Design and Analysis of Frequency-Tunable Amplifiers using Varactor ...
Circuits Syst Signal Process (2011) 30:705–720 DOI 10.1007/s00034-011-9309-6 C O G N I T I V E R A D I O - B A S E D W I R E L E S S C O M M U N I C AT I O N D E V I C E S
Design and Analysis of Frequency-Tunable Amplifiers using Varactor Diode Topologies Tayfun Nesimoglu
Received: 7 February 2010 / Revised: 10 September 2011 / Published online: 10 May 2011 © Springer Science+Business Media, LLC 2011
Abstract The design of frequency-tunable amplifiers is investigated and the tradeoff between linearity, efficiency and tunability is revealed. Several tunable amplifiers using various varactor diode topologies as tunable devices are designed by using loadpull techniques and their performances are compared. The amplifier using anti-series distortion-free varactor stack topology achieves 38% power added efficiency and it may be tuned from 1.74 to 2.36 GHz (about 35% tunable range). The amplifier using anti-series/anti-parallel topology is tunable from 1.74 to 2.14 GHz (about 23% tunable range) and provides 42% power added efficiency. It is demonstrated that tunable amplifiers using distortion-free varactor stack topologies provide better power added efficiency than the tunable amplifiers using reverse biased varactor diodes and their linearity is similar to that of a conventional amplifier. These amplifiers may facilitate the realization of frequency agile radio frequency transceiver front-ends and may replace several parallel connected amplifiers used in conventional multimode radios. Keywords Amplifiers · Tunable amplifiers · Impedance matching · Reconfigurable matching networks · Reconfigurable radio · Software defined radio 1 Introduction The objective of Software Defined Radio (SDR) is to provide a flexible radio that is capable of operating over a continuously evolving set of communication standards. This work was initiated at University of Bristol within a Toshiba Research Europe Ltd. project. Much of the work reported here was carried out at Middle East Technical University, Northern Cyprus Campus (METU-NCC) and funded by the Scientific and Technical Research Council of Turkey (TUBITAK) under the project code 110E105 and partly funded by the METU-NCC under the project code FEN-1. T. Nesimoglu () Middle East Technical University, Northern Cyprus Campus, Kalkanli, Guzelyurt, Mersin 10, Turkey e-mail: [email protected]
706
Circuits Syst Signal Process (2011) 30:705–720
Fig. 1 Uplink and downlink frequencies of commercial communications standards between 870 MHz and 2.5 GHz. The Digital Audio Broadcasting (DAB), Global Positioning System (GPS) and Galileo have downlink receive frequencies only. The lowest frequency of uplink transmission is Extended-Global System for Mobile communications (E-GSM) at 876 MHz
Within a SDR transceiver there is bound to be a requirement for an amplifier that can support the multitude of standards that are currently in use and those standards that may be introduced in the future. Conventional multimode mobile equipment use up to six amplifiers connected in parallel [10] to accommodate communication standards between 0.9–2.5 GHz (see Fig. 1). These amplifier architectures increase the cost, size and weight of mobile equipment. Furthermore, radios using amplifiers with predetermined frequency bands of operation cannot accommodate standards that may be introduced in the future. Using broadband amplifiers may be considered as the simplest solution to this problem. However, broadband matching networks introduce higher loss compared to narrowband matching networks and thus broadband amplifiers offer lower power gain and efficiency than narrowband amplifiers [27]. In a receiver application, a broadband low-noise amplifier may amplify high level interferers that could not be rejected by the radio frequency (RF) front-end filter and may drive the following non-linear components, such as mixers, to saturation and thus add in-band interference to a nearby wanted signal [16, 23, 24]. Therefore, narrowband frequency-tunable RF amplifiers may enhance the performance of reconfigurable and multimode radios since channelization will be initiated early at the RF front-end. This paper suggests using narrowband frequency tunable amplifiers to achieve the broad frequency coverage that is required for reconfigurable and multimode radios. It investigates the design of frequency-tunable amplifiers using various varactor diode topologies and the impact of employing tunable matching networks on power added efficiency (PAE) and linearity. To the authors’ knowledge, the impact of using tunable matching networks on amplifier efficiency and linearity has not been in-
Circuits Syst Signal Process (2011) 30:705–720
707
vestigated previously. Although there are many tunable matching network designs, [2, 15, 25, 28, 32, 33, 35, 38, 39] examples of complete tunable amplifier modules are not many [6, 8, 11, 18, 37]. Most of the tunable amplifiers presented in the literature are designed for frequencies between 10–40 GHz and provide up to 10% tunability. This frequency band of operation and range of tunability is insufficient for the realization of the commercial SDR concept. Furthermore, no information was supplied in [6, 8, 11, 18, 37] regarding the efficiency and linearity of these tunable amplifiers. However, it is widely accepted that the linearity and efficiency of RF front-end components are bottlenecks in reconfigurable radio design [16, 36]. The frequency tunable amplifier in [18] is not a voltage controlled tunable amplifier. Its frequency of operation is set by using metal-insulator-metal interconnections at manufacturing. The frequency tunable amplifier in [11] achieve tunability by switching distributed components in the matching networks in/out by using switching devices such as micro electromechanical systems (MEMS) and achieves tunability in frequency steps. In some amplifier designs, MEMS [30] and varactor diode [14] based tunable matching networks were used to vary the load impedance presented to the transistor with the objective of enhancing the efficiency and linearity performance of the amplifier module. Distortion-free varactor stack (DFVS) topologies were first proposed by R.G. Meyer et al. to achieve tunable capacitive elements and matching networks that are highly linear and low-loss [17]. These topologies were investigated further by T. Sasaki et al. [31] and C. Huang et al. [3, 4, 13] and it has been demonstrated that by correct choice of components they may be useful for RF applications. The antiseries (AS) DFVS topology was used in [22] to realize a multiband amplifier, but no comparison was made between the performances of tunable amplifiers using different varactor diode topologies. In this work, several tunable amplifiers are designed by using load-pull techniques and their efficiency, tunability and linearity are compared. The objective is to design an amplifier that can achieve continuous tunability across a broad bandwidth by using current technology and to identify the tunable amplifier topology that can provide the best trade-off between efficiency, tunability and linearity. The details of these designs are given in the following sections.
2 Conventional Amplifier Design Load-pull analysis determines the impedance that should be presented to the input and output ports of a transistor to achieve a target specification [7]. The load-pull simulations are performed in Advanced Design System (ADS) [1] from 0.5 to 6 GHz in 500 MHz steps using a two-tone sinusoidal drive signal to a MicroWave Technology MWT-871 transistor [20]. The measurement based model of MWT-871 is available in ADS transistor library. The transistor biasing is optimized in a DC-simulation set-up for maximum power added efficiency (PAE) and the bias voltages are set as VDD = 4.8 V and VGS = −2.8 V. The PAE is a good practical metric for quantifying the efficiency of amplifiers because it takes account of the RF input power applied to the amplifier. The PAE, is
708
Circuits Syst Signal Process (2011) 30:705–720
defined as the ratio of the difference between the output and input powers (Pout − Pin ) to the DC-bias power, given by the product of the DC-bias voltage VDD and current IDD (1). ηPAE =
Pout − Pin VDD IDD
(1)
The delivered output power (Pdel), PAE, third (IM3) and fifth-order intermodulation (IM5) contours obtained by load-pull simulation at 2 GHz are shown in Fig. 2. The contour step size is 1 dB for Pdel, 3% for PAE and 3 dB for IM3 and IM5. Marker-1 (m1) shows the impedance required from the output matching network to achieve maximum PAE, m2 shows the impedance required to maximize Pdel, m4 shows the impedance required to minimize IM3 and m5 shows the impedance required to minimize IM5. From Fig. 2, it can be seen that the impedances required from the output matching network to provide maximum PAE (61.38%) and minimum IM3 (−28.22 dBc) are significantly different from each other, thus achieving a high efficiency together with high linearity by using the same matching network is not possible [12]. The lower the IM3, the lower the delivered output signal power, thus the DC power consumption of the amplifier becomes more comparable to the difference between input and output power as shown in (1) and the PAE of the amplifier is reduced at linear regions of operation. Load-pull analysis validates that linearity and efficiency are contradicting trade-off metrics; achieving one without compromising the other is a challenging task for the RF designer and requires the use of linearization and transmitter design techniques [29]. The optimum PAE, Pdel, IM3 and IM5 values that can be achieved by MWT-871 from 0.5 to 6 GHz are obtained by load-pull analysis and summarized in Fig. 3 as a function of frequency. Between 1.5–2.5 GHz the transistor provides the highest PAE. This frequency band is important for commercial communication systems, especially around 1.8 GHz there are several communication standards (see Fig. 1). The schematic of the conventional amplifier is shown in Fig. 4. The output and input matching networks are designed by load and source-pull techniques, respectively, to maximize PAE at 1.8 GHz. A low-loss high frequency laminate (GIL Technologies, GML1000) [26] is selected as the substrate material in order to reduce the insertion loss through the matching networks. The measurement based ADS models of the lumped components are used in these simulations, where Murata GQM-1885 series capacitors and LQW-18A series inductors are selected due to their high Q-factors and low effective series resistances [19]. The amplifier can provide up to 60% PAE (see Fig. 5), 22.5 dBm output power and about 12.5 dB gain (see Fig. 6). In Fig. 5, the PAE of the conventional amplifier is shown as a function of input power and compared to those of the tunable amplifiers. The IM3 and IM5 distortion characteristics of the conventional amplifier and those of the tunable amplifiers are compared in Fig. 7 as a function input power. The tunable amplifier designs are presented and their performances are discussed in the coming sections. 3 State-of-the-Art in Tunable Device Technology There is a large amount of information on the physical properties, manufacturing and packaging techniques as well as types of materials that can be used for real-
Fig. 2 Load-pull analysis at 2 GHz: (a) PAE and Pdel contours, (b) IM3 and IM5 contours. The impedance values shown by the markers are normalized to 50 (Z0 = 50 )
Circuits Syst Signal Process (2011) 30:705–720 709
710
Circuits Syst Signal Process (2011) 30:705–720
Fig. 3 Optimum PAE, Pdel, IM3 and IM5 values that can be delivered by MWT-871 from 0.5 to 6 GHz
Fig. 4 The hierarchical amplifier schematic with input and output matching networks
izing tunable circuit components. Here, a brief overview of PN-junctions (varactor diodes), MEMS and ferroelectric thin-film Barium Strontium Titanate (BST) devices is carried out. Table 1 compares the characteristics of tunable capacitors that are constructed using these technologies. It must be noted that there are many trade-offs in each device technology. For example; the linearity of a BST capacitor can be increased by using a thicker thin-film but this increases the control voltage. By using a smaller diode area, the Q-factor of a varactor can be increased at the expense of a smaller tuning range. The DC-bias voltage of an RF-MEMS capacitor can be reduced
Circuits Syst Signal Process (2011) 30:705–720
711
Fig. 5 The PAE of the conventional amplifier compared to those of the tunable amplifiers as a function of input power
Fig. 6 S-parameters of the conventional amplifier
by lowering the suspended metal plate but this also lowers the self actuation voltage which degrades the reliability and linearity of the device. Although RF-MEMS and BST capacitors have attractive features like high linearity and high Q, the control voltage of these devices are much higher than that of varactor diodes. Also obtaining off-the-shelf RF-MEMS and BST devices is difficult. Therefore, varactor diodes are still attractive for realizing tunable matching networks. Semiconductor based devices have some drawbacks such as poor linearity and low Q, thus a number of varactor diode topologies are proposed in [17, 31] in order to over-
Fig. 7 (a) IM3 and (b) IM5 characteristics of the conventional amplifier and those of the tunable amplifiers compared as a function of input power
712 Circuits Syst Signal Process (2011) 30:705–720
Circuits Syst Signal Process (2011) 30:705–720
713
Table 1 Summary of capacitor characteristics using a number of device technologies Varactor diodes Tunability
Q-factor (RF loss) Control voltage
RF-MEMS capacitors
Ferroelectric BST capacitors
High
Low
Moderate
(3:1)
(1.5–2:1)
(2–3:1)
Moderate (Q < 50)
Excellent (Q < 200)
High (Q < 100)
Low
High
Moderate
0.5 [3]. The AS/AP connection of varactor diodes (see Fig. 11(b)) reduces second (IM2) and thirdorder distortion when M > 0.5. However, complete cancellation of IM2 and IM3 requires specific values of M for different size diode area ratios of s (s = DB /DA ); cancellation of IM3 can only occur for diodes with M ≥ 0.5.
716
Circuits Syst Signal Process (2011) 30:705–720
Fig. 11 Output matching network using: (a) AS-DFVS topology, (b) AS/AP-DFVS topology Fig. 12 The tunable amplifier layout showing the top layer (copper) and the surface mount components
The diode (Skyworks SMV-1245) used in this work is a hyper-abrupt varactor diode with M = 1.7, therefore it is suitable for use in DFVS architectures. The linear capacitance of the AS and AS/AP topologies is identical, i.e. in theory; the tuning range does not improve or degrade with the number of the sections. 5.1 Tunable Amplifier using Anti-series Distortion-free Varactor Stack Topology The output matching network using the AS-DFVS topology is realized in ADS as shown in Fig. 11(a). The input matching network also uses the same topology and both matching networks are designed by load and source-pull techniques to achieve maximum PAE from the amplifier. Figure 12 shows the amplifier printed circuit board (PCB) layout with the top layer copper and surface mount components. The amplifier can be tuned from 1.74 to 2.36 GHz (see Fig. 13), i.e. 620 MHz (35.63% tunability), which is a significant improvement over the tunable amplifiers using reverse biased diode topologies. This tunability is achieved by sweeping the
Circuits Syst Signal Process (2011) 30:705–720
717
Fig. 13 S-parameters of the tunable amplifier using AS-DFVS topology
VCC from 0 to 12 V, which is the same control voltage required with a single reverse biased diode. This tunable amplifier may be used for Digital Cellular Service (DCS-1800), Personal Communications Service (PCS-1900), Digital Enhanced Cordless Telecommunications (DECT), Universal Mobile Telecommunication System (UMTS), Bluetooth and Wireless Local Area Network (WLAN) 802.11b/g (see Fig. 1). As shown in Fig. 5, it provides up to 38% PAE. Therefore, using AS-DFVS topology achieves a significant increase in the tunability without increasing the control voltage requirement and the PAE of the amplifier is similar to that of the amplifier using dual reverse biased diodes (see Fig. 8(b)). It introduces the highest IM3 (see Fig. 7(a)) among the tunable amplifiers and has similar linearity to the conventional amplifier at large input signal levels. 5.2 Tunable Amplifier Using Anti-Series/Anti-Parallel Distortion-Free Varactor Stack Topology The output matching network using AS/AP-DFVS topology is shown in Fig. 11(b). The input matching network uses the same topology and both networks are designed by load and source-pull techniques to maximize PAE. The amplifier can be tuned from 1.74 to 2.14 GHz (see Fig. 14), i.e. 400 MHz (22.98% tunability) by sweeping the VCC from 0 to 12 V. As shown in Fig. 5, it provides up to 42% PAE, which the highest PAE achieved among the tunable amplifiers. This amplifier may be used for DCS-1800, PCS-1900, DECT and UMTS. The tuning range is significantly larger than that of the amplifiers using reverse biased diode topologies but smaller than that of the amplifier using AS-DFVS topology. At large input signal levels its IM3 is only slightly worse than that of the conventional amplifier. It also generates the lowest IM5 at large input signal levels compared to the other amplifiers. 6 Conclusion It has been demonstrated that adding tunability property to an amplifier by using varactor diodes may result in a significant reduction of PAE. The tunable amplifiers
718
Circuits Syst Signal Process (2011) 30:705–720
Fig. 14 S-parameters of the tunable amplifier using AS/AP-DFVS topology
Table 2 Summary of amplifier performances Amplifier
PAE
Tunability
Control
(%)
(%)
voltage (V)
Supported communication standard(s)
Conventional amplifier
60
NA
NA
DCS-1800
Tunable amplifier using single diode
36
10.34
0–12
DCS-1800, PCS-1900, DECT
Tunable amplifier using dual diodes
39
11.76%
0–24
DCS-1800, PCS-1900, DECT
Tunable amplifier using AS-DFVS
38
35.63%
0–12
DCS-1800, PCS-1900, DECT, UMTS/TDD, UMTS/FDD, Bluetooth, WLAN 802.11b/g (US, UK, Japan)
Tunable amplifier using AS/AP-DFVS
42
22.98%
0–12
DCS-1800, PCS-1900, DECT, UMTS/TDD, UMTS/FDD
using reverse biased diode topologies achieved up to 11.76% tunability (1.7 to 1.9 GHz) and 36% PAE, i.e. 24% lower PAE than the conventional amplifier. It is shown that DFVS topologies are superior to reverse biased diode topologies in terms of tunability and PAE in a tunable amplifier application. The largest tunability of 35.63% (1.74 to 2.36 GHz) is achieved by the amplifier using AS-DFVS topology which gave 38% PAE. This range of tunability is considerably larger than that of other tunable amplifiers recorded in the literature. The tunable amplifier using AS/AP-DFVS has provided a good trade-off between tunability and PAE. It achieved a tunability of 22% (1.74 to 2.14 GHz) and gave 42% PAE. The linearity of the amplifier using AS/AP-DFVS topology is generally better than that of other amplifiers at large input signal drive levels and only slightly worse than that of conventional amplifier. The performances of conventional and tunable amplifiers are summarized in Table 2. The tunable amplifiers using DFVS topologies may replace parallel connected amplifiers used in multimode radios. Furthermore, they may be tuned continuously within a frequency range rather than switching between predetermined frequency
Circuits Syst Signal Process (2011) 30:705–720
719
bands. This enables them to accommodate communication standards that may be introduced in the future and facilitate the design of a SDR.
References 1. http://www.agilent.com/find/eesof, accessed on 4 May 2011 2. W.N. Allen, D. Peroulis, Three-bit and six-bit tunable matching networks with tapered lines, in IEEE Topical Meeting on Silicon Monolithic Integrated Circuits in RF Systems, 19–21 Jan. 2009 (2009), pp. 1–4 3. K. Buisman, L.C.N. de Vreede, L.E. Larson, M. Spirito, A. Akhnoukh, T.L.M. Scholtes, L.K. Nanver, Distortion-free varactor diode topologies for RF adaptivity, in IEEE International Microwave Symposium Digest, 12–17 June 2005 (2005), pp. 157–160 4. K. Buisman, L.C.N. de Vreede, L.E. Larson, M. Spirito, A. Akhnoukh, Y. Lin, X. Liu, L.K. Nanver, Low-distortion, low-loss varactor-based adaptive matching networks, implemented in a silicon-onglass technology, in IEEE Radio Frequency Integrated Circuits Symposium, 12–14 June 2005 (2005), pp. 389–392 5. B.E. Carey-Smith, P.A. Warr, M.A. Beach, T. Nesimoglu, Wide tuning-range planar filters using lumped-distributed coupled resonators. IEEE Trans. Microw. Theory Tech., 53(2), 777–785 (2005) 6. J.G. Colom, R. Medina, Y. Pérez, Simulation of single-stage tunable amplifier using ferroelectric materials. Taylor and Francis, Integr. Ferroelectr., 56(1), 1131–1140 (2003) 7. S.C. Cripps, RF Power Amplifiers for Wireless Communications, 2nd edn. (Artech House, London, 2006) 8. Q. Dongjiang, R. Molfino, S.M. Lardizabal, B. Pillans, P.M. Asbeck, G. Jerinic, An intelligently controlled RF power amplifier with a reconfigurable MEMS-varactor tuner. IEEE Trans. Microw. Theory Tech., Part 2, 53(3), 1089–1095 (2005) 9. K. Entesari, G.M. Rebeiz, A 12–18-GHz three-pole RF MEMS tunable filter. IEEE Trans. Microw. Theory Tech., 53(8), 2566–2571 (2005) 10. http://www.freescale.com/webapp/sps/site/prod_summary.jsp?code=RFX250-20&fsrch=1, accessed on 4 May 2011 11. A. Fukuda, H. Okazaki, S. Narahashi, T. Hirota, Y. Yamao, A 900/1500/2000-MHz triple-band reconfigurable power amplifier employing RF-MEMS switches, in IEEE International Microwave Symposium Digest, 12–17 June 2005 (2005), p. 4 12. F.M. Ghannouchi, Z. Guoxiang, F. Beauregard, Simultaneous load-pull of intermodulation and output power under two-tone excitation for accurate SSPA’s design. IEEE Trans. Microw. Theory Tech., 42(6), 929–934 (1994) 13. C. Huang, K. Buisman, M. Marchetti, L.K. Nanver, F. Sarubbi, M. Popadic, T. Scholtes, H. Schellevis, L.E. Larson, L.C.N. de Vreede, Ultra linear low-loss varactor diode configurations for adaptive RF systems. IEEE Trans. Microw. Theory Tech., 57(1), 205–215 (2009) 14. F. Jia-Shiang, A. Mortazawi, A tunable matching network for power amplifier efficiency enhancement and distortion reduction, in 2008 IEEE MTT-S International Microwave Symposium Digest (2008), pp. 1151–1154 15. H.T. Kim, S. Jung, K. Kang, J.H. Park, Y.K. Kim, Y. Kwon, Low-loss analog and digital micromachined impedance tuners at the Ka-band. IEEE Trans. Microw. Theory Tech. 49(12), 2394–2400 (2001) 16. J.R. MacLeod, T. Nesimoglu, M.A. Beach, P.A. Warr, Enabling technologies for software defined radio transceivers, in Military Communications Conference-MILCOM, October 2002, California, USA 17. R.G. Meyer, M.L. Stephens, Distortion in variable-capacitance diodes. IEEE J. Solid-State Circuits, 10(1), 47–54 (1975) 18. A. Miras, E. Legros, High-gain frequency-tunable low-noise amplifiers for 38–42.5-GHz band applications. IEEE Microw. Guided Wave Lett., 7(9), 305–307 (1997) 19. http://www.murata.com/, accessed on 4 May 2011 20. http://www.mwtinc.com/cat/fets/pdf/mwt-8.pdf, accessed on 4 May 2011 21. J. Nath, D. Ghosh, J.P. Maria, A.I. Kingon, W. Fathelbab, P.D. Franzon, M.B. Steer, An electronically tunable microstrip bandpass filter using thin-film Barium–Strontium–Titanate (BST) varactors. IEEE Trans. Microw. Theory Tech., 53(9), 2707–2712 (2005)
720
Circuits Syst Signal Process (2011) 30:705–720
22. W.C.E. Neo, L. Yu, L. Xiao-dong, L.C.N. de Vreede, L.E. Larson, M. Spirito, M.J. Pelk, K. Buisman, A. Akhnoukh, G. de Anton, L.K. Nanver, Adaptive multi-band multi-mode power amplifier using integrated varactor-based tunable matching networks. IEEE J. Solid-State Circuits, 41(9), 2166–2176 (2006) 23. T. Nesimoglu, M.A. Beach, P.A. Warr, J.R. MacLeod, Linearised mixer using frequency retranslation. IEE Electron. Lett., 37(25), 1493–1494 (2001) 24. T. Nesimoglu, M.A. Beach, J.R. MacLeod, P.A. Warr, Mixer linearisation for software defined radio applications, in IEEE Vehicular Technology Conference, September 2002, Vancouver, Canada (2002), pp. 134–138 25. A. Nieuwoudt, J. Kawa, Y. Massoud, Automated design of tunable impedance matching networks for reconfigurable wireless applications, in 45th ACM/IEEE Design Automation Conference, 8–13 June 2008 (2008), pp. 498–503 26. http://paginas.fe.up.pt/~hmiranda/etele/g1000_30.pdf, accessed on 4 May 2011 27. D.M. Pozar, Microwave Engineering (Wiley, New York, 1998) 28. S. Qin, N.S. Barker, Distributed MEMS tunable matching network using minimal-contact RF-MEMS varactors. IEEE Trans. Microw. Theory Tech., Part 2, 54(6), 2646–2658 (2006) 29. F.H. Raab, P. Asbeck, S. Cripps, P.B. Kenington, Z.B. Popovic, N. Pothecary, J.F. Sevic, N.O. Sokal, Power amplifiers and transmitters for RF and microwave. IEEE Trans. Microw. Theory Tech., 50(3), 814–826 (2002) 30. C. Sanchez-Perez, J. de Mingo, P. Garcia-Ducar, P.L. Carro, A. Valdovinos, Exploring the use of reconfigurable matching networks for efficiency and linearity improvement in RE power amplifiers under load variations, in 2010 IEEE International Microwave Workshop Series on RF Front-ends for Software Defined and Cognitive Radio Solutions (IMWS) (2010) 31. T. Sasaki, H. Hataoka, Investigation of intermodulation in a tuning varactor. IEEE Trans. Broadcast., BC-29(2), 77–81 (1983) 32. P. Scheele, F. Goelden, A. Giere, S. Mueller, R. Jakoby, Continuously tunable impedance matching network using ferroelectric varactors, in IEEE MTT-S International Microwave Symposium Digest, 12–17 June 2005 (2005), p. 4 33. J.H. Sinsky, C.R. Westgate, Design of an electronically tunable microwave impedance transformer, in IEEE MTT-S International Microwave Symposium, June 1997 (1997), pp. 647–650 34. http://www.skyworksinc.com/, accessed on 4 May 2011 35. A. Tombak, A ferroelectric-capacitor-based tunable matching network for quad-band cellular power amplifiers. IEEE Trans. Microw. Theory Tech., Part 2, 55(2), 370–375 (2007) 36. W. Tuttlebee, Software Defined Radio—Enabling Technologies (Wiley, New York, 2002). ISBN10:0470843187 37. H. Uchida, K. Ogura, Y. Konishi, S. Makino, A frequency-tunable amplifier with a simple tunable admittance inverter. Eur. Microw. Conf., 1(4–6), 4 (2005) 38. M. Unlu, K. Topalli, H.I. Atasoy, E.U. Temocin, I. Istanbulluoglu, O. Bayraktar, S. Demir, O.A. Civi, S. Koc, T. Akin, A reconfigurable RF MEMS triple stub impedance matching network, in 36th European Microwave Conference, Sept. 2006 (2006), pp. 1370–1373 39. L.Y. Vicki Chen, R. Forse, D. Chase, R.A. York, Analog tunable matching networks using integrated thin-film BST capacitors. In IEEE MTT-S International Microwave Symposium, TU5C-6, June 2004
Design and Analysis of Frequency-Tunable Amplifiers using Varactor Diode Topologies Tayfun Nesimoglu
Received: 7 February 2010 / Revised: 10 September 2011 / Published online: 10 May 2011 © Springer Science+Business Media, LLC 2011
Abstract The design of frequency-tunable amplifiers is investigated and the tradeoff between linearity, efficiency and tunability is revealed. Several tunable amplifiers using various varactor diode topologies as tunable devices are designed by using loadpull techniques and their performances are compared. The amplifier using anti-series distortion-free varactor stack topology achieves 38% power added efficiency and it may be tuned from 1.74 to 2.36 GHz (about 35% tunable range). The amplifier using anti-series/anti-parallel topology is tunable from 1.74 to 2.14 GHz (about 23% tunable range) and provides 42% power added efficiency. It is demonstrated that tunable amplifiers using distortion-free varactor stack topologies provide better power added efficiency than the tunable amplifiers using reverse biased varactor diodes and their linearity is similar to that of a conventional amplifier. These amplifiers may facilitate the realization of frequency agile radio frequency transceiver front-ends and may replace several parallel connected amplifiers used in conventional multimode radios. Keywords Amplifiers · Tunable amplifiers · Impedance matching · Reconfigurable matching networks · Reconfigurable radio · Software defined radio 1 Introduction The objective of Software Defined Radio (SDR) is to provide a flexible radio that is capable of operating over a continuously evolving set of communication standards. This work was initiated at University of Bristol within a Toshiba Research Europe Ltd. project. Much of the work reported here was carried out at Middle East Technical University, Northern Cyprus Campus (METU-NCC) and funded by the Scientific and Technical Research Council of Turkey (TUBITAK) under the project code 110E105 and partly funded by the METU-NCC under the project code FEN-1. T. Nesimoglu () Middle East Technical University, Northern Cyprus Campus, Kalkanli, Guzelyurt, Mersin 10, Turkey e-mail: [email protected]
706
Circuits Syst Signal Process (2011) 30:705–720
Fig. 1 Uplink and downlink frequencies of commercial communications standards between 870 MHz and 2.5 GHz. The Digital Audio Broadcasting (DAB), Global Positioning System (GPS) and Galileo have downlink receive frequencies only. The lowest frequency of uplink transmission is Extended-Global System for Mobile communications (E-GSM) at 876 MHz
Within a SDR transceiver there is bound to be a requirement for an amplifier that can support the multitude of standards that are currently in use and those standards that may be introduced in the future. Conventional multimode mobile equipment use up to six amplifiers connected in parallel [10] to accommodate communication standards between 0.9–2.5 GHz (see Fig. 1). These amplifier architectures increase the cost, size and weight of mobile equipment. Furthermore, radios using amplifiers with predetermined frequency bands of operation cannot accommodate standards that may be introduced in the future. Using broadband amplifiers may be considered as the simplest solution to this problem. However, broadband matching networks introduce higher loss compared to narrowband matching networks and thus broadband amplifiers offer lower power gain and efficiency than narrowband amplifiers [27]. In a receiver application, a broadband low-noise amplifier may amplify high level interferers that could not be rejected by the radio frequency (RF) front-end filter and may drive the following non-linear components, such as mixers, to saturation and thus add in-band interference to a nearby wanted signal [16, 23, 24]. Therefore, narrowband frequency-tunable RF amplifiers may enhance the performance of reconfigurable and multimode radios since channelization will be initiated early at the RF front-end. This paper suggests using narrowband frequency tunable amplifiers to achieve the broad frequency coverage that is required for reconfigurable and multimode radios. It investigates the design of frequency-tunable amplifiers using various varactor diode topologies and the impact of employing tunable matching networks on power added efficiency (PAE) and linearity. To the authors’ knowledge, the impact of using tunable matching networks on amplifier efficiency and linearity has not been in-
Circuits Syst Signal Process (2011) 30:705–720
707
vestigated previously. Although there are many tunable matching network designs, [2, 15, 25, 28, 32, 33, 35, 38, 39] examples of complete tunable amplifier modules are not many [6, 8, 11, 18, 37]. Most of the tunable amplifiers presented in the literature are designed for frequencies between 10–40 GHz and provide up to 10% tunability. This frequency band of operation and range of tunability is insufficient for the realization of the commercial SDR concept. Furthermore, no information was supplied in [6, 8, 11, 18, 37] regarding the efficiency and linearity of these tunable amplifiers. However, it is widely accepted that the linearity and efficiency of RF front-end components are bottlenecks in reconfigurable radio design [16, 36]. The frequency tunable amplifier in [18] is not a voltage controlled tunable amplifier. Its frequency of operation is set by using metal-insulator-metal interconnections at manufacturing. The frequency tunable amplifier in [11] achieve tunability by switching distributed components in the matching networks in/out by using switching devices such as micro electromechanical systems (MEMS) and achieves tunability in frequency steps. In some amplifier designs, MEMS [30] and varactor diode [14] based tunable matching networks were used to vary the load impedance presented to the transistor with the objective of enhancing the efficiency and linearity performance of the amplifier module. Distortion-free varactor stack (DFVS) topologies were first proposed by R.G. Meyer et al. to achieve tunable capacitive elements and matching networks that are highly linear and low-loss [17]. These topologies were investigated further by T. Sasaki et al. [31] and C. Huang et al. [3, 4, 13] and it has been demonstrated that by correct choice of components they may be useful for RF applications. The antiseries (AS) DFVS topology was used in [22] to realize a multiband amplifier, but no comparison was made between the performances of tunable amplifiers using different varactor diode topologies. In this work, several tunable amplifiers are designed by using load-pull techniques and their efficiency, tunability and linearity are compared. The objective is to design an amplifier that can achieve continuous tunability across a broad bandwidth by using current technology and to identify the tunable amplifier topology that can provide the best trade-off between efficiency, tunability and linearity. The details of these designs are given in the following sections.
2 Conventional Amplifier Design Load-pull analysis determines the impedance that should be presented to the input and output ports of a transistor to achieve a target specification [7]. The load-pull simulations are performed in Advanced Design System (ADS) [1] from 0.5 to 6 GHz in 500 MHz steps using a two-tone sinusoidal drive signal to a MicroWave Technology MWT-871 transistor [20]. The measurement based model of MWT-871 is available in ADS transistor library. The transistor biasing is optimized in a DC-simulation set-up for maximum power added efficiency (PAE) and the bias voltages are set as VDD = 4.8 V and VGS = −2.8 V. The PAE is a good practical metric for quantifying the efficiency of amplifiers because it takes account of the RF input power applied to the amplifier. The PAE, is
708
Circuits Syst Signal Process (2011) 30:705–720
defined as the ratio of the difference between the output and input powers (Pout − Pin ) to the DC-bias power, given by the product of the DC-bias voltage VDD and current IDD (1). ηPAE =
Pout − Pin VDD IDD
(1)
The delivered output power (Pdel), PAE, third (IM3) and fifth-order intermodulation (IM5) contours obtained by load-pull simulation at 2 GHz are shown in Fig. 2. The contour step size is 1 dB for Pdel, 3% for PAE and 3 dB for IM3 and IM5. Marker-1 (m1) shows the impedance required from the output matching network to achieve maximum PAE, m2 shows the impedance required to maximize Pdel, m4 shows the impedance required to minimize IM3 and m5 shows the impedance required to minimize IM5. From Fig. 2, it can be seen that the impedances required from the output matching network to provide maximum PAE (61.38%) and minimum IM3 (−28.22 dBc) are significantly different from each other, thus achieving a high efficiency together with high linearity by using the same matching network is not possible [12]. The lower the IM3, the lower the delivered output signal power, thus the DC power consumption of the amplifier becomes more comparable to the difference between input and output power as shown in (1) and the PAE of the amplifier is reduced at linear regions of operation. Load-pull analysis validates that linearity and efficiency are contradicting trade-off metrics; achieving one without compromising the other is a challenging task for the RF designer and requires the use of linearization and transmitter design techniques [29]. The optimum PAE, Pdel, IM3 and IM5 values that can be achieved by MWT-871 from 0.5 to 6 GHz are obtained by load-pull analysis and summarized in Fig. 3 as a function of frequency. Between 1.5–2.5 GHz the transistor provides the highest PAE. This frequency band is important for commercial communication systems, especially around 1.8 GHz there are several communication standards (see Fig. 1). The schematic of the conventional amplifier is shown in Fig. 4. The output and input matching networks are designed by load and source-pull techniques, respectively, to maximize PAE at 1.8 GHz. A low-loss high frequency laminate (GIL Technologies, GML1000) [26] is selected as the substrate material in order to reduce the insertion loss through the matching networks. The measurement based ADS models of the lumped components are used in these simulations, where Murata GQM-1885 series capacitors and LQW-18A series inductors are selected due to their high Q-factors and low effective series resistances [19]. The amplifier can provide up to 60% PAE (see Fig. 5), 22.5 dBm output power and about 12.5 dB gain (see Fig. 6). In Fig. 5, the PAE of the conventional amplifier is shown as a function of input power and compared to those of the tunable amplifiers. The IM3 and IM5 distortion characteristics of the conventional amplifier and those of the tunable amplifiers are compared in Fig. 7 as a function input power. The tunable amplifier designs are presented and their performances are discussed in the coming sections. 3 State-of-the-Art in Tunable Device Technology There is a large amount of information on the physical properties, manufacturing and packaging techniques as well as types of materials that can be used for real-
Fig. 2 Load-pull analysis at 2 GHz: (a) PAE and Pdel contours, (b) IM3 and IM5 contours. The impedance values shown by the markers are normalized to 50 (Z0 = 50 )
Circuits Syst Signal Process (2011) 30:705–720 709
710
Circuits Syst Signal Process (2011) 30:705–720
Fig. 3 Optimum PAE, Pdel, IM3 and IM5 values that can be delivered by MWT-871 from 0.5 to 6 GHz
Fig. 4 The hierarchical amplifier schematic with input and output matching networks
izing tunable circuit components. Here, a brief overview of PN-junctions (varactor diodes), MEMS and ferroelectric thin-film Barium Strontium Titanate (BST) devices is carried out. Table 1 compares the characteristics of tunable capacitors that are constructed using these technologies. It must be noted that there are many trade-offs in each device technology. For example; the linearity of a BST capacitor can be increased by using a thicker thin-film but this increases the control voltage. By using a smaller diode area, the Q-factor of a varactor can be increased at the expense of a smaller tuning range. The DC-bias voltage of an RF-MEMS capacitor can be reduced
Circuits Syst Signal Process (2011) 30:705–720
711
Fig. 5 The PAE of the conventional amplifier compared to those of the tunable amplifiers as a function of input power
Fig. 6 S-parameters of the conventional amplifier
by lowering the suspended metal plate but this also lowers the self actuation voltage which degrades the reliability and linearity of the device. Although RF-MEMS and BST capacitors have attractive features like high linearity and high Q, the control voltage of these devices are much higher than that of varactor diodes. Also obtaining off-the-shelf RF-MEMS and BST devices is difficult. Therefore, varactor diodes are still attractive for realizing tunable matching networks. Semiconductor based devices have some drawbacks such as poor linearity and low Q, thus a number of varactor diode topologies are proposed in [17, 31] in order to over-
Fig. 7 (a) IM3 and (b) IM5 characteristics of the conventional amplifier and those of the tunable amplifiers compared as a function of input power
712 Circuits Syst Signal Process (2011) 30:705–720
Circuits Syst Signal Process (2011) 30:705–720
713
Table 1 Summary of capacitor characteristics using a number of device technologies Varactor diodes Tunability
Q-factor (RF loss) Control voltage
RF-MEMS capacitors
Ferroelectric BST capacitors
High
Low
Moderate
(3:1)
(1.5–2:1)
(2–3:1)
Moderate (Q < 50)
Excellent (Q < 200)
High (Q < 100)
Low
High
Moderate
0.5 [3]. The AS/AP connection of varactor diodes (see Fig. 11(b)) reduces second (IM2) and thirdorder distortion when M > 0.5. However, complete cancellation of IM2 and IM3 requires specific values of M for different size diode area ratios of s (s = DB /DA ); cancellation of IM3 can only occur for diodes with M ≥ 0.5.
716
Circuits Syst Signal Process (2011) 30:705–720
Fig. 11 Output matching network using: (a) AS-DFVS topology, (b) AS/AP-DFVS topology Fig. 12 The tunable amplifier layout showing the top layer (copper) and the surface mount components
The diode (Skyworks SMV-1245) used in this work is a hyper-abrupt varactor diode with M = 1.7, therefore it is suitable for use in DFVS architectures. The linear capacitance of the AS and AS/AP topologies is identical, i.e. in theory; the tuning range does not improve or degrade with the number of the sections. 5.1 Tunable Amplifier using Anti-series Distortion-free Varactor Stack Topology The output matching network using the AS-DFVS topology is realized in ADS as shown in Fig. 11(a). The input matching network also uses the same topology and both matching networks are designed by load and source-pull techniques to achieve maximum PAE from the amplifier. Figure 12 shows the amplifier printed circuit board (PCB) layout with the top layer copper and surface mount components. The amplifier can be tuned from 1.74 to 2.36 GHz (see Fig. 13), i.e. 620 MHz (35.63% tunability), which is a significant improvement over the tunable amplifiers using reverse biased diode topologies. This tunability is achieved by sweeping the
Circuits Syst Signal Process (2011) 30:705–720
717
Fig. 13 S-parameters of the tunable amplifier using AS-DFVS topology
VCC from 0 to 12 V, which is the same control voltage required with a single reverse biased diode. This tunable amplifier may be used for Digital Cellular Service (DCS-1800), Personal Communications Service (PCS-1900), Digital Enhanced Cordless Telecommunications (DECT), Universal Mobile Telecommunication System (UMTS), Bluetooth and Wireless Local Area Network (WLAN) 802.11b/g (see Fig. 1). As shown in Fig. 5, it provides up to 38% PAE. Therefore, using AS-DFVS topology achieves a significant increase in the tunability without increasing the control voltage requirement and the PAE of the amplifier is similar to that of the amplifier using dual reverse biased diodes (see Fig. 8(b)). It introduces the highest IM3 (see Fig. 7(a)) among the tunable amplifiers and has similar linearity to the conventional amplifier at large input signal levels. 5.2 Tunable Amplifier Using Anti-Series/Anti-Parallel Distortion-Free Varactor Stack Topology The output matching network using AS/AP-DFVS topology is shown in Fig. 11(b). The input matching network uses the same topology and both networks are designed by load and source-pull techniques to maximize PAE. The amplifier can be tuned from 1.74 to 2.14 GHz (see Fig. 14), i.e. 400 MHz (22.98% tunability) by sweeping the VCC from 0 to 12 V. As shown in Fig. 5, it provides up to 42% PAE, which the highest PAE achieved among the tunable amplifiers. This amplifier may be used for DCS-1800, PCS-1900, DECT and UMTS. The tuning range is significantly larger than that of the amplifiers using reverse biased diode topologies but smaller than that of the amplifier using AS-DFVS topology. At large input signal levels its IM3 is only slightly worse than that of the conventional amplifier. It also generates the lowest IM5 at large input signal levels compared to the other amplifiers. 6 Conclusion It has been demonstrated that adding tunability property to an amplifier by using varactor diodes may result in a significant reduction of PAE. The tunable amplifiers
718
Circuits Syst Signal Process (2011) 30:705–720
Fig. 14 S-parameters of the tunable amplifier using AS/AP-DFVS topology
Table 2 Summary of amplifier performances Amplifier
PAE
Tunability
Control
(%)
(%)
voltage (V)
Supported communication standard(s)
Conventional amplifier
60
NA
NA
DCS-1800
Tunable amplifier using single diode
36
10.34
0–12
DCS-1800, PCS-1900, DECT
Tunable amplifier using dual diodes
39
11.76%
0–24
DCS-1800, PCS-1900, DECT
Tunable amplifier using AS-DFVS
38
35.63%
0–12
DCS-1800, PCS-1900, DECT, UMTS/TDD, UMTS/FDD, Bluetooth, WLAN 802.11b/g (US, UK, Japan)
Tunable amplifier using AS/AP-DFVS
42
22.98%
0–12
DCS-1800, PCS-1900, DECT, UMTS/TDD, UMTS/FDD
using reverse biased diode topologies achieved up to 11.76% tunability (1.7 to 1.9 GHz) and 36% PAE, i.e. 24% lower PAE than the conventional amplifier. It is shown that DFVS topologies are superior to reverse biased diode topologies in terms of tunability and PAE in a tunable amplifier application. The largest tunability of 35.63% (1.74 to 2.36 GHz) is achieved by the amplifier using AS-DFVS topology which gave 38% PAE. This range of tunability is considerably larger than that of other tunable amplifiers recorded in the literature. The tunable amplifier using AS/AP-DFVS has provided a good trade-off between tunability and PAE. It achieved a tunability of 22% (1.74 to 2.14 GHz) and gave 42% PAE. The linearity of the amplifier using AS/AP-DFVS topology is generally better than that of other amplifiers at large input signal drive levels and only slightly worse than that of conventional amplifier. The performances of conventional and tunable amplifiers are summarized in Table 2. The tunable amplifiers using DFVS topologies may replace parallel connected amplifiers used in multimode radios. Furthermore, they may be tuned continuously within a frequency range rather than switching between predetermined frequency
Circuits Syst Signal Process (2011) 30:705–720
719
bands. This enables them to accommodate communication standards that may be introduced in the future and facilitate the design of a SDR.
References 1. http://www.agilent.com/find/eesof, accessed on 4 May 2011 2. W.N. Allen, D. Peroulis, Three-bit and six-bit tunable matching networks with tapered lines, in IEEE Topical Meeting on Silicon Monolithic Integrated Circuits in RF Systems, 19–21 Jan. 2009 (2009), pp. 1–4 3. K. Buisman, L.C.N. de Vreede, L.E. Larson, M. Spirito, A. Akhnoukh, T.L.M. Scholtes, L.K. Nanver, Distortion-free varactor diode topologies for RF adaptivity, in IEEE International Microwave Symposium Digest, 12–17 June 2005 (2005), pp. 157–160 4. K. Buisman, L.C.N. de Vreede, L.E. Larson, M. Spirito, A. Akhnoukh, Y. Lin, X. Liu, L.K. Nanver, Low-distortion, low-loss varactor-based adaptive matching networks, implemented in a silicon-onglass technology, in IEEE Radio Frequency Integrated Circuits Symposium, 12–14 June 2005 (2005), pp. 389–392 5. B.E. Carey-Smith, P.A. Warr, M.A. Beach, T. Nesimoglu, Wide tuning-range planar filters using lumped-distributed coupled resonators. IEEE Trans. Microw. Theory Tech., 53(2), 777–785 (2005) 6. J.G. Colom, R. Medina, Y. Pérez, Simulation of single-stage tunable amplifier using ferroelectric materials. Taylor and Francis, Integr. Ferroelectr., 56(1), 1131–1140 (2003) 7. S.C. Cripps, RF Power Amplifiers for Wireless Communications, 2nd edn. (Artech House, London, 2006) 8. Q. Dongjiang, R. Molfino, S.M. Lardizabal, B. Pillans, P.M. Asbeck, G. Jerinic, An intelligently controlled RF power amplifier with a reconfigurable MEMS-varactor tuner. IEEE Trans. Microw. Theory Tech., Part 2, 53(3), 1089–1095 (2005) 9. K. Entesari, G.M. Rebeiz, A 12–18-GHz three-pole RF MEMS tunable filter. IEEE Trans. Microw. Theory Tech., 53(8), 2566–2571 (2005) 10. http://www.freescale.com/webapp/sps/site/prod_summary.jsp?code=RFX250-20&fsrch=1, accessed on 4 May 2011 11. A. Fukuda, H. Okazaki, S. Narahashi, T. Hirota, Y. Yamao, A 900/1500/2000-MHz triple-band reconfigurable power amplifier employing RF-MEMS switches, in IEEE International Microwave Symposium Digest, 12–17 June 2005 (2005), p. 4 12. F.M. Ghannouchi, Z. Guoxiang, F. Beauregard, Simultaneous load-pull of intermodulation and output power under two-tone excitation for accurate SSPA’s design. IEEE Trans. Microw. Theory Tech., 42(6), 929–934 (1994) 13. C. Huang, K. Buisman, M. Marchetti, L.K. Nanver, F. Sarubbi, M. Popadic, T. Scholtes, H. Schellevis, L.E. Larson, L.C.N. de Vreede, Ultra linear low-loss varactor diode configurations for adaptive RF systems. IEEE Trans. Microw. Theory Tech., 57(1), 205–215 (2009) 14. F. Jia-Shiang, A. Mortazawi, A tunable matching network for power amplifier efficiency enhancement and distortion reduction, in 2008 IEEE MTT-S International Microwave Symposium Digest (2008), pp. 1151–1154 15. H.T. Kim, S. Jung, K. Kang, J.H. Park, Y.K. Kim, Y. Kwon, Low-loss analog and digital micromachined impedance tuners at the Ka-band. IEEE Trans. Microw. Theory Tech. 49(12), 2394–2400 (2001) 16. J.R. MacLeod, T. Nesimoglu, M.A. Beach, P.A. Warr, Enabling technologies for software defined radio transceivers, in Military Communications Conference-MILCOM, October 2002, California, USA 17. R.G. Meyer, M.L. Stephens, Distortion in variable-capacitance diodes. IEEE J. Solid-State Circuits, 10(1), 47–54 (1975) 18. A. Miras, E. Legros, High-gain frequency-tunable low-noise amplifiers for 38–42.5-GHz band applications. IEEE Microw. Guided Wave Lett., 7(9), 305–307 (1997) 19. http://www.murata.com/, accessed on 4 May 2011 20. http://www.mwtinc.com/cat/fets/pdf/mwt-8.pdf, accessed on 4 May 2011 21. J. Nath, D. Ghosh, J.P. Maria, A.I. Kingon, W. Fathelbab, P.D. Franzon, M.B. Steer, An electronically tunable microstrip bandpass filter using thin-film Barium–Strontium–Titanate (BST) varactors. IEEE Trans. Microw. Theory Tech., 53(9), 2707–2712 (2005)
720
Circuits Syst Signal Process (2011) 30:705–720
22. W.C.E. Neo, L. Yu, L. Xiao-dong, L.C.N. de Vreede, L.E. Larson, M. Spirito, M.J. Pelk, K. Buisman, A. Akhnoukh, G. de Anton, L.K. Nanver, Adaptive multi-band multi-mode power amplifier using integrated varactor-based tunable matching networks. IEEE J. Solid-State Circuits, 41(9), 2166–2176 (2006) 23. T. Nesimoglu, M.A. Beach, P.A. Warr, J.R. MacLeod, Linearised mixer using frequency retranslation. IEE Electron. Lett., 37(25), 1493–1494 (2001) 24. T. Nesimoglu, M.A. Beach, J.R. MacLeod, P.A. Warr, Mixer linearisation for software defined radio applications, in IEEE Vehicular Technology Conference, September 2002, Vancouver, Canada (2002), pp. 134–138 25. A. Nieuwoudt, J. Kawa, Y. Massoud, Automated design of tunable impedance matching networks for reconfigurable wireless applications, in 45th ACM/IEEE Design Automation Conference, 8–13 June 2008 (2008), pp. 498–503 26. http://paginas.fe.up.pt/~hmiranda/etele/g1000_30.pdf, accessed on 4 May 2011 27. D.M. Pozar, Microwave Engineering (Wiley, New York, 1998) 28. S. Qin, N.S. Barker, Distributed MEMS tunable matching network using minimal-contact RF-MEMS varactors. IEEE Trans. Microw. Theory Tech., Part 2, 54(6), 2646–2658 (2006) 29. F.H. Raab, P. Asbeck, S. Cripps, P.B. Kenington, Z.B. Popovic, N. Pothecary, J.F. Sevic, N.O. Sokal, Power amplifiers and transmitters for RF and microwave. IEEE Trans. Microw. Theory Tech., 50(3), 814–826 (2002) 30. C. Sanchez-Perez, J. de Mingo, P. Garcia-Ducar, P.L. Carro, A. Valdovinos, Exploring the use of reconfigurable matching networks for efficiency and linearity improvement in RE power amplifiers under load variations, in 2010 IEEE International Microwave Workshop Series on RF Front-ends for Software Defined and Cognitive Radio Solutions (IMWS) (2010) 31. T. Sasaki, H. Hataoka, Investigation of intermodulation in a tuning varactor. IEEE Trans. Broadcast., BC-29(2), 77–81 (1983) 32. P. Scheele, F. Goelden, A. Giere, S. Mueller, R. Jakoby, Continuously tunable impedance matching network using ferroelectric varactors, in IEEE MTT-S International Microwave Symposium Digest, 12–17 June 2005 (2005), p. 4 33. J.H. Sinsky, C.R. Westgate, Design of an electronically tunable microwave impedance transformer, in IEEE MTT-S International Microwave Symposium, June 1997 (1997), pp. 647–650 34. http://www.skyworksinc.com/, accessed on 4 May 2011 35. A. Tombak, A ferroelectric-capacitor-based tunable matching network for quad-band cellular power amplifiers. IEEE Trans. Microw. Theory Tech., Part 2, 55(2), 370–375 (2007) 36. W. Tuttlebee, Software Defined Radio—Enabling Technologies (Wiley, New York, 2002). ISBN10:0470843187 37. H. Uchida, K. Ogura, Y. Konishi, S. Makino, A frequency-tunable amplifier with a simple tunable admittance inverter. Eur. Microw. Conf., 1(4–6), 4 (2005) 38. M. Unlu, K. Topalli, H.I. Atasoy, E.U. Temocin, I. Istanbulluoglu, O. Bayraktar, S. Demir, O.A. Civi, S. Koc, T. Akin, A reconfigurable RF MEMS triple stub impedance matching network, in 36th European Microwave Conference, Sept. 2006 (2006), pp. 1370–1373 39. L.Y. Vicki Chen, R. Forse, D. Chase, R.A. York, Analog tunable matching networks using integrated thin-film BST capacitors. In IEEE MTT-S International Microwave Symposium, TU5C-6, June 2004
