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Superconducting Microwave Applications: Filters
Superconducting Microwave Applications: Filters$ N Klein, Jülich Research Center, Jülich, Germany H Chaloupka, University of Wuppertal, Wuppertal, Germany GK Sujan, University of Malaya, Kuala Lumpur, Malaysia r 2016 Elsevier Inc. All rights reserved.
1 2 3 4 5 5.1 5.2 6 6.1 6.2 7 References
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Fundamentals of Microwave Absorption of High-Temperature Superconductors Technology of High-Temperature Superconducting Thin Film Devices Planar HTS Resonators Planar Multipole Filter Topologies Planar High-Temperature Superconducting Filters and Subsystems Filters Subsystems Tuneable and Switchable Filters Ferroelectric Varactors Ferrites Impact of High-Temperature Superconducting Subsystems for Future Microwave Systems
1 2 3 4 5 5 7 7 8 8 9 9
Fundamentals of Microwave Absorption of High-Temperature Superconductors
The microwave response of a superconductor can be understood by two physical phenomena. First, by the Meissner effect (Waldram, 1996; Essén and Fiolhais, 2012; Hirsch, 2012, 2013), which causes any magnetic field applied to the surface of a superconductor to decrease exponentially inside the superconductor on the length scale of the London penetration depth lL, which is about 160 nm for the most relevant high-temperature superconductor (HTS) compound YBa2Cu3O7 (called ‘YBCO’) at T-0. The London penetration depth increases with temperature according to [lL(0)/lL(T)]2E1 (T/Tc)2 (Tc ¼ transition temperature, with Tc ¼ 92 K for YBCO). As T approaches Tc, lL (T) converges to the normal metal skin depth. Below about 0.8Tc, lL (T) is nearly frequency independent up to several 100 GHz. The second fact is that at finite temperatures below Tc, Cooper pairs (corresponding to ‘ballistic’ charge carriers without dissipation) and quasi-particles (corresponding to normal conducting charge carriers obeying Ohm's law with a temperature dependent conductivity s1(T)) coexist (see e.g., Klein, 1997). According to this simple physical picture, the electrodynamic response of a superconductor can be described by a complex valued conductivity: s ¼ s1 ðT Þ is2 ðT Þ ¼ s1 ðT Þ
i om0 l2L ðT Þ
½1
The imaginary part of the conductivity corresponds to the inductive response of the Cooper pairs. The explicit relationship between s2 and lL follows from the London equations. It should be emphasized that the rigorous treatment of the electrodynamic response of a superconductor requires a quantum mechanical treatment based on BCS theory including some peculiarities of hightemperature superconducting oxides (Klein, 1997; Hein, 1999). In the context of this article, only a basic understanding of the microwave response being necessary for the understanding of superconducting filters can be provided. At microwave frequencies s1{s2 holds true resulting in a simple expression for the surface resistance and reactance of a superconductor (by a Taylor expansion of eqn [1]): RS ¼
1 2 0 o m2 s1 ðT Þl3L ðT Þ; 2
XS ðT Þ ¼ om0 lL ðT Þ
½2
In contrast to normal metals, the surface resistance exhibits a quadratic frequency dependence. The absolute values for thin films of YBCO at a temperature of 77 K are shown in Figure 1. According to this data, there is a clear advantage by orders of magnitude for using HTS for the whole range of microwave communications bands. Above 77 K, Rs increases strongly toward the critical temperature due to the strong increase of the London penetration depth. Below 77 K, Rs decreases gradually toward zero temperature by less than one order of magnitude. ☆
Change History: September 2015. G.K. Sujan added an abstract, six keywords, and seven most recent references within the text.
Reference Module in Materials Science and Materials Engineering
doi:10.1016/B978-0-12-803581-8.01821-X
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Superconducting Microwave Applications: Filters
Figure 1 Measured surface resistance of epitaxially grown YBCO films grown at different laboratories at T¼77 K in comparison to that of copper.
The surface resistance data discussed so far correspond to the linear regime corresponding to low levels of microwave magnetic fields. For higher field levels corresponding to higher values of the stored field energy, nonlinearities occur resulting either in an increase of Rs and/or intermodulation distortion (Hein, 1999). This is of particular importance, because – as a result of magnetic field displacement – planar conductors possess a strongly peaked edge current density (enhanced by about one order of magnitude). This effect can only be avoided by employing ‘edge current free’ modes in circular disk or ring resonators. Typically, intermodulation distortion as well as a field dependent surface resistance occurs at field levels, which depend strongly on the film quality. As an example, misoriented grains in the strongly anisotropic materials and grain boundaries give rise to strong nonlinearities. The nonlinear effects in HTS films are strongly temperature dependent, in particular close to Ts (Klein, 1997; Hein, 1999). Therefore, operation temperatures of 50–65 K are more favorable than 77 K. As discussed in Section 5, temperatures in this range can be attained by low-power closed-cycle cryocoolers.
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Technology of High-Temperature Superconducting Thin Film Devices
In most cases, HTS planar microwave devices rely on epitaxially grown films of YBCO grown (Zhang et al., 2012) by vacuum deposition techniques. Nonvacuum techniques like spraying or sol–gel (Alford et al., 1997) represent very challenging developments with the focus on low-cost production. However, the properties of such films are still behind that of epitaxial film. However, for some applications like coating of large area microwave cavities for base-station filters, HTS thick films are in use (Remilliard et al., 2001). For a review about the growth of YBCO films see Wӧrdenweber (1999). Apart from YBCO, thin films with reasonable microwave properties have been prepared from the thallium-based compounds Tl2Ba2CaCu2O8 (TcE105 K) and Tl2Ba2Ca2Cu3O10 (TcE115 K) (Klein, 1997; Wӧrdenweber, 1999; Liu et al., 2015). For the thallium-based and the more recently discovered mercury-based compounds with Ts values up to 140 K, epitaxial growth is very difficult because of the volatility of thallium and mercury, respectively. HTS films with reasonable and qualified microwave properties can be grown on wafers up to a diameter greater than 4 in; the most common sizes are 2 in and 3 in for microwave applications (Wӧrdenweber, 1999). A very important step was the preparation of double-sided coatings, which have turned out to be essential for planar microwave devices, where the ground plane needs to be superconducting in order to achieve high quality factors. Substrates for planar HTS microwave devices need to fulfill the criteria for expitaxial growth plus moderated values of the dielectric constant (ɛrr25) and a low level of dielectric losses (tan δr105). The most commonly used substrate materials are lanthanum aluminate (LaAlO3, ɛrE23), magnesium oxide (MgO, ɛrE10), and sapphire (Al2O3, ɛrE10) (see Krupka et al., 1994; Zuccaro et al., 1997). The fabrication of a planar microwave device is based on a patterning process. As a first step, masks are prepared according to the layout of the structure. A conventional photolithographic procedure based on a photoresist layer followed by chemical or ion
Superconducting Microwave Applications: Filters
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beam etching is applied for patterning of the HTS wafers. In order to provide electrical contacts to microstrip connectors and to the housing, the HTS films are often covered with an in situ gold layer prior to patterning. The feature sizes are typically not smaller than 10 mm, but due to RF current crowding at the edges, the performance of planar microwave devices becomes quite sensitive to the quality of the patterning process. After process optimization no significant degradation of the microwave properties remains.
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Planar HTS Resonators
Typically, the building blocks of HTS filters are planar HTS resonators (Guo et al., 2012). In general, a microwave resonator is characterized by its resonant frequency f0, its unloaded quality factor Q0 of the selected resonant mode(s), and its spectrum of spurious modes. The unloaded quality factor of a resonator is determined by the stored energy W and the dissipated power Pdiss Q0 ¼
2pf0 W Pdiss
½3
Pdiss contains loss contribution from the circuit layer and the unpatterned ground plane, dielectric losses from the substrate materials in use, and radiation losses (or metal losses from the housing). The dielectric losses are characterized by the loss tangent tan δ of the substrate material. Neglecting radiation losses, the unloaded quality factor is given by Z Z er E 2 dV om0 H 2 dV 1 RS S Z ¼ κtanδ þ ; κ ¼ Z ; G¼ Z V ½4 Q0 G E 2 dV þ er E 2 dV H 2 dA VS
S
C
with κ representing the filling factor indicating the normalized fraction of electric field energy stored in the dielectric substrate (S). Typically, κ values are slightly smaller than 1. The quantity G is a geometric factor (in O) representing the surface integral of the squared RF magnetic field over the conducting parts (C). In case of planar resonators G is roughly proportional to the substrate thickness. For conventional metals, the dielectric losses are small in comparison to metal losses. For HTS resonators, substrate losses can play a significant role. The integrals in eqn [4] with subscript ‘V’ are volume integrals over the entire volume of the resonator, i.e., substrate plus housing. Figure 2 shows typical examples of HTS planar resonators which have been used as building blocks of multipole filter structures. Planar HTS resonators are either formed by segments of quasi-TEM (transverse electromagnetic) transmission lines defining the resonances to be at frequencies where the length L equals a multiple of half a guided wavelength (Figures 2(b) and 2(c)) or lumped element resonators each composed of a discrete inductor L and capacitor C (see Figure 2(a) and Hieng et al., 2001) with its resonance at a frequency f ¼ 1/[2p(LC)1/2]. In many cases hybrids of lumped elements and microstrip lines are used, for example, folded microstrip lines disrupted by a capacitive gap (Figure 2(d); Hong et al., 1999). In order to obtain a high value of Q for microstrip and lumped element structures, the ground plane needs to be formed by a HTS film, for example, in general
Figure 2 Typical planar resonators being used as building blocks for planar HTS filters (design by Superconductor Technologies Inc.): quasilumped element (a), microstrip (b), coplanar waveguide (c), folded microstrip with integrated capacitors (d), and two-dimensional disk resonator (e). Omitting the capacitive gap in the folded microstrip design (d) leads to a ring resonator (if circular shaped), which also represents a quite commonly used microstrip resonator design.
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Superconducting Microwave Applications: Filters
double-sided films are required in order to achieve ultimate performance. As an alternative, coplanar resonators have been used (Figure 2(c)) with some compromise on Q in comparison to microstrip lines of the same size but with the advantage of single sided coating. However, until now no high-performance multipole filters based on coplanar resonators have been built. For the highest Q and ultimate power handling capability circular two-dimensional disk resonators excited in the TM010-mode have been used (Figure 2(e)), also requiring double-sided coating (Kolesov et al., 1997). The structures shown in Figure 2 are generally not restricted to superconductors, but only here the achievable quality factors are comparable or higher than the ones of bulky cavities or dielectric resonators at room temperature. Therefore, there is strong potential in high-temperature superconductor technology for the miniaturization of high-performance microwave devices and circuits.
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Planar Multipole Filter Topologies
The class of microwave filters which can mostly benefit from HTS technology is characterized by some common structural features (‘topologies’). Filters of this class are passive and reciprocal two-ports, where the incident power is transmitted within certain frequency intervals (passbands) and reflected within the stopbands. Rejection in the stopbands is achieved by reflection. Unavoidable dissipation causes a degradation of the filter performance. For a given amount of dissipation, the degree of degradation depends on the filter parameters. In turn, this determines whether an HTS realization is beneficial or not. In the most common filter topology all resonators are identical, possessing the same resonant frequency f0 in the uncoupled state. A structure where input and output ports are coupled via one resonator only, represent a one-pole filter with a Lorentzian shaped transmission characteristic. If losses can be neglected, the frequency bandwidth (frequency interval where the transmission factor is higher than a prescribed value) of a one-pole filter is controlled by the strength of the coupling between resonator and ports. In order to achieve a frequency response closer to the rectangular frequency response of an ideal filter, a multiple-resonant (multipole) filter structure needs to be employed. In the most common filter topology, multiple-resonant structures are realized by a set of identical resonators of unperturbed resonant frequency f0, which are mutually coupled. Mutual coupling of N resonators results in a splitting into N (in general) different frequencies. In the case that each resonator supports two orthogonal resonant modes (dual-mode resonator), N represents the number of operational modes. Each coupling path (direct connection between resonator i and j) is characterized by its coupling coefficient kij, which is related to the frequency splitting of f0 into fe and fo for the even and odd mode, respectively, by kij ¼ (fe fo)/f0. In the special case of pure adjacent resonator coupling (ki,j ¼ 0 for iaj71), a single chain between input and output port is formed. This allows one to approximate a rectangular bandpass response with transition width δf decreasing with increasing order N (see Figure 3). Different approximations for the insertion loss response are possible. The most popular is the Chebyshev response with equal-ripple response of the (reflective) passband insertion loss (Matthaei et al., 1980). The required order (number of resonators or operational modes) increases with increasing ratio between the passband width Df and the transition width δf. For a given order N the transition width δf can be further reduced by introducing transmission zeros in the stopband close to the band edge. These transmission zeros cannot be realized if the coupling topology is restricted to adjacent resonator coupling. Additional coupling between non-adjacent resonators (‘cross-couplings’) with appropriate coupling sign and strength is required. Filters with
Figure 3 Typical frequency response of a passband filter with 2 transmission zeros in the stopbands (Df ¼passband width, δf¼transition width).
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Figure 4 Filter topology with resonators, adjacent resonator coupling, and non-adjacent resonator coupling (cross-coupling).
cross-couplings are characterized by the ratio between the number of transmission zeros at finite frequencies and the filter order and referred to as quasi-elliptic or elliptic filters (Figure 4; Klauda et al., 2000). In analogy to spectral-analysis where frequency resolution increases with integration time, the skirt steepness (in dB MHz1) of a filter determines the minimum time duration in which the signal has to be stored in the filter structure. This time duration t can be described by means of the frequency-dependent group delay which is the frequency derivative of the transmission phase and corresponds to the delay of a narrowband (bandwidth approaching zero) pulse passing through the filter. The group delay time t allows for a simple relationship between the field energy W stored in the resonators to the incident power Pinc W ¼ tPinc
½5
Up to now, degradations of the filter response caused by losses were ignored. The in-band insertion loss Ldiss Ldiss Pin ot ¼ 10 log ¼ 10 log 1 þ Q dB Pout
½6
is increased due to the finite unloaded quality factor Q by an amount which is proportional to the group delay. The insertion loss is associated with an unwanted power reduction of in-band signals as well as with an unwanted amplitude distortion caused by the frequency dependence of t. The latter effect leads to a rounding of the insertion loss response at frequencies close to the band edge where the group delay has a maximum. Therefore, the achievable skirt steepness for a bandpass filter depends on the unloaded quality factor and on the filter topology (Klauda et al., 2000): So4 103
Q0 ξ f
½7
The dimensionless quantity ξ has a value of 0.33 for Chebyshev and 1 for elliptic filters (the values for quasi-elliptic filters are in between) (where S is measured in dB MHz1 and f in GHz).
5 5.1
Planar High-Temperature Superconducting Filters and Subsystems Filters
Since the late 1990s, tremendous progress has been achieved in the development of HTS planar filters and their integration in subsystems, mostly for base stations in mobile communication (Willemsen, 2001). For HTS planar filters the resonator types shown in Figure 2 and others have been used. The main emphasis was to develop filters for base stations with steep skirts coming as close as possible to the Q-requirements discussed in the previous section. In most cases, these are (quasi) elliptic filters with 8–17 poles or Chebyshev filters with up to 30 poles. Figure 5 shows an example of an eight-pole quasi-elliptic filter based on folded microstrip resonators similar to ‘c’ in Figure 2. In this case of monomode resonators, coupling coefficients of different signs were achieved by changing between electric and magnetic field coupling of the resonators. For a 17-pole elliptic filter at 1.8 GHz with 5% relative bandwidth (resonator Q0 ¼ 50.000 at 65 K) a steepness of skirts of 85 dB MHz1 was demonstrated (Figure 6). Such a high performance cannot be achieved with any other filter technology. In addition, high quality filters based on microstrip resonators have been developed for C-band satellite transponders. Figure 7 shows a three channel IMUX test module developed at Bosch SatCom GmbH in Germany. This test module, which is considered
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Superconducting Microwave Applications: Filters
Figure 5 Example of an HTS-planar filter with 8 poles and quasi-elliptic characteristic (from Hong et al., 1999).
Figure 6 Measured characteristic of a HTS planar 17-pole elliptic filter (from Kolesov et al., 2000).
Figure 7 Photograph of a three-channel IMUX module based on HTS planar filters as part of a cryogenic C-band satellite transponder. The HTS filters are indicated as large black squares (from Klauda et al., 2000).
Superconducting Microwave Applications: Filters
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Figure 8 Commercial HTS subsystem for potential use in base stations. The filters and the LNA are inside a Dewar vacuum (left side), the metal cylinder in the right part of the assembly is the compressor of the Stirling-type refrigerator (from Kolesov et al., 2000).
to be part of a space experiment, consists of three HTS quasi-elliptic eight-pole channel filters, cryogenic circulators, a cryogenic preamplifier, and a wide band HTS input filter (Klauda et al., 2000). Due to the nonlinear surface resistance of HTS films (see Section 1) power handling of HTS filters is limited. In general, one can claim that planar HTS filters with edge-parallel currents in their resonators can handle power levels in the mW range without significant intermodulation distortions. Applications to transmit circuits with typical power levels of several 10 W can only be handled by employing the edge-current free disk resonator.
5.2
Subsystems
The most important ‘enabling technology’ for applications of HTS in telecommunications is cryotechnology. Cooling by liquid nitrogen is unacceptable, because the amount of maintenance for each base station should be as small as possible. The situation for satellite communications is even more severe, because the lifetime of a geostationary satellite is at least 10 year. The most convenient way of cooling is to use Stirling-type closed-cycle refrigerators consisting of a small stainless steel compressor with helium gas pressure of a few bar and a cold finger with a displacer inside, both connected by a thin stainless steel tube. Typically, a compressor with an a.c. 50 Hz power consumption of 100–200 W with the size of one or two beer cans provides a cooling power of 3–10 W at 77 K, which is the typical amount of cooling power needed for a HTS subsystem, consisting of about three filters and one cryogenic LNA (low-noise amplifier). For the sake of filter performance the base station subsystems are operating between 60 and 70 K, and the satellite systems at 77 K because cooler efficiency is a crucial parameter with respect to system mass reduction (Klauda et al., 2000; Willemsen, 2001). Figure 8 shows a commercial system for potential use in wireless base stations (Kolesov et al., 2000). The filters are assembled inside a Dewar vacuum (left side), the metal cylinder in the right part of the assembly is the compressor of the Stirling-type refrigerator. In 2002, companies are focussing on improving the coolers with respect to lifetime (currently about 3–5 year for continuous operation) and cost reduction.
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Tuneable and Switchable Filters
Tuneable and switchable filters are supposed to have a strong potential for future receiver front-ends (Li et al., 2014). First, for military communications systems, most flexible interference suppression is an important issue. Second, for future mobile communication systems beyond the currently installed third-generation systems, most flexible allocation of bandwidth may require high-performance reconfigurable filters (see also Section 7). In general, the figure-of-merit (FOM) of a tuneable resonator is given by FOM ¼
Df Q f
½8
with Df/f being the relative frequency tuning range and Q the unloaded quality factor of the resonator. The most commonly investigated techniques which can be used for HTS tuneable devices are based on ferroelectrics and ferrites. For the future also micromechanical switches (MEMS) are considered to be relevant for planar HTS circuits (see e.g., Rebeiz and Muldavin, 2001).
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Superconducting Microwave Applications: Filters
Figure 9 Tuneable lumped element 2-pole bandpass filter based on a SrTiO3 loaded interdigited capacitor (a) and experimental result for measured filter response (b) (from Marcilhac et al., 2001).
6.1
Ferroelectric Varactors
These are very attractive for the integration with passive HTS microwave circuits because of the agile dielectric materials which can be grown as epitaxial heterostructures with YBCO. The current efforts are concentrated on thin films of SrTiO3 (SrTiO3 does not exhibit a ferroelectric phase transition but the temperature dependence of the permittivity exhibits a Curie–Weiss law similar to ferroelectric above its Curie temperature). Thin films exhibit lower ɛr values in comparison to the bulk single crystals, but a stronger tuneability above about 60 K. Similarly, the dielectric losses at microwave frequencies are in the range of 102 (see e.g., Petrov et al., 1998) in comparison to several 104 for bulk single crystals (Vendik et al., 1998). The FOMs achieved at microwave frequencies for single varactors or tuneable resonators are in the range of about 100. Figure 9(a) shows an example of a planar HTS resonator incorporating a ferroelectric varactor based on a YBCO/SrTiO3 multilayer structure. With such resonators a tuneability by about 10% was achieved (Marcilhac et al., 2001, B Marcilhac, private communication). Such resonators can be used to construct multipole bandpass filters (Figure 9(b)).
6.2
Ferrites
These represent a very common way of frequency tuning utilizing the magnetic field and magnetization dependence of a permeability tensor. In general, the microwave properties of a ferrite biased by a d.c. magnetic field H0 in z-direction are defined by the permeability tensor which is in the lossless case (see e.g., Pozar, 1998) 3 iκ 0 m 07 5 0 m0 o0 om oom with m ¼ m0 1 þ 2 and κ ¼ m0 2 o0 o2m o0 o2m 2
m 6 ½m ¼ 4 iκ 0
½9
The angular frequencies o0 ¼ m0gH0 and os ¼ m0gMs are proportional to the external magnetic field H0 and the saturation magnetization Ms with g¼ 1.759 1011 C kg1 being the gyromagnetic ratio. This proportionality corresponds to a ratio of 2.8 MHz G1 between the value of frequency f ¼ o/2p and magnetic field. Large tuning ranges can be achieved by exploiting the ferrimagnetic resonance (o¼ o0) in a YIG sphere. However, the losses are quite high and therefore combinations with HTS are not worth considering. In addition, high magnetic fields applied during operation may result in a significant degradation of the surface resistance of the employed HTS film. One attractive possibility is to use latching devices, where the magnetization of the ferrite can be switched between the remanent magnetization values Mr and þ Mr (usually slightly lower than Ms) employing short current pulses applied through a coil. This principle has been employed successfully for the realization of planar HTS phase shifters (Oates et al., 1997). Tuneable resonators and simple Chebyshev filters with a small number of poles have been demonstrated, the FOM values are about several hundred. However, there are several drawbacks associated with ferrimagnetic tuning: (i) The growth of HTS on ceramic YIG or other ferrites is difficult because no epitaxial growth can be achieved; epitaxial growth of single crystal YIG substrates has been achieved, but the substrates are very expensive and only available in small dimensions. Therefore, the working solutions rely on flip-chip assemblies.
Superconducting Microwave Applications: Filters
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(ii) The particular form of the m-tensor sets strong limits on possible tuning and phase shifting topologies. (iii) Experimentally, the losses below about 5 GHz increase dramatically due to ferrimagnetic resonance losses of partially magnetized segments of the ferrite material in use (Ms of YIG corresponds to 4.9 GHz). As an alternative to YIG, Ga- or Al-doped YIG with lower values of Ms have been used (Yeo and Lancaster, 2001). One of the challenges is the development and optimization of ferrites with tailored properties at cryogenic temperatures.
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Impact of High-Temperature Superconducting Subsystems for Future Microwave Systems
The superior performance of HTS filters, namely high selectivity combined with a very low passband insertion loss can be used to enhance the performance of receiver front ends with respect to both interference resistivity as well as a reduced receiver noise figure. Receiver front-ends are analog subsystems, placed in between the antenna ports and the analog-to-digital converters (ADCs). Their function comprises pre-amplification, down-conversion and some filter functions. It is important to distinguish between the different filter functions. Channel (carrier) selection and/or separation in principle can be performed by analog filters in the microwave or the intermediate frequency (IF) section, or by software-controlled digital filters in the digital part. In 2002, analog channel selection in the IF represents the best choice. Future receivers are expected to utilize more and more digital channel selection (‘software defined radio’). Transparent transponders with signal processing exclusively in the microwave regime represent an exception from this trend. In contrast to channel selection, other filter functions need to be performed in the microwave regime. These functions are the suppression of image reception in superheterodyne receivers and the rejection of strong out-of-band interferers. The second function stems from the necessity to prevent strong interfering signals from entering the LNAs and mixers, where they would cause saturation, desensitisation, and intermodulation effects due to the nonlinear response of these active devices. Cryogenic units for base-transceiver stations (BTS) of wireless communication networks became commercially available in the late 1990s. These units comprise HTS bandpass filters followed by cryogenic LNAs, both integrated in an enclosed vacuum which incorporates the cryocooler. In order to meet the different requirements associated with frequency allocation in a first-generation analog and second- and third-generation digital systems, these systems are available for different center frequencies and bandwidths, as well as with multiple passbands and with narrowband stopbands embedded in wider passbands. The number of filterLNA chains in one cryogenic unit equals the number of antenna ports (sector antennas and diversity antennas) implemented in a one BTS. For the evaluation of system benefits offered by cryogenic front-ends, the issue of a significantly improved interference suppression due to steeper filter skirts and the issue of an improved sensitivity due to the reduced receiver noise figure should be clearly distinguished. The first feature becomes significant in the case of wireless systems which have to operate in areas with strongly interfering systems with unwanted signals at frequencies closely spaced to the edge frequencies of the desired signal. Here, the improved selectivity is transformed into a lower intermodulation noise level and hence into improving the quality of service. Alternatively, this advantage can be transformed into reduced guard-band widths and hence in an enhanced spectral efficiency and capacity. In case of spread-spectrum systems, like the third-generation W-CDMA standard, HTS stopband filters with extremely narrow bandwidths can be used to reject narrowband interferers falling into the wideband operational frequency band. The reduced receiver noise figure of cryogenic filter-LNA configurations originates from three different effects, namely the reduced noise temperature of the cooled LNA, the reduced thermal noise of the filter due to the lower physical temperature, and the reduced contribution of the amplifier noise due to the decreased passband insertion loss of the filter. Reduced receiver noise becomes important in noise-limited situations (e.g., rural areas), where it transforms into a lower number of required BTSs or an improved coverage for a fixed number of BTSs. Typically, the noise figure of a BTS with the cryogenic front end at the ground (noise figure degeneration due to lossy cable between antenna and front-end) resembles the noise figure of a conventional, but mast-mounted front-end.
References Alford, N. McN., Penn, S.J., Button, T.W., 1997. High-temperature superconducting thick films. Supercond. Sci. Technol. 10, 169–185. Essén, H., Fiolhais, M.C., 2012. Meissner effect, diamagnetism, and classical physics − A review. Am. J. Phys. 80, 164–169. Guo, J., Sun, L., Zhou, S., et al., 2012. A 12-pole K-band wideband high-temperature superconducting microstrip filter. IEEE T. Appl. Supercon. 22, 1500106. Hein, M., 1999. Tracts in Modern Physics: High-Temperature Superconductor Thin Films at Microwave Frequencies, vol. 155. New York, NY: Springer. Hieng, T.S., Huang, F., Lancaster, M.J., 2001. Highly miniature HTS microwave filters. IEEE T. Appl. Supercon. 11, 349–352. Hirsch, J., 2012. The origin of the Meissner effect in new and old superconductors. Physica Scripta 85, 035704. Hirsch, J., 2013. Kinetic energy driven superfluidity and superconductivity and the origin of the Meissner effect. Physica C: Superconductivity 493, 18–23. Hong, J.-S., Lancaster, M.J., Greed, R.B., et al., 1999. Thin film HTS passive microwave components for advanced communications systems. IEEE T. Appl. Supercon. 9, 3839–3896.
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Klauda, M., Kaesser, T., Mayer, B., et al., 2000. Superconductors and cryogenics for future communication systems. IEEE T. Microw. Theory. 48, 1227–1239. Klein, N., 1997. Electrodynamic properties of oxide superconductors. Juelich report, July 3773. Post-doctoral thesis, Juelich Research Centre. Kolesov, S., Aminov, B., Kaiser, T., et al., 2000. Cryogenic BTS receiver front end demonstrator. Proceedings of 30th European Microwave Conference, vol. 3, pp. 230–232. Kolesov, S., Chaloupka, H., Baumfalk, A., Kaiser, T., 1997. Planar HTS structures for high-power applications in communication systems. J. Supercond. 10, 179–187. Krupka, J., Geyer, R.G., Kuhn, M., Hinken, J.H., 1994. Dielectric properties of single crystals of Al2O3, LaAlO3, NdGaO3, SrTiO3, and MgO at cryogenic temperatures. IEEE T. Microw. Theory 42, 1886–1890. Li, C., Bian, Y., Li, G., et al., 2014. A tunable high temperature superconducting bandpass filter realized using semiconductor varactors. IEEE T. Appl. Supercon. 24, 1–5. Liu, X., Wang, P., Xie, W., et al., 2015. Millimeter wave characteristics of intrinsic Josephson junctions with planar equiangular spiral antenna in misaligned Tl2Ba2CaCu2O8 thin film. Phys. C: Supercond. Appl. 519, 1–4. Marcilhac, B., Crete, D.G., Lemaitre, Y., et al., 2001. Frequency agile microwave devices based on Y−Ba−Cu−O/Sr−Ti−O/La−Al−O structures. IEEE T. Appl. Supercon. 11, 438–441. Matthaei, G., Young, L., Jones, E.M.T., et al., 1980. Microwave Filters, Impedance-Matching Networks and Coupling Structures. Dedham: Artech House. Oates, D.E., Dionne, G.F., Temme, D.H., Weiss, J.A., 1997. Superconductor ferrite phase shifters and circulators. IEEE T. Appl. Supercon. 7, 2347–2350. Petrov, P.K., Carlsson, E.F., Larsson, P., Friesel, M., Ivanov, Z.G., 1998. Improved SrTiO3 multilayers for microwave application: Growth and properties. J. Appl. Phys. 84, 3134–3140. Pozar, D.M., 1998. Microwave Engineering. New York, NY: John Wiley. Rebeiz, G.M., Muldavin, J.B., 2001. RF MEMS switches and switch circuits. IEEE Microwave Magazine, pp. 59−71. Remilliard, S.K., Abdelmonem, A., Radzikowski, P.O., Lazzaro, N.D., Applegate, D.S., 2001. Field deployable microwave filters made from superconductive thick films. J. Supercond. 14, 47–56. Vendik, O.G., Ter-Martirosyan, L.T., Zubko, S.P., 1998. Microwave losses in incipient ferroelectrics as functions of the temperature and the biasing field. J. Appl. Phys. 84, 993–998. Waldram, J.R., 1996. Superconductivity of Metals and Cuprates. Bristol: Institute of Physics. Willemsen, B.A., 2001. HTS filter subsystems for wireless telecommunications. IEEE T. Appl. Supercon. 11, 60–67. Wördenweber, R., 1999. Growth of high-Tc thin films. Supercond. Sci. Technol. 12, R86–R102. Yeo, K.S.K., Lancaster, M.J., 2001. High-temperature superconducting ferrite phase shifter latching structures. IEEE T. Appl. Supercon. 11, 430–433. Zhang, X., He, X., Zhang, Q., et al., 2012. A HTS balun on lanthanum aluminate substrate. Physics Procedia 36, 425–428. Zuccaro, C., Winter, M., Klein, N., Urban, K., 1997. Microwave absorption in single crystals of lanthanum aluminate. J. Appl. Phys. 82, 5695–5704.
1 2 3 4 5 5.1 5.2 6 6.1 6.2 7 References
1
Fundamentals of Microwave Absorption of High-Temperature Superconductors Technology of High-Temperature Superconducting Thin Film Devices Planar HTS Resonators Planar Multipole Filter Topologies Planar High-Temperature Superconducting Filters and Subsystems Filters Subsystems Tuneable and Switchable Filters Ferroelectric Varactors Ferrites Impact of High-Temperature Superconducting Subsystems for Future Microwave Systems
1 2 3 4 5 5 7 7 8 8 9 9
Fundamentals of Microwave Absorption of High-Temperature Superconductors
The microwave response of a superconductor can be understood by two physical phenomena. First, by the Meissner effect (Waldram, 1996; Essén and Fiolhais, 2012; Hirsch, 2012, 2013), which causes any magnetic field applied to the surface of a superconductor to decrease exponentially inside the superconductor on the length scale of the London penetration depth lL, which is about 160 nm for the most relevant high-temperature superconductor (HTS) compound YBa2Cu3O7 (called ‘YBCO’) at T-0. The London penetration depth increases with temperature according to [lL(0)/lL(T)]2E1 (T/Tc)2 (Tc ¼ transition temperature, with Tc ¼ 92 K for YBCO). As T approaches Tc, lL (T) converges to the normal metal skin depth. Below about 0.8Tc, lL (T) is nearly frequency independent up to several 100 GHz. The second fact is that at finite temperatures below Tc, Cooper pairs (corresponding to ‘ballistic’ charge carriers without dissipation) and quasi-particles (corresponding to normal conducting charge carriers obeying Ohm's law with a temperature dependent conductivity s1(T)) coexist (see e.g., Klein, 1997). According to this simple physical picture, the electrodynamic response of a superconductor can be described by a complex valued conductivity: s ¼ s1 ðT Þ is2 ðT Þ ¼ s1 ðT Þ
i om0 l2L ðT Þ
½1
The imaginary part of the conductivity corresponds to the inductive response of the Cooper pairs. The explicit relationship between s2 and lL follows from the London equations. It should be emphasized that the rigorous treatment of the electrodynamic response of a superconductor requires a quantum mechanical treatment based on BCS theory including some peculiarities of hightemperature superconducting oxides (Klein, 1997; Hein, 1999). In the context of this article, only a basic understanding of the microwave response being necessary for the understanding of superconducting filters can be provided. At microwave frequencies s1{s2 holds true resulting in a simple expression for the surface resistance and reactance of a superconductor (by a Taylor expansion of eqn [1]): RS ¼
1 2 0 o m2 s1 ðT Þl3L ðT Þ; 2
XS ðT Þ ¼ om0 lL ðT Þ
½2
In contrast to normal metals, the surface resistance exhibits a quadratic frequency dependence. The absolute values for thin films of YBCO at a temperature of 77 K are shown in Figure 1. According to this data, there is a clear advantage by orders of magnitude for using HTS for the whole range of microwave communications bands. Above 77 K, Rs increases strongly toward the critical temperature due to the strong increase of the London penetration depth. Below 77 K, Rs decreases gradually toward zero temperature by less than one order of magnitude. ☆
Change History: September 2015. G.K. Sujan added an abstract, six keywords, and seven most recent references within the text.
Reference Module in Materials Science and Materials Engineering
doi:10.1016/B978-0-12-803581-8.01821-X
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2
Superconducting Microwave Applications: Filters
Figure 1 Measured surface resistance of epitaxially grown YBCO films grown at different laboratories at T¼77 K in comparison to that of copper.
The surface resistance data discussed so far correspond to the linear regime corresponding to low levels of microwave magnetic fields. For higher field levels corresponding to higher values of the stored field energy, nonlinearities occur resulting either in an increase of Rs and/or intermodulation distortion (Hein, 1999). This is of particular importance, because – as a result of magnetic field displacement – planar conductors possess a strongly peaked edge current density (enhanced by about one order of magnitude). This effect can only be avoided by employing ‘edge current free’ modes in circular disk or ring resonators. Typically, intermodulation distortion as well as a field dependent surface resistance occurs at field levels, which depend strongly on the film quality. As an example, misoriented grains in the strongly anisotropic materials and grain boundaries give rise to strong nonlinearities. The nonlinear effects in HTS films are strongly temperature dependent, in particular close to Ts (Klein, 1997; Hein, 1999). Therefore, operation temperatures of 50–65 K are more favorable than 77 K. As discussed in Section 5, temperatures in this range can be attained by low-power closed-cycle cryocoolers.
2
Technology of High-Temperature Superconducting Thin Film Devices
In most cases, HTS planar microwave devices rely on epitaxially grown films of YBCO grown (Zhang et al., 2012) by vacuum deposition techniques. Nonvacuum techniques like spraying or sol–gel (Alford et al., 1997) represent very challenging developments with the focus on low-cost production. However, the properties of such films are still behind that of epitaxial film. However, for some applications like coating of large area microwave cavities for base-station filters, HTS thick films are in use (Remilliard et al., 2001). For a review about the growth of YBCO films see Wӧrdenweber (1999). Apart from YBCO, thin films with reasonable microwave properties have been prepared from the thallium-based compounds Tl2Ba2CaCu2O8 (TcE105 K) and Tl2Ba2Ca2Cu3O10 (TcE115 K) (Klein, 1997; Wӧrdenweber, 1999; Liu et al., 2015). For the thallium-based and the more recently discovered mercury-based compounds with Ts values up to 140 K, epitaxial growth is very difficult because of the volatility of thallium and mercury, respectively. HTS films with reasonable and qualified microwave properties can be grown on wafers up to a diameter greater than 4 in; the most common sizes are 2 in and 3 in for microwave applications (Wӧrdenweber, 1999). A very important step was the preparation of double-sided coatings, which have turned out to be essential for planar microwave devices, where the ground plane needs to be superconducting in order to achieve high quality factors. Substrates for planar HTS microwave devices need to fulfill the criteria for expitaxial growth plus moderated values of the dielectric constant (ɛrr25) and a low level of dielectric losses (tan δr105). The most commonly used substrate materials are lanthanum aluminate (LaAlO3, ɛrE23), magnesium oxide (MgO, ɛrE10), and sapphire (Al2O3, ɛrE10) (see Krupka et al., 1994; Zuccaro et al., 1997). The fabrication of a planar microwave device is based on a patterning process. As a first step, masks are prepared according to the layout of the structure. A conventional photolithographic procedure based on a photoresist layer followed by chemical or ion
Superconducting Microwave Applications: Filters
3
beam etching is applied for patterning of the HTS wafers. In order to provide electrical contacts to microstrip connectors and to the housing, the HTS films are often covered with an in situ gold layer prior to patterning. The feature sizes are typically not smaller than 10 mm, but due to RF current crowding at the edges, the performance of planar microwave devices becomes quite sensitive to the quality of the patterning process. After process optimization no significant degradation of the microwave properties remains.
3
Planar HTS Resonators
Typically, the building blocks of HTS filters are planar HTS resonators (Guo et al., 2012). In general, a microwave resonator is characterized by its resonant frequency f0, its unloaded quality factor Q0 of the selected resonant mode(s), and its spectrum of spurious modes. The unloaded quality factor of a resonator is determined by the stored energy W and the dissipated power Pdiss Q0 ¼
2pf0 W Pdiss
½3
Pdiss contains loss contribution from the circuit layer and the unpatterned ground plane, dielectric losses from the substrate materials in use, and radiation losses (or metal losses from the housing). The dielectric losses are characterized by the loss tangent tan δ of the substrate material. Neglecting radiation losses, the unloaded quality factor is given by Z Z er E 2 dV om0 H 2 dV 1 RS S Z ¼ κtanδ þ ; κ ¼ Z ; G¼ Z V ½4 Q0 G E 2 dV þ er E 2 dV H 2 dA VS
S
C
with κ representing the filling factor indicating the normalized fraction of electric field energy stored in the dielectric substrate (S). Typically, κ values are slightly smaller than 1. The quantity G is a geometric factor (in O) representing the surface integral of the squared RF magnetic field over the conducting parts (C). In case of planar resonators G is roughly proportional to the substrate thickness. For conventional metals, the dielectric losses are small in comparison to metal losses. For HTS resonators, substrate losses can play a significant role. The integrals in eqn [4] with subscript ‘V’ are volume integrals over the entire volume of the resonator, i.e., substrate plus housing. Figure 2 shows typical examples of HTS planar resonators which have been used as building blocks of multipole filter structures. Planar HTS resonators are either formed by segments of quasi-TEM (transverse electromagnetic) transmission lines defining the resonances to be at frequencies where the length L equals a multiple of half a guided wavelength (Figures 2(b) and 2(c)) or lumped element resonators each composed of a discrete inductor L and capacitor C (see Figure 2(a) and Hieng et al., 2001) with its resonance at a frequency f ¼ 1/[2p(LC)1/2]. In many cases hybrids of lumped elements and microstrip lines are used, for example, folded microstrip lines disrupted by a capacitive gap (Figure 2(d); Hong et al., 1999). In order to obtain a high value of Q for microstrip and lumped element structures, the ground plane needs to be formed by a HTS film, for example, in general
Figure 2 Typical planar resonators being used as building blocks for planar HTS filters (design by Superconductor Technologies Inc.): quasilumped element (a), microstrip (b), coplanar waveguide (c), folded microstrip with integrated capacitors (d), and two-dimensional disk resonator (e). Omitting the capacitive gap in the folded microstrip design (d) leads to a ring resonator (if circular shaped), which also represents a quite commonly used microstrip resonator design.
4
Superconducting Microwave Applications: Filters
double-sided films are required in order to achieve ultimate performance. As an alternative, coplanar resonators have been used (Figure 2(c)) with some compromise on Q in comparison to microstrip lines of the same size but with the advantage of single sided coating. However, until now no high-performance multipole filters based on coplanar resonators have been built. For the highest Q and ultimate power handling capability circular two-dimensional disk resonators excited in the TM010-mode have been used (Figure 2(e)), also requiring double-sided coating (Kolesov et al., 1997). The structures shown in Figure 2 are generally not restricted to superconductors, but only here the achievable quality factors are comparable or higher than the ones of bulky cavities or dielectric resonators at room temperature. Therefore, there is strong potential in high-temperature superconductor technology for the miniaturization of high-performance microwave devices and circuits.
4
Planar Multipole Filter Topologies
The class of microwave filters which can mostly benefit from HTS technology is characterized by some common structural features (‘topologies’). Filters of this class are passive and reciprocal two-ports, where the incident power is transmitted within certain frequency intervals (passbands) and reflected within the stopbands. Rejection in the stopbands is achieved by reflection. Unavoidable dissipation causes a degradation of the filter performance. For a given amount of dissipation, the degree of degradation depends on the filter parameters. In turn, this determines whether an HTS realization is beneficial or not. In the most common filter topology all resonators are identical, possessing the same resonant frequency f0 in the uncoupled state. A structure where input and output ports are coupled via one resonator only, represent a one-pole filter with a Lorentzian shaped transmission characteristic. If losses can be neglected, the frequency bandwidth (frequency interval where the transmission factor is higher than a prescribed value) of a one-pole filter is controlled by the strength of the coupling between resonator and ports. In order to achieve a frequency response closer to the rectangular frequency response of an ideal filter, a multiple-resonant (multipole) filter structure needs to be employed. In the most common filter topology, multiple-resonant structures are realized by a set of identical resonators of unperturbed resonant frequency f0, which are mutually coupled. Mutual coupling of N resonators results in a splitting into N (in general) different frequencies. In the case that each resonator supports two orthogonal resonant modes (dual-mode resonator), N represents the number of operational modes. Each coupling path (direct connection between resonator i and j) is characterized by its coupling coefficient kij, which is related to the frequency splitting of f0 into fe and fo for the even and odd mode, respectively, by kij ¼ (fe fo)/f0. In the special case of pure adjacent resonator coupling (ki,j ¼ 0 for iaj71), a single chain between input and output port is formed. This allows one to approximate a rectangular bandpass response with transition width δf decreasing with increasing order N (see Figure 3). Different approximations for the insertion loss response are possible. The most popular is the Chebyshev response with equal-ripple response of the (reflective) passband insertion loss (Matthaei et al., 1980). The required order (number of resonators or operational modes) increases with increasing ratio between the passband width Df and the transition width δf. For a given order N the transition width δf can be further reduced by introducing transmission zeros in the stopband close to the band edge. These transmission zeros cannot be realized if the coupling topology is restricted to adjacent resonator coupling. Additional coupling between non-adjacent resonators (‘cross-couplings’) with appropriate coupling sign and strength is required. Filters with
Figure 3 Typical frequency response of a passband filter with 2 transmission zeros in the stopbands (Df ¼passband width, δf¼transition width).
Superconducting Microwave Applications: Filters
5
Figure 4 Filter topology with resonators, adjacent resonator coupling, and non-adjacent resonator coupling (cross-coupling).
cross-couplings are characterized by the ratio between the number of transmission zeros at finite frequencies and the filter order and referred to as quasi-elliptic or elliptic filters (Figure 4; Klauda et al., 2000). In analogy to spectral-analysis where frequency resolution increases with integration time, the skirt steepness (in dB MHz1) of a filter determines the minimum time duration in which the signal has to be stored in the filter structure. This time duration t can be described by means of the frequency-dependent group delay which is the frequency derivative of the transmission phase and corresponds to the delay of a narrowband (bandwidth approaching zero) pulse passing through the filter. The group delay time t allows for a simple relationship between the field energy W stored in the resonators to the incident power Pinc W ¼ tPinc
½5
Up to now, degradations of the filter response caused by losses were ignored. The in-band insertion loss Ldiss Ldiss Pin ot ¼ 10 log ¼ 10 log 1 þ Q dB Pout
½6
is increased due to the finite unloaded quality factor Q by an amount which is proportional to the group delay. The insertion loss is associated with an unwanted power reduction of in-band signals as well as with an unwanted amplitude distortion caused by the frequency dependence of t. The latter effect leads to a rounding of the insertion loss response at frequencies close to the band edge where the group delay has a maximum. Therefore, the achievable skirt steepness for a bandpass filter depends on the unloaded quality factor and on the filter topology (Klauda et al., 2000): So4 103
Q0 ξ f
½7
The dimensionless quantity ξ has a value of 0.33 for Chebyshev and 1 for elliptic filters (the values for quasi-elliptic filters are in between) (where S is measured in dB MHz1 and f in GHz).
5 5.1
Planar High-Temperature Superconducting Filters and Subsystems Filters
Since the late 1990s, tremendous progress has been achieved in the development of HTS planar filters and their integration in subsystems, mostly for base stations in mobile communication (Willemsen, 2001). For HTS planar filters the resonator types shown in Figure 2 and others have been used. The main emphasis was to develop filters for base stations with steep skirts coming as close as possible to the Q-requirements discussed in the previous section. In most cases, these are (quasi) elliptic filters with 8–17 poles or Chebyshev filters with up to 30 poles. Figure 5 shows an example of an eight-pole quasi-elliptic filter based on folded microstrip resonators similar to ‘c’ in Figure 2. In this case of monomode resonators, coupling coefficients of different signs were achieved by changing between electric and magnetic field coupling of the resonators. For a 17-pole elliptic filter at 1.8 GHz with 5% relative bandwidth (resonator Q0 ¼ 50.000 at 65 K) a steepness of skirts of 85 dB MHz1 was demonstrated (Figure 6). Such a high performance cannot be achieved with any other filter technology. In addition, high quality filters based on microstrip resonators have been developed for C-band satellite transponders. Figure 7 shows a three channel IMUX test module developed at Bosch SatCom GmbH in Germany. This test module, which is considered
6
Superconducting Microwave Applications: Filters
Figure 5 Example of an HTS-planar filter with 8 poles and quasi-elliptic characteristic (from Hong et al., 1999).
Figure 6 Measured characteristic of a HTS planar 17-pole elliptic filter (from Kolesov et al., 2000).
Figure 7 Photograph of a three-channel IMUX module based on HTS planar filters as part of a cryogenic C-band satellite transponder. The HTS filters are indicated as large black squares (from Klauda et al., 2000).
Superconducting Microwave Applications: Filters
7
Figure 8 Commercial HTS subsystem for potential use in base stations. The filters and the LNA are inside a Dewar vacuum (left side), the metal cylinder in the right part of the assembly is the compressor of the Stirling-type refrigerator (from Kolesov et al., 2000).
to be part of a space experiment, consists of three HTS quasi-elliptic eight-pole channel filters, cryogenic circulators, a cryogenic preamplifier, and a wide band HTS input filter (Klauda et al., 2000). Due to the nonlinear surface resistance of HTS films (see Section 1) power handling of HTS filters is limited. In general, one can claim that planar HTS filters with edge-parallel currents in their resonators can handle power levels in the mW range without significant intermodulation distortions. Applications to transmit circuits with typical power levels of several 10 W can only be handled by employing the edge-current free disk resonator.
5.2
Subsystems
The most important ‘enabling technology’ for applications of HTS in telecommunications is cryotechnology. Cooling by liquid nitrogen is unacceptable, because the amount of maintenance for each base station should be as small as possible. The situation for satellite communications is even more severe, because the lifetime of a geostationary satellite is at least 10 year. The most convenient way of cooling is to use Stirling-type closed-cycle refrigerators consisting of a small stainless steel compressor with helium gas pressure of a few bar and a cold finger with a displacer inside, both connected by a thin stainless steel tube. Typically, a compressor with an a.c. 50 Hz power consumption of 100–200 W with the size of one or two beer cans provides a cooling power of 3–10 W at 77 K, which is the typical amount of cooling power needed for a HTS subsystem, consisting of about three filters and one cryogenic LNA (low-noise amplifier). For the sake of filter performance the base station subsystems are operating between 60 and 70 K, and the satellite systems at 77 K because cooler efficiency is a crucial parameter with respect to system mass reduction (Klauda et al., 2000; Willemsen, 2001). Figure 8 shows a commercial system for potential use in wireless base stations (Kolesov et al., 2000). The filters are assembled inside a Dewar vacuum (left side), the metal cylinder in the right part of the assembly is the compressor of the Stirling-type refrigerator. In 2002, companies are focussing on improving the coolers with respect to lifetime (currently about 3–5 year for continuous operation) and cost reduction.
6
Tuneable and Switchable Filters
Tuneable and switchable filters are supposed to have a strong potential for future receiver front-ends (Li et al., 2014). First, for military communications systems, most flexible interference suppression is an important issue. Second, for future mobile communication systems beyond the currently installed third-generation systems, most flexible allocation of bandwidth may require high-performance reconfigurable filters (see also Section 7). In general, the figure-of-merit (FOM) of a tuneable resonator is given by FOM ¼
Df Q f
½8
with Df/f being the relative frequency tuning range and Q the unloaded quality factor of the resonator. The most commonly investigated techniques which can be used for HTS tuneable devices are based on ferroelectrics and ferrites. For the future also micromechanical switches (MEMS) are considered to be relevant for planar HTS circuits (see e.g., Rebeiz and Muldavin, 2001).
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Superconducting Microwave Applications: Filters
Figure 9 Tuneable lumped element 2-pole bandpass filter based on a SrTiO3 loaded interdigited capacitor (a) and experimental result for measured filter response (b) (from Marcilhac et al., 2001).
6.1
Ferroelectric Varactors
These are very attractive for the integration with passive HTS microwave circuits because of the agile dielectric materials which can be grown as epitaxial heterostructures with YBCO. The current efforts are concentrated on thin films of SrTiO3 (SrTiO3 does not exhibit a ferroelectric phase transition but the temperature dependence of the permittivity exhibits a Curie–Weiss law similar to ferroelectric above its Curie temperature). Thin films exhibit lower ɛr values in comparison to the bulk single crystals, but a stronger tuneability above about 60 K. Similarly, the dielectric losses at microwave frequencies are in the range of 102 (see e.g., Petrov et al., 1998) in comparison to several 104 for bulk single crystals (Vendik et al., 1998). The FOMs achieved at microwave frequencies for single varactors or tuneable resonators are in the range of about 100. Figure 9(a) shows an example of a planar HTS resonator incorporating a ferroelectric varactor based on a YBCO/SrTiO3 multilayer structure. With such resonators a tuneability by about 10% was achieved (Marcilhac et al., 2001, B Marcilhac, private communication). Such resonators can be used to construct multipole bandpass filters (Figure 9(b)).
6.2
Ferrites
These represent a very common way of frequency tuning utilizing the magnetic field and magnetization dependence of a permeability tensor. In general, the microwave properties of a ferrite biased by a d.c. magnetic field H0 in z-direction are defined by the permeability tensor which is in the lossless case (see e.g., Pozar, 1998) 3 iκ 0 m 07 5 0 m0 o0 om oom with m ¼ m0 1 þ 2 and κ ¼ m0 2 o0 o2m o0 o2m 2
m 6 ½m ¼ 4 iκ 0
½9
The angular frequencies o0 ¼ m0gH0 and os ¼ m0gMs are proportional to the external magnetic field H0 and the saturation magnetization Ms with g¼ 1.759 1011 C kg1 being the gyromagnetic ratio. This proportionality corresponds to a ratio of 2.8 MHz G1 between the value of frequency f ¼ o/2p and magnetic field. Large tuning ranges can be achieved by exploiting the ferrimagnetic resonance (o¼ o0) in a YIG sphere. However, the losses are quite high and therefore combinations with HTS are not worth considering. In addition, high magnetic fields applied during operation may result in a significant degradation of the surface resistance of the employed HTS film. One attractive possibility is to use latching devices, where the magnetization of the ferrite can be switched between the remanent magnetization values Mr and þ Mr (usually slightly lower than Ms) employing short current pulses applied through a coil. This principle has been employed successfully for the realization of planar HTS phase shifters (Oates et al., 1997). Tuneable resonators and simple Chebyshev filters with a small number of poles have been demonstrated, the FOM values are about several hundred. However, there are several drawbacks associated with ferrimagnetic tuning: (i) The growth of HTS on ceramic YIG or other ferrites is difficult because no epitaxial growth can be achieved; epitaxial growth of single crystal YIG substrates has been achieved, but the substrates are very expensive and only available in small dimensions. Therefore, the working solutions rely on flip-chip assemblies.
Superconducting Microwave Applications: Filters
9
(ii) The particular form of the m-tensor sets strong limits on possible tuning and phase shifting topologies. (iii) Experimentally, the losses below about 5 GHz increase dramatically due to ferrimagnetic resonance losses of partially magnetized segments of the ferrite material in use (Ms of YIG corresponds to 4.9 GHz). As an alternative to YIG, Ga- or Al-doped YIG with lower values of Ms have been used (Yeo and Lancaster, 2001). One of the challenges is the development and optimization of ferrites with tailored properties at cryogenic temperatures.
7
Impact of High-Temperature Superconducting Subsystems for Future Microwave Systems
The superior performance of HTS filters, namely high selectivity combined with a very low passband insertion loss can be used to enhance the performance of receiver front ends with respect to both interference resistivity as well as a reduced receiver noise figure. Receiver front-ends are analog subsystems, placed in between the antenna ports and the analog-to-digital converters (ADCs). Their function comprises pre-amplification, down-conversion and some filter functions. It is important to distinguish between the different filter functions. Channel (carrier) selection and/or separation in principle can be performed by analog filters in the microwave or the intermediate frequency (IF) section, or by software-controlled digital filters in the digital part. In 2002, analog channel selection in the IF represents the best choice. Future receivers are expected to utilize more and more digital channel selection (‘software defined radio’). Transparent transponders with signal processing exclusively in the microwave regime represent an exception from this trend. In contrast to channel selection, other filter functions need to be performed in the microwave regime. These functions are the suppression of image reception in superheterodyne receivers and the rejection of strong out-of-band interferers. The second function stems from the necessity to prevent strong interfering signals from entering the LNAs and mixers, where they would cause saturation, desensitisation, and intermodulation effects due to the nonlinear response of these active devices. Cryogenic units for base-transceiver stations (BTS) of wireless communication networks became commercially available in the late 1990s. These units comprise HTS bandpass filters followed by cryogenic LNAs, both integrated in an enclosed vacuum which incorporates the cryocooler. In order to meet the different requirements associated with frequency allocation in a first-generation analog and second- and third-generation digital systems, these systems are available for different center frequencies and bandwidths, as well as with multiple passbands and with narrowband stopbands embedded in wider passbands. The number of filterLNA chains in one cryogenic unit equals the number of antenna ports (sector antennas and diversity antennas) implemented in a one BTS. For the evaluation of system benefits offered by cryogenic front-ends, the issue of a significantly improved interference suppression due to steeper filter skirts and the issue of an improved sensitivity due to the reduced receiver noise figure should be clearly distinguished. The first feature becomes significant in the case of wireless systems which have to operate in areas with strongly interfering systems with unwanted signals at frequencies closely spaced to the edge frequencies of the desired signal. Here, the improved selectivity is transformed into a lower intermodulation noise level and hence into improving the quality of service. Alternatively, this advantage can be transformed into reduced guard-band widths and hence in an enhanced spectral efficiency and capacity. In case of spread-spectrum systems, like the third-generation W-CDMA standard, HTS stopband filters with extremely narrow bandwidths can be used to reject narrowband interferers falling into the wideband operational frequency band. The reduced receiver noise figure of cryogenic filter-LNA configurations originates from three different effects, namely the reduced noise temperature of the cooled LNA, the reduced thermal noise of the filter due to the lower physical temperature, and the reduced contribution of the amplifier noise due to the decreased passband insertion loss of the filter. Reduced receiver noise becomes important in noise-limited situations (e.g., rural areas), where it transforms into a lower number of required BTSs or an improved coverage for a fixed number of BTSs. Typically, the noise figure of a BTS with the cryogenic front end at the ground (noise figure degeneration due to lossy cable between antenna and front-end) resembles the noise figure of a conventional, but mast-mounted front-end.
References Alford, N. McN., Penn, S.J., Button, T.W., 1997. High-temperature superconducting thick films. Supercond. Sci. Technol. 10, 169–185. Essén, H., Fiolhais, M.C., 2012. Meissner effect, diamagnetism, and classical physics − A review. Am. J. Phys. 80, 164–169. Guo, J., Sun, L., Zhou, S., et al., 2012. A 12-pole K-band wideband high-temperature superconducting microstrip filter. IEEE T. Appl. Supercon. 22, 1500106. Hein, M., 1999. Tracts in Modern Physics: High-Temperature Superconductor Thin Films at Microwave Frequencies, vol. 155. New York, NY: Springer. Hieng, T.S., Huang, F., Lancaster, M.J., 2001. Highly miniature HTS microwave filters. IEEE T. Appl. Supercon. 11, 349–352. Hirsch, J., 2012. The origin of the Meissner effect in new and old superconductors. Physica Scripta 85, 035704. Hirsch, J., 2013. Kinetic energy driven superfluidity and superconductivity and the origin of the Meissner effect. Physica C: Superconductivity 493, 18–23. Hong, J.-S., Lancaster, M.J., Greed, R.B., et al., 1999. Thin film HTS passive microwave components for advanced communications systems. IEEE T. Appl. Supercon. 9, 3839–3896.
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Superconducting Microwave Applications: Filters
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