Estudio de estructuras planas innovadoras para el desarrollo de circuitos pasivos de microondas
- Autores: Armando Fernández Prieto
- Directores de la Tesis: Francisco Medina Mena (dir. tes.), Jesus Maria Martel Villagran (dir. tes.)
- Lectura: En la Universidad de Sevilla ( España ) en 2013
- Idioma: español
- Tribunal Calificador de la Tesis: Juan Fernando Martín Antolín (presid.), Rafael Rodríguez Boix (secret.), Philippe Ferrari (voc.), Eva Rajo Iglesias (voc.), Roberto Gómez Garcia (voc.)
- Materias:
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- Resumen
The termmicrowaves is used to describe the electromagnetic waves with frequencies ranging from 300 MHz to 300 GHz, which correspond to wavelengths (in free space) from 1 m to 1 mm. Electromagnetic waves with frequencies between 30 GHz and 300 GHz are called millimeter waves since their corresponding wavelengths are in the millimeter range (1-10 mm). Below the microwave frequency spectrum is the radio-frequency (RF) spectrum, whose lowest frequency limit is located at 300 KHz. At this frequency, the free space wavelength is 1 km. Most of RF and microwave applications are related to wireless networking and communication systems, but also find application in radar systems, environmental remote sensing and medical systems, among others. In many of these systems, the desired signal passing through the circuit must be separated from undesired frequency components that can contaminate the input signal and then degrade the device performance. The process of eliminating undesired signals is usually performed by means of filters. In circuit theory, a filter is an electrical two-port network that alters the amplitude and/or phase characteristics of a signal with respect to frequency. Ideally, a filter does not add new frequencies to the input signal, nor it will change the component frequencies of that signal, but it will change the relative amplitudes of the various frequency components and/or their phase relationships.
It can be admitted that filter theory began in 1915 when George A. Campbell in the United States of America and KarlWillyWagner in Germany independently invented the electric-wave filter. As a result of that, filter theory evolved along to independent lines, known in the literature as classical filter theory and modern filter theory. Classical filter theory concerns the design of passive lumped element filters using the method of imageparameters, and was developed in the 1920s by Campbell, Zobel and others. The method is relatively simple and involves the specification of passband and stopband characteristics for a simple cascade of two-port networks. The main disadvantage of this method is that it is not possible to incorporate an arbitrary frequency response into the design.
However, for more precise and accurate results, modern filter theory is much to be preferred.
Modern filter theory is based on the use of the insertion-loss method, and is more general and efficient than the classical theory. It was developed in the 1930s by Cauer, Darlington, and others, and it is divided into two distinct parts: the approximation of the filter specifications by a transfer function and the design of a network which realizes the transfer function.
There are five basic filter types: low-pass filter (low frequency signals passes without meaningful attenuation while frequencies above a certain value ¿ which is known as cutoff frequency ¿ are rejected), band-pass filter (it allows signals with frequencies comprised between two cutoff values to pass, attenuating signals at other frequencies), band-stop filter (it is the opposite of the bandpass filter), high-pass filter (it is the opposite of the low-pass filter) and all-pass or phase-shift filter (its function is to change the phase without affecting the amplitude).
Filters may be classified in several ways. For example, filters can be used to process analog signals, that is, signals which are functions of a continuous-time variable. These filters receive the name of analog filters. On the other hand, when filters are used to process digital signals, they are usually referred as digital filters. Depending on the type of elements used in their design (and fabrication), filters can be also classified into passive or active filters. In this thesis, only analog and passive filters will be considered. Lumpedelement filter design by the insertion-loss method starts with a low-pass prototype filter normalized in terms of impedance and frequency (source impedance Rs = 1 and cutoff frequency !c = 1 rad/s), which is composed of a combination of capacitors and inductors.
The values of these lumped-elements will depend on the form of the chosen transfer function (Butterworth, Chebyshev, elliptic, etc). This low-pass prototype can be frequency and impedance scaled to give high-pass, band-pass or band-stop responses.
Lumped-element design method works well at low frequencies, but at microwave/RF frequencies two important problems arise. First, inductors and capacitors are difficult to implement at microwave/RF frequencies and are available only for a limited range of values. In addition, at microwave frequencies, the distance between filter components is not negligible since the dimensions are on the order of the electrical wavelength. This means that both capacitors and inductors must be implemented by using of distributedelements such as open-circuited and short-circuited transmission lines, resonators, coupled transmission lines, etc. The process of converting lumped-elements into transmission line sections is accomplished with the help of the Richard¿s transformation. Once lumped-elements have been transformed into distributed-elements, Kuroda¿s identities may be used to physically separate filter elements by means of transmission line sections.
In the frequency range of interest, the response of the filter implemented with distributed elements must be as similar as possible to the corresponding response of the filter implemented with lumped components. At high frequencies, the distributedelements filter response will depart from the lumped-elements filter response due to the appearance of second order distributed effects.
In the past, different technologies have been used to implement microwave distributed filters (coaxial, waveguide, dielectric resonators, etc), but nowadays planar technology has gained the interest of many filter designers. Planar structures such as stripline, microstrip lines, slot-lines or coplanar waveguide are low in cost, compact in size and capable of being easily integrated with active devices to form microwave integrated circuits.
Furthermore, the operation frequency range of these circuits is very broad since several types of substrates can be used, including those of high dielectric permittivity commonly used in high-frequency applications. Among the most classical distributed filters, parallel-coupled lines filters, inter-digital filters, combline filters and hairpin filters deserve special mention. For more information about distributed filters history, design and development, we refer the interested reader to the excellent paper published in 1984 by professors Ralph Levy and Seymour Cohn. Despite its good performance, distributed filters are not suitable for applications in which high miniaturization levels are required (the filter size is on the order of the guided wavelength). Furthermore, due to the distributed characteristics of the transmission lines, these filters will suffer from the problem of spurious bands (unwanted bands located at integer multiples of the center frequency). To solve these problems, a number of resonators with a first quasi-static resonance (for this resonance the resonator dimensions are much smaller than the guided wavelength) have been developed in the last years. For these resonators, the higher order resonance frequencies will have much higher values than the first quasi-static resonance, so that the spurious bands will be far apart from the first band. These type of filters are usually referred in the literature as quasi-lumped filters. However, when compared with distributed filters, quasi-lumped filters present two main drawbacks: first, the achievable fractional bandwidth values are very limited since the coupling level between quasi-lumped resonators is very weak. In addition, the quality factor for these resonators is typically smaller than that of the distributed ones (ohmic losses in small conductor strips supporting high density currents may be very important), leading to significant power loss in the passband. This fact is specially important when the filter bandwidth is very narrow. However, this problem can be solved by using High-Temperature- Superconductors (HTS), but this entails higher costs and the limitations imposed by the use of the cryogenic coolers.
In this thesis, we intend to contribute to the development of both new distributed and quasi-lumped filters. In the second and third chapters we present two distributed filter configurations implemented in planar technology. Specifically, in chapter 2 a new parallel-coupled CPW bandpass filter for spurious band suppression is presented. In this filter, a floating conductor strip is introduced below the coupled-lines sections. In this manner, it is possible to achieve the suppression of the first spurious band while keeping the integrity of the fundamental passband. Meanwhile, in chapter 3, three new filters (two band-pass filters and one stop-band filter) based on the use of open-circuited stubs with slots in the ground plane are presented. As is well known, this type of filters requires very high characteristic impedance values for the stubs when wide bandwidth bandpass filters or narrow bandwidth bandstop filters are desired. By introducing slots in the ground plane this problem can be partially solved, relaxing in this way the margin of achievable characteristic impedances for the problematic stubs.
The second part of this thesis, which corresponds to chapter 4, is focused on the design of two differential-lines for transmitting differential-signals with strong commonmode rejection. The application of this structure to the design of quasi-lumped balanced single-band and dual-band bandpass filters is described. Differential signals usually involves a pair of traces (wires) between the transmitter and the receiver. Differential signals are sent in pairs with the same amplitude but with mutual opposite phases. One wire carries the positive signal and the other wire carries the negative signal. Since both signals are equal in amplitude but opposite in phase, there is no return signal through the ground plane (one wire is the ground of the other). Differential signaling in analog circuits has been utilized for more than 50 years. During the last decades, it has also become popular in digital circuit design after low voltage differential signaling (LVDS) became something common for high-speed digital signals systems. LVDS are widely used in advanced electronics such as laptop computers, test and measurement instruments, medical and automotive equipment. In modern high-speed digital communication systems, with the increasing clock frequencies and short edge rise/fall times, crosstalk and electromagnetic interferences (EMI) are critical problems that deserve to be treated carefully.
Ideally, differential-signals offer high immunity to EMI radiation and crosstalk when compared with single-ended signals. The main advantage of differential signaling with respect to single-ended signaling is that any introduced noise equally affects both the differential transmission lines if the two lines are tightly coupled together. Since only the difference of voltage between the lines is considered, the introduced common-mode noise can be rejected at the receiver device. However, due to manufacturing imperfections, signal unbalance will occur resulting in energy conversion from differential-mode to common-mode and vice versa, which is known as cross-mode conversion. The presence of common-mode will lead to the signal quality degradation. In this thesis, two different designs of differential-lines are presented in order to reduce common-mode transmission. The first differential pair is implemented in double-side microstrip/CPW technology. It will be shown how by etching LC resonators periodically in the ground plane, just below the differential-lines, it is possible to reject common-mode propagation over a wide frequency range while the differential signals remain unaffected. The proposed differential pair will be introduced as input/output lines of a balanced singleband bandpass filter based on electrically coupled folded stepped impedance resonators (FSIRs). The same structure will be combined with a new balanced dual-band bandpass filter based on embedded resonators. The poor common-mode performance of the original passband filters is drastically improved thanks to the use of a couple of input/ output cells without degrading the differential signal behavior. When comparing our differential-pair with other structures proposed in the literature we observe some advantages concerning bandwidth and compactness. The second pair of differential-lines is implemented in a multilayer Liquid Crystal Polymer (LCP) substrate. The use of multilayer technology provides some advantages with respect to the double-side MIC technology (for instance, it is possible to implement devices with solid ground plane, which is important for system integration). The differential pair proposed here has three metal layers. Two parallel-coupled lines are implemented in the top metal layer. A periodic array of parallel-LC resonators that are short-circuited to ground by means of via-holes is introduced in the middle layer, just below the coupled pair. It will be shown how under common-mode operation the structure produces evanescent waves in the frequency range of interest, thus avoiding common-mode propagation in the selected band. On the other hand, the differential-mode will propagate for all frequencies since the structure behaves as a conventional transmission line. As it was done with the first differentialpair, this multilayer structure is used as input line of a balanced FSIR bandpass filter to show the improvement of the common-mode performance.
Although this thesis is mainly focused on the design of microwave filters, in the last chapter we will address another topic that has gained great interest in the last years: the extraordinary transmission (ET) of electromagnetic waves. To understand the phenomenon of extraordinary transmission we must go back to 1944, when Bethe published a work in which he solved the diffraction problem of plane waves through a threedimensional aperture in a metallic screen. He found that the total power transmitted through a circular aperture perforated in a infinitely thin metallic screen is proportional to (a )4 , being a the aperture radius and the wavelength of the incident radiation. In the limit when a , only a negligible fraction of the incident power will pass through the aperture. More than forty years after the original work of Bethe, A. Roberts checked by a numerical code that the effect of including the finite size (thickness) of the metallic screen further decreases the transmission through the aperture. Bethe¿s theory seemed to explain these facts in a satisfactory manner until in 1998, T.W. Ebbesen and co-workers discovered by chance strong transmission peaks in metallic screens perforated with 2- dimensional cylindrical holes whose diameters were significantly smaller than the corresponding wavelength. This phenomenon, in apparent contradiction with Bethe¿s theory for small apertures was called extraordinary optical transmission. This discovery boosted the research on the details of the interaction of electromagnetic waves with periodic distributions of apertures or scatterers. Some members of my research group focused the analysis of this class of optical problems by means of techniques and models proceeding of the classical microwaves literature. Following this research line, in chapter 5 we present a microstrip implementation of a system exhibiting an electromagnetic response thatmimics the response of compound gratings investigated in the Optics community.
