Analytical Design and Optimization of a WR-3 Waveguide Diplexer Synthesized using Direct Coupled Resonator Cavities Project in Applied Physics, Uppsala University, January 2017 Authors: Markus Back, Rickard Viik Master Programme in Engineering Physics, Uppsala University Supervisor: Dragos Dancila Department of Engineering Sciences, Solid State Electronics, Uppsala University Abstract A WR-3 coupled waveguide resonator diplexer is designed, analytically, using the insertion loss method, and subsequently simulated and optimized in HFSS. The design features ten iris coupled resonator cavities, assembled with a power divider in a T-junction topology. The diplexer channel filters yield a 5th order Chebyshev type frequency response, centered around 265 GHz and 300 GHz, respectivley. The resulting diplexer channels have bandwidths of 13 GHz and 11.6 GHz, respectivley, and a maximum passband return loss of -6.35 dB for channel A and -6.95 dB for channel B. A usable diplexer should have a passband return loss of at most -20 dB. Further optimization or, alternatively, changing the features of the design is needed to reduce the passband ripple to a level for which the diplexer is usable in practice. Possible improvements can be made by making the channel passbands narrower or, alternatively, increasing the number of resonators in the channel filters. 1 Contents 1 Introduction 4 1.1 Introduction to Microwave Technology . .4 1.2 Project Description . .5 2 Theory 6 2.1 Waveguides & Resonance Cavities . .6 2.1.1 Waveguides . .6 2.1.2 Resonance Cavities . .8 2.2 Filter Theory . .9 2.2.1 Scattering Parameters . .9 2.2.2 Chebyshev Filter Design by the Insertion Loss Method . 10 2.2.3 Chebyshev Low-Pass Prototype . 12 2.2.4 LP Prototype to Bandpass Transformation . 13 2.2.5 Waveguide Resonator Filters . 14 2.3 Diplexers . 15 3 Method 17 3.1 Design Specifications . 17 3.2 Analytical Filter Design . 17 3.3 Extraction of Iris Opening Widths . 19 3.4 Filter Simulation & Tuning in HFSS . 20 3.5 Diplexer Simulation & Tuning in HFSS . 22 4 Results and Discussion 24 4.1 Filter Design . 24 4.1.1 Initial Design Performed with Analytical Calculations and CMS . 24 4.1.2 Optimized Design (HFSS) . 25 4.2 Diplexer Design . 27 5 Summary and Conclusions 31 2 List of abbreviations AC - Alternating Current BP - Bandpass BS - Band-stop CMS - Coupling Matrix Synthesis EHF - Extremely High Frequency EM - Electromagnetic HFSS - High Frequency Structure Simulator HP - High-Pass IL - Insertion Loss LP - Low-Pass MEMS - Micro-Electro-Mechanical Systems PEC - Perfect Electric Conductor PMC - Perfect Magnetic Conductor RF - Radio Frequency RL - Return Loss / Reflection Loss SHF - Super High Frequency TE - Transverse Electric TEM - Transverse Electromagnetic TM - Transverse Magnetic UHF - Ultra High Frequency 3 1 Introduction 1.1 Introduction to Microwave Technology Microwaves have widespread use in many fields of technology such as telecommunication [1], military and law enforcement systems [2], astronomic remote sensing [3], heating [1], medical technology [4], etc. The use of microwaves became important for military use during World War II for the purpose of high resolution radar detection of ships and airplanes [1, 4, 3]. Furthermore, many materials exhibit resonance phenomena due to interaction with EM waves in the microwave region, which also makes microwaves useful for molecular/nuclear spectroscopy for material analysis [3]. The frequency interval of electromagnetic (EM) radiation which corresponds to microwaves ranges from ca 300 MHz to 300 GHz [4]. The microwave region can be divided into the subsets Ultra High Frequency (UHF), Super High Frequency (SHF) and Extremely High Frequency (EHF), as shown in table 1. Table 1: Microwave frequency bands Frequency band Frequency (GHz) Wavelength (m) UHF 0.3 - 3 1 - 0.1 SHF 3 - 30 0.1 - 0.01 EHF 30 - 300 0.01 - 0.001 Furthermore, the frequency region of 300 GHz - 3000 GHz, contiguous to EHF, is known as sub- millimeter waves or THz waves. All of the aforementioned technological application areas of microwaves employ the use of mi- crowave filters in some way or another. The use of filters is motivated by the need to select certain frequency bands for microwave systems to operate within, while simultaneously rejecting unwanted frequencies. Much of the theory of microwave filters was developed in the 1950's by Matthaei, Young, Jones and others, which resulted in an extensive handbook containing standard methods for filter de- sign which is still relevant today [5]. There are several methods of design and synthesis of microwave filters, the most common ones including the use of microstrips, striplines or waveguides. For high power and low loss devices in the microwave region, the preferred method is to use waveguides [1]. For lower frequencies, the low loss property of waveguides comes at the prize of bulky structures with high fabrication cost, which may make other devices such as striplines or microstrips more feasible for those frequencies. An important application of microwave filters is the case where several communications devices operating on different frequency bands are required to be received on a common antenna and sub- sequently sent on along to different outputs. One way to prevent interference between the different devices is to project the signals from each device onto the antenna using a multiplexer. A multiplexer is constructed by combining several microwave filters (one for each frequency band) with a power distribution network. The multi-band signal coming from the shared antenna is inserted into the multiplexer, which splits the multi-band signal and separates it into several single-band channels. In each channel, a microwave filter allows transmission of a single frequency band, while rejecting the 4 others, thus preventing cross-talk between the different channels. A multiplexer with only two separate frequency band channels is called a diplexer. 1.2 Project Description An important reason for the suitability of high frequency microwaves or THz waves for certain appli- cations, as opposed to lower frequency waves, is that the size of microwave systems are often inversely proportional to the operating frequency. Thus, higher operating frequencies allow for more compact systems, which makes possible Micro-Electro-Mechanical Systems (MEMS)[6] such as lab-on-a-chip technology, as well as facilitate the need for smaller and lighter communication devices in e.g. air- planes, ships and spacecrafts where limitations to weight and size are of high importance. Furthermore, as technology progresses, more and more of the microwave spectrum is used up by existing technology. This pushes research into development of technological solutions, able to operate in higher frequency ranges, such as extremely high frequency microwaves and sub-millimeter waves. The larger context of this project is a collaborative effort (MEMS THz Systems (SSF)) between Uppsala University (UU), Royal Institute of Technology (KTH) and the Swedish Defence Research Agency (FOI) to develop proof-of-concept prototypes of MEMS operating in the THz frequency band of electromagnetic waves [7]. The goal of the project presented in this paper is to demonstrate the design and optimization of a diplexer operating within the frequency range of 220-325 GHz. This frequency range corresponds to EHF to THz microwaves, making hollow rectangular waveguides suitable as a basis for the design. The channel filters of the diplexer can thus be realized by a series of connected waveguide cavities (resonators), coupled to one another by small apertures (irises). The diplexer is then constructed by connecting each channel filter to a waveguide T-junction. The recommended dimensions for rectan- gular waveguides operating in this frequency range is specified by the WR-3 standard. The chosen methodology for the design of the demonstrated diplexer is based on methods found in [1, 5, 8, 9, 10]. 5 2 Theory In order to design a coupled resonator waveguide diplexer, some theoretical background study has been required. Literature has been studied to understand the nature of waveguides, and how these can be used to allow transmission of EM (electromagnetic) signals through different types of RF (Radio Fre- quency) and microwave systems [1]. Furthermore, section 2.1.2 discusses how waveguide sections with terminated ends function as electromagnetic resonance cavities, making them well suited for applica- tions in signal modulation (e.g. microwave filter technology). EM filters are an essential component of coupled resonator waveguide diplexers. Section 2.2.1 briefly discusses so called scattering parameters [11], which describe the frequency response of such filters. A useful method for designing Chebyshev type bandpass filters is described in sections 2.2.2 - 2.2.4, which can be realized by electromagnetically coupled waveguide resonance cavities [1, 12, 13]. Finally, section 2.3 presents the general purpose and configuration of a microwave diplexer [10]. 2.1 Waveguides & Resonance Cavities 2.1.1 Waveguides Waveguides are conducting structures that allow waves to propagate through them along a certain path. These structures are useful in high frequency AC electronics, where the frequency is high enough that the propagating wave nature of the alternating electromagnetic fields cannot be ignored. Differ- ent types of waveguides allow for different types of waves to propagate through them and they can consist of one continuous piece of conducting material or of several conductors put together. Waveg- uides can either be empty, or be filled with some dielectric medium. For electromagnetic waves, the modes of the waves allowed to propagate through the waveguide are dependent on the dimensions of the waveguide and of the composition of the conductors that makes up the waveguide. The dif- ferent possible modes of propagation for electromagnetic waves are TE (transverse electric; meaning that the electric field has at least one component in the transverse direction relative to the direction of propagation), TM (transverse magnetic) and TEM (transverse electromagnetic). TEM waves are supported by transmission lines and waveguides consisting of more than one conductor, e.g.