Dual-Band RF Circuits and Components for Multi-Standard Software Defined Radios

Abstract

The advent of multi-standard and multi-band software defined radio (SDR) applications has necessitated the design and deployment of dual-band RF components and circuits considering the numerous advantages of such designs over the traditional narrow band circuits and components. For example, a dual-band power amplifier (PA) not only simplifies the hardware complexity but also provides higher reconfigurability [1] and hence makes it a front runner for deployment in SDR architectures [2]–[3]. Furthermore, the evolution of communication technologies demands the use of dualband/ multi-band RF circuits so as to acc ommodate many standards simultaneously for facilitating and guaranteeing the backward compatibility of future standards (such as 4 G) based system for smooth network migration and upgrades. These technological requirements have also led to commercial introduction of dual-band base stations and repeaters [4]–[6]. Furthermore, the advancement in CMOS and other MMIC technologies, although, is challenging the transmission line based passive circuit techniques but the high power handling ability of transmission line based circuits are potentially very useful in applications such as the design of high power/high efficiency PAs and transmitters. This article elaborates on the techniques employed in the design of transmission line based dual-band RF components in the context of multi-band/multi-mode SDR architecture, highlighting the problems which need to be addressed during the design process.

Introduction

ide-band circuits, although, are more generic and best suited for reconfigurable transceiver architecture but are severely limited in applications such as impedance matching [7–14]. Many pioneer researchers such as Bode [9], Fano [10], Youla [11], and Carlin et al. [12–13], have conducted their research to describe the limit of broadband impedance matching. Initial work by Bode was however focused on a load consisting of a resistance and a capacitor in parallel [9]. Fano [10], Youla [11] and Carlin et al. [12–13] later developed the gain bandwidth restriction to an arbitrary load. In fact, the theory of Youla and Carlin is focused on the determination of the feasibility of matching an arbitrary load, so as to obtain a target reflection coefficient as a function of frequency [14].

For matching applications, the hypothesis of Fano establishes that arbitrary impedance cannot be matched to a pure resistance over the whole frequency spectrum or even at all frequencies within a finite frequency band [10]. Instead the hypothesis suggests possibilities for obtaining matching at desired number of frequencies provided the required impedances have finite resistive components at those frequencies. Consequently the design of wide-band matching, which is a pre-requisite for obtaining optimum efficiency and linearity over the specified band from non-linear components such as PA, is not feasible especially for the situation when the intended bandwidth covers two distinct communication standards far apart in terms of their carrier frequencies. In such situations, dual-band/multi-band matching is highly useful as they provide optimum solution over a limited range of bandwidth around the chosen carrier frequencies of operation [1], [15].

The dual-band matching is also useful in receiver circuits such as diode based mixers. Such an application generally needs a broadband rat-race or branchline coupler with an octave bandwidth, which is difficult to fabricate and has limited performance [16]–[17]. In addition, there is always an issue of simultaneously matching the diodes to the respective optimum reflection coefficients at LO and RF especially when the LO and RF are far from each other. In practical designs, mismatch is allowed at LO as it has high power than RF [16]–[17]. A dual-band matching, however, can provide match at both LO and RF which will lead to eventual reduction in LO power consumption. Furthermore, other applications in passive RF circuit field mostly utilize cascading of several single sections for obtaining broad-band performances. This results into increased cost, size and acomplexity which consequently limit the usefulness of such circuits. It can thus be concluded that the dual-band/multi-band RF circuits have potential applications until there is some breakthrough research for catapulting the design of broad-band circuits.

In this article, the fundamental concept of dispersive circuits and their applications in dual-band circuitry is presented which is then followed by several examples of dual-band RF passive circuits and their associated design and miniaturization methodologies as well as dual-band impedance matching technique for high power applications. Finally, an example of dual-band wireless transmitter, suitable for SDR applications, is described that utilizes various dual-band RF circuits in conjunction with hybrid RF-digital pre-distortion (hybrid RF-DPD) setup realized on a field programmable gate array (FPGA) platform [18].

Multi-Band/Multi-Mode Software Defined Radio: An Architectural Overview

Software defined radio (SDR) is the radio terminal where the key parameters of the radios are defined in software and in which fundamental aspects of the radio’s operation can be reconfigured by upgrading the software [3]. Although software plays an important role in SDR backend where the signal processing functionality is the key operation, yet this role is considered peripheral while hardware plays the dominant role in the SDR frontend. These roles of hardware and software are changing continuously over time, and with the advent of new technology the SDR architecture is moving towards software radio (SR) where receiver digitization will be at (or very near to) the antenna and software programmed in high-speed signal processing element will perform all the processing required for the radio [19]–[22]. Fig. 1 shows a typical block diagram of SDR terminal, where the analog to digital conversion and vice versa is performed at some stage downstream from the antenna typically after low noise amplification and down conversion to a lower frequency in subsequent stages. However, several variations have been proposed in the literature [23]–[25], among which Fig. 1 is built on most common existing state of art in transceiver design. In such a configuration, the software can play a vital role in obtaining multi-mode capability but multi-band capability is mainly served by hardware in the RF front end.

Adopting multi-band architecture over wideband in implementing SDR front-end also reduces burden over the design of band-select filters after antenna without hampering the performance in presence of undesired interference. These band-select filters are used to select desired band of operation as per the intended standard of communication (e.g. WCDMA, WiMax etc.).

In the case of PA design, any mismatch from the optimal loads can severely affect efficiency and linearity of the transmitter. This, mismatch can occur due to (1) the bandwidth limitation of matching network as imposed by Bode, Fano, Youla and Carlin etc. [7–14] and (2) change in antenna input impedance. The latter case occurs due to change in antenna environment (e.g. mutual coupling of the antenna with the nearby object can cause detune of the antenna resonant frequency) [26], whereas, the former case is related to broad-band matching circuits, where, there is compromise in terms of level of mismatch tolerated as the bandwidth of operation increases [7–14]. With the mismatch at the PA output and between the antenna and PA, the efficiency and linearity of the transmitter reduces drastically [26]–[27].

The efficiency is very important in concern to the transmitters as it primarily contributes towards power consumption in a typical wireless communication network. Moreover, to increase spectral efficiency, the modulation resulting into envelop varying signals having high PAPR (e.g. 64 QAM) are commonly used which poses constraints over the linearity of the PA in the transmitter, resulting into adjacent channel leakage and interference with the other standards operating in a nearby frequency range. Although, in order to meet spectral mask of 3G and 4G communication standards, a separate linearization technique must be adopted, still the PA designer should also seek for an optimum solution in terms of efficiency and linearity (IMD, ACLR etc.) through optimum matching condition. As an example, the power added efficiency (PAE) and IMD contours of a 1W GaN HEMT depicted in Fig. 2 clearly identifies that there is substantial degradation in PAE and linearity as the matching impedance moves away from the optimal solution. These contours provide an indication of the trade-off that can be adopted in the design of matching circuits for optimal PAE, Pout and IMD.

It is evident from Fig. 2(a) that the maximum Pout and PAE are 28 dBm and 21% respectively when the device is measured corresponding to the lower fundamental tone (ω₁). The IMD contours in Fig. 2(b) demonstrates that the best matching, Γ_la depicted as the shaded overlapping contours of upper and lower IMDs, for relatively good linearity of 24 dBm results into a poor PAE of 5%. However the results also show that the matching region for the optimal PAE and P_out, shown as the shaded portion and depicted as Γ_la, provides a poor linearity. Therefore, depending on the design specifications the best matching conditions can be traded-off in order to achieve the best PAE, P_out, and IMD.

It should be, however, noted that even the choice of matching for the optimal PAE and linearity at a certain frequency may not result in best PAE and linearity over a band due to presence of mismatch occurring across the band [7–14]. It is due to this reason that multi-band/ dual-band circuits are employed, when the intended carrier frequencies are widely separated, for optimal operation of the radio.

The mismatch due to the change in the antenna input impedance is more difficult to manage and technology such as smart antenna where the adaptive variation in directivity and null-placement can reduce the effect of the object in the vicinity [3], are employed. Another approach adopted to overcome this problem is to design fully adaptive system that can adjust output power, load-line or bias with the change of the antenna impedance resulting into optimum performance in changing antenna environment [26].

Dispersive Circuits and Their Applications in Dual–Band Circuitry

The most common approach adopted in the design of dual-band circuits is to replace each transmission line sections in a conventional single-band design with a 2-port dispersive structure. These dispersive structures possess specific image impedance and phase constant which corresponds to the required values of the characteristic impedance and electric lengths at the respective two frequencies. For example, each section in a dual-band branch-line hybrid requires a phase shift of 90° or its odd-multiple with characteristic impedances, 50 Ω or 35.35 Ω, at the chosen two frequencies which is same as desired for the traditional single-band hybrid [29]. For a standard transmission line segment, the image impedance is same as its characteristic impedance at two frequencies but the corresponding electric length is linear function of frequency. In other words, if n is the frequency ratio of the two chosen frequencies f₁ and f₂ then electric length at f₂ will be n times the electric length at f₁. It consequently leads to a simple premise that a circuit having controllable non-linear behavior of phase with respect to frequency can be customized to achieve a specific electric length or its multiple at any two frequencies of operation which are independent of the frequency ratio of the two frequencies. Fig. 3, which depicts the relationship between the frequency ratio and electric length, clearly conveys this idea that by controlling the non-linear phase characteristics through design parameters based on the type of circuit chosen, the desired electric lengths at the two frequencies can be achieved for any frequency ratio.

The circuits/2-port networks which have nonlinear phase characteristic with frequency are known as dispersive circuits and in principle the dispersion is responsible for frequency dependent phase/group velocity characteristic in such circuits. Stub loaded transmission line is the most common 2-port network exhibiting dispersive effect. In these structures the phase characteristic can be shaped by the stub and the parameters of the loaded line [30]–[32]. In addition, these circuits exhibit frequency dependent behavior of both image impedance as well as phase characteristics and therefore shaping of the phase characteristic also changes the image impedance and thereby necessitating simultaneous solutions for both these features during the design [30]–[31]. Alternatively these structures can also be thought as filters and studied through the image theory concept but this aspect is beyond the scope of this article.

It is worth discussing that, although s-parameters analysis is more rigorous and practical in analyzing the RF and Microwave circuits, image impedance and ABCD matrix approach can be used in much easier way to analyze and design of certain circuits where the transmission lines are involved as main design elements [33]. Example of these circuits are hybrids [29], [32], [34], Wilkinson power divider [29], [32], [35], delay line [29], [32] etc., where the key goal is to obtain desired performance using specific value of characteristic impedance and electrical length of the transmission line at the desired frequency.

In such cases, the theory of image filter design provides a direct relationship of the characteristic impedance and electric length of the emulated transmission line to the ABCD parameters to a 2-port network imitating the transmission line behavior. Indeed, due to this reason, this approach is sometimes preferred over network synthesis approach [7–8], while designing the dual-band circuits, where, a dispersive 2-port network is used to emulate the behavior of transmission line of certain characteristic impedance and electrical length at two frequencies of operation. Thus rather than shaping the input impedance (hence reflection coefficient) using a certain polynomial characteristics (such as Tchebyscheff, Butterworth etc.) [7]–[8], the image impedance and image propagation constant characteristics are shaped [30]. These characteristics to a certain limiting case can be considered equivalent to characteristic impedance and electrical length of a transmission line over a finite band and hence imitate the properties of the transmission line with required specifications.

Analysis of RF Passive Dual–Band Circuits

RF passive dual-band circuits such as power dividers, branch-line hybrid/rat-race baluns, phase-offset lines, delay lines etc. are designed using transmission lines with fix characteristic impedances and desired electric lengths at the specified frequencies. As a case study, design methodologies for realizing power divider and hybrids for dual-band operation as well as a common technique for miniaturizing these circuits are analysed in this section. However, it should be understood that these techniques are equally applicable for the design of any transmission line based dual-band circuits.

Stub-Loaded Transmission Line in Dual-Band Hybrid/Baluns Applications

The transmission line segments in branch-line/rat-race couplers are quarter wave length long whose ABCD parameters are given in equation (1) [29], [32]

To satisfy (1) at two distinct frequencies, a 2-port dispersive structure is required which can be achieved through the use of either lumped components [36] or transmission line sections [30]–[31], [37]–[39]. The lumped components based designs are smaller in size but suffer from the limited bandwidth. In addition, these designs are dependent on the inductor models for achieving the required accuracy. The transmission line based designs, although, are larger in size but have the potential to provide superior performance if designed properly.

There have been two techniques to achieve dualband quarter-wave operation from a transmission line. First method is stub loading at the center of the transmission line [30] while the other is stub loading at the ends of the transmission line [31], [37]–[39]. Figs. 4(a) and 4(b) depict both these scenarios for the case of dual-band branch-line coupler. The transmission lines in these figures are dispersive and therefore capable of providing dual-band operation if their characteristics are shaped appropriately.

The center-tapped stub-loaded line (as shown in Fig. 4(c)) behaves as dual-band quarter-wave transformer if equations (2) and (3), derived from its respective ABCD matrix [30], are simultaneously valid and satisfy the ABCD parameters in (1).

where, Z_S,T and u_S,T are the characteristic impedance and electric length of unloaded line, Z_T
is the overall image impedance of the loaded line, and B_S,T is the susceptance of the stub loading the line in Fig. 4(c). A detail derivation of transforming a center-tapped stub-loaded dispersive structure in a dual-band quarter wave transformer is given in shaded block.

Similarly, a transmission line with edge-loading, as shown in Fig. 4 (d), behaves as dual-band quarter-wave transformer and emulates ABCD parameters given in (1) if expressions in equations (4) and (5) hold simultaneously [31].

where, Z_S,PI and Θ_S,PI are the characteristic impedance and electric length of unloaded line loaded with a stub possessing susceptance B_S,PI and Z_T is the overall image impedance of the loaded line in Fig. 4(d). A detail derivation of transforming a dispersive structure with stub loading at the edges in a dual-band quarter wave transformer is given in shaded block.

The electric lengths u_S,T in (2)–(3) and Θ_S,PI in (4)–(5) varies with frequency and for them to satisfy (1) simultaneously at two distinct frequencies the expression in (6) should hold true [30]–[31].

where, n is the frequency ratio f₂/f₁ with f₁ being the smaller frequency and p equals 1 for the principle argument of sine and tangent function of (2)–(5) corresponding to the smallest physical length of unloaded line in Figs. 4(c) and 4(d).

The negative and positive signs in (1) correspond to electric lengths 90° and 270° respectively. It can therefore be concluded that any odd multiple of electric length 90° provides same performance as quarter-wave transformer. For the dual-band situation, therefore, it has been practically found that there exist two solutions for (6) that provide the requisite dual-band quarter-wave transformers at two distinct frequencies [30]–[31]. First solution is achieved with electric length 90°, corresponding to the negative sign in (6), for both the frequencies. While the second solution is obtained with electric length 90° in first frequency and 270° in the second frequency and corresponds to the positive sign in (6). For smaller frequency ratios, the first case gives larger physical dimensions as compared to the second case [30]–[31].

The most common design approach is to vary frequency ratio n in (6) for obtaining different values of electric length Θ_S,T or Θ_S,PI for which the structure presents a required image impedance Z_T (and hence emulate a quarter-wave transformer with a required value of characteristic impedance Z_T) with a realizable value of Z_S,T or Z_S,PI. The realizable value of Z_S,T or Z_S,PI depends on the minimum width of line that can be fabricated precisely with the fabrication facility. Therefore the minimum possible width of transmission line puts a constraint over the maximum value of Z_S,T or Z_S,PI. The standard design curves regulating the center-tapped and edge loaded structures for emulating dual-band quarter-wave transmission line of 50 Ω characteristic impedance are shown in Figs. 5(a) and 5(b) respectively.

Upon determining the values of Z_S,T or Z_S,PI for particular values of Θ_S,T or Θ_S,PI, n, and Z_T, the corresponding values for the other values of Z_T can easily be predicted by the linear relation given by (2) and (4) as described in [30]. Once the conditions for Z_S,T or Z_S,PI and the associated Θ_S,T or Θ_S,PI are obtained such that the structures in Fig. 4 can emulate an image impedance of ±Z_T at the two specified frequencies, the respective values of B_S,T should satisfy (3) for the center-tapped loaded structure and BS,PI should satisfy (5) for the edge-loaded structure. In most practical designs the stubs are realized by using either an open circuit or a short circuit transmission line. In such a scenario, the stub parameters for center-tapped stub loading of a transmission line are given by expression in (7) [39].

where, Z_P,T is the characteristic impedance and Θ_P,T is the electric length of the stub. Similarly, for the edge-loaded structure the stub parameters are given by the expression in (8) [39].

where, Z_P,PI is the characteristic impedance and Θ_P,PI is the electric length of the stub.

For (7) and (8) to repeat at the two distinct frequencies, an expression given in (9) can be derived [30]–[31].

where, q is the integer with value 1 for principle argument of the tangent function in (7) and (8) and n is the frequency ratio.

For each realizable value of Z_S,T and Z_S,PI obtained from Fig. 5(a) and Fig. 5(b) respectively, for a particular required value of Z_T and n, the values of Θ_P,T or Θ_P,PI can be obtained using (9). These selected values of Θ_P,T or Θ_P,PI along with other design parameters can then be used to obtain value of Z_P,T for center-tapped loaded line and Z_P,PI for the edge-loaded using equation (7) or (8) respectively. It should however be kept in mind that the selection of the values of Z_P,T or Z_P,PI are dependent on the technology used for fabrication. It is also evident from (7) and (8) that for particular values of Z_T, Z_S,T or Z_S,PI and Θ_P,T or Θ_P,PI the design parameter, Z_P,T or Z_P,PI, is linearly proportional to Z_T. Therefore, once the design parameters for a particular n and Z_T are known, the values of the corresponding Z_P,T or Z_P,PI for any other values of Z_T for the same n can also be determined [30].

Fig. 6(a) presents a photograph of dual-band rat-race coupler operating at 1960 MHz and 3500 MHz, which has been designed using center-tapped stub loaded dispersive structure, whereas Figs. 6(b)–(d) depict the measured dual-band performance of this rat-race coupler [30]. The insertion loss of less than 3.9 dB, return loss greater than 16 dB, and isolation better than 20 dB over the band of 80 MHz, centered on the two selected frequencies of 1960 and 3500 MHz, achieved from this design provides a simple proof of concept of the use of stub-loaded center-tapped dispersive structure in the design of dual-band rat-race coupler. The use of edge-loaded dispersive structure is shown in the design of a dual-band branch-line coupler operating at 1960 MHz and 3500 MHz whose photograph is shown in Fig. 7(a) and the corresponding measured results are given in Figs. 7(b)–(d). Once again the achieved results of 3.41 dB insertion loss, return loss of 20 dB, and isolation of 20 dB over the band of 80 MHz, provide a proof of concept of the edge-loaded dispersive structure in the design of dual-band branch-line coupler.

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