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Insertion loss and unloaded quality factor
The expression showed above is utilized to calculate the Qu value of a single resonator. However, it is a matter of interest to calculate the performance of a whole passband microwave filter in terms of the dissipative characteristics of its resonators. From a circuital point of view, the resonators that integrate the filter can be modeled by the equivalent RLC circuits shown in Figure 5 [2]. Figure 5a depicts a circuit integrated by an inductance L connected in series with a capacitance C and a resistance R. In a similar way, Figure 5b details another equivalent circuit, composed by an inductance L connected in parallel with a capacitance C and a conductance G.
Planar technologies.
Planar microwave filter technologies are an advancement that arrived later than the waveguide technologies, which were developed at first. They are distinguished for its compactness, low-cost and its easy fabrication and integration with other electronic circuits [1]. On the other hand, their Qu values are relatively low, which results in high insertion loss and poor selectivity and also they are not suitable for high-power applications. Planar technologies include microstrip, stripline, coplanar and slot lines between others.
Planar technologies are based basically in a dielectric substrate and one or two metallic layers which are deposited on the up side, bottom side or both of them. The election of the dielectric substrate is based on its electric, mechanic and thermal characteristics. The metallic layers are composed of high conductivity metals such as silver, gold or copper. After, techniques as serigraphy and electrolysis are employed to carry out the metal deposition process. Finally, the structure is implemented by means of etching methods such as the lithography, subtractive and additive process and vias drilling using mechanical drills or laser depending of the substrate material [10].
Microstrip technology.
This technology consists of a metallic line placed on top of a substrate and a ground plane constituted by a metallic surface that covers the bottom side. In such structure the substrate serves as a propagation medium of electromagnetic fields. The propagation mode in the microstrip line is not purely TEM because of the difference in the εr values between the air and the substrate, which makes that the fields in the air propagate faster than the fields inside the dielectric. Figure 6 depicts the classical structure of a microstrip line as well as its field distribution.
Passband filter topologies.
In the literature it is reported an appreciable number of filter topologies with passband characteristics. They could be classified in two categories depending of their bandwidth. Middle and wideband filters, whose fractional bandwidth is between 20 and 80% and narrowband filters, which exhibit a fractional bandwidth lower than 20%. A brief description of the topologies that belongs to each group is presented as follows.
Middle and wideband filters.
This category comprises the filters whose FBW is between 20 and 80%. This type of filters is mainly utilized in telecommunications and radar applications enabled to work with high data rates. The classic topology to meet such requirements is the stubs filter, integrated with λg/4 short-circuited stubs or with λg/2 open-circuited stubs [2].
Stubs filter topology.
The stubs filter is composed by shunt stubs which are 0/4 long for the case of the short-circuited stubs filter and 0/2 for the open-circuited stubs filter, connected by 0/4 long admittance inverters, where 0 is the guided wavelength in the propagation medium at the central frequency f0. The synthesis procedure involves the calculus of the characteristic admittances of both stub lines and the admittance inverters considering the given specification, and then their respective dimensions [1].
Waveguide technology.
The waveguide technology was the base of the first reported microwave filters and continues to play a key role in the design of communication systems, particularly for satellite payloads. They are characterized for its high power handling capability and low loss due to its elevated Qu values (Qu > 10000), which enables the synthesis of filter functions with very selective responses (FBW of 2% or lower). Despite its excellent performance, their weigth and bulkiness are well-known drawbacks of this technology [1]. For these reasons, they occupy an important area inside the payload and therefore they contribute significantly to the satellite’s lunching price [28]. Waveguide filters can be classified in three categories: dielectric resonator filters, waveguide filters and cavity filters, whose characteristics are described as follows.
Dielectric resonator filters.
Dielectric resonator filters are composed by high permittivity dielectric blocks of circular or rectangular geometrical shapes and magnetic walls resulting from the permittivity difference between the dielectric and the air. The inter-resonator couplings are realized through the air and the input/output couplings are implemented by using microstrip lines or a coaxial cable. Due to the utilization of dielectrics with high permittivity values, this kind of filters are less bulky and heavy compared to metallic cavity filters, achieving at the same time high Qu values. Despite the mentioned advantages, the loss increment of the excitation systems as the operation frequency is increased and the tuning complexity are the main drawbacks of this type of filter. Figure 15 shows a filter developed in [29] based on this technology, which uses dual mode resonators in order to reduce the total footprint of the structure.
Waveguide filters.
Waveguide filters are composed by a traditional waveguide in which some metal plates are positioned conveniently to form a series of cavities coupled by irises. The coupling nature (electric or magnetic) is determined by the position of these coupling structures. The design equations for these filter technology are well known and documented [30]. An example of a rectangular waveguide filter is depicted at Figure 16 [31].
The loss level of the technology is reduced thanks to the absence of dielectric and the utilization of high conductivity metallization in the delimiting walls. For this reason, they are utilized in high frequency applications, such as RF-front ends and satellites emission chains, which require low loss, high selectivity and a wide spurious free band [32]. The disadvantages of the technology lie on its significant associated footprint, due to the reduced value of εr and the difficulty to develop complex filter functions when particular modes are used.
Cavity filters.
Cavity filters are composed by metallic cavities built inside a metal block. Their inter-resonator couplings are made through the utilization of apertures etched in the cavity walls. Theoretical equations to determine the cavities dimensions and design abacus to calculate the coupling structures between the filter elements are available in [1]. Dual mode cavities with two orthogonal polarizations at the same frequency could be employed to reduce the footprint of the filter. Then, filters of 2N order can be created with N resonators. A 45o discontinuity regarding the excitation axis, usually performed by using tuning screws or slots, is introduced to couple the dual mode polarizations. Figure 17 depicts a dual-mode cavity filter [33].
Table of contents :
GENERAL INTRODUCTION.
1. CHAPTER 1: STATE OF THE ART ON MICROWAVE FILTERS AND LTCC TECHNOLOGY. BASIC CONCEPTS ABO
1.1. UT MICROWAVE FILTERS.
1.1.1. Generalities about passband filters.
1.1.2. Performance parameters of a passband filter
1.1.3. Quality factors.
1.1.3.1. Loaded quality factor.
1.1.3.2. External quality factor.
1.1.3.3. Unloaded quality factor.
1.1.3.4. Insertion loss and unloaded quality factor
1.1.3.5. Definition of relative permittivity.
1.2. FILTER DESIGN TECHNOLOGIES.
1.2.2.1. Coplanar technology.
1.2.2.2. Stripline technology.
1.2.2.3. Multilayer technology.
1.2.3.1. Middle and wideband filters.
1.2.3.2. Narrowband filters.
1.2.3.2.1. Coupled line filters
1.2.3.2.2. Open-Loop filters
1.2.4.1. Dielectric resonator filters.
1.2.4.2. Waveguide filters.
1.2.4.3. Cavity filters.
1.2.5. Additive technology.
1.2.6. Substrate Integrated Waveguide (SIW).
1.2.6.1. LTCC technology.
1.2.6.1.1. Generalities.
1.2.6.1.2. Substrate Heraeus Heratape CT765.
1.2.6.1.3. Choice of foundry.
1.2.6.1.4. Design rules.
1.3. CONCLUSION.
2. CHAPTER 2: DESIGN AND IMPLEMENTATION OF A SIW FILTER IN HIGH K LTCC TECHNOLOGY.
2.1. INTRODUCTION
2.2. DESCRIPTION OF THE FILTER ELECTRICAL SPECIFICATION IN S BAND.
2.3. SIW FILTER DESCRIPTION.
2.3.1. Synthesis of the SIW filter in S band.
2.3.1.1. Cavity dimensioning considering the central frequency and the Qu factor.
2.3.1.2. Analysis of the relation between the Qu factor and the electrical performance of the filter.
2.3.1.3. Choice of topology.
2.3.1.4. Coupling coefficients matrix.
2.3.2. Characterization of the external quality factor 𝑸𝑬 and the inter-resonators coupling coefficients 𝑲𝒊, 𝒋.
2.3.2.1. Calculation of the external quality factor QE
2.3.2.2. Calculation of the inter-resonator coupling coefficient 𝑲𝒊, 𝒋.
2.3.2.3. Microstrip-SIW transition.
2.4. PHYSICAL IMPLEMENTATION OF THE VERTICALLY STACKED SIW FILTER.
2.4.1. Electromagnetic simulation of the initial structure.
2.4.2. Insertion of staggered metallic vias around the SIW filter structure.
2.4.3. Electromagnetic simulation of the vertically stacked SIW filter structure after the metallic vias insertion.
2.5.1. Simulation of the vertically stacked SIW filter structure after the modification of the relative permittivity value to εr=57.8.
2.5.2. Measurment of the vertically stacked SIW filter.
2.6.1. Material type dispersion on the substrate relative permittivity.
2.6.2. Technological type dispersions on the filter dimension.
2.7. MULTIPHYSICS ANALYSIS OF THE SIW FILTER CONCERNING EXTERIOR TEMPERATURE VARIATIONS.
2.8. INTRODUCTION OF AN ADJUSTMENT DEVICE FOR BIDIRECTIONAL FREQUENCY POST TUNING.
2.8.1. Adjustment principle of a SIW resonator towards high and low frequencies.
2.8.2. Insertion of the adjusting device on the vertically stacked SIW filter.
2.9. CONCLUSIONS.
3. CHAPTER 3: DESIGN AND IMPLEMENTATION OF A HIGH-K LTCC STUBS FILTER IN LTCC TECHNOLOGY.
3.1. INTRODUCTION.
3.2. SYNTHESIS OF A QUARTER WAVELENGTH STUBS FILTER IN A PLANAR CONFIGURATION IN STRIPLINE TECHNOLOGY.
3.2.1. General description.
3.2.2. Filter specifications.
3.2.3. Stubs filter synthesis in stripline technology in a planar configuration.
3.3. HIGH K LTCC MULTILAYER QUARTER WAVELENGTH STUBS FILTER IN STRIPLINE TECHNOLOGY.
3.3.1. Description of the proposed design approach.
3.3.2. Filter synthesis after the reduction of the substrate thickness associated to the stubs lines.
3.3.3. Physical implementation of the filter topology.
3.4. ELECTROMAGNETIC SIMULATION OF THE STRIPLINE STUBS FILTER STRUCTURE AFTER THE STAGGERED VIAS INSERTION.
3.4.1. Measurement of the 6th order stubs filter.
3.5. IMPLEMENTATION OF THE HIGH-K LTCC MULTILAYER STUBS FILTER IN STRIPLINE TECHNOLOGY FOR THE S BAND SPECIFICATION.
3.5.1. Measurements of the stripline stubs filter for the S band.
3.6. STUDY OF DISPERSIONS FOR THE HIGH-K LTCC STUBS FILTER IN STRIPLINE TECHNOLOGY.
3.6.1. Dispersion of material type on the substrate relative permittivity.
3.6.2. Dispersion of technological type on the dimensions of the stripline stubs filter.
3.7. MULTIPHYSICS ANALYSIS OF THE STRIPLINE STUBS FILTER CONCERNING EXTERIOR TEMPERATURE VARIATIONS.
3.8. INTRODUCTION OF AN ADJUSTMENT DEVICE FOR UNIDIRECTIONAL FREQUENCY POST TUNING.
3.8.1. Adjustment principle of a stub resonator towards low frequencies
3.8.2. Unidirectional tuning of the S band stubs filter.
3.8.3. Simulation of the S band filter with the insertion of the post tuning devices.
3.9. CONCLUSIONS.
4. CHAPTER 4: GENERAL CONCLUSION AND PERSPECTIVES.
4.1. GENERAL CONCLUSION.
4.2. PERSPECTIVES.
BIBLIOGRAPHY.
