Investigation of novel passive phase shifter concepts in. microscale millimetre wave applications STEFAN HAMEL

Transcription

1 Investigation of novel passive phase shifter concepts in microscale millimetre wave applications STEFAN HAMEL Master s Degree Project in Microsystem Technology Supervisor: Nutapong Somjit, KTH Stockholm, Sweden Examiner: Dr. Joachim Oberhammer, KTH Stockholm, Sweden Co-Supervisor: Prof. Dr. Helmut Schlaak, TU Darmstadt, Germany Kungliga Tekniska Högskolan, Stockholm September 2007

2 Abstract This thesis presents a new phase shifter concept working at the frequency of 110 GHz. At this frequency, it is reasonable to use a rectangular waveguide, since the existing devices, such as coplanar waveguide based phase shifters, have high losses at the very high frequency. This new type of phase shifter works on the principle of changing electromagnetic wave propagation characteristics in the waveguide with different dielectric permittivity by mechanically moveable silicon membrane. From the simulation it is represented that one stage of silicon bridge can achieve phase shift of 50, with return loss of -22 db and insertion loss of -0,10 db, in the upstage position of the dielectric slab, and return loss of -35 db and insertion loss of -0,11 db, in the downstage, respectively. To perform higher phase shift, seven stages of the silicon bridges are introduced. This provides the maximum phase shift of 350, with return loss of lower than -19 db and insertion loss of approximately -3 db. The device provides bandwidth of approximately 1.2 GHz concerning the reflection coefficient below -10 db. Investigation of Novel Phase Shifter Applications ii

3 Table of contents 1. Introduction Phase shifter Motivation Tasks 3 2. Basic theory of Rectangular Waveguides TE m0 Modes of a partially loaded waveguide Calculation and design method 5 3. Simulation of Rectangular Waveguide Phase Shifter Ansoft HFSS vs. CST Microwave Studio Standard rectangular waveguide as phase shifter Simulation of the standard rectangular waveguide Simulation of the single stage phase shifter stage phase shifter array based on the SRWG Review of the Simulation of the SRWG Phase shifter with impedance matching Basic Simulations for the impedance matched RWG Simulation of the single stage silicon bridge properties Review of the Simulation of the matched-impedance rectangular waveguide Fabrication Choice of actuation scheme Prototype of phase shifters Processing the dielectric slabs Processing the rectangular waveguide Assembling the holder Discussion and Outlook Acknowledgements Bibliography Appendix 31 Investigation of Novel Phase Shifter Applications iii

4 List of Figures Figure 1: Phased array antenna schematic...1 Figure 2: Anticollision radar principle. (a) Fixed beam, (b) Steerable beam...2 Figure 3: Partially loaded RWG...4 Figure 4: Simulation of SRWG calculated by HFSS...8 Figure 5: Cross-section of SRWG in downstage position...9 Figure 6: Cross-section of SRWG in upstage position...9 Figure 7: Scheme of variation of the length...9 Figure 8: Length of one silicon-slab in downstage position of SRWG-based phase shifter...10 Figure 9: Length of silicon-slab in details (around 405 µm)...10 Figure 10: Length of silicon-slab in details (around 2440 µm)...11 Figure 11: Length of silicon in upstage position of SRWG...11 Figure 12: Determination of width of one silicon slab in downstage for SRWG...12 Figure 13: S-parameter in upstage position of the SRWG...13 Figure 14: S-parameter in downstage position of the SRWG...13 Figure 15: S-parameter with perfect conductor-sheet in upstage position...14 Figure 16: S-parameter with a perfect conductor-sheet in downstage position...14 Figure 17: Variation of the offset in three examples. (a) Offset equals 0 µm (upstage), (b) Offset equals 413 µm, (c) Offset equals 826 µm (downstage)...14 Figure 18: Relation between S-parameter and bridge offset...15 Figure 19: Optimisation of distances between two bridges in downstage...15 Figure 20: Frequency response of an array of two bridges in downstage and 1 mm distance...16 Figure 21: Sketch of phase shifter with three stages up and four stages down...16 Figure 22: Simulation of phase shifter with 7 stage silicon bridge...17 Figure 23: Sketch of mi-rwg. (a) front side (b) cut-axis along propagation direction...18 Figure 24: Simulation of mi-rwg...19 Figure 25: Length of silicon bridge for mi-rwg in downstage position...19 Figure 26: S-parameter in downstage position of the mi-rwg...20 Figure 27: Optimisation of distances between two bridges in downstage for the mi-rwg...20 Figure 28: Micrometer screw...24 Figure 29: Micrometer screw with the first part of the clamp...24 Figure 30: Clamped seven stages...25 Figure 31: Complete setup of the prototype...25 Figure 32: The prototype with 3 stages up and 4 stages down...26 Figure 33: Rectangular waveguide in Cartesian coordinate system...b Figure 34: Simulation of array with 7 stages. All 7 slabs are in upstage position... I Figure 35: Simulation of array with 7 stages. 6 upstage / 1 downstage...j Figure 36: Simulation of array with 7 stages. 5 upstage / 2 downstage...k Figure 37: Simulation of array with 7 stages. 4 upstage / 3 downstage... L Figure 38: Simulation of array with 7 stages. 3 upstage / 4 downstage... M Figure 39: Simulation of array with 7 stages. 2 upstage / 5 downstage...n Figure 40: Simulation of array with 7 stages. 1 upstage / 6 downstage...o Figure 41: Simulation of array with 7 stages. All 7 slabs are in downstage position... P Figure 42: Holder part 1...Q Figure 43: Holder part 2 distance = 0 mm...r Figure 44: Holder part 2 distance = 1 mm... S Investigation of Novel Phase Shifter Applications iv

5 List of Charts Table 1: Comparison of existing phase shifter applications...3 Table 2: Summary of results of SRWG...6 Table 3: Comparison between Ansoft HFSS and CST Microwave Studio...7 Table 4: S-parameter of the SRWG at 110 GHz...8 Table 5: Comparison between the two promising lengths (HFSS)...12 Table 6: Comparison between added conductor layer and pure silicon...14 Table 7: 7 stage phase shifter array reflection, transmission and bandwidth...17 Table 8: Comparison between one stage in upstage and downstage of mi-rwg (HFSS)...20 Table 9: Different possible actuation schemes...22 Table of Abbreviations Abbreviation CMOS CPW FDTD FEM FET FIT IC KOH MEMS mi-rwg PEC PIN-Diode RWG SRWG TE TM VNA WLAN Meaning Complementary Metal Oxide Semiconductor Coplanar Waveguide Finite-Difference Time Domain Finite-Element Method Field-effect transistor Finite-Integration Technique Integrated Circuit Potassium Hydroxide Micro-Electro-Mechanical System Matched Impedance Rectangular Waveguide Perfect Electric Conductor Positive Intrinsic Negative-Diode Rectangular Waveguide Standard Rectangular Waveguide Transverse Electric Transverse Magnetic Vector Network Analyser Wireless Local Area Network Table of Symbols Fundamental constants Quantity Value Unit Denotation c 0 2, ms -1 Speed of light µ 0 4π 10-7 VsA -1 m -1 Permeability constant ε 0 8, AsV -1 m -1 Dielectric constant Investigation of Novel Phase Shifter Applications v

6 Symbols Quantity Unit Denotation a m inner diameter of the rectangular waveguide (height) B T magnetic flux density b m inner diameter of the rectangular waveguide (width) b* m inner diameter of the matched-impedance RWG (width) f Hz frequency / design frequency f cmn Hz cut-off frequency of the mn th mode D Cm -2 electric displacement field E Vm -1 electric field Ex/y/z Vm -1 electric field in x/y/z-direction H Am -1 magnetic field H x/y/z Am -1 magnetic field in x/y/z-direction J Am -2 free current density j - imaginary unit k m -1 wavenumber / propagation constant k c m -1 cut-off wavenumber / propagation constant l m length of the rectangular waveguide m - m th mode of the propagating wave n - n th mode of the propagating wave S 11 db reflection coefficient S 21 db transmission coefficient Si length m length of one silicon bridge v p ms -1 phase velocity Z 0 Ω line impedance Z wave Ω wave impedance α Np m -1 attenuation constant β rad m -1 phase constant δ M skin depth η Ω intrinsic impedance λ 0 m wavelength λ 10 m cut-off wavelength of the first mode λ c m cut-off wavelength λ g m guided wavelength in the RWG λ L m cut-off wavelength of the RWG λ Si m wavelength in the silicon-slab ρ Cm -3 free electric charge density σ Au Sm -1 conductivity of gold x m -1 curl operator m -1 divergence operator Investigation of Novel Phase Shifter Applications vi

7 Chapter 1: Introduction 1. Introduction This chapter gives a brief introduction into the phase shifter technologies, its applications and ways of how they are realised nowadays. Then assignments of this thesis are presented. To classify RF MEMS components, one can distinguish between active and passive components [1, 2]. Active components provide power gain in an electric circuit; passive components do not show this behaviour and extract energy from the circuit. Variable capacitors are typically used as active components, whereas transmission lines, filters, couplers, switches and tuners are most often in passive devices [2]. Active components: Passive components: Variable capacitors Transmission lines Filters Couplers Switches Tuners Still, one can also find active filters and transmission lines. In this thesis a digital tuneable phase shifter device is designed. This type represents passive transmission lines. 1.1 Phase shifters Phase shifter applications are commonly used in transport telematics and in wireless communication e.g. short-length high-speed communication links and automotive radar. In both cases directional-beams are formed by phased array antenna systems where phase shifter is one of the important components: Figure 1: Phased array antenna schematic Figure 1 shows that different scan directions can be achieved by varying appropriate phase shifts. Nowadays, phase shifter used for automotive radar system shown in Figure 2 work at 24 GHz and can be realised by coplanar waveguides (CPW) or microstrip transmission line technologies [3-7]. Although they are easy to implement and have very low profile, they also have high losses at the very high frequency. Investigation of Novel Phase Shifter Applications 1

8 Chapter 1: Introduction Figure 2: Anticollision radar principle. (a) Fixed beam, (b) Steerable beam (1) 1.2 Motivation At high frequency it is possible to design a phase shifter system with rectangular waveguides (RWG), because CPW- and microstrip phase shifter systems have very high loss and RWG is small enough to be implemented on integrated circuits (IC). The other interesting characteristic is the possibility to have larger influence of the electromagnetic field propagating along the transmission line. As an example, using CPW-based phase shifter only a part of electromagnetic field can be disturbed by MEMS-structures, because the other part of the field also propagates in the substrate, the influence of the MEMS-structure is normally low. By using RWG-based phase shifter, the dielectric influences the complete field, since it completely propagates inside the RWG. This new type of phase shifter works on the principle of changing electromagnetic wave propagation characteristics in the waveguide with different effective permittivity by mechanically moveable silicon membrane. Table 1 compares existing phase shifter technologies to each other. (1) Example based on [8] F. Schäfer, F. Gallée, G.Landrac, and M. Ney, "Optimum Reflector Shapes for Anticollision Radar at 76 GHz," Microwave opt Technol Lett, vol. 24, pp , Investigation of Novel Phase Shifter Applications 2

9 Chapter 1: Introduction Table 1: Comparison of existing, passive phase shifter applications Reference [3] [4] [5] [6] [7] Type PIN FET CPW microstrip GaAs Frequency [GHz] Return Loss better than Average Insertion Loss -25 db -18 db -25 db -17 db -15 db 3.8 db 0.9 db 0.5 db 0.5 db 4.2 db Bandwidth (2) 15 GHz 3 GHz 25 GHz 5 GHz n.a. Chip Size (WxL) [mm] Impedance Transmiss. Line Possible phase shift 1.8 x x x x 0.8 n.a. n.a. < 50 Ω 62 Ω 50 Ω 74 Ω n.a Phase increment n.a. 4 bit bit (90 or 180 ) bit / 90 each continuous (3) 1.3 Tasks Aim of this thesis is to design, fabricate and evaluate a novel phase shifter based on a RWG with moveable dielectric slab. The geometries of waveguide and dielectric are calculated and verified by simulations. The simulation programs used in this thesis are Ansoft HFSS (4), an FEM- and frequency domain based simulator, and CST Microwave Studio (5), an FIT/FDTD- and time domain based simulator. Once the design is complete the fabrication of the waveguide with the dielectric layers is selected as well as an appropriate actuation scheme for moving the dielectric bridges. The phase shifter is designed to work at the frequency of 110 GHz. For evaluation, prove of this concept is done by using standard, WR-06-type RWG [1, p. 706]. Silicon is used as the tuneable dielectric bridge coated with gold layer. (2) At the frequency band. Return loss better than -10 db (3) Using 50 Schottky-diodes, phase shift provided by change of voltage bias (4) (5) Investigation of Novel Phase Shifter Applications 3

10 Chapter 2: Basic theory of Rectangular Waveguides 2. Basic theory of Rectangular Waveguides In this chapter the theory of partially loaded rectangular waveguides and its calculations will be presented. Important parameters, such as the wave number, phase shift or reflection and transmission coefficient, will be defined. Then the theoretical behaviour of waves in a siliconloaded waveguide is derived. Finally the geometries of the rectangular waveguide (RWG) are calculated [1]. 2.1 TE m0 Modes of a partially loaded waveguide The basic theory behind electromagnetic wave propagation and the rectangular waveguides is given in Appendix A. This section will directly derive the behaviour in partially loaded RWGs. As long as the RWG will only be partially loaded with a dielectric, some more boundary conditions than in the unloaded case can be introduced. Solutions for a partially loaded RWG have already been presented and can be adopted for our problem [1, 9, 10]. Since the RWG is twice bigger than high a vertically loaded RWG is suitable, due to the requirements of low displacement. Figure 3: Partially loaded RWG Figure 3 shows a partially loaded RWG in vertical direction, with the inner geometries a and b. The RWG is filled with a dielectric component, whose relative dielectric coefficient must differ from that from air k = 0 2 a h z, for 0 y t, (1) y 2 y k d h z = 0, for t y b, (2) Where k a and k d are the cut-off wavenumbers for the air-filled and the dielectric region, respectively. So, the propagation constant β can be defined as a β = k k, for 0 y t, (3) 2 2 rk0 kd β = ε, for t y b, (4) Investigation of Novel Phase Shifter Applications 4

11 Chapter 2: Basic theory of Rectangular Waveguides The resulting differential equation can be solved by double integration, which introduces the four integration constants A, B, C and D. The result can be described with respect to ensure phase matching of the fields of both regions at the interface (y = t). Acos( ka y) + B sin( ka y), for 0 y t, hz = (5) C cos( kd ( b y) ) + D sin( kd ( b y) ), for t y b, From the electromagnetic theory it is known that there is no E-component into the propagation direction for TE-modes and that the x-component of the H equals zero. This is due to the abbreviation for solving the field in Cartesian coordinates (Appendix A, (23)). The boundary value problem at the point t for the solution of h z gives an infinite number of results, due to an unlimited number of modes. Still, every solution consists of a tangential component, which introduces extreme values for different offsets of the dielectric. kd tan ( kat) + ka tan[ kd ( b t) ] = 0 (6) 2.2 Calculation and design method As mentioned, the required operating frequency is 110 GHz; therefore, a waveguide with cut-off frequency of 90 GHz is sufficient for this purpose. To calculate the diameters of the waveguide one can take advantage of the following assumptions (in linear, homogeneous material). To give a rough estimation of optimised lengths for one silicon bridge and the distance between two bridges, the wavelengths in each material are interested and thus investigated. Assuming free and linear space: - Free-space wavelength: 8 1 c ms λ 0 = = = mm (7) f 110 GHz 10 - Wavelength in silicon: 8 1 c ms λ Si = = = mm (8) f ε 110 GHz 11,9 10 r Table 2 gives results for the standard rectangular waveguide (SRWG) filled with linear homogeneous material, such as air, based on [1]. The inner geometries a and b of the RWG are calculated. The width a equals to mm and the width b to mm. The derived parameters, shown in Table 2 and Appendix A, represent existing waveguides designed for D-Band-applications, working at 110 to 170 GHz. The propagating E-field must have nodal points at conducting walls. Thus at least half of the wavelength must fit in the transversal direction. To maximise the transmission in silicon one should choose a length for the silicon of approximately Si Si length λ = 0, or its multiples. Table 2 shows the impedance of the SRWG to be 667 Ω. This stand-alone phase shifter can prove the principle, but is not suitable to implement it to work on chip, since other components of the circuit require system impedance of 50 Ω. To match this requirement the height b must be decreased to match 50 Ω. The height b will be calculated in the following sections, based on (9). mm Investigation of Novel Phase Shifter Applications 5

12 Chapter 2: Basic theory of Rectangular Waveguides Z wave kη λ! G 2b = = 377Ω 50Ω β λ0 a (9) Table 2: Summary of results of SRWG Quantity TE mn Mode TE 10 Mode (Air, 110 GHz) a µε 2 fc mm b η a 2 µ ε mm Ω k ω µε m k mπ nπ c a + b m -1 2 β 2 k c k m -1 λ c λ g λ mn v p Z wave δ (6) m a 2π kc 2π β n + b ω β kη β 2 ωµ 0 σ Au mm mm mm 531 ms Ω 0,237 µm (6) Assuming gold walls Investigation of Novel Phase Shifter Applications 6

13 Chapter 3: Simulation of Rectangular Waveguide Phase Shifter 3. Simulation of Rectangular Waveguide Phase Shifter This chapter presents the setup and results of the designed phase shifter. First, the two simulation programs, Ansoft HFSS and CST Microwave Studio, are described. Then phase shifter based on standard rectangular waveguide (SRWG) is designed and implemented (see also Chapter 4: Fabrication). The results of CPW-based phase shifter are also compared in this chapter. Since the SRWG shows a high wave impedance of 667 Ω, it is not suitable to use this device in the circuit with the impedance of 50 Ω required. Finally, a matched impedance rectangular waveguide (mi-rwg) is designed and optimised. It shows special geometries, which suite the restrain of impedance close to 50 Ω. This device will not be fabricated nor evaluated in this thesis, since prove can be performed by the SRWG-based phase shifter. The setups for the simulations are presented in Appendix C. 3.1 Ansoft HFSS vs. CST Microwave Studio The FEM-based Ansoft High Frequency Structure Simulator (HFSS) solves the E-field in frequency-domain; this means HFSS solves the E-field as a function of frequency. The other parameters of interest have to be computed. Using the Maxwell s equations, the program calculates the H-field indirectly from the electric field. From these two values, the other parameters, such as radiation, are estimated. The time-domain parameters are obtained through the Inverse Fourier Transformation. HFSS uses a frequency stepping algorithm, which solves the E-field for one certain frequency at a time with a frequency sweep function. The FIT/FDTD-based CST Microwave Studio solves the E-field in time-domain. This transient analysis computes the E-field as a function of time directly. The magnetic field can then be obtained through the Maxwell s equations and solved as a function of time as well. As in HFSS, CST Microwave Studio will then compute the related parameters. The frequency-domain parameters are calculated through the Fourier Transformation. Since CST Microwave Studio uses time step algorithm only one time step is computed at a time. Table 3 gives a brief overview of the two programs, related to this thesis. Table 3: Comparison between Ansoft HFSS and CST Microwave Studio Ansoft HFSS CST Microwave Studio algorithm based on FEM FIT / FDTD E-field frequency-domain (direct) time-domain (direct) H-field computed (indirect) computed (indirect) frequency-domain parameters directly solved Fourier Transformation time-domain parameters Inverse Fourier Transform. directly solved step algorithm frequency time Both frequency and time domain solvers give restrains on the simulation setup. In HFSS narrow band simulation is faster than wide band, since the frequency sweep has to simulate less frequency points. In CST Microwavestudio wide band analysis are performed faster than narrow band, because of the Fast Fourier Transform, which gives very narrow pulses. Investigation of Novel Phase Shifter Applications 7

14 Chapter 3: Simulation of Rectangular Waveguide Phase Shifter 3.2 Standard rectangular waveguide as phase shifter To design a phase shifter based on a SRWG working at 110 GHz, D-Band, is chosen as a required frequency band (Appendix B). The calculation method and parameter for the SRWG is found from the previous chapter Simulation of the standard rectangular waveguide An approximation of the geometries and characteristics of the SRWG can be extracted from Table 2. The first simulation roughly confirms the calculated values, especially the inner geometry of the SRWG which is 1651 x 826 µm. The important characteristics, such as the cutoff frequency which is at 90 GHz, are confirmed. Figure 4 shows the simulation results, performed by CST Microwave Studio in which S(1)11 is the return loss and S(1)21 the insertion loss of the first mode and S(2)11, S(2)21 of the second mode respectively: Figure 4: Simulation of SRWG calculated by HFSS The graph shows that this type of SRWG has a cut-off frequency of 90 GHz and good transmission coefficients for the first mode at the desired frequency range (Table 4). Table 4: S-parameter of the SRWG at 110 GHz S-Parameter Value [db] S(1)11 Reflection coefficient of the first mode S(1)21 Transmission coefficient of the first mode S(2)11 Reflection coefficient of the second mode S(2)21 Transmission coefficient of the second mode Simulation of the single stage phase shifter The desired waveguide has a width of mm and a height of mm. The calculated length of one silicon stage and the distance of two bridges will be shown in this step. Then the reflection coefficient S 11, transmission coefficient S 22 and the phaseshift φ of one stage can be represented. Investigation of Novel Phase Shifter Applications 8

15 Chapter 3: Simulation of Rectangular Waveguide Phase Shifter The following simulations are performed in downstage (Figure 5) or upstage of the dielectric slab (Figure 6). Figure 5: Cross-section of SRWG in downstage position Figure 6: Cross-section of SRWG in upstage position The optimisation of the length l of the silicon bridge is performed in the downstage position of the silicon slab, where the dielectric fully fills the SRWG (Figure 7). The length, l, also corresponds to the length of the metallic cover and the hole in the RWG, where the dielectric will be inserted. From Figure 7 it can be seen that the small gap is introduced between the dielectric slab including metallic cover and the RWG. This is to take losses due to surface roughness and uncertainties at the manufacturing step into account. Ideally, no gap between the dielectric and RWG occurs, but this will not be possible in reality, since the friction might destroy the device s contacts. The gap is introduced with 50 µm on each side and respected in all following simulations. This causes also that the results will never reach points of complete lossless, but reproduces the simulation results in the more reliable way. Figure 7: Scheme of variation of the length Figure 8 shows that in the downstage position of the dielectric slab, the S-parameter for the return loss S 11 and insertion loss S 21 have periodic characteristics. Investigation of Novel Phase Shifter Applications 9

16 Chapter 3: Simulation of Rectangular Waveguide Phase Shifter Figure 8: Length of one silicon-slab in downstage position of SRWG-based phase shifter The simulation shows that in downstage of the dielectric bridge the return loss is minimised at a length of silicon of 405 µm and 2440 µm, respectively. Equation (8) shows that the wavelength λ Si in silicon at 110 GHz is approximately 790 µm. So the value of 405 µm or its multiples like 2440 µm approximately correspond to half of the wavelength in the dielectric. For the length of 405 µm, the return loss from the simulation is db and for 2440 µm - 35 db. Both interesting lengths are simulated in more detail. Figure 9: Length of silicon-slab in details (around 405 µm) Investigation of Novel Phase Shifter Applications 10

17 Chapter 3: Simulation of Rectangular Waveguide Phase Shifter Figure 10: Length of silicon-slab in details (around 2440 µm) In the same way the silicon-length in upstage position must be optimised. Figure 11: Length of silicon in upstage position of SRWG This simulation does not give such clear results as the one performed for the downstage position, where the periodic characteristic allows optimisations of the length. For lengths around 400 µm and between approximately 2300 to 2800 µm the return loss S 11 is below -15 db and the insertion loss S 21 close to 0 db. To provide best possible performance, the two lengths minimising the return loss S 11 have to show also good behaviour in the upstage of the bridge. Table 5 compares the simulated values for S 11 and S 21 in upstage and downstage of the dielectric slab. Investigation of Novel Phase Shifter Applications 11

18 Chapter 3: Simulation of Rectangular Waveguide Phase Shifter Table 5: Comparison between the two promising lengths (HFSS) upstage downstage Si length [µm] S 11 [db] S 21 [db] S 11 [db] S 21 [db] φ In upstage of the dielectric, the return loss is much lower for the shorter length of the dielectric, whereas in downstage the longer dielectric has a lower return loss. In both positions of the dielectric the 2440 µm long dielectric shows better performance, but these does not vary much. The significant criterion to choose 2440 µm as the length of the silicon is the higher possible phase shift. The tolerances for the fabrication are much higher for a length of 2440 µm. Furthermore, the miniaturise ability for a prototype is not postulated. One can chose a length of 2440 µm, without harming any restrains into this direction. From the electromagnetic theory for RWG we know that the maximum E-field arises in the middle of the RWG for TE 10 -mode. A smaller dielectric concentrated in the middle of the SRWG introduces more disturbance, reflection and higher loss consequently. This will be verified by the simulation presented in Figure 12: Figure 12: Determination of width of one silicon slab in downstage for SRWG The silicon slab is always centred in the middle of the RWG. As assumed, the wider the siliconslab is the better the transmission line works, in terms of loss characteristics. A fully loaded SRWG gives the following results for a frequency sweep in upstage (Figure 13) and downstage position (Figure 14) of the dielectric slab. The distance from in- and outlet from the wave ports to the dielectric is 1 mm (this value will later be verified as being the optimum distance between a wave port and the dielectric bridge). Investigation of Novel Phase Shifter Applications 12

19 Chapter 3: Simulation of Rectangular Waveguide Phase Shifter Figure 13: S-parameter in upstage position of the SRWG Figure 14: S-parameter in downstage position of the SRWG Compared to an unmodified RWG, the top side of the waveguide is missing, where the dielectric slabs are inserted. In the upstage position of the dielectric bridge, losses occur because of the field penetrating the dielectric block from the bottom side. The field then can be strayed onto the outside of the RWG. An approach is tested to decrease these effects. A 25-µm thick layer of perfect conductivity is applied onto the bottom side of the dielectric slab. The consideration has to be drawn between an increase of the disturbance, which leads to higher loss and reflection, and better performance of the SRWG with the dielectric in upstage position. In this case a conducting wall suppresses radiation through the dielectric layer. The behaviour of the system in up- and downstage are simulated. Investigation of Novel Phase Shifter Applications 13

20 Chapter 3: Simulation of Rectangular Waveguide Phase Shifter Figure 15: S-parameter with perfect conductor-sheet in upstage position Figure 16: S-parameter with a perfect conductor-sheet in downstage position Table 6: Comparison between added conductor layer and pure silicon upstage downstage S11 [db] S21 [db] S11 [db] S21 [db] Without PEC-layer With PEC- layer One can see that the perfect conductance layer will not upgrade the behaviour. It even worsens the return loss in the downstage position dramatically. This approach will be discarded. The third variable of the dielectric phase shifter, the offset of one bridge, is analysed. The offset is the key issue behind the phase shifter, but has just minor influence on design parameters, such as width or height of the RWG. Figure 17 gives an example for three different offsets of the dielectric bridge. Figure 17: Variation of the offset in three examples. (a) Offset equals 0 µm (upstage), (b) Offset equals 413 µm, (c) Offset equals 826 µm (downstage) The simulation shown in Figure 18 clarifies that the phase shifter should either be used in completely upstage or downstage. This corresponds to possible solutions of (6), where the tangential behaviour was postulated. So, the phase shifter does only show useable results concerning the transmission losses for zero or full offset and minor usability around 500 µm. Investigation of Novel Phase Shifter Applications 14

21 Chapter 3: Simulation of Rectangular Waveguide Phase Shifter Figure 18: Relation between S-parameter and bridge offset In the next step the distance between the stages is optimised. This also influences the optimised distance between the in- and outlet (waveports) and the first / last bridge of section An array of two slabs is set up to investigate this variable. Figure 19: Optimisation of distances between two bridges in downstage The best performance for two stages in downstage is incident at a distance of approximately 1000 µm to each other. In this case the return loss S 11 is equal to db and the transmission S 21 is equal to db. The change of the distance between two stages shows only minor effects on the transmission coefficient, S 21, as shown in Figure 19. The frequency response for this length is shown in Figure 20. Investigation of Novel Phase Shifter Applications 15

22 Chapter 3: Simulation of Rectangular Waveguide Phase Shifter Figure 20: Frequency response of an array of two bridges in downstage and 1 mm distance stage phase shifter array based on the SRWG To fulfil the maximum phase shift, seven dielectric stages are introduced. The seven stages realise a phase shift of 350 in steps of 50. Each distance between two stages is 1 mm. The length of the SRWG, which will be later fabricated, is equal to 50 mm including the two flanges on both ends. The simulation setups and results for all simulations are given in the Appendix C and D. Figure 21 shows a sketch of the phase shifter to be simulated. In this example three dielectric layers are in an upstage position (to the left) and four in downstage position (on the right hand side). Figure 21: Sketch of phase shifter with three stages up and four stages down Investigation of Novel Phase Shifter Applications 16

23 Chapter 3: Simulation of Rectangular Waveguide Phase Shifter Table 7: 7 stage phase shifter array reflection, transmission and bandwidth (7) S11 [db] S21 [db] phase shift [ ] -10 db-bandwidth [GHz] 0 stages down stage down stages down stages down stages down stages down stages down stages down Table 7 and Figure 22 show the phase shifter based on a rectangular waveguide gives promising results concerning the reflection coefficient and bandwidth. The performance in term of the insertion loss is comparably poor since the simulation was driven with gaps of 50 µm between the RWG and the silicon-slabs. The gaps were introduced to rebuild the reality in a more reliable way, especially concerning construction uncertainties and other factors such as surface roughness. The phase shifter based on the SRWG will be constructed. The following steps are described in the following chapter. Figure 22: Simulation of phase shifter with 7 stage silicon bridge Review of the Simulation of the SRWG The Simulation shows that it is possible to design a phase shifter based on rectangular waveguides. Using SRWG, seven dielectric stages of 2.44 mm length are inserted with the distance of 1 mm. The total length of the phase shifter including the inlet and the outlet is mm. This setup achieves seven phase shifts in 50 steps. The transmission coefficient S 21 is forecasted to be between db for all seven stages up and -3 db in downstage. The reflection coefficient S 11 is below -19 db for all cases. A maximum bandwidth of 1.2 GHz is possible. (7) Bandwidth between the two cross-sections of S 11 at -10 db Investigation of Novel Phase Shifter Applications 17

24 Chapter 3: Simulation of Rectangular Waveguide Phase Shifter 3.3 Phase shifter with impedance matching Prove of the phase shifter principle is possible with SRWG used without connections to other system components. The application of the phase shifter is on chip implementation, working with other components requiring the system impedance to be 50 Ω. Since the SRWG has an impedance of 667 Ω it is suitable to match the impedance of the RWG-based phase shifter to 50 Ω. The matched impedance RWG (mi-rwg) will not be prosecuted further than the simulation state, since prove of the concept will be performed with SRWG-based phase shifter. By rearranging the wave impedance shown in Table 2, the influence of the two geometries a and b* can be seen in (10), as [11] defines. kη λ! G 2b* Z = = 377Ω 50Ω (10) wave β λ0 a Since the width a is directly correlated to the cut-off frequency f cmn this parameter must not be changed. The free-space wavelength λ 0 and guided wavelength λ G are constants as well, assuming a TE m0 wave-propagation. From (10) the only remaining parameter to change is the height b* of the RWG: 50 2,727 1,651mm b * = 61,9 µ m (11) 377 4,827 2 Assuming that the impedance will decrease the more dielectric is inserted, the target impedance of the unloaded RWG is chosen well above 50 Ω. A height b* of 70 µm gives a wave impedance of Ω. Figure 23 sketches the mi-rwg. Its width a equals to the width of the SRWG (1651 µm). The new height b* derived out of equation (11), equals to approximately 70 µm. Figure 23: Sketch of mi-rwg. (a) front side (b) cut-axis along propagation direction Investigation of Novel Phase Shifter Applications 18

25 Chapter 3: Simulation of Rectangular Waveguide Phase Shifter Basic Simulations for the impedance matched RWG The mi-rwg shows the same cut-off frequency and propagation behaviour as the SRWG, independent from the height. The S-parameter S(1)11 is the return loss and S(1)21 the insertion loss of the first mode and S(2)11, S(2)21 of the second mode respectively, as previously shown in Figure 4. Figure 24: Simulation of mi-rwg Simulation of the single stage silicon bridge properties As for the SRWG, the length of one silicon bridge is optimised in the downstage position. Figure 25 shows that the length of the silicon in the thinner RWG gives the same results concerning the S-parameters as the SRWG does. Figure 25: Length of silicon bridge for mi-rwg in downstage position Investigation of Novel Phase Shifter Applications 19

26 Chapter 3: Simulation of Rectangular Waveguide Phase Shifter A frequency sweep for the RWG with silicon-length of 2440 µm, gives the result shown in Figure 26. Figure 26: S-parameter in downstage position of the mi-rwg The phase shift that can be achieved from upstage to downstage is 40. To achieve a maximal phase shift eight silicon stages are required. The S-parameters for both up- and downstage of one stage are presented in Table 8: Table 8: Comparison between one stage in upstage and downstage of mi-rwg (HFSS) upstage downstage S11 [db] S21 [db] S11 [db] S21 [db] φ In the next step, the distance between two stages is optimised: Figure 27: Optimisation of distances between two bridges in downstage for the mi-rwg Investigation of Novel Phase Shifter Applications 20

27 Chapter 3: Simulation of Rectangular Waveguide Phase Shifter The reflection coefficient S 11 in Figure 27 does not show such clear results as for the SRWGoptimisation, which is shown in Figure 19. The optimised behaviour, concerning the reflection, is in distance ranges between 1000 to 1300 µm, where the return loss S 11 is below -30 db and insertion loss S 21 between -1.5 db and -1.8 db. For following simulations a distance of 1200 µm between the two stages must be assumed Review of the Simulation of the matched-impedance rectangular waveguide The section of the mi-rwg can be seen as a brief outlook. Performing the same simulations as done for the SRWG, the mi-rwg can be optimised. Its geometrical structure for a design frequency f of 110 GHz (f cmn of 90 GHz) is 1651 µm width and 70 µm in height. This design gives an impedance of approximately 50 Ω. The length of each dielectric slab Si length is 2440 µm. This result corresponds to the designed length of the silicon in the SRWG-case. So does the distance between two stages: distances around 1000 µm give the best performance concerning the reflection coefficient S 11. Since each stage performs a phase shift of 40, eight stages should be introduced for further designs based on the mi-rwg. The mi-rwg will not be prosecuted. Investigation of Novel Phase Shifter Applications 21

28 Chapter 4: Fabrication 4. Fabrication This chapter presents the mechanical construction of the phase shifter and the fabrication techniques used in this thesis. The device was manufactured based on a SRWG. This mainly influences the choice of a proper actuation scheme, since the distance is 826 µm, compared to a lower travel requirement of 50 µm for the impedance matched approach, which will not be prosecuted further than the simulation state. The WR-6 SRWG was bought from Millimeter Wave Products Inc. (8). Including the two flanges, it has a total length of 5 cm. This is sufficient for our application, since the total length of seven stages, the bridge distances and inlet / outlet margin is well below 3 cm in the optimised state. The seven opening slots where the dielectric bridges will be induced have a length of 2.5 mm and can be milled mechanically. The distance between two bridges is 1 mm. From the theory it is known that the transmission losses will be reduced, when the dielectric slabs have no distance or multiple of quarter of the guided wavelength λ g. These two cases will be also taken into account and fabricated. 4.1 Choice of actuation scheme The phase shift in the SRWG is performed by a full insertion of the dielectric slab, which means a distance of 826 µm. This gives restrains onto possible active principles in micromechanical devices with respect to typical displacements [12]: Table 9: Different possible actuation schemes Actuation principle Typical displacements Suitability Electrohydraulic > 1 mm Yes Electromagnetic > 1 mm Yes Electropneumatic > 1 mm Yes Electrostatic < 10 µm No Electrostrictive < 10 µm No Magnetostrictive < 10 µm No Micrometer-screw > 1 mm Yes Piezoelectric Stack Bending < 50 µm < 2 mm No (9) Yes The electrostatic, magnetostrictive and electrostrictive principle plus the piezoelectric stack actuator cannot perform the required displacement of 826 µm. For the evaluation it might be of interest to measure stages in between the upstage and downstage mode. The electromagnetic and electropneumatic principles have problems, when they are driven in very low displacement modes (e.g. stick slip effect). The resolutions of these devices are not suitable in our case. The remaining principles piezoelectric (bending) and electromagnetic actuator plus the micrometer-screw do all fulfil the requirements proposed by our setup. They all provide enough displacement and high resolution. One drawback for the piezoelectric actuator is that they only have low forces (< 2 N). This may not be sufficient for moving seven stages at once, which would be the easiest implementation. (8) (9) Lever can increase the travel, but requires more design work Investigation of Novel Phase Shifter Applications 22

29 Chapter 4: Fabrication Since this the goal of this project is prove of the concept of designing a new type of phase shifter, it is sufficient to implement the actuation scheme for the dielectric bridges as easy as possible. Depending on the design of the micrometer-screw a displacement of 1 mm with a resolution of well below 10 µm is possible. In this thesis, the solution with a micrometer-screw is performed. For further applications an electromagnetic (especially the electrodynamics) principle should be chosen. With some restrains, one can also think of a piezoelectric implementation. One restrain for the construction arises from the evaluation process. To provide the possibility to measure every single bit, the bridges must be deflectable separately. Since a micrometer-screw is used, a realisation by applying up to seven tubes holding the dielectric is suitable. The tubes must therefore be easy to attach or remove from the micrometer-screw. 4.2 Prototype of phase shifters Three different prototypes are set up. Every prototype consists of seven silicon stages to shift the phase. The difference between each is the distance of two dielectric slabs. The simulation in Figure 19 shows that the optimised distance is 1 mm. From the theory one could expect good transmission behaviour at distances of 0 µm and the half of the length of the guided-wavelength (around 2.41 mm) as well. These values were not simulated, but will be characterised by measurements Processing the dielectric slabs The dielectric slabs are fabricated out of entire silicon-wafer with the thickness of 826 µm. Starting with a 1300 µm-thick, n-type Si-wafer the required thickness can be done by KOHetching in the clean-room in Kista. The etching-rate of the KOH-bath (concentration 30%, temperature 100 C) was approximately 2 µm/min. On top of the wafers two different layers are sputtered: (Si-wafer) 50 nm TiW 1.5 µm Au; (Si-wafer) 50 nm TiW 1 µm Au 1.5 µm TiW; The TiW-layer has no influence on this project and the phase shifting properties, but provides with better adhesion between the wafer and the gold layer. The main difference between the two types of silicon-slabs is the thickness of the gold. After the sputtering process the slabs are sawed out of the wafer. The geometry of each slab is set to be 2440 x 1550 µm. The width of the dielectric slab does not correspond to the simulation of the seven-stage phase shifter, but should still provide good propagation coefficients, as shown from the simulation of the width in Section Processing the rectangular waveguide The three RWGs are made of bronze. All three are processed with slits on top to insert the dielectric slabs. The one RWG containing the dielectric slabs without any distance has a long hole of mm length, adjusted to the middle of the RWG. The two RWGs providing a distance between two stages are milled as well. The distance between two slits corresponds to the optimised distance between two stages of 1 mm and the theoretical approach of 1.22 mm, with respect to the quarter of the guided wavelength λ g. To minimise the risk of that the dielectric slabs could stuck in the RWGs each slit will be milled longer than the required 2.44 mm. The length of each slit is exactly 2.5 mm. Investigation of Novel Phase Shifter Applications 23

30 Chapter 4: Fabrication Assembling the holder From Section 4.1 a micrometer screw is chosen for actuating dielectric slabs. This approach offers a good controllability over the offset of the silicon bridges. The micrometer screw (Figure 28) is attached to a fastener, not shown in this picture. Figure 28: Micrometer screw Onto this micrometer screw a holder is mounted (Figure 29): Figure 29: Micrometer screw with the first part of the clamp In the next step, the seven stages are clamped to the holder with a second block, which is fixed by screws. Three different types of blocks are manufactured. They differ in the distance between the trenches in which the stages can be mounted. Each trench is designed to be over the middle of each dielectric slab. The distances between the stages are 0 mm, 1 mm (based on the simulations) and 1.22 mm (based on the theory of wave propagation). On each dielectric slab a 2 cm long aluminium tube is glued to prevent harming the slabs while clamping. Investigation of Novel Phase Shifter Applications 24

31 Chapter 4: Fabrication Figure 30: Clamped seven stages Finally, this device will be mounted on top of the processed RWG, which will be inserted into the Vector Network Analyser (VNA) for Characterisation (not shown in the following picture): Figure 31: Complete setup of the prototype Figure 32 shows the fabricated device mounted to a holder in the laboratory of the Microsystem Technology Group at KTH. Investigation of Novel Phase Shifter Applications 25

32 Chapter 4: Fabrication Figure 32: The prototype with 3 stages up and 4 stages down Investigation of Novel Phase Shifter Applications 26

33 Chapter 5: Discussion and Outlook 5. Discussion and Outlook This report gives a digital phase shifter based on rectangular waveguide technology. The principle is presented and designed in theory and verified by simulations. The phase shifter is designed for operating at 110 GHz. To prove the principle a standard rectangular waveguide for D-Band applications (WR-07) is used. Its cut-off frequency of GHz gives a margin for safe applications at the design frequency. For implementation as an on-chip solution, the impedance must fit the system requirements of 50 Ω. The manufacturing of the matched-impedance RWG was not part of this thesis, because of its complex and timeconsuming manufacturing which could not be fit to the time restrictions of the present master thesis. The simulations show that 50 µm of silicon cause a phase shift of 1. To fulfil the maximum phase shift seven stages of 2440 µm length are introduced. Each dielectric slab shifts the phase of 50. To ease the characterisation a distance of 1 mm between two stages is introduced. The simulations forecast a reflection coefficient S 11 in a range of (all stages down) to db and the transmission coefficient S 21 between (all stages up) to db (all stages down). This means that at least half of the inserted energy will be transmitted to the outlet of the device. A bandwidth of approximately 1.2 GHz concerning S 11 being below -10 db. Three different prototypes are manufactured and presented. They mainly differ in the distance between two dielectric stages. One solution offers the direct contact of two silicon slabs, which should ideally prevent losses. A second prototype is based on the theory of propagating electromagnetic waves, claiming that a maximum of energy will be transported for a distance corresponding to a quarter of the wavelength. So the distance between two stages is 2.41 mm. A third approach is the outcome of the optimisation performed by the simulations. In this case the distance is 1 mm and the simulated results are presented above. All three types of phase shifter will be characterised at the VTT Technical Research Centre of Finland (Valtion teknillinen tutkimuskeskus, VTT) in Helsinki, Finland. The new design based on rectangular waveguide technology is competitive to existing shifter concepts, such as those based on coplanar waveguides, microstrip PIN-diodes or FETs [6, 13-16]. These phase shifter are compared in Table 1. The new phase shifter based on rectangular waveguide technology combines the advantages of existing phase shifter design. Depending on the number of stages phase shifts over full 360 degrees is possible. The new phase shifter is designed to work on frequencies higher than 100 GHz. The only limitation of this value was the possibility of characterisation. Higher design frequencies mostly rely on the waveguide itself. The insertion loss is in ranges of -1.8 to -3 db. CPW- and microstrip-phase shifters with insertion loss of more than -1 db exist, but work at lower frequencies. The simulations are performed with a 50 µm-gap between RWG and dielectric to represent losses, caused by losses, such as surface roughness. This value was arbitrarily chosen, a better performance in concerning the insertion loss might be possible. The maximum return loss of the RWG phase shifter is less than db. This is the best value compared to the existing technologies, working at their typical frequencies below 100 GHz. During the simulation and fabrication process several problems occurred. The simulations performed with the single stages to derive values such as the length of the dielectric slabs, was possible without any problems. Simulating the complete array of seven dielectric stages evoked problems, based on the simulation tools CST Microwave Studio and Ansoft HFSS. To be able to run the simulation, the model has to be simplified as much as possible. Thus, the walls of the SRWG are replaced by the boundary of the model, which was chosen to be a perfect conductor. With this setup HFSS gives trustable results, but Microwave Studio doubled the cut-off frequency of the SRWG to be approximately 180 GHz. Since this value depends on the width a of the Investigation of Novel Phase Shifter Applications 27

34 Chapter 5: Discussion and Outlook waveguide, which was unchanged, were these results implausible. HFSS gives plausible results concerning the insertion and transmission losses. In HFSS one key function making the analysis easier is missing. The user is not able to wrap the phase as Microwave Studio does. The output of the phase of the S 21 -parameter is fixed between ±180. Since the phase change over the frequency contains several periods is the evaluation between the results hard. One problem during the fabrication process was that the required height of the dielectric slab was realised out of the thickness of silicon-wafer. Since wafer with a thickness of 826 µm are not available on the market, a decision between ordering a special wafer with the certain thickness and realising the thickness by KOH-etching in Kista had to be made. Companies, which were able to provide the thickness, have a limitation on the number of wafer to order. Since it does not make sense to buy at least 30 wafer for at least 80 /each, the decision was made to etch the wafer to the required thickness. Using KOH-etch the thickness was controllable and reached 826 µm ±0.6%. The drawback of the etching is that the surface roughness of the silicon block is higher than the roughness of polished wafers. Still, this technology should be enhanced. It offers improvements, especially concerning the bandwidth and insertion loss above 100 GHz. By optimising and fabricating the matched-impedance rectangular waveguide implementation into line transmitting systems is possible. Investigation of Novel Phase Shifter Applications 28

35 Chapter 6: Acknowledgements 6. Acknowledgements Finally, I want to thank some people, who helped me realising this work. Nutapong Somjit for giving me the chance doing a Master Thesis at KTH; Kjell Norén for supporting me building up the mechanical structure; Martin Lapisa, Mikael Sterner and Stefan Braun for helping me building up the mechanical structure in Kista; The whole MST-lab and especially Niklas Roxhed for inspiring conversations concerning my Thesis; Prof. Dr. H. Schlaak from TU Darmstadt for co-supervising my Thesis; Investigation of Novel Phase Shifter Applications 29

36 Chapter 7: Bibliography 7. Bibliography [1] D. Pozar, Microwave Engineering vol. 2. Hoboken, NJ, USA: John Wiley & Sons, Inc., [2] G. Rebeiz, RF MEMS: Design, Theory and Technology. Hoboken, NJ, USA: John Wiley & Sons, Inc, [3] J. Putnam, M. Barter, K. Wood, and J. LeBlanc, "A Monolithic GaAs PIN Switch Network For A 77 GHz Automotive Collision Warning Radar," IEEE MTT-S Int. Microwave Symp. Dig, pp , [4] K. Maruhashi, H. Mizutani, and K. Ohata, "A Ka-band 4-bit monolithic phase shifter using unresonated FETswitches," Microwave Symposium Digest, vol. 1, pp , Jun [5] J. B. Rizk and G. M. Rebeiz, "W-Band CPW RF MEMS Circuits on Quartz Substrates," IEEE Transactions on Microwave Theory and Techniques, vol. 51, pp , Jul [6] G. P. Gauthier, J.-P. Raskin, L. P. B. Katehi, and G. M. Rebeiz, "A 94-GHz Aperture- Coupled Micromachined Microstrip Antenna," IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, vol. 47, p. 6, Dec [7] A. S. Nagra, J. Xu, E. Erker, and R. A. York, "Monolithic GaAs Phase Shifter Circuit with Low Insertion Loss and Continuous Phase Shift at 20 GHz," IEEE MICROWAVE AND GUIDED WAVE LETTERS, vol. 9, p. 3, Jan [8] F. Schäfer, F. Gallée, G.Landrac, and M. Ney, "Optimum Reflector Shapes for Anticollision Radar at 76 GHz," Microwave opt Technol Lett, vol. 24, pp , [9] B. Zheng and Z. Shen, "Analysis of Dielectric-Loaded Waveguide Slot Antennas by the Hybrid Mode-Matching/Moment Method," IEICE Transactions on Communications, vol. E88-B, Number 8, pp , [10] P. H. Vartanian, W. P. Ayres, and A. L. Helgesson, "Propagation in Dielectric Slab Loaded Rectangular Waveguide," IEEE Transactions on Microwave Theory and Techniques, vol. 6, pp , [11] T. Weiland, "Script to Technical Electrodynamics WS 2005/2006," Darmstadt: TU Darmstadt, 2005, pp [12] R. Isermann, Mechatronische Systeme - Grundlagen vol. 1. korrigierter Nachdruck - Studienausgabe. Munich, Germany: Springer Verlag, [13] L. He, F. Hong, and Y. Li, "94 GHz phase-shift-keying modulator," International Journal of Infrared and Millimeter Waves, vol. Volume 17, p. 7, Feb [14] C. T. Charles and A. D. J., "Design considerations for integrated CMOS reflective-type phase shifters," Analog Integrated Circuits and Signal Processing, vol. Volume 50, Number 3 / März 2007, p. 9, Feb [15] J. S. Hayden and G. M. Rebeiz, "Low-Loss Cascadable MEMS Distributed X-Band Phase Shifter," IEEE MICROWAVE AND GUIDED WAVE LETTERS, p. 3, [16] S. Hamedi-Hagh and C. Salama, "A novel C-band CMOS phase shifter for communication systems," Proc. Int. Symp. on Circuits and Systems, vol. 2, p. 4, May [17] Millimeter_Wave_Products, "MIWV Catalog June 2006," Investigation of Novel Phase Shifter Applications 30

37 Chapter 8: Appendix 8. Appendix A. Electromagnetic and rectangular waveguide theory A A.1 Maxwell s equations A A.2 Helmholtz equation A A.3 Rectangular waveguide B B. Millimetre Wave RWG Information C C. Simulation Setups D C.1 Simulation of a SRWG calculated by HFSS, Figure 4 D C.2 Length of one silicon-slab in downstage position of the SRWG, Figure 8 D C.3 Length of one silicon-slab in detail (around 405 µm), Figure 9 E C.4 Length of one silicon-slab in detail (around µm), Figure 10 E C.5 Length of the silicon-slab in upstage position, Figure 11 E C.6 Width of one silicon-slab, Figure 12 E C.7 S-parameter in the upstage position of the SRWG, Figure 13 E C.8 S-parameter in the downstage position of the SRWG, Figure 14 F C.9 S-parameter with a perfect conductor in the downstage / upstage position of the SRWG, Figure 15 / Figure 16: F C.10 S-parameter dependency on the bridge offset, Figure 18 G C.11 Optimisation between two stages, Figure 19 G C.12 S-parameter for an array of two stages, distance 1 mm, Figure 20 G C.13 Length of one silicon-slab in downstage position of the mi-rwg, Figure 25 G C.14 S-parameter in downstage position for the mi-rwg, Figure 26 H C.15 Optimisation between two stages for the mi-rwg, Figure 27 H D. Simulation Results for the 7-stage array I D.1 All 7 slabs in upstage position I D.2 6 slabs in upstage position, 1 slab in downstage J D.3 5 slabs in upstage position, 2 slabs in downstage position K D.4 4 slabs in upstage position, 3 slab in downstage L D.5 3 slabs in upstage position, 4 slab in downstage M D.6 2 slabs in upstage position, 5 slab in downstage N D.7 1 slabs in upstage position, 6 slab in downstage O D.8 All 7 slabs in downstage position P E. Technical Drawings Q Investigation of Novel Phase Shifter Applications 31

38 A. Electromagnetic and rectangular waveguide theory This part of the Appendix gives the fundamental theory behind the project. Starting with the Maxwell s equations the field propagation in a rectangular waveguide is affiliated. A.1 Maxwell s equations The four Maxwell s equations (12) - (15) are in the differential form given by: B E = (12) t D H = J + (13) t B = 0 (14) D = ρ (15) In free-space, the electric and magnetic field intensities and flux densities are connected by (16) and (17): B µ H (16) D = 0 = 0 ε E (17) Assuming a conductive and therefore lossy medium (12) and (13) can be redefined as: E = jωµ H (18) H = jωε E + σ E (19) A.2 Helmholtz equation By taking the curl of (18) and using the vector identity A = A( A) 2 A one can simplify the result to the wave equation: 2 2 σ E + ω µε 1 j E = 0 (20) ωε In the same way an equation for H can be derived: 2 2 σ H + ω µε 1 j H ωε = 0 (21) In a source free, isotropic, homogeneous and linear material the propagation constant k is defined as k = ω µε. Since a dielectric layer is introduced in this project, we have to define the complex propagation constant σ γ = α + jβ = jω µε 1 j (22) ωε where α represents the attenuation constant and β the phase constant. A

39 Chapter 8: Appendix A.3 Rectangular waveguide This section presents the theory and calculations of rectangular waveguide filled with air. A RWG, as shown in Figure 33, consists of four metallic walls, where one can assume a perfect conductivity σ. It is filled with a linear, homogeneous material, which gives a constant permittivity ε and permeability µ. The propagation of the wave is in ±z-direction. Figure 33: Rectangular waveguide in Cartesian coordinate system In the RWG only two waveforms exist: TM-waves, with no propagation of the H-field into the z- direction, described by (20), or TE-waves where the E-field equals to zero, (21). The general solution can be derived as a superposition of both wavetypes. In this thesis we are going to use the TE m0 Modes of the waveguide. From (20) and (21) we can solve the three Cartesian components of the E- and the H-field for TE m0 waves, where k c represents the cut-off wavenumber and β the propagation constant of different modes (23) - (26). β H z H x = j 2 (23) k c x β H z H y = j 2 (24) k c y ωµ H z Ex = j 2 (25) k c x ωµ H z Ey = j 2 (26) k c y With the assumption that we only have an H-field into the propagation direction z, we can define H z in this direction from the Helmholtz equation (21) k = H z (27) x y z Investigation of Novel Phase Shifter Applications B

40 Chapter 8: Appendix B. Millimetre Wave RWG Information This table shows typical values for RWG, which are presented from Millimeter Wave Products Inc. [17] (p. 169, Appendix A). This table focuses on frequency bands over 100 GHz. Waveguide Frequency Range [GHz] Wavelength Range λ 0 [mm] Guide Wavelength Range λ G /λ 0 TE 10 Cutoff Frequency [GHz] TE 10 Cutoff Wavelength λ C [mm] Inside Dimensions [mm] WG Band WR ,997 2,725 1,620 1,185 59,0 5,08 2,50 x 1,270 WR ,331 2,141 1,746 1,177 73,8 4,06 2,032 x 1,016 WR ,725 1,763 1,771 1,183 90,8 3,30 1,651 x 0,826 WR ,141 1,176 1,777 1, ,7 2,59 1,295 x 0,648 Corresponding values can be found in [1] (p. 706, Appendix I). Recommended Frequency Range [GHz] TE 10 Cutoff Frequency [GHz] EIA Designation WR-XX Inside Dimensions [cm] Outside Dimensions [cm] Band W ,01 WR-10 0,254 x 0,127 0,458 x 0,330 F ,84 WR-8 0,203 x 0,102 0,406 x 0,305 D ,85 WR-6 0,170 x 0,083 0,368 x 0,286 G ,75 WR-5 0,130 x 0,065 0,333 x 0,268 In both cases the dimensions and properties do not vary much. With a desired signal frequency of 110 GHz, a D-Band-RWG is the convenient solution (WR-6). Investigation of Novel Phase Shifter Applications C

41 Chapter 8: Appendix C. Simulation Setups The simulation programs used in this thesis are Ansoft HFSS (10) using a FEM-based analysis and the FIT/FDTD-based CST Microwave Studio (11). Both programs are described and compared in Section 3.1. C.1 Simulation of a SRWG calculated by HFSS, Figure 4 Simulation program: CST Microwave Studio Variable: Frequency GHz, step size 1 GHz - Geometry: RWG: width mm, height mm, length 30 mm. Material thickness: 1 mm; - Setup: Units: µm/ghz/ns; Background: Normal; Monitors: E-Field, Frequency 110 GHz, Fmin 0 GHz, Fmax 220 GHz; Mesh: Type Hexahedral, Lines per wavelength 15, Lower mesh limit 15, Mesh line ratio 10; Transient Solver Parameters: Accuracy -30 db, Source Type: Port 1, Mode: All (3); Number of Frequency Samples 20; Steady state: Number of pulses 200, Energy balance limits 0,02; Solver: Samples 1001; C.2 Length of one silicon-slab in downstage position of the SRWG, Figure 8 Simulation program: Ansoft HFSS Variable: Length of the silicon-slab µm, step size 50 µm - Geometry: RWG: width 1,651 mm, height 0,826 mm, length variable (length of the siliconslab plus the inlet and outlet, each 1 mm). Material thickness: 1 mm; Silicon-slab: width 1,651 mm, height 0,826 mm, length variable, offset 0,826 µm; Distance between RWG and silicon-slab: 50 µm - Setup: Number of passes 20, Delta S 0,01, Frequency 110 GHz Simulation program: CST Microwave Studio Variable: Length of the silicon-slab µm, step size 50 µm - Geometry: RWG: width 1,651 mm, height 0,826 mm, length variable. Material thickness: 1 mm; Silicon-slab: width µm, height 0,826 mm, length variable, offset 0,826 µm; Distance between RWG and silicon-slab: 50 µm - Setup: Units: µm/ghz/ns; Background: Normal; Monitors: E-Field, Frequency 110 GHz, Fmin 80 GHz, Fmax 220 GHz; Mesh: Type Hexahedral, Lines per wavelength 15, Lower mesh limit 15, Mesh line ratio 10; Transient Solver Parameters: Accuracy -30 db, Source Type: Port 1, Mode: All (2); Number of Frequency Samples 20; Steady state: Number of pulses 100, Energy balance limits 0,03; Solver: Samples 1001; Sweep: length of the silicon (30) (10) (11) Investigation of Novel Phase Shifter Applications D

42 Chapter 8: Appendix C.3 Length of one silicon-slab in detail (around 405 µm), Figure 9 Simulation program: Ansoft HFSS Variable: Length of the silicon-slab µm, step size 20 µm - Geometry: RWG: width 1,651 mm, height 0,826 mm, length variable (length of the siliconslab plus the inlet and outlet, each 1 mm). Material thickness: 1 mm; Silicon-slab: width 1,651 mm, height 0,826 mm, length variable, offset 0,826 µm; Distance between RWG and silicon-slab: 50 µm - Setup: Number of passes 20, Delta S 0,01, Frequency 110 GHz C.4 Length of one silicon-slab in detail (around µm), Figure 10 Simulation program: Ansoft HFSS Variable: Length of the silicon-slab µm, step size 20 µm - Geometry: RWG: width 1,651 mm, height 0,826 mm, length variable (length of the siliconslab plus the inlet and outlet, each 1 mm). Material thickness: 1 mm; Silicon-slab: width 1,651 mm, height 0,826 mm, length variable, offset 0,826 µm; Distance between RWG and silicon-slab: 50 µm - Setup: Number of passes 20, Delta S 0,01, Frequency 110 GHz C.5 Length of the silicon-slab in upstage position, Figure 11 Simulation program: Ansoft HFSS Variable: Length of the silicon-slab µm, step size 50 µm - Geometry: RWG: width 1,651 mm, height 0,826 mm, length variable (length of the siliconslab plus the inlet and outlet, each 1 mm). Material thickness: 1 mm; Silicon-slab: width 1,651 mm, height 0,826 mm, length variable, offset 0 µm; Distance between RWG and silicon-slab: 50 µm - Setup: Number of passes 20, Delta S 0,01, Frequency 110 GHz C.6 Width of one silicon-slab, Figure 12 Simulation program: Ansoft HFSS Variable: Width of the silicon-slab µm, step size 50 µm - Geometry: RWG: width 1,651 mm, height 0,826 mm, length µm. Material thickness: 1 mm; Silicon-slab: width variable, height 0,826 mm, length µm, offset 0,826 µm; Distance between RWG and silicon-slab: 50 µm - Setup: Number of passes 20, Delta S 0,01, Frequency 110 GHz C.7 S-parameter in the upstage position of the SRWG, Figure 13 Simulation program: Ansoft HFSS Variable: Frequency GHz, step size 1 GHz - Geometry: RWG: width 1,651 mm, height 0,826 mm, length µm. Material thickness: 1 mm; Silicon-slab: width µm, height 0,826 mm, length µm, offset 0 µm; Distance between RWG and silicon-slab: 50 µm - Setup: Number of passes 20, Delta S 0,02, Frequency variable Investigation of Novel Phase Shifter Applications E

43 Chapter 8: Appendix Simulation program: CST Microwave Studio Variable: Frequency GHz, step size 1 GHz - Geometry: RWG: width 1,651 mm, height 0,826 mm, length µm. Material thickness: 1 mm; Silicon-slab: width µm, height 0,826 mm, length µm, offset 0 µm; Distance between RWG and silicon-slab: 50 µm - Setup: Units: µm/ghz/ns; Background: Normal; Monitors: E-Field, Frequency 110 GHz, Fmin 80 GHz, Fmax 220 GHz; Mesh: Type Hexahedral, Lines per wavelength 15, Lower mesh limit 15, Mesh line ratio 10; Transient Solver Parameters: Accuracy -20 db, Source Type: Port 1, Mode: All (2); Number of Frequency Samples 20; Steady state: Number of pulses 100, Energy balance limits 0,03; Solver: Samples 1001 C.8 S-parameter in the downstage position of the SRWG, Figure 14 Simulation program: Ansoft HFSS Variable: Frequency GHz, step size 1 GHz - Geometry: RWG: width 1,651 mm, height 0,826 mm, length µm. Material thickness: 1 mm; Silicon-slab: width µm, height 0,826 mm, length µm, offset 0,826 µm; Distance between RWG and silicon-slab: 50 µm - Setup: Number of passes 20, Delta S 0,02, Frequency variable Simulation program: CST Microwave Studio Variable: Frequency GHz, step size 1 GHz - Geometry: RWG: width 1,651 mm, height 0,826 mm, length µm. Material thickness: 1 mm; Silicon-slab: width µm, height 0,826 mm, length µm, offset 0,826 µm; Distance between RWG and silicon-slab: 50 µm - Setup: Units: µm/ghz/ns; Background: Normal; Monitors: E-Field, Frequency 110 GHz, Fmin 80 GHz, Fmax 220 GHz; Mesh: Type Hexahedral, Lines per wavelength 15, Lower mesh limit 15, Mesh line ratio 10; Transient Solver Parameters: Accuracy -20 db, Source Type: Port 1, Mode: All (2); Number of Frequency Samples 20; Steady state: Number of pulses 100, Energy balance limits 0,03; Solver: Samples 1001 C.9 S-parameter with a perfect conductor in the downstage / upstage position of the SRWG, Figure 15 / Figure 16: Simulation program: Ansoft HFSS Variable: Frequency GHz, step size 1 GHz - Geometry: RWG: width 1,651 mm, height 0,826 mm, length µm. Material thickness: 1 mm; Silicon-slab: width µm, height 0,826 mm, length µm, offset 0,826 µm / 0 µm; Perfect Conductor: width µm, height 25 µm, length µm; Distance between RWG and silicon-slab: 50 µm - Setup: Number of passes 20, Delta S 0,02, Frequency variable Investigation of Novel Phase Shifter Applications F

44 Chapter 8: Appendix C.10 S-parameter dependency on the bridge offset, Figure 18 Simulation program: Ansoft HFSS Variable: offset µm, step size 25 µm - Geometry: RWG: width 1,651 mm, height 0,826 mm, length µm. Material thickness: 1 mm; Silicon-slab: width µm, height 0,826 mm, length µm, offset variable; Distance between RWG and silicon-slab: 50 µm - Setup: Number of passes 20, Delta S 0,01, Frequency 110 GHz Simulation program: CST Microwave Studio Variable: offset µm, step size 25 µm - Geometry: RWG: width 1,651 mm, height 0,826 mm, length µm. Material thickness: 1 mm; Silicon-slab: width µm, height 0,826 mm, length µm, offset variable; Distance between RWG and silicon-slab: 50 µm - Setup: Units: µm/ghz/ns; Background: Normal; Monitors: E-Field, Frequency 110 GHz, Fmin 80 GHz, Fmax 220 GHz; Mesh: Type Hexahedral, Lines per wavelength 15, Lower mesh limit 15, Mesh line ratio 10; Transient Solver Parameters: Accuracy -20 db, Source Type: Port 1, Mode: All (2); Number of Frequency Samples 20; Steady state: Number of pulses 500, Energy balance limits 0,02; Solver: Samples 1001 C.11 Optimisation between two stages, Figure 19 Simulation program: Ansoft HFSS Variable: bridge distance µm, step size 50 µm - Geometry: RWG: width 1,651 mm, height 0,826 mm, length µm. Material thickness: 1 mm; Silicon-slab: width µm, height 0,826 mm, length µm, offset 826 µm; Distance between RWG and silicon-slab: 50 µm; Distance between two stage: variable - Setup: Number of passes 20, Delta S 0,06, Frequency 110 GHz C.12 S-parameter for an array of two stages, distance 1 mm, Figure 20 Simulation program: Ansoft HFSS Variable: Frequency GHz, step size 1 GHz - Geometry: RWG: width 1,651 mm, height 0,826 mm, length µm. Material thickness: 1 mm; Silicon-slab: width µm, height 0,826 mm, length µm, offset 0,826 µm; Perfect Conductor: width µm, height 25 µm, length µm; Distance between RWG and silicon-slab: 50 µm; Distance between two stage: 1 mm - Setup: Number of passes 20, Delta S 0,02, Frequency variable C.13 Length of one silicon-slab in downstage position of the mi-rwg, Figure 25 Simulation program: Ansoft HFSS Variable: Length of the silicon-slab µm, step size 50 µm - Geometry: RWG: width 1,651 mm, height 40 µm, length variable (length of the silicon-slab plus the inlet and outlet, each 1 mm). Material thickness: 1 mm; Silicon-slab: width 1,651 mm, height 0,826 mm, length variable, offset 40 µm; Distance between RWG and silicon-slab: 50 µm - Setup: Number of passes 20, Delta S 0,03, Frequency 110 GHz Investigation of Novel Phase Shifter Applications G

45 Chapter 8: Appendix C.14 S-parameter in downstage position for the mi-rwg, Figure 26 Simulation program: Ansoft HFSS Variable: Frequency GHz, step size 1 GHz - Geometry: RWG: width 1,651 mm, height 50 µm, length µm. Material thickness: 1 mm; Silicon-slab: width µm, height 50 µm, length µm, offset 50 µm; Distance between RWG and silicon-slab: 50 µm - Setup: Number of passes 20, Delta S 0,02, Frequency variable C.15 Optimisation between two stages for the mi-rwg, Figure 27 Simulation program: Ansoft HFSS Variable: bridge distance µm, step size 50 µm - Geometry: RWG: width 1,651 mm, height 50 µm, length µm. Material thickness: 1 mm; Silicon-slab: width µm, height 50 µm, length µm, offset 50 µm; Distance between RWG and silicon-slab: 50 µm; Distance between two stage: variable - Setup: Number of passes 20, Delta S 0,05, Frequency 110 GHz Investigation of Novel Phase Shifter Applications H

46 Chapter 8: Appendix D. Simulation Results for the 7-stage array All eight simulations where performed by Ansoft HFSS. The general setup for the simulations is: - Analysis Setup: Number of Passes: 20, Max. Refinement per Pass: 20%, Minimum Convergenced Passes: 1; - Sweep Setup: Type: Discrete, Start Frequency: 80 GHz, Stop Frequency: 140 GHz, Step Size: 0,5 GHz The only difference, besides the geometrical setup is the factor Maximum Delta S, defining the accuracy of the simulation. D.1 All 7 slabs in upstage position Maximum Delta S: 0,1; S 11 (f = 110 GHz): -21,15 db; S 21 (f = 110 GHz): -1,83 db Figure 34: Simulation of array with 7 stages. All 7 slabs are in upstage position Investigation of Novel Phase Shifter Applications I

47 Chapter 8: Appendix D.2 6 slabs in upstage position, 1 slab in downstage Maximum Delta S: 0,09; S 11 (f = 110 GHz): -22,80 db; S 21 (f = 110 GHz): -1,86 db Figure 35: Simulation of array with 7 stages. 6 upstage / 1 downstage Investigation of Novel Phase Shifter Applications J

48 Chapter 8: Appendix D.3 5 slabs in upstage position, 2 slabs in downstage position Maximum Delta S: 0,09; S 11 (f = 110 GHz): -20,50 db; S 21 (f = 110 GHz): -2,06 db Figure 36: Simulation of array with 7 stages. 5 upstage / 2 downstage Investigation of Novel Phase Shifter Applications K

49 Chapter 8: Appendix D.4 4 slabs in upstage position, 3 slab in downstage Maximum Delta S: 0,1; S 11 (f = 110 GHz): -28,55 db; S 21 (f = 110 GHz): -2,16 db Figure 37: Simulation of array with 7 stages. 4 upstage / 3 downstage Investigation of Novel Phase Shifter Applications L

50 Chapter 8: Appendix D.5 3 slabs in upstage position, 4 slab in downstage Maximum Delta S: 0,08; S 11 (f = 110 GHz): -26,57 db; S 21 (f = 110 GHz): -2,47 db Figure 38: Simulation of array with 7 stages. 3 upstage / 4 downstage Investigation of Novel Phase Shifter Applications M

51 Chapter 8: Appendix D.6 2 slabs in upstage position, 5 slab in downstage Maximum Delta S: 0,08; S 11 (f = 110 GHz): -34,47 db; S 21 (f = 110 GHz): -2,45 db Figure 39: Simulation of array with 7 stages. 2 upstage / 5 downstage Investigation of Novel Phase Shifter Applications N

52 Chapter 8: Appendix D.7 1 slabs in upstage position, 6 slab in downstage Maximum Delta S: 0,08; S 11 (f = 110 GHz): -25,99 db; S 21 (f = 110 GHz): -2,55 db Figure 40: Simulation of array with 7 stages. 1 upstage / 6 downstage Investigation of Novel Phase Shifter Applications O

53 Chapter 8: Appendix D.8 All 7 slabs in downstage position Maximum Delta S: 0,07; S 11 (f = 110 GHz): -18,97 db; S 21 (f = 110 GHz): -3,00 db Figure 41: Simulation of array with 7 stages. All 7 slabs are in downstage position Investigation of Novel Phase Shifter Applications P