier in just one conversion stage. The resulting baseband signal is then filteredwith a low-pass filter, which can be integrated, to select the desired channel [1, 4]. Since the signal and its image are separated by twice the IF, this zero IF approachimplies that the desired channel is its own image. Thus, the homodyne receiver doesnot require image rejection. All processing is performed at the baseband, and wehave the more relaxed possible requirements for filters and A/Ds. Using modern modulation schemes, the signal has information in the phase andamplitude, and the downconversion requires accurate quadrature signals. The blockdiagram of a homodyne receiver is shown in Fig. 2.3. The filter before the LNAis optional [27], but it is often used to suppress the noise and interference outsidethe receiver band. This simple approach permits a highly integrated, low area, lowpower, and low-cost realization. Direct conversion receivers have several disadvantages with respect to hetero-dyne receivers, which do not allow the use of this architecture in more demandingapplications. These disadvantages are related to flicker noise, channel selection, LO(local oscillator) leakage, quadrature errors, DC offsets, and intermodulation:(a) Ficker noise – The flicker noise from any active device has a spectrum close to DC. This noise can corrupt substantially the low frequency baseband signals, which is a severe problem in MOS implementation (1/f corner is about 200 kHz). LPF A/D RF LO LNA BPF DSP –90º LPF A/DFig. 2.3 Homodyne receiver
  21. 21. 2.2 Receiver Architectures 11(b) Channel selection – At the baseband the desired signal must be filtered, ampli- fied, and converted to the digital domain. The low-pass filter must suppress the out-of-channel interferers. The filter is difficult to implement, since it must have low-noise and high linearity.(c) LO leakage – LO signal coupled to the antenna will be radiated, and it will inter- fere with other receivers using the same wireless standard. In order to minimize this effect, it is important to use differential LO and mixer outputs to cancel common mode components.(d) Quadrature error – Quadrature error and mismatches between the amplitudes of the I and Q signals corrupt the downconverted signal constellation (e.g., in QAM). This is the most critical aspect of direct-conversion receivers, because modern wireless applications have different information in I and Q signals, and it is difficult to implement accurate high frequency blocks with very accurate quadrature relationship.(e) DC offsets – Since the downconverted band extends down to zero frequency, any offset voltage can corrupt the signal and saturate the receiver’s baseband output stages. Hence, DC offset removal or cancellation is required in direct-conversion receivers.(f) Intermodulation – Even order distortion produces a DC offset, which is signal dependent. Thus, these receivers must have a very high IIP2 (input second har- monic intercept point)The direct conversion approach requires very linear LNAs and mixers, high fre-quency local oscillators with precise quadrature, and use of a method for achiev-ing submicrovolt offset and 1/f noise. All these requirements are difficult to fulfillsimultaneously.2.2.3 Low-IF ReceiversHeterodyne receivers have important limitations due to the use of external im-age reject filters. Homodyne receivers have some drawbacks because the signalis translated directly to the baseband. Thus, there is interest in the developmentof new techniques to reject the image without using filters. An architecture thatcombines the advantages of both the IF and the zero-IF receivers is the low-IFarchitecture. The low-IF receiver is a heterodyne receiver that uses special mixing circuitsthat cancel the image frequency. A high quality image reject filter is not necessaryanymore, while the disadvantages of the zero-IF receiver are avoided. Since image reject filters are not required, it is possible to use a low IF, allowingthe integration of the whole system on a single chip. The low IF relaxes the IFchannel select filter specifications, and, since it works at a relatively low frequency,it can be integrated on-chip, sometimes digitally. In a low-IF receiver the value of IFis once to twice the bandwidth of the wanted signal. For example, an IF frequency
  22. 22. 12 2 Transceiver Architectures and RF Blocksof few hundred kHz can be used in GSM applications (200 kHz channel bandwidth),as described in [4]. Quadrature carriers are necessary in modern modulation schemes, and in low IFreceivers they have an additional use: accurate quadrature signals are essential toremove the image signal. This removal depends strongly on component matchingand LO (local oscillator) quadrature accuracy. Two image reject mixing techniques can be used, which have been proposed byHartley and by Weaver. The Hartley architecture [28] has the block diagram represented in Fig. 2.4. TheRF signal is first mixed with the quadrature outputs of the local oscillator. Afterlow-pass filtering of both mixers’ outputs, one of the resulting signals is shifted by90◦ , and a subtraction is performed, as shown in Fig. 2.4. In order to show how theimage is canceled we must consider the signals at points 1, 2, and 3 (Fig. 2.4). We assume that xRF (t) = VRF cos(␻RF t) + VIM cos(␻IM t) (2.1)where VIM and VRF are, respectively, the amplitude of image and RF signals, and␻IM is the image frequency. It follows that VRF VIM x1 (t) = sin[(␻LO − ␻RF )t] + sin[(␻LO − ␻IM )t] (2.2) 2 2 VRF VIM x2 (t) = cos[(␻LO − ␻RF )t] + cos[(␻LO − ␻IM )t] (2.3) 2 2 Equation (2.2) can be written as: VRF VIM x1 (t) = − sin[(␻RF − ␻LO )t] + sin[(␻LO − ␻IM )t] (2.4) 2 2 sin (ω LO t) 1 3 LPF 90° RF LO IF Input Output –90° 2 LPF cos (ω LO t)Fig. 2.4 Hartley architecture (single output)
  23. 23. 2.2 Receiver Architectures 13 Since a shift of 90◦ is equivalent to a change from cos(␻t) to sin(␻t): VRF VIM x3 (t) = cos[(␻RF − ␻LO )t] − cos[(␻LO − ␻IM )t] (2.5) 2 2 Adding (2.5) and (2.3) cancels the image band and yields the desired signal. InHartley’s approach, the quadrature downconversion followed by a 90◦ phase shiftproduces in the two paths the same polarities for the desired signal, and oppositepolarities for image. The main drawback of this architecture is that the receiver isvery sensitive to the local oscillator quadrature errors and to mismatches in the twosignal paths, which cause incomplete image cancellation. The relationship between the image average power (PIM ) and the signal averagepower (PS ) is [1]: PIM V 2 (VLO + ⌬VLO )2 − 2VLO (VLO + ⌬VLO ) cos(␪) + VLO 2 = IM (2.6) PS VRF (VLO + ⌬VLO )2 + 2VLO (VLO + ⌬VLO ) cos(␪) + VLO 2 2where VLO is the amplitude of local oscillator, ⌬VLO is the amplitude mismatch, and␪ is the quadrature error. Noting that VIM 2 /VRF 2 is the image-to-signal ratio at the receiver input (RF),the image rejection ratio (IRR) is defined as PIM /PS at the IF output divided byVIM 2 /VRF 2 . PIM PS IRR = 2 out (2.7) VIM 2 VRF in The resulting equation can be simplified if the mismatch is small (⌬VLO VLO )and the quadrature error ␪ is small [1, 2]: 2 ⌬VLO + ␪2 VLO IRR ≈ (2.8) 4 Note that we have considered only errors of the amplitude and phase in the localoscillator. Mismatches in mixers, filters, adders, and phase shifter will also con-tribute to the IRR. In integrated circuits, without using calibration techniques, thetypical values for amplitude mismatch are 0.2–0.6 dB and for the quadrature error3−5◦ , leading to an image suppression of 25 to 35 dB [1, 2, 28, 29]. The second type of image-reject mixing is performed by the Weaver architecture[30], represented in Fig. 2.5. This is similar to the Harley architecture, but the 90◦phase shift in one of the signal paths is replaced by a second mixing operation inboth signal paths: the second stage of I and Q mixing has the same effect of the90◦ phase shift used in the Hartley approach. As with the Hartley receiver, if the
  24. 24. 14 2 Transceiver Architectures and RF Blocks LPF RF IF or BB LO1 LO2 Input Output –90° –90° LPFFig. 2.5 Weaver architecture with single outputphase difference of the two local oscillator signals is not exactly 90◦ , the image isno longer completely cancelled. The Weaver architecture has the advantage that the RC-CR mismatch effect (thiseffect will be discussed in detail in Section 2.6) on the 90◦ phase shift after the down-conversion in the Hartley architecture is avoided and the second order distortion in Channel Secondary Image RE Input ωLO1 2ωLO2 – ωIN + 2ωLO1 ωIN ω Channel Secondary First Image IF 2ωLO2 – ωIN + ωLO1 ωLO2 ωIN – ωLO1 ω Channel Secondary Second Image IF ωIN – ωLO1 – ωLO2 ωFig. 2.6 Secondary image problem in the Weaver architecture
  25. 25. 2.3 Transmitter Architectures 15 LPF BB I LPF RF Input BB Q LPF LPF I Q I Q LO1 LO2Fig. 2.7 Weaver architecture with quadrature outputsthe signal path can be removed by the filters following the first mixing. However,as the Hartley architecture, the Weaver architecture is sensitive to mismatches inamplitude and quadrature error of the two LO signals. It suffers from an imageproblem (in the second mixing operation) if the second downconversion is not tothe baseband, as shown in Fig. 2.6. In this case the low pass filters, must be replacedby bandpass filters, to suppress the secondary image, but, the image suppression iseasier at IF than at RF. The receiver of Fig. 2.5 needs to be modified to provide baseband quadratureoutputs, which are necessary in modern wireless applications. We need 6 mixersto cancel the image and separate the quadrature signals, as shown in Fig. 2.7. Thesecond two mixers in Fig. 2.5 are replaced by two pairs of quadrature mixers, andtheir outputs are then properly combined [2]. This modified Weaver architecture isused in low-IF receivers [31].2.3 Transmitter ArchitecturesTransmitter architectures can be divided into two main groups:– Heterodyne – that use an intermediate frequency;– Direct upconversion – that converts directly the signal to the RF band.2.3.1 Heterodyne TransmittersThe heterodyne upconversion, represented in Fig. 2.8, is the most often used archi-tecture in transmitters. In heterodyne transmitters the baseband signals are modu-lated in quadrature (modern transmitters must handle quadrature signals) to the IF,since it is easier to provide accurate quadrature outputs at IF than at RF. The IF filterthat follows rejects the harmonics of the IF signal, and reduces the transmitted noise.
  26. 26. 16 2 Transceiver Architectures and RF Blocks D/A LO IF RF DSP PA BPF BPF –90° D/A LOFig. 2.8 Heterodyne transmitterThe IF modulated signal is then upconverted, amplified (by the power amplifier),and transmitted by the antenna. A heterodyne transmitter requires an RF band-pass filter to suppress (50–60 dB)the unwanted sideband after the upconversion, in order to meet spurious emissionlevels imposed by the standards. This filter is typically passive and built with expen-sive off-chip components [1, 4]. This topology does not allow full integration of thetransmitter, due to the off-chip passive components in IF and RF filters.2.3.2 Direct Upconversion TransmittersIn this type of transmitter, shown in Fig. 2.9, the baseband signal is directly upcon-verted to RF. The RF carrier frequency is equal to the LO frequency, at the mixersinput. A quadrature upconversion is required by modern modulations schemes. This topology can be easily integrated, because there is no need to suppressany mirror signal generated during the upconversion. As in the receiver, the localoscillator frequency is the carrier frequency [4]. D/A LO HF DSP PA BPF –90° D/AFig. 2.9 Direct upconversion transmitter
  27. 27. 2.4 Oscillators 17 The main disadvantage is the “injection pulling” or “injection locking” of thelocal oscillator by the high level PA output. The resulting spectrum can not besuppressed by a bandpass filter, because it has the same frequency as the wantedsignal. To avoid this effect the isolation required is normally higher than 60 dB. As in the receiver case, a solution that tries to combine the advantages of bothdirect and heterodyne upconversion was proposed in [32, 33]. In this case the base-band signals are converted to a low IF, and are then upconverted to the final carrierfrequency using an image-reject mixing technique to reject the unwanted sideband,thus avoiding the use of an RF filter after the upconversion. Thus, an integratedcircuit realization is possible, with lower area and cost than with a conventionalheterodyne approach.2.4 Oscillators2.4.1 Barkhausen CriterionThe basic function of an oscillator is to convert DC power into a periodic signal.A sinusoidal oscillator generates a sinusoid with frequency ␻0 and amplitude V0(Fig. 2.10), vOUT (t) = V0 cos(␻0 t + ␪) (2.9) For digital applications, oscillators generate a clock signal, which is a square-waveform with period T0 . Sinusoidal oscillators can be analyzed as a feedback system, shown in Fig. 2.11,with the transfer function. Yout ( j␻) H ( j␻) = (2.10) X in ( j␻) 1 − H ( j␻)␤( j␻) Amplitude [V] P[dBm] V0 t[s] ω0 ω[rad/s] (a) (b)Fig. 2.10 Sinusoidal oscillator output: (a) Time domain; (b) Frequency domain
  28. 28. 18 2 Transceiver Architectures and RF BlocksFig. 2.11 Feedback systemblock diagram β( jω) Xin ( jω) Yout ( jω) + + + H( jω) The necessary conditions concerning the loop gain for steady-state oscillationwith frequency ␻0 are known as the Barkhausen conditions. The loop gain must beunity (gain condition), and the open-loop phase shift must be 2k␲, where k is aninteger including zero (phase condition). |H ( j␻0 )␤( j␻0 )| = 1 (2.11) arg[H ( j␻0 )␤( j␻0 )] = 2k␲ (2.12) The Barkhausen criterion gives the necessary conditions for stable oscillations,but not for start-up. For the oscillation to start, triggered by noise, when the systemis switched on, the loop gain must be larger than one, |H ( j␻)␤( j␻)| > 1 [34].2.4.2 Phase-Noise2.4.2.1 DefinitionIn modern transceiver applications the most important difference between idealand real oscillators is the phase-noise. The noise generated at the oscillator out-put causes random fluctuation of the output amplitude and phase. This meansthat the output spectrum has bands around ␻0 and its harmonics (Fig. 2.12).With the increasing order of the harmonics of ␻0 the power in the sidebandsdecreases [35]. The noise can be generated either inside the circuit (due to active and passivedevices) or outside (e.g., power supply). Effects such as nonlinearity and periodic P [dBm] White noiseFig. 2.12 Spectrum of flooroscillator output with ω0 2ω0 3ω0phase-noise ω[rad/s]
  29. 29. 2.4 Oscillators 19variation of circuit parameters make it very difficult to predict phase-noise [36]. Thenoise causes fluctuations of both amplitude and phase. Since, in practical oscillatorsthere is an amplitude stabilization scheme, which attenuates amplitude variations,phase-noise is usually dominant. The oscillator noise can be characterized eitherin the frequency domain (phase-noise), or in the time domain (jitter). The firstis used by analog and RF designers, and the second is used by digital designers[35–37]. There are several ways to quantify the fluctuations of phase and amplitude inoscillators (a review of different standards and measurement methods is presentedin [38]). They are often characterized in terms of the single sideband noise spec-tral density, L(␻), expressed in decibels below the carrier per hertz (dBc/Hz). Thischaracterization is valid for all types of oscillators and is defined as: P(␻m ) L(␻m ) = (2.13) P(␻0 )where: P(␻m ) is the single sideband noise power at a distance of ␻m from the carrier (␻0 ) in a 1 Hz bandwidth; P(␻0 ) is the carrier power. The advantage of this parameter is its ease of measurement. This can be doneby using a spectrum analyzer (which is a general-purpose equipment, but will in-troduce some errors) or with phase or frequency demodulators with well knownproperties (which are dedicated and expensive equipment). Note that the spectraldensity (2.13) includes both phase and amplitude noise, and they can not be sep-arated. However, practical oscillators have an amplitude stabilization mechanism,which strongly reduces the amplitude noise, while the phase-noise is unaffected.Thus, equation (2.13) is dominated by the phase-noise and L(␻m ) is known simplyas “phase-noise”. The carrier-to-noise ratio (CNR) can also be used to specify the oscillator phase-noise. The CNR in a 1 Hz frequency band at the distance of ␻m from the carrier ␻0 ,is defined as: CNR(␻m ) = 1/L(␻m ) (2.14)2.4.2.2 Quality FactorThe Quality Factor (Q) is the most common figure of merit for oscillators, and it isrelated to the total oscillator phase-noise. Q is usually defined within the context ofsecond order systems. There are three possible definitions of Q [1]: (1) Leeson in [39] considers a single resonator network with −3 dB bandwidthB and resonance frequency ␻0 (Fig. 2.13),
  30. 30. 20 2 Transceiver Architectures and RF BlocksFig. 2.13 Q definition for a H(s)second order system 3 dB ω0 ω B ␻0 Q= (2.15) BA second order bandpass filter has a transfer function: ␻0 s K Q H (s) = ␻0 (2.16) s2 + s + ␻2 0 Qwhere K is the mid-band gain and Q is the pole quality factor (the same Q of (2.15)).For Q 1 the transfer function is symmetric as shown in Fig. 2.13. In practice thisapproximation is valid for Q ≥ 5. This definition of Q is suitable for filters, andcan be used in oscillators if we consider the resonator circuit as a second orderfilter. (2) A second definition of Q considers a generic circuit and relates the maximumenergy stored and the energy dissipated in a period [2]: Maximum energy stored in a period Q = 2␲ (2.17) Energy dissipated in a period This definition is usually applied to a general RLC circuit and relates the maxi-mum energy stored (in C or L) and the energy dissipated (by R) in a period. As anexample, we apply the definition to an RLC series circuit. The energy is stored inthe inductor and the capacitor, and the maximum energy stored in the inductor andthe capacitor is the same. The energy stored in an inductor (WL ) is: T di(t) WL = i(t)L dt = L Ir2ms (2.18) dt 0where Ir ms is the root-mean-square current in the inductor. The energy dissipated in a resistor (W R ) per cycle (in the period T0 ) is: W R = Ir2ms RT0 (2.19)
  31. 31. 2.4 Oscillators 21 The value of Q is: L Ir2ms L ␻0 L Q = 2␲ 2 RT = 2␲ f 0 = (2.20) Ir ms 0 R R We can also use the energy stored in the capacitor: T dν(t) WC = ν(t)C dt = C Vr2 ms (2.21) dt 0where Vr ms is the root-mean-square voltage in the capacitor, and Vr ms = Ir ms /(␻0 C).Then, the value of Q is: C Vr2 (C Ir2ms )/(␻2 C 2 ) 1 Q = 2␲ ms = 2␲ f 0 0 = (2.22) Ir2ms RT0 R Ir2ms ␻0 C R Equation (2.17) is a general definition, which does not specify which elementsstore or dissipate energy. (3) In the third definition of Q the oscillator is considered as a feedback systemand the phase of the open-loop transfer function H (j␻) is evaluated at the oscillationfrequency, ␻osc , which is not necessarily the resonance frequency [36]. In a singleRLC circuit the oscillation frequency is the resonance frequency, but with coupledoscillators the oscillation frequency can be different, as we will show in Chapter 5.The oscillator Q is defined as: 2 2 ␻0 dA d␪ Q= + (2.23) 2 d␻ d␻where A is the amplitude and ␪ is the phase of H (j␻). This definition, called open-loop Q, was proposed in [36], and takes into account the amplitude and phase vari-ations of the open-loop transfer function. This Q definition is often applied to a single resonator as shown in Fig. 2.14. This definition is very useful to calculate the oscillator quality factor, which hasits maximum value at the resonance frequency, and it will be used in Chapter 5 tocalculate the degradation of the oscillator quality factor if the oscillation frequency is H( jω) θ = ∠H( jω) L C RFig. 2.14 Definition of Q ω0 ωbased on open-loop phaseslope
  32. 32. 22 2 Transceiver Architectures and RF Blocksdifferent from the resonance frequency. We will also use this definition in Chapter 6to calculate the quality factor of a two-integrator oscillator.2.4.2.3 Leeson-Cutler Phase-Noise EquationThe most used and best known phase-noise model is the Leeson-Cutler semi empir-ical equation proposed in [39–41]. It is based on the assumption that the oscillatoris a linear time invariant system. The following equation for L(␻m ) is obtained [42]: 2FkT ␻0 2 ␻1/ f 3 L(␻m ) = 10 log 1+ 1+ (2.24) PS 2Q␻m |␻m |where: k – Boltzman constant; T – absolute temperature; PS – average power dissipated in the resistive part of the tank; ␻0 – oscillation frequency; Q – quality factor (also known as loaded Q); ␻m – offset from the carrier; ␻1/ f 3 – corner frequency between 1/ f 3 and 1/ f 2 zones of the noise spectrum (represented in Fig. 2.15); F – empirical parameter, called excess noise factor. A detailed study of this parameter, which includes nonlinear effects for LC oscillators, was done in [43]. A different model to predict the oscillator phase-noise was presented recentlyin [42]. This is a linear time-variant model, which, according to the authors, givesaccurate results without any empirical or unspecified factor. In Fig. 2.15, a typical asymptotic output noise spectrum of an oscillator is shown. This plot has three different regions [35]: (ω) (dBc/Hz) –30 dB/decade –20 dB/decade white noise floorFig. 2.15 A typical (3) (2) (1)asymptotic noise spectrum at ω0 ω1 ω2 ωthe oscillator output
  33. 33. 2.4 Oscillators 23(1) For frequencies far away from the carrier, the noise of the oscillator is due towhite-noise sources from circuits, such as buffers, which are connected to the oscil-lator, so there is a constant floor in the spectrum.(2) A region [␻1 −␻2 ] with a −20 dB/decade slope is due to FM of the oscillator byits white noise sources.(3) In the region close to the carrier frequency, with frequencies between ␻0 and ␻1there is a −30 dB/decade slope due to the 1/f noise of the active devices.2.4.2.4 Importance of Phase-Noise in Wireless CommunicationsThe phase-noise in the local oscillator will spread the power spectrum around thedesired oscillation frequency. This phenomenon will limit the immunity against ad-jacent interferer signals: in the receiver path we want to downconvert a specificchannel located at a certain distance from the oscillator frequency; due to the os-cillator phase-noise, not only the desired channel is downconverted to an interme-diate frequency, but also the nearby channels or interferers, corrupting the wantedsignal [35] (Fig. 2.16). This effect is called “reciprocal mixing”. In the case of the transmitter path the phase-noise tail of a strong transmittercan corrupt and overwhelm close weak channels [35] (Fig. 2.17). As an example,if a receiver detects a weak signal at ␻2 , this will be affected by a close transmittersignal at ␻1 with substantial phase-noise. Interferer Interferer Signal SignalFig. 2.16 Phase-noise effecton the receiver and theundesired downconversion ω0 ω ωIF ω Close Transmitter SignalFig. 2.17 Phase-noise effecton the transmitter path ω 1 ω2 ω
  34. 34. 24 2 Transceiver Architectures and RF Blocks2.4.3 Examples of OscillatorsOscillators can be divided into two main groups: quasi-linear and strongly non-linear oscillators [34]. Strongly non-linear or relaxation oscillators are usually realized by RC-activecircuits. In this book we will present a detailed study of relaxation oscillators. Themain advantage of this type of oscillators is that only resistors and capacitors areused together with the active devices (inductors, which are costly elements in termsof chip area, are not needed); the main drawback of relaxation oscillators is theirhigh phase-noise. In addition to the relaxation oscillator, another RC oscillator willbe studied: the two-integrator oscillator. This oscillator is very interesting because itcan have either linear or non-linear behaviour, as we will see in detail in Chapter 6. LC oscillators are usually quasi-linear oscillators. They can use as resonatorelement: dielectric resonators, crystals, striplines, and LC tanks. These oscillatorsare known by their good phase-noise performance, since Q is normally much higherthan one. In this book we are interested in oscillators capable to produce two outputs inaccurate quadrature. We will study relaxation RC oscillators and LC oscillators withan LC tank (usually called simply LC oscillators), because they can be cross-coupledto provide quadrature outputs. We also study a third type of oscillator: the two-integrator oscillator, which has inherent quadrature outputs. In the next part of thissection we present examples of an RC relaxation oscillator and of an LC oscillator.2.4.3.1 Relaxation OscillatorsRelaxation oscillators are widely used in fully integrated circuits (because theydo not have inductors), in applications with relaxed phase-noise requirements [9],typically as part of a phase-locked loop. However, these oscillators have not beenpopular in RF design because they have noisy active and passive devices [1]. VCC R R M M C I IFig. 2.18 Relaxationoscillator
  35. 35. 2.4 Oscillators 25 In Fig. 2.18 we present an example of an RC relaxation oscillator. This oscillatorhas been referred to as a first order oscillator, since its behaviour can be describedin terms of first order transients [8, 44]. It operates by alternately charging and dis-charging a capacitor between two threshold voltage levels that are set internally. Theoscillation frequency cannot be determined by the Barkhausen criterion (this is nota linear oscillator) and it is inversely proportional to capacitance.2.4.3.2 LC OscillatorIn order to illustrate the Barkhausen criterion, the LC oscillator can be used becauseit is a quasi-linear oscillator. Oscillation will occur at the frequency for which theamplitude of the loop gain is one and the phase is zero. The LC oscillator modelis represented in Fig. 2.19: the transfer function is H ( j␻) = gm and ␤( j␻) is theimpedance of the parallel RLC circuit. R ␤( j␻) = (2.25) ␻ ␻0 1+ j − Q ␻0 ␻where C Q=R (2.26) L 1 ␻0 = √ (2.27) LC At the resonance frequency (␻0 ) the inductor and capacitor admittances canceland the loop gain is |H (j␻0 )␤( j␻0 )| = gm R = 1: the active circuit has a negativeresistance, which compensates the resistance of the parallel RLC circuit. This con-dition is necessary, but not sufficient, because, for the oscillation to start, the loopgain must be higher than 1, gm > 1/R. In Fig. 2.20 a typical LC oscillator, used in RF transceivers, is shown. This isknown as LC oscillator with LC-tank, and it is also called differential CMOS LC gm C R LFig. 2.19 LC-oscillatorbehavioural model
  36. 36. 26 2 Transceiver Architectures and RF BlocksFig. 2.20 CMOS LC VCCOscillator with LC tank L L C M M C IFig. 2.21 Equivalent +vx–resistance of thedifferential pair ix vx vx – 2 2 vx vx vx vx – gm –gm 2 2 2 2oscillator, or negative gm oscillator. The cross-coupled NMOS transistors (M) gen-erate a negative resistance, which is in parallel with the lossy LC tank (Fig. 2.21). In Fig. 2.21 the small signal model of the differential pair is shown. Since the circuit is symmetric, the controlled sources have the currents shown inFig. 2.21, and the equivalent resistance of the differential pair is: vx 2 Rx = =− (2.28) ix gm Thus, the differential pair realizes a negative resistance (Fig. 2.21) that compen-sates the losses in the tank circuit.2.5 MixersMixers are a fundamental block of RF front-ends. Nowadays, a research effort isdone to realize a fully integrated front-end, to obtain cost and space savings. Inte-grated mixers are usually a separate block of the receiver; however, the possibility
  37. 37. 2.5 Mixers 27of combining the LNA and the mixer [45] has been considered. In this book we willinvestigate the combination of the oscillator and the mixer in a single block. Conventional mixers have an open-loop structure, in which the output is obtainedby the multiplication of a local oscillator signal and an input signal (RF signal, inthe receiver path). For quadrature modulation and demodulation two independentmixers are required, which imposes severe constrains on the matching of circuitcomponents. The integration of the mixing function in quadrature oscillators has theadvantage of relaxing these constraints, as will be shown in Chapter 4 of this book. In this section we review the most important characteristics of mixers: noise fig-ure, second and third order intermodulation points, 1-dB compression point, gain,input and output impedance, and isolation between ports. Different types of imple-mentations will be reviewed [1, 2].2.5.1 Performance Parameters of MixersThe noise factor (NF) is the ratio of the signal-to-noise ratios at the input and at theoutput. It is an important measure of the performance of the mixer, indicating howmuch noise is added by it. The noise factor of a noiseless system is unity, and it ishigher in real systems. SNRIN NF = (2.29) SNROUT The intermodulation distortion (IMD) is a measure of the mixers linearity. In-termodulation distortion is the result of two or more signals interacting in a nonlinear device to produce additional unwanted signals. Two interacting signals willproduce intermodulation products at the sum and difference of integer multiples ofthe original frequencies. For two input signals at frequencies f 1 and f 2 , the output components will havefrequencies m f 1 ± n f 2 , where m and n are integers. The second and third-orderintercept points (IP2 and IP3 ) can be defined for the input (IIP2 and IIP3 ), or forthe output (OIP2 and OIP3 ), as represented in Fig. 2.22. Here, the desired output(P1 ) and the third order IM output (P3 ) are represented as a function of the inputpower. IIP3 and OIP3 are the input and output power, respectively, at the point ofintersection (extrapolated) of the two lines. The IIP3 can be determined for any inputpower (PIN ) from the difference of power between the signal and third harmonic(⌬P) as shown in Fig. 2.22 [1]. It can be shown that there is a relationship betweenthe IIP3 and ⌬P for a given PIN [1], as indicated in Fig. 2.22. Using the same procedure, we can obtain the IP2 , and the respective input andoutput intercept points (IIP2 and OIP2 ), which are obtained from the intersectionpoint of P1 and the second order IM output power (not represented in Fig. 2.22). In a receiver with IF (heterodyne), the third-order intermodulation distortion isthe most important. If two input tones at f 1 + f LO and f 2 + f LO are close in frequency,the intermodulation components at 2 f 2 − f 1 and 2 f 1 − f 2 will be close to f 1 and
  38. 38. 28 2 Transceiver Architectures and RF Blocks POUT (dBm) IP3 OIP3 P1 f1 f2 ΔP ΔP P3 2f1 − f2 2f2 − f1 f ΔP IIP3 = ΔP + PIN (dBm) 2 2 IIP3 PIN (dBm) (a) (b)Fig. 2.22 (a) Calculation of IIP3. (b) Graphical Interpretation f 2 , making them difficult to filter without also removing the desired signal. Higherorder intermodulation products are usually less important, because they have loweramplitudes, and are more widely spaced. The remaining third order products, 2 f 1 + f 2 and 2 f 2 + f 1 , do not present a problem. The second-order intermodulation distortion is important in direct conversion(homodyne receivers). In this case, intermodulation due to two input signals( f 1 and f 2 ), can be close to DC ( f 2 − f 1 and f 1 − f 2 ), and lie in the signal band(Fig. 2.23). Thus, a mixer that converts directly to the baseband has very stringentIP2 requirements. Another specification concerning distortion is the 1-dB compression point. Thisis the output power when it is one dB less than the output power of an extrapolatedlinear amplifier with the same gain (Fig. 2.24). The conversion gain of a mixer can be defined in terms of either voltage or power.– The voltage conversion gain is defined as the ratio of rms voltage of the IF signal to the rms voltage of the RF signal. Signal Signal f1 − f2 f2 − f1 fLO f1 + fLO f2 + fLO 0 f1 f2 RF Baseband fLOFig. 2.23 Second order distortion in a direct conversion mixer
  39. 39. 2.5 Mixers 29Fig. 2.24 Calculationof P-1dB 1 dB POUT (dB) P–1dB PIN (dB) VOUT Voltage Gain(dB) = 20 log (2.30) VIN– The power conversion gain is defined as the IF power delivered to a load (RL ) divided by the available power from an RF source with resistance RS . POUT Power Gain(dB) = 10 log (2.31) PIN (available)If the load impedance is equal to the source impedance (for example 50 ⍀) then thevoltage and power conversion gains are equal. In conventional heterodyne receivers the input impedance of the mixer must be50 ⍀ because we need an external image reject filter, which should be terminated by50 ⍀ impedance. In other receiver architectures, which do not need off-chip filters(e.g., low IF receiver), there is no need for 50 ⍀ matching, but the mixer input needsto be matched to the LNA output. The isolation between the mixer ports is critical. This quantifies the interactionamong the RF, IF (or baseband for homodyne receivers), and LO ports. The LO toRF feedthrough results in LO leakage to the LNA, and eventually to the antenna;the RF to LO feedthrough allows strong interferers in the RF path to interact withthe local oscillator that drives the mixer. The LO to IF feedthrough is undesirablebecause substantial LO signal at the IF output will disturb the following stages.2.5.2 Different Types of MixersThere are several types of possible implementations for a mixer. The choice ofthe implementation is based on linearity, gain, and noise figure requirements. Thesimplest mixer is a switch, implemented by a CMOS transistor [1]. The circuit ofFig. 2.25 is referred to as a passive mixer; although having an active element, thetransistor, this acts as a switch, and does not provide gain. This type of mixers,
  40. 40. 30 2 Transceiver Architectures and RF BlocksFig. 2.25 Mixer using a vLOswitch vRF vIF RLtypically has no DC consumption, has high linearity and high bandwidth, and issuitable for use in microwave circuits. There are other possible implementations, as shown in Figs. 2.26 and 2.27,which, by contrast, provide gain, and reduce the effect of noise generated by sub-sequent stages; they are referred to as active mixers. These are widely used in RFsystems, and most of them are based on the differential pair. They can be divided intosingle-balanced mixers, where the LO frequency is present in the output spectrumand double-balanced mixers, which use symmetry to remove the LO frequency fromthe output. In the single-balanced mixer, the differential pair has the LO signal at the inputand the current source is controlled by the other input signal (RF signal in downcon-version, as shown in Fig. 2.26). It converts the RF input voltage to a current, whichis steered either to one or to the other side of the differential pair. This mixer hasthe advantage that it is simple to design and operates with a single-ended RF input. VCC R R vIF M1 M2 vLO vRF M3Fig. 2.26 Activesingle-balanced mixer

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