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1

Hosking, Michael William. "Microstrip ring resonator at microwave frequencies : applications to superconducting and normal circuits." Thesis, University of Portsmouth, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.336916.

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2

Farooqui, Muhammad Fahad. "Compact circularly polarized slot-ring antenna and microstrip bandpass filter using triangular open-loop resonators." Texas A&M University, 2006. http://hdl.handle.net/1969.1/4969.

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In this thesis two different research topics are undertaken, both in the area of compact RF/microwave circuits design. The first topic involves the design of a compact circularly polarized (CP) slot-ring antenna. A study of several compact CP microstrip and slotline antennas reported in the past has been carried out. In this research, a method of reducing the size of a printed slot-ring antenna is proposed. The reduction in size is achieved by introducing meandered-slot sections in the ring. Circular polarization is achieved by introducing an asymmetry, also a meandered-slot section, and feeding the antenna at an angle of 45o from the asymmetry using a microstrip feed line. The minimum axial ratio of 0.4 dB is obtained at 2.46 GHz, which is the operating frequency of the antenna. The size of the proposed antenna is reduced by about 50% compared to a conventional CP slot-ring antenna and it displays a CP bandwidth of about 2.5%. The simulated and measured results are presented, and they are in good agreement. The small size of the antenna makes it very suitable for use in modern RF/microwave wireless systems which require compact, low cost, and high performance circuits. Moreover, its CP behavior makes it more attractive for applications such as satellite communications. The second topic in the thesis involves the design of a compact microstrip bandpass filter using triangular open-loop resonators. A new compact three-pole microstrip bandpass filter using four triangular open-loop resonators is presented. A fourth resonator is placed to provide cross-coupling in the structure which gives a better skirt rejection. The measured pass-band center frequency is 2.85 GHz. The filter demonstrates about 7% bandwidth with insertion loss of less than 1 dB in the passband, a return loss of greater than 15 dB and out-of-band rejection of greater than 30 dB. The simulated and measured results are in good agreement. The proposed filter is very attractive for use in modern wireless systems which require bandpass filters having compact size, low insertion loss, high selectivity, and good out-of-band rejection.
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3

Limaye, Aparna U. "Size reduction of microstrip antennas using left-handed materials realized by complementary split-ring resonators /." Link to online version, 2006. https://ritdml.rit.edu/dspace/handle/1850/2428.

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4

Sousa, Neto Marinaldo Pinheiro de. "Um estudo de metamaterial em antenas de microfita." Universidade Federal do Rio Grande do Norte, 2014. http://repositorio.ufrn.br:8080/jspui/handle/123456789/15247.

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Made available in DSpace on 2014-12-17T14:55:19Z (GMT). No. of bitstreams: 1 MarinaldoPSN_TESE.pdf: 2731148 bytes, checksum: 7c2caa3355d4d42f0702baf0d147bf97 (MD5) Previous issue date: 2014-04-25<br>Universidade Federal do Rio Grande do Norte<br>Metamaterials have attracted a great attention in recent years mostly due to their electromagnetic properties not found in nature. Since metamaterials began to be synthesized by the insertion of artificially manufactured inclusions in a medium specified host , it provides the researcher a broad collection of independent parameters such as the electromagnetic properties of the material host. In this work was presents an investigation of the unique properties of Split Ring Resonators and compounds metamaterials was performed. We presents a theoretical and numerical analysis , using the full-wave formalism by applying the Transverse Transmission Line - LTT method for the radiation characteristics of a rectangular microstrip antenna using metamaterial substrate, as is successfully demonstrated the practical use of these structures in antennas. We experimentally confirmed that composite metamaterial can improved the performance of the structures considered in this thesis<br>Os metamateriais tem atra?do uma grande aten??o nas ?ltimas d?cadas, principalmente devido as suas propriedades eletromagn?ticas n?o encontradas na natureza. Desde que os metamateriais passaram a ser sintetizados atrav?s da inser??o de inclus?es artificialmente fabricadas num meio hospedeiro especificado, isto propicia ao pesquisador uma larga cole??o de par?metros independentes, tais como as propriedades eletromagn?ticas do material hospedeiro. Neste trabalho foi realizada uma investiga??o das propriedades ?nicas dos Ressoadores em Anel Partido (Split Ring Ressonators - SRR) e dos metamateriais compostos. Apresentou-se uma an?lise te?rica e num?rico-computacional, utilizando o formalismo de onda completa atrav?s da aplica??o do m?todo da Linha de Transmiss?o Transversa LTT, para as caracter?sticas ressonantes de uma antena de microfita com patch retangular utilizando substrato metamaterial, assim como ? demonstrado com sucesso ? utiliza??o pr?tica dessas estruturas em antenas. Esta utiliza??o pr?tica ? confirmada experimentalmente
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5

Lai, Lian-Shing, and 賴良星. "Physical properties of YBCO microstrip ring resonator with a split gap." Thesis, 2001. http://ndltd.ncl.edu.tw/handle/17287449071313649079.

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碩士<br>國立交通大學<br>電子物理系<br>89<br>The thesis can be divided into three parts. The first is to investigate the microwave properties of high-Tc superconductor ring resonators with various split gap structures. The second part is to use the microwave data of wave impedance, from which the important physical parameters such as Q values, surface impedance, penetration depth and energy gap, have been deduced. The third part attempts to delineate the physical properties of YBCO thin films with various oxygen contents. A detailed process of fabrication of the epitaxial YBCO thin films as well as the microwave ring resonators will be described at first. Using these resonators the generation of the frequency response can be justified by the computer simulation of Ansoft software, in which a perfect conductor, instead of the superconductor, has been taken. From the experimental observation, the case of the superconducting ring resonator appears the resonate frequency as same as that in the conductor. Although both of them have the behavior of the same frequency response, it has possessed the Meissner effect for the superconductor. Incidentally their resonate frequencies are determined by their own boundary conditions. Finally a number of salient results in the microwave measurement allow us to get several important parameters, with which the basic nature of the high-Tc superconductivity in the underdoped case can be elucidated. For instances, the energy gap 2Δ0/kBTc=8±0.2 and Fermi liquid correction factor <1, can be yielded. Moreover, the reduced temperature T/Tc dependence of the superfluid density is shown to be independent of doping concentration, which reflects a fact that the Cu-O chain in the YBCO material is irrelevant in the consideration of superconductor properties, and the pairing mechanism occurs on the CuO2 planes thoroughly.
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6

Zeng, Huey-Kai, and 鄭慧愷. "Study of Microwave Properties of the YBCO Thin Film Using Microstrip Ring Resonator." Thesis, 2001. http://ndltd.ncl.edu.tw/handle/63121601204478223984.

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博士<br>國立交通大學<br>電子物理系<br>89<br>Superconducting ring resonators with or without a gap were successfully fabricated using double-side YBa2Cu3O7-δ (YBCO) films deposited on LaAlO3 (LAO) substrates. Measurement of the microwave surface impedance, Zs(T) = Rs(T) + jXs(T), allows us to determine the complex conductivity, s(T), in the ab-plane of YBCO thin films. Using results of Zs(T) and s(T) together with the modified two-fluid model, the temperature and frequency dependences of London penetration depth and quasiparticle scattering lifetime can be systematically studied by varying the oxygen contents of the same resonator structure. Some salient results found in the dissertation are listed below: I.Form the measurement of the resonance frequency and thus the phase velocity in the ring resonator the dielectric constant of the LAO substrate was estimated to be er @ 25.7 at 5 K. II.By placing a narrow gap located at symmetrical position with respect to the coupling lines in the ring resonator, we observed that original fundamental resonating modes splits into a dual-mode with different resonating frequencies. One occurs at one half and the other at three halves of the original frequency, respectively. It leads us to easily provide some behaviors of frequency dependence of several physical quantities with the same microstructure in a unique manner. Moreover, an equivalent mutual-inductance circuit model is suggested to account for the occurrence of the dual mode resonance. The validity of the model let us easily give the justification of the relation between the surface loss and frequencies, i.e., Rs µ w2. III.(a) For fully oxygenated case (d = 0.05), the resonator exhibits a quality factor Q > 104 around 15 K, and Dl(T) = l(T)-l(5K) displays a linear behavior (Dl/T = 4.8 Å/K) at the low temperature regions (T < Tc/3). With increasing d (e.g. d = 0.2, 0.4), although Dl is still linear in temperature, the slope changes with increasing oxygen deficiency. (b) Following the model suggested by Scalapiano et al., the energy gap could be derived and the value of the ratio of energy gap to the critical temperature, we found 2D(0)/kBTc, around 5.3±1.4, which is independent of the doping concentrations. (c) The function of l(T) versus the normalized temperature T/Tc exhibits a universal form. It implies a unique high-Tc mechanism in the underdoped cuprate, which is occurred in the CuO2 planes only. The values of l(5K) with various oxygen contents are 150±14 (d = 0.05), 216±16 (d = 0.2) and 282±20 nm (d = 0.4), respectively and found to be independent of frequencies. IV.The scattering rate of the low-excitation quasiparticles versus normalized temperature appears as a universal exponential form, 1/t(T) µ eaT/Tc. The relaxation time in the low temperature limit is around t @ 3.76 ´ 10-11 sec, which is 500 times more than that at the critical temperature. Then the energy due to such scattering from the uncertainty principle is found to be around 1.75 ´ 10-2 mev. V.The real part of the complex conductivity s(T) after reaches a plateau in the low temperature limit. The effect is clearly contradicted to that found by a single crystal. We prospect that it might be a lot of dislocation distributed in the ab plane for our samples thin films. Such defect of dislocation takes a great effect on the quasiparticle scattering in the low temperature limit. We also found that the residual conductivity depends upon the doping concentration of oxygen contents. VI.The current model suggested by Wen and Lee was analyzed in a quantitative manner. We noted that the Fermi-liquid correction factor, a2, predicted by the model could be obtained with the values around 0.5, which might correspond to prospect the mechanism of high-Tc in the underdoped case to be a single Boson condensation possibly.
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7

SHIE, CHING-HENG, and 謝青航. "Dual-Mode Double-Ring Resonator for Microstrip Band-Pass Filter Design and Analysis." Thesis, 2003. http://ndltd.ncl.edu.tw/handle/61123412212221939142.

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碩士<br>國防大學中正理工學院<br>電子工程研究所<br>91<br>In this thesis, the Double-Ring filter is proposed to improve the bandwidth of conventional ring filters. The possibility of the Double-Ring filter will be verified by measurements and simulations. The mode coupling techniques of the Double-Ring resonator can be classified as two types: (1) The Directive coupled-mode, (2) The Cross coupling-mode. Both of Double-Ring filter and Extended Double-Ring filter belong to the Directive coupled-mode. By the measurements and simulations the possibility of the mode coupling techniques can be verified. By this contribution the Double-Ring filter and the Extended Double-Ring filter all have the characteristic of pass-band. In the experiment design, we can fit the filter by the techniques of adjusting values, bridging capacitance and cascade-stage, and it can be served as a reference for Double-Ring filter design. From the matching techniques, the Double-Ring filter is designed and compared with Butterworth filter, Single-Ring filter and Chebyshev filter for the advantages. The measurements and the simulations are similar.
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8

蔡致遠. "Design of Microstrip Ring Resonator Bandpass Filters with a Miniaturized Area and Desirable Upper Stopband Characteristics." Thesis, 2005. http://ndltd.ncl.edu.tw/handle/84204197241453804031.

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碩士<br>國立交通大學<br>電信工程系所<br>93<br>An optimal ring resonator and a new square loop resonator are proposed for designing miniaturized dual-mode bandpass filters. In the first resonator, the center of each side of the loop resonator is tapped with a capacitive arrow-shape open stub. The whole resonator encloses four coupled compact miniaturized hairpin resonators. The slow-wave effect caused by the capacitively load can reduce the fundamental frequency of the loop resonator. As a result, this miniaturized loop resonator can be used to synthesis a miniaturized dual-mode bandpass filter. In the second resonator, the fundamental frequencies and higher order resonant harmonics of ring resonators with different numbers of impedance steps are analyzed against the length and impedance ratios of the hi-Z and low-Z segments. It is found that the optimal numbers of impedance steps and length can be obtained for a given hi-Z to low-Z impedance ratio to minimize the filter size and maximize the upper rejection bandwidth. Both the proposed bandpass filters not only have good spurious-free performances, but also achieve more than 50% size reductions, as compared with a conventional dual-mode ring bandpass filter. The measured results show a good match with the simulated responses.
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9

Lok, U.-Hou, and 陸裕豪. "Two New Microstrip Bandpass Filter Designs:Parallel-Coupled Corrugated Stages with Multispurious Suppression and Quasi-Elliptic Function Response with Quadra-Mode Coupled-Ring Resonator." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/97044625209398689486.

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碩士<br>國立交通大學<br>電信工程系所<br>95<br>Coupled-line stages are designed with corrugated periods to accurately allocate inherent transmission zeros at three leading even harmonics of design frequency, fo. The corrugation is finely trimmed so that the eigenmode phase velocities at these frequencies can be equalized. Through adjusting number of corrugation periods of a stage, frequencies of the zeros can be arbitrarily scaled up to a certain extent. In this way, a parallel-coupled line bandpass filter with a cascade of several such stages can be synthesized to be free of spurious harmonics up to at least 10fo, with aid of tapped input/output coupling scheme. The spurious harmonics from 11fo to 16fo are further suppressed by bandstop characteristics of periodic structure. The measured data of the fabricated bandpass filter show a rejection level of better than 30 dB in the upper stopband up to 18fo. Double-ring resonator with two open stubs is proposed to design quadra-mode bandpass filters. Two open stubs are horizontally attached to the inner ring. By appropriately adjusting the length or width of stubs, it is possible to control an extra zero existing in the double-ring structure. In addition, perturbation patches are introduced to inner and outer rings to split up the four poles for synthesizing a bandpass filter with high selectivity and relatively wide passband. In order to validate the proposed idea, two quadra-mode bandpass filters with fractional bandwidth of 10% and 15% are fabricated. Measured results show that the in-band insertion losses are less than 1.1dB. Simulation data are also plotted for comparison.
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10

(8120606), Zhaoyang Li. "Design and Simulation of Microwave Filters Using Non-uniform Transmission Line and Superformula." Thesis, 2019.

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In this study, a novel and systematic methodology for the design and optimization of lowpass filters (LPFs), and multiorder-bandpass filters (BPFs) are proposed. The width of the LPF signal traces consistently follow Fourier truncated series, and the thickness of the substrate as well. By studying different lengths and other physical constraints, the design meets predefined electrical requirements. Moreover, superformula is used in split ring resonators (SRRs) designs to obtain a BPF response and significant structural compactness. Non-uniform transmission lines, as well as superformula equations, are programmed in MATLAB, which is also used for analytical validations. Traces are drawn in AutoCAD. The substrate of LPF is constructed in Pro/e. Finally, the optimized layouts are imported to Ansys High Frequency Structure Simulation (HFSS) software for simulation and verification. Nonuniform LPFs are optimized over a range of 0-6 GHz with cutoff frequency 3.5 GHz. Superformula implemented multiorder-BPFs are optimized with cutoff frequency of 1.1 GHz.
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11

Chung, Wei-Chih, and 鍾崴至. "The design of the microstrip ring resonators." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/m9a8fc.

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碩士<br>國立中央大學<br>通訊工程研究所<br>94<br>Abstract In the thesis, the design of the microstrip ring resonators is discussed, and new feeding strategies are proposed. Due to a variety of resonators employed in circuit design, the feeding(or energy-coupling) strategy is always an important issue. Thus, a better coupling strategy will be applied and the size of the circuit configuration will be improved at the same time in the thesis. The full-wave electromagnetic simulator, IE3D, will be used in the design. Circuits will be realized using FR4 printed-circuit boards. The design will be validated by the comparison with experimental results.
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12

Shu, Hsin Yi, and 許心怡. "Bandpass Filter Constructed with Asymmetrical Compact Microstrip Resonators and Dual-mode Ring Resonators." Thesis, 2009. http://ndltd.ncl.edu.tw/handle/41807203892840972537.

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碩士<br>長庚大學<br>電子工程學研究所<br>97<br>In general, RF wireless signals transit in atmosphere. In order to reject unwanted radio waves or noises, a band-pass filter can be used to reject noise in stopband. Therefore, this paper presents two kinds of band-pass filter. The first one is an asymmetrical response band-pass filter with three transmission zeros, the design principle uses traditional π-network of second-order band-pass filter inductively coupled combining of capacitance to ground and coupling capacitance mechanisms to achieve the two lower bands and upper band zeros. The most important thing is that this mechanism of cross coupling capacitance does not affect the passband performance .The measured insertion loss of the passband is less than 3dB, and three transmission zeros of less than -20dB attenuation at 10GHz, 16.7GHz and 60GHz. Second type of filter is dual-mode ring resonator, which has advantages of simple structure, easy implementation, and two transmission zeros at upper and lower. In Chapter III, we selected this simple symmetrical structure with high-quality dual-mode ring resonator as a filter. Using multi-layer metal process of TSMC 0.18μm CMOS to make sandwich MIM structure as the feed and perturbation capacitor, it can easily adjust the input and output ports of the feed location, and using a smaller area to achieve sufficient coupling to match the circuit. Also, we make analysis for the perturbation impact of transmission zeros and bandwidth. Besides, the ring resonator is also combined with multi-layer metal, by changing the characteristic impedance of microstrip line to increase flexibility of circuit design to get the better pass-band and stop-band characteristics. Finally, we implement a successful operation in the 60GHz dual-mode ring bandpass filter, and meander the ring to reduce the area of 40 percent, the overall area of 0.56 × 0.73 mm2, insertion loss is less than 4dB, transmission zeros at 46GHz and 88GHz get the attenuation lower than -20dB. In Chapter IV, we use the design method shown in Chapter III to make a dual-mode dual-band bandpass filter in the pHEMT process which provided by semiconductor companies WIN. 60GHz is unlicensed band which can find applications in such as point-to-point wireless LANs and broadband internet access.77GHz is another unlicensed band for adaptive cruise control on cars. The measurement conform both of the 60GHz and 77GHz frequency bands of specification. Insertion loss of passband are less than 3dB, there is more than -30dB attenuation zeros located at 51, 70, and 91GHz. Those results fit the specification of 60 and 77 GHz systems. The total area is 0.91×0.46 mm2. Index Terms: Bandpass filter、transmission zero、dualband filter、dual-mode ring resonator
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Chen, Chi-Wei, and 陳志偉. "A Compact Size Microstrip Diplexer Design Based On Complementary Split Ring Resonators." Thesis, 2011. http://ndltd.ncl.edu.tw/handle/40090961022392355661.

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碩士<br>國立交通大學<br>電信工程研究所<br>100<br>In this thesis, we proposed miniaturization bandpass filters (BPFs) design based on complementary split ring resonators (CSRRs) with two different operating frequency. The two BPFs are operated at 2.45 GHz and 1.85 GHz, respectively. The complementary split ring resonator, which is one kind of the meta-material, since it has unique electromagnetic characteristics, therefore there are many academic literatures about CSRRs which are applied on miniaturization of antennas and microwave circuits. In the first part of this thesis, a BPF is implemented by utilizing CSRRs and microstrip line coupled interdigital-capacitors to realize necessary circuit components. The open stubs are used to improve the selectivity of the higher edge of the passband, and we proposed the equivalent circuit to explain the frequency responses which are affected by the parts of the BPF. In the last part of this thesis, we use the proposed BPF to design the compact size microstrip diplexer. By simulation and measurement results, the diplexer has good characteristic responses, such as transmission loss (1.1 dB and 1.4 dB),signal suppression (29.6 dB and 41.21 dB),and 3 dB fractional bandwidth (12.85% and 8.91%). Moreover, the diplexer occupy a small area and has the dimensions of 51 mm×29 mm about 0.42λg × 0.2λg.
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14

Leon and 李喆龍. "The technique to suppress the second harmonic of microstrip bandpass filter with Split Ring Resonators." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/97026361874382457090.

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碩士<br>樹德科技大學<br>電腦與通訊研究所<br>94<br>In the RF communicative world, the quality of wireless signals is key factor. The filters are a kind of important component application in the RF field. In this thesis, we used the physics technique “Split Ring Resonators (SRRs)” which is based on the “Dual –Mode Ring Resonator” structure application of RF filters, and suppressed the second harmonic successfully. Using the technique of Split Ring Resonators had many advantages. In this research we found the Split Ring Resonators were designed easily in many structures and didn’t change the major structure. The result of the Split Ring Resonator’s work could suppress the second harmonic in 1.0 GHz to 10.0 GHz and didn’t change the major frequency.
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15

Jhang, Syuan-Wai, and 張軒維. "Accurate Parameters Extraction of Complementary Split-Ring Resonators and Its Applications for Designing Microstrip Filters." Thesis, 2011. http://ndltd.ncl.edu.tw/handle/75556925740249605876.

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碩士<br>大葉大學<br>電機工程學系<br>99<br>This paper presents an accurate design technique for a low-pass filter with complementary split-ring resonators (CSRR).We extract the complementary split-ring resonators (CSRR) equivalent circuit component values for designing filter.The CSRR not only can significantly increase the characteristic impendance of microstrip line,but also improve stopband performance by rejecting the higher order passband.For increasing efficiency and reducing the area of circuits, we usually utilize the defected ground structure, but the conventional design did not consider the parasitic effect of stub at high frequency﹒The parasitic effect may result in significant frequency deviation.In order to improve the accuracy of the low pass filter design with CSRR, an equation to find the parasitic inductance is suggested.This inductance is used to modify the frequency deviation of low pass filter.
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Lai, Liang-Shing, and 賴良星. "Study of Physical Properties of YBCO and Ca-YBCO Thin Films Using Microstrip Ring and Line Resonators." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/34479860965227823154.

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博士<br>國立交通大學<br>電子物理系所<br>94<br>Superconducting microstrip ring and line resonators were successfully fabricated using double-side YBa2Cu3O7-δ (YBCO) and Y0.7Ca0.3Ba2Cu3O7-δ (Ca-YBCO) thin films deposited on LaAlO3 (LAO) substrates by pulsed laser deposition. By controlling the oxygen contents of the same resonator, the hole concentration p determined from the empirical relation, Tc/Tc,max=1-82.6(p-0.16)2, was controlled from the over- to the underdoped regime. The microwave surface impedance measurements, Zs(T) = Rs(T) + jXs(T), allow us to determine the complex conductivity, ��(T), in the ab-plane of YBCO and Ca-YBCO thin films. Using results of Zs(T) and ��(T) together with the modified two-fluid model, the doping and temperature dependences of London penetration depth, superfluid density and complex conductivity can be systematically studied. In particular, these experimental results can be used to test the current theoretical models of high-Tc superconductivity, especially for Lee’s model, Wen and Lee’s model, Emery and Kivelson’s model and Vishveshwara and Fisher’s model. Some salient results found in the dissertation are listed below: I. From the measurements of the temperature dependence of resonance frequency in the microstrip ring and line resonators, the absolute values of the ab-plane London penetration depth at 5K were obtained for YBCO and Ca-YBCO thin films with various hole concentrations by using Chang’s formula together with the help of THz measurements. For example, was obtained to be at optimum doping, and this result was consistent with the one obtained from single crystal measurement ( ) or thin film measurement ( ). II. In the underdoped regime, the measured superfluid density is proportional to critical temperature Tc. This relation has been revealed by the Uemura relation. However, for all doping levels (from over- to underdoped regime), the measured superfluid density is proportional to the product of critical temperature (Tc) and the d.c. conductivity at Tc. This universal relation can be explained by using Ferrell-Glover-Tinkham (FGT) sum rule. Furthermore, the doping dependence of the normalized superconducting energy gap can be obtained from the FGT sum rule. Compare to the doping dependence of the superconducting d-wave gap directly measured by scanning tunneling spectroscopy (STS), the doping dependence of is consistent with that measured by STS. This indirect evidence not only leads further support that the superconducting energy gap is of d-wave symmetry but also point out that the charge is conserved in the ab-plane of the cuprates. III. The complex conductivity �� = ��1 - j��2 extracted from experiments together with the help of some theoretical model gives the evidence that the real part of complex conductivity, ��1, and the imaginary part of it, ��2, both have thermal activation gap. This result is consistent with the prediction of Lee’s model. It thus points out that the classical thermal fluctuations play an important role on physical properties of the high temperature state of high-Tc superconducting cuprates. Also, by fitting ��2 with , it was found that a characteristic energy scale emerges. is higher than Tc, when . The phase diagram of versus hole concentration p is similar to that predicted by Emery and Kivelson’s model. Hence, we propose that would be the upper bound on the phase ordering temperature in the underdoped regime, and in the overdoped regime, is corresponding to the mean field transition temperature . IV. There are two cases for the temperature dependence of ��1 in the low temperature regime (T < 0.1 Tc). Case 1, ��1(T) reaches a plateau in the low temperature limit. Case 2, ��1(T) decreases with temperature in the low temperature limit. However, in both cases, ��1(T) contains a thermal activation gap . The meaning of the thermal activation gap in ��1(T) can be attributed to the energy barrier for quasiparticle tunneling in the weak-link structures. And also, in case 1, the cuprate is the thermal insulator in the superconducting state according to the Vishveshwara and Fisher’s model. But for case 2, the real part conductivity ��1(T) contains an extra linear-T contribution, which has been also observed for pure crystals, as reported by Hardy et al. We propose that the linear-T contribution is due to the delocalized quasiparticles free from the effects of weak links. According to Vishveshwara and Fisher, the delocalized quasiparticles would further result in the thermal metal phase in the superconducting state. Thus, for case 2, the ��1(T) results imply that there are two phases, the thermal-metal and the thermal-insulator, in the superconducting state of some samples displaying the clean limit behaviors similar to those observed in high purity single crystal. The fact reveals that the feature of is very sensitive to the degree of disorder in the cuprate samples. V. As the temperature approaching 0 K, ��1(T) has a finite residual value, which we denoted as ��1(5K). According to Lee’s model, impurity scattering, particularly in the unitary limit, produces low energy quasiparticles in a two-dimensional d-wave superconductor even with small impurity concentrations. In our thin film samples, these quasiparticles are localized because the mean free path of quasiparticles ( ) is smaller than the localization length ( ). In this condition, the conductivity ��1(T) approaches to a universal value at , where is the coherence length and is the lattice constant. Moreover, Durst and Lee proposed a theoretical model based on Lee’s model that the universal value should be corrected by the Fermi liquid correction factor ��2 and the vertex correction factor , which accounts for the charge current renormalization and anisotropic impurity potential, respectively. Based on the residual conductivity ��1(5K) obtained in our experiments, we found that the value of is about 1.5±1.0, which is consistent with that predicted by the Durst and Lee’s model. In fact, we have observed that a flattening of the temperature dependence of in the low temperature limit, which is also consistent with that predicted by Lee’s model. All of these results revealed that the quasiparticles have the tendency of being localized in a two-dimensional superconductor with small impurity concentrations or disorder. VI. The Fermi-liquid model, proposed by Wen and Lee in 1998 to describe the basic nature of low-lying excitations, was analyzed in a quantitative manner. The obtained Fermi-liquid correction factor, ��, was formed to be always smaller than one ( ) over the entire doping range (from underdoped to overdoped) and is almost independent of hole concentration p, which is consistent with that predicted by Wen and Lee’s model ( ). The results revealed that the basic nature of quasiparticles in the superconducting state can be attributed to the normal Fermi-liquid in all doping levels. VII. The imaginary part of complex conductivity ��2(T) has a thermal activation gap , which shows the thermal-averaged Josephson coupling energy of superfluid (Cooper pairs) in forming the long range order across the barriers macroscopically. VIII. A closed form of the empirical formula of the real part and the imaginary part is obtained respectively. From that, the phase diagram of several energy scales versus hole concentration p was presented. The phase diagram is very similar to the one predicted by Emery and Kivelson’s model based on the classical phase fluctuations on explaining the Cooper pair formation for high-Tc superconductors. We conjecture that the formation of superconducting state in the high-Tc superconducting thin films is owing to the phase fluctuations mechanism. The experimental results have revealed that a number of the basic natures of quasiparticles in the superconducting state can be attributed to the normal Fermi liquid in the all levels of doping. When T > Tc, the classical phase fluctuations play a key role in forming the Cooper pairs of short range order. When T �� Tc, the superconductivity with a long range order is formed by the Josephson tunneling of superfluid (Cooper pairs). In the superconducting state (T < Tc), the ��2(T) was attributed to the effect of Josephson tunneling in the weak links in our disordered samples. However, for all of the experiments in the microwave measurements till now there are two cases for ��1(T). One of them is that ��1(T) can be completely attributed to the effect of quasiparticle tunneling in the weak links. It means that the quasiparticles are localized, and ��1(T) is in thermal insulator phase in the superconducting state. Another is that ��1(T) can be partly attributed to the effect of quasiparticle tunneling through the weak links, i.e. quasiparticles are localized, and partly attributed to the effect of delocalized quasiparticles. In this case, ��1(T) indicates that the system contains both the thermal insulator and the thermal metal phases. All of the above results have led us to the conjecture that in the HTSC, there are two different energy scales which correspond to two temperatures: Tc below which coherence is established, and some higher temperature where the pairs are formed. These two scales are close to each other, in the all levels of doping. The conjecture is also to endow the two associated superconducting phases - the thermal metal and the thermal insulator – and the critical point between them.
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