Microstrip bộ lọc cho các ứng dụng lò vi sóng RF (P7)

CHAPTER 7 Advanced Materials and Technologies High-temperature superconductors (HTS), ferroelectrics, micromachining or mi- croelectromechanical systems (MEMS), hybrid or monolithic microwave integrated circuits (MMIC), active filters, photonic bandgap (PBG) materials/structures, and low-temperature cofired ceramics (LTCC) are among recent advanced materials and technologies that have stimulated the rapid development of new microstrip and other filters. This chapter summarizes some of these important materials and tech- nologies, particularly regarding the applications to microstrip or stripline filters. 7.1 SUPERCONDUCTING FILTERS High-temperature superconductivity is at the forefront of today’s filter technology and is changing the way we design communication systems, electronic systems, medical instrumentation, and military microwave systems [1–4]. Superconducting filters play an important role in many applications, especially those for the next generation of mobile communication systems [12–17]. Most superconducting fil- ters are simply microstrip structures using HTS thin films [18–44]. For the design of HTS microstrip filters, it is essential to understand some important properties of superconductors and substrates for growing HTS films. These will be described in the following section. 7.1.1 Superconducting Materials Superconductors are materials that exhibit a zero intrinsic resistance to direct cur- rent (dc) flow when cooled below a certain temperature. The temperature at which the intrinsic resistance undergoes an abrupt change is referred to as the critical tem- 191 Microstrip Filters for RF/Microwave Applications. Jia-Sheng Hong, M. J. Lancaster Copyright © 2001 John Wiley & Sons, Inc. ISBNs: 0-471-38877-7 (Hardback); 0-471-22161-9 (Electronic) perature or transition temperature, denoted by T c . For alternating current (ac) flow, the resistance does not go to zero below T c , but increases with increasing frequency. However, at typical RF/microwave frequencies (in the cellular band, for example), the resistance of a superconductor is perhaps one thousandth of that in the best ordi- nary conductor. It is certainly low enough to make significant improvement in per- formances of RF/microwave microstrip filters. Although superconductors were first discovered in 1911, for almost 75 years af- ter the discovery, all known superconductors required a very low transition tempera- ture, say 30 Kelvin (K) or lower; this limited the applications of these early super- conductors. A revolution in the field of superconductivity occurred in 1986 with the discovery of superconductors with transition temperatures greater than 77 K, the boiling point of liquid nitrogen. These superconductors are therefore referred to as the high-temperature superconductors (HTS). The discovery of the HTS made world headlines since it made many practical applications of superconductivity pos- sible. Since then, the development of microwave applications has proceeded vary rapidly, particularly HTS microstrip filters. The growth of HTS films and the fabrication of HTS microstrip filters are com- patible with hybrid and monolithic microwave integrated circuits. Although there are many hundreds of high-temperature superconductors with varying transition temperatures, yttrium barium copper oxide (YBCO) and thallium barium calcium copper oxide (TBCCO) are by far the two most popular and commercially available HTS materials. These are listed in Table 7.1 along with their typical transition tem- peratures [5]. 7.1.2 Complex Conductivity of Superconductors Superconductivity may be explained as a consequence of paired and unpaired elec- trons travelling within the lattice of a solid. The paired electrons travel, under the in- fluence of an electric field, without resistive loss. In addition, due to the thermal en- ergy present in the solid, some of the electron pairs are split, so that some normal electrons are always present at temperatures above absolute zero. It is therefore pos- sible to model the superconductor in terms of a complex conductivity ␴ 1 – j ␴ 2 , and such a model is called the two-fluid model [1–2]. A simple equivalent circuit is depicted in Figure 7.1, which describes complex conductivity in superconductor. J denotes the total current density and J s and J n are the current densities carried by the paired and normal electrons respectively. The to- tal current in the circuit is split between the reactive inductance and the resistance, which represents dissipation. As frequency decreases, the reactance becomes lower 192 ADVANCED MATERIALS AND TECHNOLOGIES TABLE 7.1 Typical HTS materials Materials T c (K) YBa 2 Cu 3 O 7-x (YBCO) Ϸ 92 Tl 2 Ba 2 Ca 1 Cu 2 O x (TBCCO) Ϸ 105 and more of the current flows through the inductance. When the current is constant, namely at dc, this inductance completely shorts the resistance, allowing resistance- free current flow. As a consequence of the two-fluid mode, the complex conductivity may be given by ␴ = ␴ 1 – j ␴ 2 = ␴ n ΂΃ 4 – j ΄ 1 – ΂΃ 4 ΅ (7.1) where ␴ n is the normal state conductivity at T c and ␭ 0 is a constant parameter that will be explained in the next section. Note that the calculation of (7.1) is not strictly valid close to T c . 7.1.3 Penetration Depth of Superconductors Normally the approximation ␴ 2 ӷ ␴ 1 can be made for good quality superconductors provided that the temperature is not too close to the transition temperature, where more normal electrons are present. Making this approximation, an important para- meter called the penetration depth, based on the two-fluid model, is given by ␭ = (7.2a) Substituting ␴ 2 from (7.1) into (7.2a) yields ␭ = (7.2b) Thus ␭ 0 is actually the penetration depth as the temperature approaches zero Kelvin. Depending on the quality of superconductors, a typical value of ␭ 0 is about 0.2 ␮m for HTS. ␭ 0 ᎏᎏ Ί 1 ๶ – ๶ ΂ ๶ ๶ ᎏ T T c ᎏ ΃ 4 ๶ 1 ᎏ ͙ ␻ ෆ ␮ ෆ ␴ ෆ 2 ෆ T ᎏ T c 1 ᎏ ␻␮␭ 0 2 T ᎏ T c 7.1 SUPERCONDUCTING FILTERS 193 J J s J n σ 2 σ 1 Normal Current Super Current FIGURE 7.1 Simple circuit model depicting complex conductivity. The penetration depth is actually defined as a characteristic depth at the surface of the superconductor such that an incident plane wave propagating into the super- conductor is attenuated by e –1 of its initial value. It is analogous to the skin depth of normal conductors, representing a depth to which electromagnetic fields penetrate superconductors, and it defines the extent of a region near the surface of a super- conductor in which current can be induced. The penetration depth ␭ is independent of frequency, but will depend on temperature, as can be seen from (7.2b). This de- pendence is different from that of the skin depth of normal conductors. Recall that the skin depth for normal conductors is ␦ = Ί ๶ (7.3) where ␴ n is the conductivity of a normal conductor and is purely real. However, pro- vided we are in the limit where ␴ n is independent of frequency, the skin depth is a function of frequency. Another distinguishing feature of superconductors is that a dc current or field cannot penetrate fully into them. This is, of course, quite unlike normal conduc- tors, in which there is full penetration of the dc current into the material. As a mat- ter of fact, a dc current decays from the surface of superconductors into the mate- rial in a very similar way to an ac current, namely, proportional to e –z/ ␭ L , where z is the coordinate from the surface into the material and ␭ L is the London penetra- tion depth. Therefore, ␭ L is a depth where the dc current decays by an amount e –1 compared to the magnitude at the surface of superconductors. In the two-fluid model, the value of the dc superconducting penetration depth ␭ L will be the same as that of the ac penetration depth ␭ given in (7.2) for ␭ being independent of fre- quency. 7.1.4 Surface Impedance of Superconductors Another important parameter for superconducting materials is the surface imped- ance. In general, solving Maxwell’s equation for a uniform plane wave in a metal of conductivity ␴ yields a surface impedance given by Z s = = Ί ๶ (7.4) where E t and H t are the tangential electric and magnetic fields at the surface. This definition of the surface impedance is general and applicable for superconductors as well. For superconductors, replacing ␴ by ␴ 1 – j ␴ 2 gives Z s = Ί ๶ (7.5a) j ␻␮ ᎏᎏ ( ␴ 1 – j ␴ 2 ) j ␻␮ ᎏ ␴ E t ᎏ H t 2 ᎏ ␻␮␴ n 194 ADVANCED MATERIALS AND TECHNOLOGIES whose real and imaginary parts can be separated, resulting in Z s = R s + jX s = ΂ + j ΃ (7.5b) with k = ͙ ␴ ෆ 1 2 ෆ + ෆ ␴ ෆ 2 2 ෆ . Using the approximations that k Ϸ ␴ 2 and ͙1 ෆ ± ෆ ␴ ෆ 1 / ෆ ␴ ෆ 2 ෆ Ϸ 1 ± ␴ 1 /(2 ␴ 2 ) for ␴ 2 ӷ ␴ 1 , and replacing ␴ 2 with ( ␻␮␭ 2 ) –1 , we arrive at R s = and X s = ␻␮␭ (7.6) It is important to note that for the two-fluid model, provided ␴ 1 and ␭ are independent of frequency, the surface resistance R s will increase as ␻ 2 . This is of practical signif- icance for justifying the applicability of superconductors to microwave devices as compared with normal conductors, which will be discussed later. R s will depend on temperature as well. Figure 7.2 illustrates typical temperature-dependent behaviors of R s , where R 0 is a reference resistance. Also, the surface reactance in (7.6) may be expressed as X s = ␻ L, where the inductance L = ␮␭ is called the internal or kinetic in- ductance. The significance of this term lies in its temperature dependence, which will mainly account for frequency shifting of superconducting filters against temperature. For demonstration, Figure 7.3 shows a typical temperature dependence of an HTS microstrip meander, open-loop resonator, obtained experimentally, where the reso- nant frequency f 0 is normalized by the resonant frequency at 60 K. The temperature ␻ 2 ␮ 2 ␴ 1 ␭ 3 ᎏᎏ 2 ͙k ෆ – ෆ ␴ ෆ 1 ෆ + ͙k ෆ + ෆ ␴ ෆ 1 ෆ ᎏᎏᎏ k ͙k ෆ + ෆ ␴ ෆ 1 ෆ – ͙k ෆ – ෆ ␴ ෆ 1 ෆ ᎏᎏᎏ k ͙ ␻ ෆ ␮ ෆ ᎏ 2 7.1 SUPERCONDUCTING FILTERS 195 FIGURE 7.2 Temperature dependence of surface resistance of superconductor. stability of cooling systems for HTS filters can be better than 0.5 K; therefore, the fre- quency shifting would not be an issue for most applications. Films of superconducting material are the main constituents of filter applications, and it is crucial for these applications that a good understanding of the properties of these films be obtained. The surface impedance described above is actually for an in- finitely thick film; it can be modified in order to take the finite thickness of the film into account. If t is the thickness of the film, then its surface impedance is [1] Z f = R s Ά coth ΂΃ + · + jX s coth ΂΃ (7.7) where R s and X s are given by (7.6). Again ␴ 2 ӷ ␴ 1 is assumed in the derivation of the expression. The effect of the finite thickness of thin film tends to increase both the surface resistance and the surface reactance of thin film. Figure 7.4 plots the surface resistance of the thin film as a function of t/ ␭ , indicating that in order to re- duce the thin film surface resistance, the thin film thickness should be greater than three to four times the penetration depth. This is similar to the requirement for nor- mal conductor thin film microwave devices, where the conductor thickness should at least three to four times thicker than the skin depth. At this point, it is worthwhile comparing the surface resistance of HTS with that of normal conductors. For a normal conductor, the surface resistance and surface re- actance are equal and are given by R s = X s = Ί ๶ (7.8) ␻␮ ᎏ 2 ␴ n t ᎏ ␭ 1 ᎏ sinh 2 ΂ ᎏ ␭ t ᎏ ΃ t ᎏ ␭ t ᎏ ␭ 196 ADVANCED MATERIALS AND TECHNOLOGIES FIGURE 7.3 Temperature-dependent resonant frequency of a HTS microstrip resonator. Both are proportional to the square root of frequency. Because the surface resistance of a superconductor increases more rapidly (as frequency squared), there is a fre- quency at which the surface resistance of normal conductors actually becomes lower than that of superconductors. This has become known as the crossover frequency. Figure 7.5 shows the comparison of the surface resistance of YBCO at 77 K with cop- per, as a function of frequency. The typical values used to produce this plot are: ț YBCO thin film surface resistance (10 GHz and 77 K) = 0.25 m⍀ ț Copper surface resistance (10 GHz and 77 K) = 8.7 m⍀ ț Copper surface resistance (10 GHz and 300 K) = 26.1 m⍀ In this case, the crossover frequency between copper and HTS films at 77 K is about 100 GHz. It can also be seen from Figure 7.5 that at 2 GHz the surface resistance of HTS thin film at 77 K is a thousand times smaller than that of copper at 300 K. Based on the discussion on microstrip resonator quality factors in Chapter 4, we may reasonably assume that a copper microstrip resonator has a conductor quality factor Q c = 250 at 2 GHz and 300 K. Since the conductor Q is inversely proportional to the surface re- sistance, if the same microstrip resonator is made of HTS thin film, it follows imme- diately that the Q c for the HTS microstrip resonator can be larger than 250 × 10 3 . 7.1.5 Nonlinearity of Superconductors Microwave materials exhibit nonlinearity when they are subject to an extreme elec- tromagnetic field, namely, their material properties such as conductivity, permittivi- 7.1 SUPERCONDUCTING FILTERS 197 FIGURE 7.4 Surface resistance of superconducting thin films as a function of normalized thickness. ty, and permeability become dependent on the field. This is also true for HTS mate- rials. It has been known that the surface resistance of an HTS film, which is related to the conductivity as described above, will be degraded even when the RF peak magnetic field in the film is only moderately high [6–8]. In the limit when the peak magnetic field exceeds a critical value, the surface resistance rises sharply as the HTS film starts losing its superconducting properties. This critical value of the RF peak magnetic field is known as the critical field and may be denoted by H rf,c . The H rf,c may be related to a dc current density by J c = (7.9) where ␭ L is the London penetration depth, which has the same value as that of ␭ giv- en by (7.2), and the J c is called the critical current density. J c is an important parame- ter for characterization of HTS materials. It is temperature-dependent and has a typ- H rf,c ᎏ ␭ L 198 ADVANCED MATERIALS AND TECHNOLOGIES FIGURE 7.5 Comparison of the surface resistance of YBCO at 77 K with copper as a function of fre- quency. ical value of about 10 6 A/cm 2 at 77 K for a good superconductor. Note that (7.9) is valid only when the HTS film is several times thicker than the penetration depth. Nonlinearity in the surface resistance not only increases losses of HTS filters, but also causes intermodulation and harmonic generation problems. This, in gener- al, limits the power handling of HTS filters. In many applications such as in a re- ceiver, where HTS filters are operated at low powers, the nonlinear effects are either negligible or acceptable. For high-power applications of HTS filters, the power-han- dling capability of an HTS filter can, in general be increased in two ways. The first method, from the HTS material viewpoint, is to increase the critical current density J c by improving the material or to operate the filter at a lower temperature; J c will increase as the temperature is decreased. The second method, from microwave de- sign viewpoint, is to reduce the maximum current density in the filter by distribut- ing the RF/microwave current more uniformly over a larger area. High-power HTS filters handling up to more than 100 W have been demonstrated [37–44]. 7.1.6 Substrates for Superconductors Superconducting films have to be grown on some sort of substrate that must be in- ert, compatible with the growth of good quality film, and also have appropriate mi- crowave properties for the application purpose. In order to achieve good epitaxial growth, the dimensions of the crystalline lattice at the surface of the substrate should match the dimensions of the lattices of the superconductors. If this is not the case, strain can be set up in the films, producing dislocations and defects. In some cases, the substrates can react chemically, causing impurity levels to rise and the quality of the film to fall. Cracks can be caused in the film if the thermal expan- sions of the substrate and film are not appropriately matched. Some of the above problems can be overcome by the application of a buffer layer between the films and the substrates. In addition, the surface of substrates should be smooth and free from defects and twinning if possible. These cause unwanted growth and mecha- nisms that can lead to nonoptimal films. For microwave applications, it is of funda- mental importance that the substrates have a low dielectric loss tangent (tan ␦ ). If the loss tangent is not low enough, then the advantage of using a superconductor can be negated. It is also desirable in most applications that the dielectric constant, or ␧ r , of a substrate not change much with temperature, improving the temperature stability of the final applications. Whatever the dielectric constant, it must be repro- ducible and not change appreciably from batch to batch. This is very important for mass production. With all the above requirements, it is not surprising that an ideal substrate for HTS films has not been found yet. Nevertheless, a number of excellent substrates, producing high-quality films with good microwave properties, are in common use. Among these, the most widely used and commercially available substrates are lan- thanum aluminate (LaAlO 3 or LAO), magesium oxide (MgO), and sapphire (Al 2 O 3 ) [9–11]. LaAlO 3 has a higher dielectric constant than MgO and sapphire but is gen- erally twinned. Sapphire is a low loss and low cost substrate but its dielectric con- stant is not isotropic and it requires a buffer layer to grow good HTS films. MgO is, 7.1 SUPERCONDUCTING FILTERS 199 in general, a very good substrate for applications but is mechanically brittle. Table 7.2 lists some typical parameters of these substrates. For sapphire substrate, the val- ues of relative dielectric constants are given for both parallel and perpendicular to the c-axis (crystal axis) because of anisotropy. 7.1.7 HTS Microstrip Filters HTS microstrip filters are simply microstrip filters using HTS thin films instead of conventional conductor films. In general, owing to very low conductor losses, the use of HTS thin films can lead to significant improvement of microstrip filter per- formance with regard to the passband insertion loss and selectivity. This is particu- larly substantial for narrow-band filters, which play an important role in many ap- plications. Some typical high-performance HTS filters are briefly described in the following paragraphs. A 19-pole HTS microstrip bandpass filter on a 75 mm diameter wafer has been de- veloped [18]. The HTS filter has the same configuration as the pseudocombline fil- ter discussed in Chapter 5 and uses an array of 19 straight half-wavelength microstrip resonators. It was designed for the 900 MHz cellular communication band with 25 MHz bandwidth and is fabricated using double-side-coated YBCO films on a 0.5 mm thick LaAlO 3 substrate. The YBCO films are thicker than 0.4 ␮m. The filter pattern- ing is accomplished by ion beam milling. The backside YBCO film is coated with a silver/gold layer using an ion beam deposition technique at room temperature. This normal metal layer provided an electrical contact between the ground plane and the filter package. Measurement of the packaged filter at 77 K showed a dissipation loss of 0.5 dB, corresponding to an average unloaded Q-factor of 10,000. For narrow-band applications, a so-called hairpin-comb filter configuration [20] may be used, in which the hairpin resonators all have the same orientation (see Fig- ure 7.6) in order to achieve a weak coupling between adjacent resonators with a small spacing. An 11-pole HTS microstrip filter of this type on a 50 mm diameter wafer, where the 0.3 mm line width and the 1.3 mm inside spacing for each of the hairpin resonators were determined based on the effectiveness of space usage [33], has been produced. This HTS microstrip filter was developed for PCS (personal communications services) applications. It was designed to have a 10 MHz passband centered at 1.775 GHz and was fabricated using double-sided YBCO films on a 0.5 mm thick LaAlO 3 substrate. The YBCO films were about 0.3 ␮m thick. The film was patterned by conventional photolithography and the argon ion-milling method. 200 ADVANCED MATERIALS AND TECHNOLOGIES TABLE 7.2 Substrates for HTS films substrate ␧ r (typical) tan ␦ (typical) LaAlO 3 24.2 @ 77K 7.6 × 10 –6 @ 77K and 10 GHz MgO 9.6 @ 77K 5.5 × 10 –6 @ 77K and 10 GHz Sapphire 11.6 || c-axis @ 77K 1.5 × 10 –8 @ 77K and 10 GHz 9.4 Ќ c-axis @ 77K [...]... (MEMS) provide a class of new devices and components which display superior high-frequency performance and enable new system capabilities For a general definition, a MEMS is a miniature device or an array of devices combining electrical and mechanical components and fabricated with integrated circuit (IC) batch-processing techniques [75–76] There are several MEMS fabrication techniques, including surface... has no ability to effectively improve filter selectivity Therefore, it does not constitute a particularly attractive choice for achieving frequency selectivity Nevertheless, it may be of interest for miniaturizing wideband active filters using MMIC technology [92] Among the advantages of the cascade method are its design simplicity and low sensitivity of filter characteristics to variations in circuit... into drilling holes on the substrate [105] 7.6.2 PBG Microstrip Filters The above-described microstrip PBG structures themselves may be seen as lowpass or bandstop filters because of their frequency characteristics However, these PBG structures can be integrated with many microstrip filters discussed in the previous chapters to improve filter performance, such as to increase the maximum attenuation... elements would be too large at lower frequencies, say below approximately 5 GHz 7.4.2 MMIC Microstrip Filters There are advantages in filter design using established MMIC foundry layout and fabrication processes Yield for a passive MMIC filter run is close to 100% and RF performance is extremely repeatable MMIC filter performance is not comparable to standard hybrid MIC and waveguide filter technology, due... material [49] 7.2.3 Tunable Microstrip Filters There are different ways to incorporate ferroelectrics into microstrip filters to make the filters electrically tunable For example, ferroelectric thin films can be implemented into a two-layered microstrip structure, as shown in Figure 7.11 This structure has been recently investigated for developing ferroelectric tunable microstrip filters [50–52], and... microwave filter selectivity is to use active transversal and recursive filtering techniques [97–99] In a classic analog transversal filter, an incident signal is divided into a multiplicity of subcomponents that are individually amplitude-weighted and timedelayed before they are combined into a composite output signal Filter action originates from constructive and destructive interference among the subcomponents... negative resistance method 220 ADVANCED MATERIALS AND TECHNOLOGIES (a) (b) FIGURE 7.17 (a) Layout of the three-pole active microstrip bandpass filter P1 and P2 are the RF ports Bias is applied to the pins labeled D1, D2, D3, G1, G2, and G3 (b) Measured performance of the active microstrip filter with HEMTs biased on and off (Taken from [96], © 1997 IEEE.) 7.6 PHOTONIC BANDGAP (PBG) FILTERS 221 FHR10X... for the microstrip components The individual circuits are mounted on a single THERMKON carrier using silver-loaded epoxy The overall footprint of the filter is 0.652 × 1.365 inches The HEMTs were biased at a drain current of approximately 5 mA and VDS = 2.0 V The effect of the negative resistors on the filter performance is clearly displayed in Figure 7.17(b) This figure shows the measured performance... However, applying the PBG concept allows one to extend his/her horizon of imagination greatly when conceiving novel structures to control the behavior of electromagnetic waves, whether they are guided waves, surface 222 ADVANCED MATERIALS AND TECHNOLOGIES waves, or radiation waves For example, microstrip lowpass and band reject filters can be achieved by modifying the dielectric substrate and/or ground... developed for microstrip circuits [106–107] These require forming of a periodic pattern through the substrate of microstrip Obviously, many different types of such PBG structures may be created, such as square lattice with square hole, triangular lattice with square hole, and honeycomb lattice with circular or square hole [110], which possess distinct stopbands for quasi-TEM wave propagation in microstrip . 7.1.4 Surface Impedance of Superconductors Another important parameter for superconducting materials is the surface imped- ance. In general, solving Maxwell’s. conductivity ␴ yields a surface impedance given by Z s = = Ί ๶ (7.4) where E t and H t are the tangential electric and magnetic fields at the surface. This