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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)
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
192 ADVANCED MATERIALS AND TECHNOLOGIES
perature or transition temperature, denoted by Tc. For alternating current (ac) flow, the resistance does not go to zero below Tc, 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 s1 – js2, 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 Js and Jn 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
TABLE 7.1
Materials
Typical HTS materials
Tc (K)
YBa2Cu3O7-x (YBCO) < 92 Tl2Ba2Ca1Cu2Ox (TBCCO) < 105
Super Current Js
J
7.1 SUPERCONDUCTING FILTERS 193
σ2
Jn σ1 Normal Current
FIGURE 7.1 Simple circuit model depicting complex conductivity.
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
s = s1 – js2
= sn1Tc 24 – j vml0 31 – 1Tc 244 (7.1)
where sn is the normal state conductivity at Tc and l0 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 Tc.
7.1.3 Penetration Depth of Superconductors
Normally the approximation s2 @ s1 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
l = Ïwwww (7.2a)
Substituting s2 from (7.1) into (7.2a) yields l0
l = !§§§§§ (7.2b)
Thus l0 is actually the penetration depth as the temperature approaches zero Kelvin. Depending on the quality of superconductors, a typical value of l0 is about 0.2 mm for HTS.
194 ADVANCED MATERIALS AND TECHNOLOGIES
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 l 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
d = !vmsn (7.3)
where sn is the conductivity of a normal conductor and is purely real. However, pro-vided we are in the limit where sn 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/lL, where z is the coordinate from the surface into the material and lL is the London penetra-tion depth. Therefore, lL 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 lL will be the same as that of the ac penetration depth l given in (7.2) for l 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 s yields a surface impedance given by
Zs = } = !jvm (7.4)
where Et and Ht 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 s by s1 – js2 gives
jvm
s (s1 – js2)
(7.5a)
7.1 SUPERCONDUCTING FILTERS 195
whose real and imaginary parts can be separated, resulting in
Zs = Rs + jXs
= Ïwvmw 1Ïw+wwsw – Ïwk –wwsw + j Ïw–wwsw + Ïkw+wwsw 2 (7.5b)
with k = Ïwsww+wsw. Using the approximations that k < s2 and Ïw1w±wsw/sww < 1 ± s1/(2s2) for s2 @ s1, and replacing s2 with (vml2)–1, we arrive at
v2m2s1l3 s 2
and Xs = vml (7.6)
It is important to note that for the two-fluid model, provided s1 and lare independent of frequency, the surface resistance Rs will increase as v2. 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. Rs will depend on temperature as well. Figure 7.2 illustrates typical temperature-dependent behaviors of Rs, where R0 is a reference resistance. Also, the surface reactance in (7.6) may be expressed as Xs = vL, where the inductance L = mlis 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 f0 is normalized by the resonant frequency at 60 K. The temperature
FIGURE 7.2 Temperature dependence of surface resistance of superconductor.
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