19 research outputs found

    Low-noise amplifiers for integrated multi-mode direct-conversion receivers

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    The evolution of wireless telecommunication systems during the last decade has been rapid. During this time the design driver has shifted towards fast data applications instead of speech. In addition, the different systems may have a limited coverage, for example, limited to urban areas only. Thus, it has become important for a mobile terminal to be able to use different wireless systems, depending on the application chosen and the location of the terminal. The choice of receiver architecture affects the performance, size, and cost of the receiver. The superheterodyne receiver has hitherto been the dominant radio architecture, because of its good sensitivity and selectivity. However, superheterodyne receivers require expensive filters, which, with the existing technologies, cannot be integrated on the same chip as the receiver. Therefore, architectures using a minimum number of external components, such as direct conversion, have become popular. In addition, compared to the superheterodyne architecture, the direct-conversion architecture has benefits when multi-mode receivers, which are described in this thesis, are being designed. In this thesis, the limitations placed on the analog receiver by different system specifications are introduced. The estimations for the LNA specifications are derived from these specifications. In addition, the limitations imposed by different types of receiver architectures are described. The inductively-degenerated LNA is the basis for all the experimental circuits. The different components for this configuration are analyzed and compared to other commonly-used configurations in order to justify the use of an inductively-degenerated LNA. Furthermore, the design issues concerning the LNA-mixer interface in direct-conversion receivers are analyzed. Without knowing these limitations, it becomes difficult to understand the choices made in the experimental circuits. One of the key parts of this thesis describes the design and implementation of a single-chip multi-mode LNA, which is one of the key blocks in multi-mode receivers. The multi-mode structures in this thesis were developed for a direct-conversion receiver where only one system is activated at a time. The LNA interfaces to a pre-select filter and mixers and the different LNA components are analyzed in detail. Furthermore, the design issues related to possible interference from additional systems on single-chip receivers are analyzed and demonstrated. A typical receiver includes variable gain, which can be implemented both in the analog baseband and/or in the RF. If the variable gain is implemented in the RF parts, it is typically placed in the LNA or in a separate gain control stage. Several methods that can be used to implement a variable gain in the LNA are introduced and compared to each other. Furthermore, several of these methods are included in the experimental circuits. The last part of this thesis concentrates on four experimental circuits, which are described in this thesis. The first two chips describe an RF front-end and a direct-conversion receiver for WCDMA applications. The whole receiver demonstrates that it is possible to implement A/D converters on the same chip as sensitive RF blocks without significantly degrading receiver performance. The other two chips describe an RF front-end for WCDMA and GSM900 applications and a direct-conversion receiver for GSM900, DCS1800, PCS1900 and WCDMA systems. These ICs demonstrate the usability of the circuit structure developed and presented in this thesis. The chip area in the last multi-mode receiver is not significantly increased compared to corresponding single-system receivers.reviewe

    Ultra Small Antenna and Low Power Receiver for Smart Dust Wireless Sensor Networks

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    Wireless Sensor Networks have the potential for profound impact on our daily lives. Smart Dust Wireless Sensor Networks (SDWSNs) are emerging members of the Wireless Sensor Network family with strict requirements on communication node sizes (1 cubic centimeter) and power consumption (< 2mW during short on-states). In addition, the large number of communication nodes needed in SDWSN require highly integrated solutions. This dissertation develops new design techniques for low-volume antennas and low-power receivers for SDWSN applications. In addition, it devises an antenna and low noise amplifier co-design methodology to increase the level of design integration, reduce receiver noise, and reduce the development cycle. This dissertation first establishes stringent principles for designing SDWSN electrically small antennas (ESAs). Based on these principles, a new ESA, the F-Inverted Compact Antenna (FICA), is designed at 916MHz. This FICA has a significant advantage in that it uses a small-size ground plane. The volume of this FICA (including the ground plane) is only 7% of other state-of-the-art ESAs, while its efficiency (48.53%) and gain (-1.38dBi) are comparable to antennas of much larger dimensions. A physics-based circuit model is developed for this FICA to assist system level design at the earliest stage, including optimization of the antenna performance. An antenna and low noise amplifier (LNA) co-design method is proposed and proven to be valid to design low power LNAs with the very low noise figure of only 1.5dB. To reduce receiver power consumption, this dissertation proposes a novel LNA active device and an input/ouput passive matching network optimization method. With this method, a power efficient high voltage gain cascode LNA was designed in a 0.13um CMOS process with only low quality factor inductors. This LNA has a 3.6dB noise figure, voltage gain of 24dB, input third intercept point (IIP3) of 3dBm, and power consumption of 1.5mW at 1.0V supply voltage. Its figure of merit, using the typical definition, is twice that of the best in the literature. A full low power receiver is developed with a sensitivity of -58dBm, chip area of 1.1mm2, and power consumption of 2.85mW

    High performance building blocks for wireless receiver: multi-stage amplifiers and low noise amplifiers

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    Different wireless communication systems utilizing different standards and for multiple applications have penetrated the normal people's life, such as Cell phone, Wireless LAN, Bluetooth, Ultra wideband (UWB) and WiMAX systems. The wireless receiver normally serves as the primary part of the system, which heavily influences the system performance. This research concentrates on the designs of several important blocks of the receiver; multi-stage amplifier and low noise amplifier. Two novel multi-stage amplifier typologies are proposed to improve the bandwidth and reduce the silicon area for the application where a large capacitive load exists. They were designed using AMI 0.5 m ” CMOS technology. The simulation and measurement results show they have the best Figure-of-Merits (FOMs) in terms of small signal and large signal performances, with 4.6MHz and 9MHz bandwidth while consuming 0.38mW and 0.4mW power from a 2V power supply. Two Low Noise Amplifiers (LNAs) are proposed, with one designed for narrowband application and the other for UWB application. A noise reduction technique is proposed for the differential cascode Common Source LNA (CS-LNA), which reduces the LNA Noise Figure (NF), increases the LNA gain, and improves the LNA linearity. At the same time, a novel Common Gate LNA (CG-LNA) is proposed for UWB application, which has better linearity, lower power consumption, and reasonable noise performance. Finally a novel practical current injection built-in-test (BIT) technique is proposed for the RF Front-end circuits. If the off-chip component Lg and Rs values are well controlled, the proposed technique can estimate the voltage gain of the LNA with less than 1dB (8%) error

    RF techniques for IEEE 802.15.4: circuit design and device modelling

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    The RF circuitry in the physical layer of any wireless communication node is arguably its most important part. The front-end radio is the hardware that enables communication by transmitting and receiving information. Without a robust and high performance front-end, all other higher layers of signal processing and data handling in a wireless network are irrelevant. This thesis investigates the radio circuitry of wireless-networked nodes, and introduces several proposals for improvement. As an emerging market, analysis starts by examining available and ratified network standards suitable for low power applications. After identifying the IEEE 802.15.4 standard (commercially known as ZigBee) as the one of choice, and analysing several front-end architectures on which its transceiver circuitry can be based, an application, the Tyre Pressure Monitoring System (TPMS) is selected to examine the capabilities of the standard and its most suitable architecture in satisfying the application’s requirements. From this compatibility analysis, the most significant shortcomings are identified as interference and power consumption. The work presented in this thesis focuses on the power consumption issues. A comparison of available high frequency transistor technologies concludes Silicon CMOS to be the most appropriate solution for the implementation of low cost and low power ZigBee transceivers. Since the output power requirement of ZigBee is relatively modest, it is possible to consider the design of a single amplifier block which can act as both a Low Noise Amplifier (LNA) in the receiver chain and a Power Amplifier (PA) on the transmitter side. This work shows that by employing a suitable design methodology, a single dual-function amplifier can be realised which meets the required performance specification. In this way, power consumption and chip area can both be reduced, leading to cost savings so vital to the widespread utilisation of the ZigBee standard. Given the importance of device nonlinearity in such a design, a new transistor model based on independent representation of each of the transistor’s nonlinear elements is developed with the aim of quantifying the individual contribution of each of the transistors nonlinear elements, to the total distortion. The methodology to the design of the dual functionality (LNA/PA) amplifier starts by considering various low noise amplifier architectures and comparing them in terms of the trade-off between noise (required for LNA operation) and linearity (important for PA operation), and then examining the behaviour of the selected architecture (the common-source common-gate cascode) at higher than usual input powers. Due to the need to meet the far apart performance requirements of both the LNA and PA, a unique amplifier design methodology is developed The design methodology is based on simultaneous graphical visualisation of the relationship between all relevant performance parameters and corresponding design parameters. A design example is then presented to demonstrate the effectiveness of the methodology and the quality of trade-offs it allows the designer to make. The simulated performance of the final amplifier satisfies both the requirements of ZigBee’s low noise and power amplification. At 2.4GHz, the amplifier is predicted to have 1.6dB Noise Figure (NF), 6dBm Input-referred 3rd-order Intercept Point (IIP3), and 1dB compression point of -3.5dBm. In low power operation, it is predicted to have 10dB gain, consuming only 8mW. At the higher input power of 0dBm, it is predicted to achieve 24% Power-Added Efficiency (PAE) with 8dB gain and 22mW power consumption. Finally, this thesis presents a set of future research proposals based on problems identified throughout its development

    High performance RF and baseband building blocks for wireless receivers

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    Because of the unique architecture of wireless receivers, a designer must understand both the high frequency aspects as well as the low-frequency analog considerations for different building blocks of the receiver. The primary goal of this research work is to explore techniques for implementing high performance RF and baseband building blocks for wireless applications. Several novel techniques to improve the performance of analog building blocks are presented. An enhanced technique to couple two LC resonators is presented which does not degrade the loaded quality factor of the resonators which results in an increased dynamic range. A novel technique to automatically tune the quality factor of LC resonators is presented. The proposed scheme is stable and fast and allows programming both the quality factor and amplitude response of the LC filter. To keep the oscillation amplitude of LC VCOs constant and thus achieving a minimum phase noise and a reliable startup, a stable amplitude control loop is presented. The proposed scheme has been also used in a master-slave quality factor tuning of LC filters. An efficient and low-cost architecture for a 3.1GHz-10.6GHz ultra-wide band frequency synthesizer is presented. The proposed scheme is capable of generating 14A novel pseudo-differential transconductance amplifier is presented. The proposed scheme takes advantage of the second-order harmonic available at the output current of pseudo-differential structure to cancel the third-order harmonic distortion. A novel nonlinear function is proposed which inherently removes the third and the fifth order harmonics at its output signal. The proposed nonlinear block is used in a bandpass-based oscillator to generate a highly linear sinusoidal output. Finally, a linearized BiCMOS transconductance amplifier is presented. This transconductance is used to build a third-order linear phase low pass filter with a cut-off frequency of 264MHz for an ultra-wide band receiver. carrier frequencies

    Continuous-time low-pass filters for integrated wideband radio receivers

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    This thesis concentrates on the design and implementation of analog baseband continuous-time low-pass filters for integrated wideband radio receivers. A total of five experimental analog baseband low-pass filter circuits were designed and implemented as a part of five single-chip radio receivers in this work. After the motivation for the research work presented in this thesis has been introduced, an overview of analog baseband filters in radio receivers is given first. In addition, a review of the three receiver architectures and the three wireless applications that are adopted in the experimental work of this thesis is presented. The relationship between the integrator non-idealities and integrator Q-factor, as well as the effect of the integrator Q-factor on the filter frequency response, are thoroughly studied on the basis of a literature review. The theoretical study that is provided is essential for the gm-C filter synthesis with non-ideal lossy integrators that is presented after the introduction of different techniques to realize integrator-based continuous-time low-pass filters. The filter design approach proposed for gm-C filters is original work and one of the main points in this thesis, in addition to the experimental IC implementations. Two evolution versions of fourth-order 10-MHz opamp-RC low-pass filters designed and implemented for two multicarrier WCDMA base-station receivers in a 0.25-”m SiGe BiCMOS technology are presented, along with the experimental results of both the low-pass filters and the corresponding radio receivers. The circuit techniques that were used in the three gm-C filter implementations of this work are described and a common-mode induced even-order distortion in a pseudo-differential filter is analyzed. Two evolution versions of fifth-order 240-MHz gm-C low-pass filters that were designed and implemented for two single-chip WiMedia UWB direct-conversion receivers in a standard 0.13-”m and 65-nm CMOS technology, respectively, are presented, along with the experimental results of both the low-pass filters and the second receiver version. The second UWB filter design was also embedded with an ADC into the baseband of a 60-GHz 65-nm CMOS radio receiver. In addition, a third-order 1-GHz gm-C low-pass filter was designed, rather as a test structure, for the same receiver. The experimental results of the receiver and the third gm-C filter implementation are presented

    Integration of broadband direct-conversion quadrature modulators

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    To increase spectral efficiency, transmitters usually send only one of the information carrying sidebands centered around a single radio-frequency carrier. The close-lying mirror, or image, sideband will be eliminated either by the filtering method or by the phasing method. Since filter Q-values rise in direct relation to the transmitted frequencies, the filtering method is generally not feasible for integrated microwave transmitters. A quadrature modulator realizes the phasing method by combining signals phased at quadrature (i.e. at 90° offsets) to produce a single-sideband (SSB) output. In this way output filtering can be removed or its specifications greatly relieved so as to produce an economical microwave transmitter. The proliferation of integrated circuit (IC) technologies since the 1980s has further boosted the popularity of quadrature modulator as an IC realization makes possible the economical production of two closely matched doubly balanced mixers, which suppress carrier and even-order spurious leakage to circuit output. Another strength of IC is its ability to perform microwave quadrature generation accurately on-chip, and thereby to avoid most of the interconnect parasitics which could ruin high-frequency quadrature signaling. Nevertheless, all quadrature modulator implementations are sensitive to phasing and amplitude errors, which are born as a result of mismatches, from the use of inaccurate differential signaling, and from inadequacies in the phasing circuitry itself. A 2° phase error is easily produced, and it reduces the image-rejection ratio (IRR) to −30 dBc. Therefore, as baseband signals synthesized by digital signal processing (DSP) are sufficiently accurate, this thesis concentrates on analyzing and producing the microwave signal path of a direct-conversion quadrature modulator with special emphasis on broadband, multimode radio-compatible operation. A model of the direct-conversion quadrature modulator operation has been developed, which reveals the effect the circuit non-linearities and mismatch-related offsets have on available performance. Further, theoretical proof is given of the well-known property of improving differential signal balance that cascaded differential pairs exhibit. Among the practical results, a current reuse mixer has been developed, which improves the transmitted signal-to-noise-ratio (SNR) by 3 dB, with a maximum measured dynamic range of +158 dB. The complementary bipolar process was further used to extend the bipolar push-pull stage bandwidth to 9.5 GHz. At the core of this work is the parallel switchable polyphase (PP) filter quadrature generator that was developed, since it makes possible accurate broadband IQ generation without the high loss that usually results from the application of PP filtering. Two IQ modulator prototypes were realized to test simulated and theoretically derived data: the 0.8 ”m SiGe IC achieves an IRR better than −40 dBc over 0.75-3.6 GHz, while the 0.13 ”m digital bulk CMOS IC achieves better than −37 dBc over 0.56-4.76 GHz. For this IRR performance the SiGe prototype boasts the inexpensive solution of integrated baluns, while the CMOS one utilizes a coil-transmission line hybrid transformer at its LO input to drive the switchable PP filters.Taajuuksien kĂ€ytön tehostamiseksi lĂ€hettimet lĂ€hettĂ€vĂ€t yleensĂ€ vain toisen informaatiota sisĂ€ltĂ€vistĂ€ sivukaistoistaan yhdelle radiotaajuuksiselle kantoaallolle keskitettynĂ€. Viereinen peilitaajuus eli sivukaista vaimennetaan joko suodattamalla tai vaiheistamalla signalointia sopivasti. Koska suodattimen hyvyysluvut nousevat suorassa suhteessa kĂ€ytettyyn taajuuteen, ei suodatusmenetelmĂ€ ole yleensĂ€ mahdollinen mikroaaltotaajuusalueen lĂ€hettimissĂ€. Kvadratuurimodulaattori toteuttaa vaiheistusmenetelmĂ€n yhdistĂ€mĂ€llĂ€ 90-asteen vaihesiirroksin vaiheistetut signaalit yksisivukaistaisen lĂ€hetteen tuottamiseksi. NĂ€in voidaan korvata lĂ€hdön suodatus joko kokonaan tai lieventĂ€mĂ€llĂ€ vaadittavia suoritusarvoja, jolloin mikroaaltoalueen lĂ€hetin voidaan tuottaa taloudellisesti. Integroitujen piiriratkaisujen yleistyminen 1980-luvulta lĂ€htien on edesauttanut kvadratuurimodulaattorin suosiota, koska integroidulle piirille voidaan taloudellisesti tuottaa kaksi hyvin ominaisuuksiltaan toisiaan vastaavaa kaksoisbalansoitua sekoitinta, ja nĂ€mĂ€ tunnetusti vaimentavat kantoaaltovuotoa ja parillisia harmoonisia piirin lĂ€hdössĂ€. Toinen integroitujen piirien vahvuus on kyky tarkkaan mikroaaltoalueen kvadratuurisignalointiin samalla piirillĂ€, jolloin vĂ€ltetÀÀn suurin osa kytkentöjen parasiittisista jotka muutoin voisivat tuhota korkeataajuuksisen 90-asteen vaiheistuksen. Kaikki kvadratuurimodulaattorit ovat joka tapauksessa herkkiĂ€ vaiheistus- ja amplitudieroille, joita syntyy komponenttiarvojen satunnaishajonnasta, epĂ€tarkan differentiaalisen signaloinnin kĂ€ytöstĂ€, ja itse vaiheistuspiiristön puutteellisuuksista. Kahden asteen vaihevirhe syntyy helposti, ja tĂ€llöin sivukaistavaimennus heikkenee -30 dBc:n tasolle. TĂ€mĂ€nvuoksi, ja olettaen ettĂ€ digitaalisella signaaliprosessorilla luotu kantataajuuksinen signalointi on riittĂ€vĂ€n tarkkaa, tĂ€mĂ€ vĂ€itöskirja keskittyy kvadratuurimodulaattorin mikroaaltotaajuuksisen signaalipolun analysointiin ja tuottamiseen painottaen erityisesti laajakaistaista, monisovellusradioiden kanssa yhteensopivaa toimivuutta. Kvadratuurimodulaattorin toimintamallia on kehitetty siten, ettĂ€ mallissa huomioidaan epĂ€lineaarisuuksien ja piirielementtien satunnaishajontojen vaikutus saavutettavalle suorituskyvylle. LisĂ€ksi on teoreettisesti todistettu sinĂ€nsĂ€ hyvin tunnettu perĂ€kkĂ€in kytkettyjen vahvistinasteiden differentiaalisen signaloinnin symmetrisyyttĂ€ parantava vaikutus. KĂ€ytĂ€nnön tuloksista voidaan mainita kehitetty virtaakierrĂ€ttĂ€vĂ€ sekoitin, joka parantaa signaali-kohinasuhdetta +3 dB, suurimman mitatun dynaamisen alueen ollessa +158 dB. Samaa komplementaarista bipolaariprosessia kĂ€ytettiin edelleen bipolaarisen vuorovaihe-asteen kaistan levittĂ€misessĂ€ 9.5 GHz:iin. YhtenĂ€ tĂ€mĂ€n työn tĂ€rkeimmistĂ€ tuloksista on kehitetty kytkimin valittavista rinnakkaisista monivaihesuodattimista koostuva kvadratuurigeneraattori, jolla on mahdollista tuottaa laajakaistaista IQ-signalointia ilman suurta hĂ€viötĂ€ joka yleensĂ€ liittyy monivaihesuodattimien kĂ€yttöön. Kaksi IQ-modulaattoriprototyyppiĂ€ toteutettiin simuloitujen ja teoreettisesti mallinnettujen tulosten testaamiseksi: 0.8 ”m SiGe integroitu piiri saavuttaa paremman sivukaistavaimennuksen kuin -40 dBc yli 0.75-3.6 GHz, kun taas 0.13 ”m digitaalipiirien tuottamiseen tarkoitetulla CMOS prosessilla toteutettu integroitu piiri saavuttaa paremman sivukaistavaimennuksen kuin -37 dBc taajuusalueella 0.56-4.76 GHz. NĂ€ihin sivukaistavaimennuksiin SiGe prototyyppi pÀÀsee edullisesti integroiduin symmetrointimuuntajin, kun taas CMOS piirillĂ€ kĂ€ytetÀÀn kela-siirtojohto-tyyppistĂ€ yhdistelmĂ€muuntajaa LO-sisÀÀntulossa josta ajetaan erikseen kytkettĂ€viĂ€ monivaihesuodattimia.reviewe

    Advanced Microwave Circuits and Systems

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    Analog baseband circuits for WCDMA direct-conversion receivers

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    This thesis describes the design and implementation of analog baseband circuits for low-power single-chip WCDMA direct-conversion receivers. The reference radio system throughout the thesis is UTRA/FDD. The analog baseband circuit consists of two similar channels, which contain analog channel-select filters, programmable-gain amplifiers, and circuits that remove DC offsets. The direct-conversion architecture is described and the UTRA/FDD system characteristics are summarized. The UTRA/FDD specifications define the performance requirement for the whole receiver. Therefore, the specifications for the analog baseband circuit are obtained from the receiver requirements through calculations performed by hand. When the power dissipation of an UTRA/FDD direct-conversion receiver is minimized, the design parameters of an all-pole analog channel-select filter and the following Nyquist rate analog-to-digital converter must be considered simultaneously. In this thesis, it is shown that minimum power consumption is achieved with a fifth-order lowpass filter and a 15.36-MS/s Nyquist rate converter that has a 7- or 8-bit resolution. A fifth-order Chebyshev prototype with a passband ripple of 0.01 dB and a −3-dB frequency of 1.92-MHz is adopted in this thesis. The error-vector-magnitude can be significantly reduced by using a first-order 1.4-MHz allpass filter. The selected filter prototype fulfills all selectivity requirements in the analog domain. In this thesis, all the filter implementations use the opamp-RC technique to achieve insensitivity to parasitic capacitances and a high dynamic range. The adopted technique is analyzed in detail. The effect of the finite opamp unity-gain bandwidth on the filter frequency response can be compensated for by using passive methods. Compensation schemes that also track the process and temperature variations have been developed. The opamp-RC technique enables the implementation of low-voltage filters. The design and simulation results of a 1.5-V 2-MHz lowpass filter are discussed. The developed biasing scheme does not use any additional current to achieve the low-voltage operation, unlike the filter topology published previously elsewhere. Methods for removing DC offsets in UTRA/FDD direct-conversion receivers are presented. The minimum areas for cascaded AC couplings and DC-feedback loops are calculated. The distortion of the frequency response of a lowpass filter caused by a DC-feedback loop connected over the filter is calculated and a method for compensating for the distortion is developed. The time constant of an AC coupling can be increased using time-constant multipliers. This enables the implementation of AC couplings with a small silicon area. Novel time-constant multipliers suitable for systems that have a continuous reception, such as UTRA/FDD, are presented. The proposed time-constant multipliers only require one additional amplifier. In an UTRA/FDD direct-conversion receiver, the reception is continuous. In a low-power receiver, the programmable baseband gain must be changed during reception. This may produce large, slowly decaying transients that degrade the receiver performance. The thesis shows that AC-coupling networks and DC-feedback loops can be used to implement programmable-gain amplifiers, which do not produce significant transients when the gain is altered. The principles of operation, the design, and the practical implementation issues of these amplifiers are discussed. New PGA topologies suitable for continuously receiving systems have been developed. The behavior of these circuits in the presence of strong out-of-channel signals is analyzed. The interface between the downconversion mixers and the analog baseband circuit is discussed. The effect of the interface on the receiver noise figure and the trimming of mixer IIP2 are analyzed. The design and implementation of analog baseband circuits and channel-select filters for UTRA/FDD direct-conversion receivers are discussed in five application cases. The first case presents the analog baseband circuit for a chip-set receiver. A channel-select filter that has an improved dynamic range with a smaller supply current is presented next. The third and fifth application cases describe embedded analog baseband circuits for single-chip receivers. In the fifth case, the dual-mode analog baseband circuit of a quad-mode receiver designed for GSM900, DCS1800, PCS1900, and UTRA/FDD cellular systems is described. A new, highly linear low-power transconductor is presented in the fourth application case. The fourth application case also describes a channel-select filter. The filter achieves +99-dBV out-of-channel IIP2, +45-dBV out-of-channel IIP3 and 23-ÎŒVRMS input-referred noise with 2.6-mA current from a 2.7-V supply. In the fifth application case, a corresponding performance is achieved in UTRA/FDD mode. The out-of-channel IIP2 values of approximately +100 dBV achieved in this work are the best reported so far. This is also the case with the figure of merits for the analog channel-select filter and analog baseband circuit described in the fourth and fifth application cases, respectively. For equal power dissipation, bandwidth, and filter order, these circuits achieve approximately 10 dB and 15 dB higher spurious-free dynamic ranges, respectively, when compared to implementations that are published elsewhere and have the second best figure of merits.reviewe
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