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The cloverleaf antenna : a compact wide-bandwidth dual-polarization feed for CHIME Deng, Meiling 2014

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The Cloverleaf Antenna:A Compact Wide-bandwidth Dual-polarization Feed forCHIMEbyMeiling DengB.Sc., Huazhong University of Science and Technology, 2012A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCEinThe Faculty of Graduate and Postdoctoral Studies(Astronomy)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)August 2014c© Meiling Deng 2014AbstractA compact, wide-bandwidth, dual-polarization cloverleaf-shaped antennahas been developed to feed the CHIME radio telescope. The antenna hasbeen tuned using a commercial antenna simulation program, CST, to have avery good impedance match to our amplifiers. Specifically, the return loss issmaller than -10dB for over an octave of bandwidth, covering the full CHIMEband from 400MHz to 800MHz and this performance has been confirmed bymeasurement. The antennas are made of conventional low-loss circuit boardsand can be mass produced economically, which is important because CHIMErequires 1280 feeds. They are compact enough to be placed 30cm apart ina linear array at any azimuthal rotation. 128 of these feeds have now beenbuilt, tested and deployed on CHIME pathfinder.iiPrefaceA discussion among myself, Mark Halpern and Tom Landecker led to de-sign of my research program, which is to use a commercial software CST todesign a wide bandwidth feed for CHIME. Later discussion among myself,Mark Halpern, Tom Landecker and Duncan Campbell-Wilson led to the real-ization that curved petal shapes in a cloverleaf feed might reduce resonancesand produce a broadband feed.The work in sections 2.1.2, 2.2 and 2.3, which sets the starting point for mysearch for a CHIME feed, was led by other members of the CHIME collab-oration, particularly Gregory Davis and Ivan Padilla. The work in section6.2 and 6.3 was done in collaboration with the whole CHIME team.Figures 2.2, 2.3, 2.4, 2.6, 5.7, 6.5 and 6.6 are made by other members of theCHIME team. There are some illustrative figures which are publicly avail-able and in each case, citation is provided in the caption. The rest of workpresented in this thesis is done by myself.The main result of this thesis has been accepted for publication in theproceedings of ANTEM 2014. The accepted paper is in appendix. (TheCloverleaf Antenna: A Compact Wide bandwidth Dual-polarization Feedfor CHIME; Meiling Deng, Duncan Campbell-Wilson for the CHIME collab-oration). I wrote the paper with help from Mark Halpern, Tom Landeckerand Duncan Campbell-Wilson. The results were presented there by the au-thor. This work won a prize as the best student paper at the conference.iiiTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . ix1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 The Existence of Dark Energy . . . . . . . . . . . . . . . . . 11.2 Properties of Dark Energy is Measurable . . . . . . . . . . . 21.2.1 Baryon Acoustic Oscillations . . . . . . . . . . . . . . 31.2.2 21cm Observation . . . . . . . . . . . . . . . . . . . . 41.3 Overview of CHIME as A New Dark Energy Experiment . . 42 Starting Point for the CHIME Feed Development . . . . . 72.1 The Four Square Antenna as the First Candidate for theCHIME Feed . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.1.1 Working Principles of the 4sq . . . . . . . . . . . . . . 92.1.2 CHIME 4sq on the Two Dish System . . . . . . . . . 112.2 The Active 4sq . . . . . . . . . . . . . . . . . . . . . . . . . . 142.3 The Four Point feed and The Four Sleeve feed . . . . . . . . 163 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.1 Grasp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.2 CST . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.2.1 CST Simulation Overview . . . . . . . . . . . . . . . 203.2.2 Test of our Approach to CST through A Dipole Model 213.2.3 Plan of Use . . . . . . . . . . . . . . . . . . . . . . . . 28ivTable of Contents4 Modeling the Current Patterns, Beam Shapes and ImpedanceSpectra of Single Feed 4sq and its Variants . . . . . . . . . 294.1 Visualizing Current Patterns and Beam Shapes . . . . . . . . 294.1.1 The 4sq and Its Petal board Model . . . . . . . . . . 294.1.2 4sq’s Variants and Their Petal Board Models . . . . . 364.1.3 Comparison of Different Feeds . . . . . . . . . . . . . 404.2 Input Impedance of Single 4sq . . . . . . . . . . . . . . . . . 414.2.1 Petal Board Model and Impedance Transformation . 414.2.2 Full Feed Model . . . . . . . . . . . . . . . . . . . . . 515 The Cloverleaf Feed . . . . . . . . . . . . . . . . . . . . . . . . 535.1 Inspiration and Confirmation of the Cloverleaf Idea . . . . . 535.2 CHIME Cloverleaf Feed . . . . . . . . . . . . . . . . . . . . . 545.2.1 Further Test of the Full Feed Model . . . . . . . . . . 545.2.2 Cloverleaf Feed Design and Optimization . . . . . . . 555.2.3 Realization of the Optimized Cloverleaf Feed Design . 576 Manufacture and Deployment of The Cloverleaf Feeds . . 616.1 Specifications of the Designed Cloverleaf Feed . . . . . . . . . 616.2 Manufacture Process . . . . . . . . . . . . . . . . . . . . . . . 636.3 Sky Data Taken from Deployed Cloverleaf Feeds . . . . . . . 667 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73vList of Tables3.1 Input impedance comparison for half-wavelength dipole fordifferent values of rN, while fixing gN=100. . . . . . . . . . . 284.1 HPBW comparison among the 4sq, 4pt and 4sl. . . . . . . . . 415.1 Designed parameters of the cloverleaf feed in CHIME band. . 576.1 Details on The Cloverleaf Feeds’ Acceptance Test. . . . . . . . 63viList of Figures1.1 Evolution history of the universe . . . . . . . . . . . . . . . . 21.2 Hyperfine splitting of neutral hydrogen . . . . . . . . . . . . . 41.3 The CHIME reflector . . . . . . . . . . . . . . . . . . . . . . . 62.1 Structure of the 4sq antenna . . . . . . . . . . . . . . . . . . . 92.2 A diagram to illustrate how the 4sq feed is balanced . . . . . 102.3 A diagram to illustrate the general idea of in-pair feeding . . 112.4 Measured performance of the CHIME 4sq . . . . . . . . . . . 132.5 The active 4sq . . . . . . . . . . . . . . . . . . . . . . . . . . 142.6 Measured beam of the active 4sq . . . . . . . . . . . . . . . . 152.7 The 4pt built as a modification of the 4sq . . . . . . . . . . . 162.8 The 4sl built as a modification of the 4sq . . . . . . . . . . . . 173.1 A simple example of Grasp model . . . . . . . . . . . . . . . . 193.2 Dipole antenna . . . . . . . . . . . . . . . . . . . . . . . . . . 213.3 The dipole model setup in CST . . . . . . . . . . . . . . . . . 243.4 Currents of the half-wavelength dipole simulated by CST . . . 263.5 Comparison of dipole’s current distributions among CST FDTD,python MoM and analytical solution . . . . . . . . . . . . . . 274.1 Petal board model of the 4sq in CST . . . . . . . . . . . . . . 304.2 Simulated current pattern of the 4sq . . . . . . . . . . . . . . 314.3 Bent dipole model for representation of the 4sq . . . . . . . . 324.4 Simulated 3D beam pattern of the 4sq at 600 MHz . . . . . . 334.5 Simulated E plane and H plane of the 4sq . . . . . . . . . . . 344.6 H plane’s beam width comparison between simulation andmeasurement . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.7 the 4pt petal board model . . . . . . . . . . . . . . . . . . . . 374.8 Simulated beam pattern of the 4pt at 600 MHz . . . . . . . . 384.9 The 4sl petal board model . . . . . . . . . . . . . . . . . . . . 394.10 Beam pattern of the 4sl at 600 MHz . . . . . . . . . . . . . . 404.11 Diagram of a transmission line and its lumped circuit model . 42viiList of Figures4.12 Diagram of impedance transformation of the transmission line 444.13 Return loss comparison between impedance transformationmethod and measurement . . . . . . . . . . . . . . . . . . . . 464.14 Zin of a single short-ended microstrip tranmission line . . . . 474.15 A model of 4sq’s petal board fed by only one microstrip trans-mission line . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494.16 Input impedance comparison between direct simulation andimpedance transformation in the context of one microstripfeeding the 4sq petal board . . . . . . . . . . . . . . . . . . . 504.17 Full feed model of the 4sq . . . . . . . . . . . . . . . . . . . . 514.18 Return loss comparison between full 4sq model simulation andmeasurement . . . . . . . . . . . . . . . . . . . . . . . . . . . 525.1 A cloverleaf prototype in MOST band . . . . . . . . . . . . . 545.2 A cloverleaf prototype in CHIME band . . . . . . . . . . . . . 555.3 Parametrization of petal shape of the cloverleaf antenna . . . 565.4 A three-stage transmission line for the cloverleaf antenna . . . 575.5 The cloverleaf feed built according to the designed parameters 585.6 Return loss comparison between measurement and simulationof the CHIME cloverleaf feed . . . . . . . . . . . . . . . . . . 595.7 Measured beam pattern of CHIME cloverleaf feed . . . . . . . 606.1 Annotations to manufacture the cloverleaf feed . . . . . . . . 626.2 Panelization of the base boards and stem boards . . . . . . . 646.3 A jig for assembling the cloverleaf feeds . . . . . . . . . . . . 656.4 The cloverleaf feeds installed on CHIME pathfinder . . . . . . 656.5 One pulse measurement of the pulsar B0329+54 from thecloverleaf feed on CHIME pathfinder . . . . . . . . . . . . . . 666.6 Holography to measure a slice of reflector beam . . . . . . . . 686.7 Grasp simulation of reflector beam and its comparison to mea-surement in terms of beam width . . . . . . . . . . . . . . . . 69viiiAcknowledgementsI would like to thank MITACS for their financial support during my masterprogram. I would like to thank many people at DRAO for their support.I am very grateful for all the help I received from the CHIME team and Ifeel honored to work with CHIME. I want to say sincere thanks to MandanaAmiri, Gregory Davis, Don Wiebe, Mateus Fandino, Rick Smegal and TomFelton who help me with great patience and long-term support. I wouldlike to say many thanks to Gary Hinshaw for his patience, encouragementand guidance. I am very appreciative of all the help, advice and insight Igot from my supervisor Mark Halpern. At last but not least, I want to saysincere thanks to Yang Lan who helped through my whole master programwith great patience, encouragement, problem-solving and devotion.ixChapter 1IntroductionThe Canadian Hydrogen Intensity Mapping Experiment (CHIME)1 [1] isan ongoing interferometric radio experiment to measure properties of darkenergy. In particular, CHIME will map neutral hydrogen distribution byobserving the 21cm hyperfine transition line in the redshift range 0.8 < z <2.5.1.1 The Existence of Dark EnergyFig. 1.1 shows the evolution history of the universe. The far left is the earliestmoment we can now probe, when a period named inflation is hypothesizedto have produced a burst of exponential growth of the universe’s size. At theend of inflation, there are photons, electrons, protons, neutrons, neutrinos,dark matter and other form of energy. Photons interact very rapidly withcharged particles so they are trapped in this hot, dense plasma. As timegoes on, the universe cools down because of expansion. When the universe’stemperature cools down to ∼3000 K, electrons and protons begin joiningtogether to form neutral hydrogen. This process frees photons and makesits free path almost size of the universe. This era is called recombination.The released photons forms Cosmic Microwave Background (CMB), whichcan be seen today from every direction with a temperature 2.7 K.Later on, local neutral hydrogen condenses due to attractive gravitationalforce. The core of those condensed neutral hydrogen has higher and highertemperature and pressure, which ignites nuclear reaction. These are the firststars generated. As time goes on, local stars get closer to each other toform first galaxies due to attractive gravitational force again. During thiswhole process, expansion of the universe is decelerating because attractivegravitational force is the only long-distance force.What is very strange is that, during the development of galaxies, expan-sion begins to accelerate. A direct measurement to support this accelerationcomes from supernovae observation by measuring their luminosity distances1http://phas.ubc.ca/chime11.2. Properties of Dark Energy is MeasurableFigure 1.1: A figure to illustrate the evolution history of the universe over13.7 billion years. Time evolves in the horizontal direction. 3D universe ata time is depicted by a cross section of the grid. Image credit:NASA/WMAP Science Team.[2, 3]. A model to explain this acceleration is dark energy (DE) [4]. Definew to be w ≡ Pρ , where P is pressure and ρ is the energy density. For normalmatter, pressure is negligible, so w ≈ 0. For radiation, w = 13 . By solvingthe Einstein equations, the energy density of dark energy evolves like:ρDE ∝ exp{−3ˆ a da′a′ [1 + w(a′)]}, (1.1)where a is size of the universe if size of the universe today is defined to be 1.Among all possible values of w, wDE = −1, which indicates constant darkenergy density through expansion, is consistent with data [5, 6].1.2 Properties of Dark Energy is MeasurableAs indicated above, properties of dark energy has not been uniquely decidedfrom the existing observations. Among different models of dark energy, there21.2. Properties of Dark Energy is Measurableare distinct predictions of expansion history, especially in the redshift range0.8 < z < 2.5, which is the range that CHIME wants to measure. Theredshift, z, is defined asz + 1 ≡ λobservedλemitted= 1a, (1.2)where λemitted is the wavelength of a signal when it was emitted, λobserved iswavelength of a signal when it is later observed.1.2.1 Baryon Acoustic OscillationsBefore recombination, photons and charged matter (electrons and protons)are coupled to each other due to Compton scattering. The universe is like avery hot, dense, simple plasma, but it is not absolutely evenly distributed.An over dense spot can be initialized by quantum fluctuations. Attractivegravitational force tends to strengthen this over dense spot, while interactionbetween photons and charged particles generates heat and creates outwardpressure. The counteracting inward gravitation and outward pressure cre-ate oscillations, which are called Baryon Acoustic Oscillations (BAO). Theseoscillations result in an outgoing spherical wave from the over dense spot.Charged particles and photons travel together with this spherical wave whiledark matter stays in the over dense spot because it interacts only gravi-tationally. The spherical wave keeps going outward until recombination ofelectrons and protons frees photons from them and releases pressure fromthe whole system. From then on, photons travel freely in space, while thecombined neutral hydrogen stays on the spherical shell and keeps attractinglocal matter to the shell due to gravitation. Therefore, a special pattern ofmatter distribution is formed and strengthened. The radius of the spheri-cal shell is called sound horizon, whose size only changes proportionally tosize of the universe. In fact, lots of over dense spots were generated beforethe recombination. Therefore, it is not one spherical shell in the universebut an interference of many of them, like the pattern in a pond with manyraindrops.Measuring the two point correlation function across a large section ofsky would reveal BAO pattern statistically. Therefore BAO can be usedas a standard ruler because comparison of its angular size to its redshiftconstitutes a measurement of the expansion history, given that its comovingsize is known from CMB measurement to be 150 Mpc.31.3. Overview of CHIME as A New Dark Energy Experiment1.2.2 21cm ObservationBAO can be seen in the neutral hydrogen distribution because neutral hydro-gen traces the matter distribution on large scales. A key feature of neutralhydrogen to make BAO measurement possible is that the neutral hydrogenemits or absorbs radio wave at 1420 MHz due to hyperfine splitting of itsatomic energy level, which is shown in Fig. 1.2. This radio wave is called HIemission or 21cm signal. In the redshift range 0.8 < z < 2.5, apparent fre-quency of HI emission will be redshifted to the range (400MHz, 800MHz).Therefore, measuring 21cm signal as a function of frequency is to measurethe matter distribution as a function of redshift. CHIME’s frequency reso-lution is set to around 0.5 MHz, which is much finer than 10 MHz frequencyresolution required to resolve BAO scale to its third harmonics.Figure 1.2: Hyperfine splitting of neutral hydrogen correspond-ing to 21cm transition. Image source: http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/h21.htmlOne of the biggest challenge in 21cm observations is to remove foregroundcontamination, which is a thousand times brighter than the 21cm signal. Theforeground removal strategy [7] is based on the fact that 21cm signal is nota smooth function of in frequency because of large scale structure in theuniverse while foreground signals from galaxies or point radio sources are allsmooth.1.3 Overview of CHIME as A New Dark EnergyExperimentThe proposed CHIME consists of five cylindrical reflectors with no movingparts, as shown in Fig. 1.3 (a). Each of them is 20 m wide, 100 m long and 541.3. Overview of CHIME as A New Dark Energy Experimentm high at focus. It is will drift scan northern half of the sky every day becauseof earth’s self rotation. Half of the sky measurement in the redshift range0.8<z<2.5 corresponds to a survey volume around 203(h−1Gpc)3, in whichboth angular size and radial size of BAO can be resolved. CHIME’s largesurvey volume is important for measuring BAO statistically. In addition,cylindrical reflectors cost much less compared with dishes since cylindricalreflectors are curved in only one dimension.To measure the universe’s expansion history around 0.8<z<2.5, CHIMEneeds to invent specialized feed deployed as element of feed array on thefocal line of reflectors. Specialized feed designed for CHIME is the topicof this thesis. CHIME needs to invent cheap Low Noise Amplifier (LNA)[8], which is right after the feed element in the analog chain. CHIME alsoneeds to invent digital FX correlator after the analog chain to do Fouriertransformation and product correlation of large amount of data.CHIME PathfinderBefore implementation of the full CHIME, CHIME pathfinder has been built.The CHIME pathfinder consists of 2 cylindrical reflectors, each of them tobe 20 m wide and 36.8 m long, at the site of DRAO, as shown in Fig. 1.3(b). Signals are received from sky through feeds on the focal line and thenamplified by the LNA. Coax cables are used to transport signal from focalline to the C-Can, which is an Radio Frequency (RF) shielded room. Filtersare followed to get signal in the 400 MHz to 800 MHz range. Then withappropriate attenuators, analog signals are digitalized by the Analog to DigitConverter (ADC), then Fourier transformed and correlated by FX correlatorfor data manipulation and analysis. This chain of CHIME pathfinder isalmost the same as that of the full CHIME. Therefore, the pathfinder isa fairly good representative of the full CHIME so that it can be used forseeking answers of some crucial questions.Several examples of those crucial questions are:• Does the current design of feed and reflector give the beam that canbe used to extract scientific signals?• Are the gain and phase of the LNA stable enough or at least tractable?• Does the FX correlator work as what we hope?• Can the overall system be calibrated?• Shall we use beamforming orN2 correlation as the calibration strategy?51.3. Overview of CHIME as A New Dark Energy ExperimentFigure 1.3: (a) Reflectors of the proposed full CHIME. (b) A picture of theCHIME pathfinder at the DRAO site.6Chapter 2Starting Point for the CHIMEFeed DevelopmentCHIME will use linear arrays of antennas placed along the focal line ofeach cylindrical reflector to examine extremely weak signals. To optimizethe Signal to Noise Ratio (SNR) of this measurement, the antennas mustefficiently transmit astronomical signals to the first stage amplifiers, whichis LNA, while introducing only minimal noise to the system. Therefore eachindividual antenna must have the following properties.1. The feed needs to have smaller than -10dB Return Loss (RL)2 across400-800 MHz range, where RL is defined asRL ≡ 10log10PrefPin= 20log10|Γ|. (2.1)Pref is the reflected power, Pin is the incident power and Γ is the re-flection coefficient due to impedance mismatch between feed and LNA.2. The feed needs to have two polarizations to fully measure the incidentfields.3. To make full use of the reflector surface, CHIME feed needs to havewide beam pattern because the focal line’s angle to the EW edges ofreflector is 90 degree and angle to the NS edges of reflector is 86 degree.4. Size of each element should be small enough so that it can be placedinto the feed array which has 30 cm separation between elements.5. The feed should be low-cost and highly repeatable to be mass producedbecause the full CHIME is going to deploy 1280 feeds in total.6. Location of phase center of all frequencies must be the same.2Here the dB expression of return loss is defined to be negative. The smaller the returnloss, the smaller the reflected power. In some cases, the dB expression of return loss mightbe defined to be positive as −10log10PrefPin72.1. The Four Square Antenna as the First Candidate for the CHIME Feed7. The feed must be low-loss to reduce system noise.The first requirement is there because low return loss results in high SNR,which is an important parameter to describe the efficiency of an experiment.SNR of CHIME isSNR = Tsky,measuredTsys= Tsky(1− |Γ|2)Tsys= TskyTsys/(1− |Γ|2), (2.2)where Tsys/(1 − |Γ|2) is the effective system temperature. The existence ofmismatch between feed and LNA results in higher effective system temper-ature. In the case of CHIME, Tsys is around 50 K, so that -5 dB returnloss of feeds results in an effective system temperature to be around 73 Kwhile -10 dB return loss of feeds results in an effective system temperatureto be around 55 K. This difference in effective system temperature, ∼ 20K, is substantial compared to the original 50 K system temperature. Onthe other hand, even with a perfect match between feed and LNA, effectivesystem temperature can only be reduced further by 5 K. Therefore, -10 dBreturn loss is decided to be the minimum requirement of the CHIME feed.2.1 The Four Square Antenna as the FirstCandidate for the CHIME FeedWe have copied the Four Square Antenna (4sq) [9–12] tuned for MolongloObservatory Synthesis Telescope (MOST) [13, 14] because the 4sq comesclose on so many of our antenna requirements. The 4sq has the advantageof dual polarization, low cost, high repeatability, wide beam pattern acrossa wide range, high polarization purity and relatively wide bandwidth, whichis around 2:1 at -5dB RL level after being scaled to the CHIME band.Structure of the 4sq is shown in Fig. 2.1. It consists of 6 printed circuitboards (PCB), which are 1 baseboard with 2 SMAs, 4 stem boards with fourmicrostrip transmission lines and 1 radiating petal board. The baseboardand stem boards together are the baluns to transform unbalanced signal atSMA port to balanced currents in the radiating petal board82.1. The Four Square Antenna as the First Candidate for the CHIME Feed(a) (b) (c)Figure 2.1: (a) Perspective view of the 4sq. (b) Top view of the 4sq, whichshows the radiating petal board. (c) Bottom view of the 4sq, which showsthe baseboard with 2 SMA and each of them connects 2 microstrip traces.All these four traces continue to four microstrip transmission lines along thefour stem boards.2.1.1 Working Principles of the 4sqDual-polarization response of the 4sq is achieved through a feeding techniquecalled the in-pair feeding.The easiest way to understand the in-pair feeding is to view the 4sq intransmitting mode. For one polarization, excitation signal is fed to one SMA.The signal is split into two to follow two curved transmission lines on thebase board, each of which leads to a transmission line on one of the stemboards. These two split signals are carried along these two stem boards untilthey reach two of the four ports at the petal board. Each port feeds a pairof adjacent petals, as shown in the left of Fig. 2.2, where the red shieldedsections are defined as a port. It can be seen that there are four ports in total.The two ports which are excited under this polarization are not adjacent toeach other. Therefore all four petals are involved as two parallel pairs.The right of Fig. 2.2 illustrates how balanced currents on petal A andpetal D are transformed from unbalanced signal on stem A. Microstrip stemboards are represented by coax cables for easier illustration. To be morespecific, bottom layer of a stem board, which is grounded, is represented bya coax’s metal shielding and top layer of a stem board, which is the microstriptrace, is represented by the center conductor of a coax. We can see that byintroducing an extra connection between petal D and bottom layer of stemD, currents on the pair of petals are balanced. This extra connection mapsto the gray shielded section in the left.92.1. The Four Square Antenna as the First Candidate for the CHIME FeedFigure 2.2: Compared with the real petal board in Fig. 2.1 (b), the left is adiagram of 4sq’s petal board which exaggerates the center part to illustratehow transmission lines’ leads on stem boards connect to petals. The fourpetals are named respectively as A, B, C and D. The four empty slots areused for insertion of the four stem boards. Stem boards are named A, B, Cand D the same order as petals. The red parts is defined as a port. Thereare four ports in total on 4sq’s petal board. The right part of this figureshows how currents on petal A and petal D are balanced from unbalancedsignals on stem A by introducing an extra connection between petal D andbottom layer of stem D. This extra connection maps to the gray shieldedsection in the left.Similarly, for the other polarization, excitation signal is fed to the otherSMA, which is split into two signals following the other two transmissionlines and feed petal board at the other two ports. All four petals then workas two parallel pairs of petals whose pattern is perpendicular to that of theprevious polarization. A simplified figure to illustrate the general idea ofin-pair feeding is shown in Fig. 2.3.102.1. The Four Square Antenna as the First Candidate for the CHIME FeedFigure 2.3: This figure shows the general picture of in pair feeding for bothpolarizations of the 4sq. The naming convention for petals and stem boardsis the same as Fig. 2.2. The details on transmission lines along the baseboard and stem boards are excluded, so it is not a circuit diagram.The 4sq’s wide bandwidth can be achieved because baluns are microstriptransmission lines, which have great flexibility to transform impedance fromthe petal board port to standard 50 Ohm at SMA.2.1.2 CHIME 4sq on the Two Dish SystemA set of 4sq, scaled to the CHIME band, were deployed on the two dish sys-tem, which is a two-element interferometer located at DRAO as the simplestinterferometer prototype of CHIME.Through the measurements with this two-dish system, we have decidedto use low-loss Teflon as substrate of baluns in the future because lossydielectrics in the balun substrate increases the system temperature.Petal boards of the MOST 4sq are double-layer and viaed to reducematerial loss. To test the effectiveness of this strategy, noise temperatures oftwo CHIME 4sq have been estimated with the two dish system. These twofeeds are exactly the same with viaed double-layer petal boards, except oneof them has FR4 based petal board while the other has Teflon based petalboard. Fig. 2.4 (a) shows the rough estimation of their noise temperature.The similar noise temperature of these two feeds proves that lossy dielectricmaterial in the petal board does not increase system temperature because ofvias. Therefore, in the future, petal board would be double-layer and viaed,with lossy but cheap FR4 as the substrate.We have found the two-dish system with the 4sq feed is noisier than thetolerable level, mainly due to 4sq’s impedance mismatch to LNA. Return lossmeasurement of the CHIME 4sq is shown in Fig. 2.4 (b). It can bee seenthat: firstly, return loss is smaller than -5dB rather than required -10 dB ina 2:1 bandwidth; secondly, that band is higher than CHIME’s desired band.112.1. The Four Square Antenna as the First Candidate for the CHIME FeedImpedance match between feed and LNA is a key aspect that is improved inthis thesis.In the manufacture point of view, the 4sq is robust enough to last severalwinters unprotected.122.1. The Four Square Antenna as the First Candidate for the CHIME Feed(a)(b)Figure 2.4: (a) Rough estimation of noise temperature of 2 4sq feeds. Oneof them has FR4 based petal board while the other one has Teflon basedpetal board. (b) Return loss measurement of the CHIME 4sq.132.2. The Active 4sq2.2 The Active 4sqRather than having LNA to be an independent element in the analog chain,LNA can be incorporated to feed, by designing a low noise amplifier circuitto feed the 4sq’s petals directly without introducing baluns. This is calledan active feed. We explore this option to eliminate the baluns and thus theloss in the baluns. An active 4sq has been designed and built by GregoryDavis, as shown in Fig. 2.5. Fig. 2.6 shows the measurement of its beampattern by Keith Vanderlinde. It can be seen that the beam patterns are notsmooth and there is non-negligible asymmetry in the co-polar beams becausethe LNA circuit does not balance petal currents well. Therefore, this kindof active feed is rejected.(a) Perspective view of the active 4sq (b) Side view of the active 4sqFigure 2.5142.2. The Active 4sqFigure 2.6: Active 4sq’s beam measured by Keith Vanderlinde in the Uni-versity of Toronto. Pol P2 is the polarization parallel to E plane, ie, xzplane. Pol P1 is the polarization parallel to H plane, ie, yz plane.152.3. The Four Point feed and The Four Sleeve feed2.3 The Four Point feed and The Four Sleeve feedThe 4sq feed has the problem of impedance mismatch to LNA, so two mod-ifications of 4sq have been tried, which are the four point feed (4pt) and thefour sleeve feed (4sl). They are also based on in-pair feeding technique.Fig. 2.7 (a) shows a picture of the 4pt and Fig. 2.7 (b) shows themeasured return loss of this 4pt. It can be seen that bandwidth of the 4ptis still far away from CHIME’s requirements.(a) (b)Figure 2.7: (a) A picture of the 4pt built as a modification of the 4sq. (b)Measured return loss of the 4pt.Fig. 2.8 (a) shows a picture of the 4sl. Each petal looks like a sleeve.There are two extra disks added on top of the petal board. They are usedto tune the impedance. Fig. 2.8 (b) shows the measured return loss of this4sl with tuning of the two disks. It can be seen that bandwidth of the 4slis pretty satisfying. However, its petal size is too big to be azimuthallyrotated in the CHIME feed array. Azimuth rotation of feed in CHIME arrayenables the ability to do more tests. Moreover, disks above the petals arefloppy and do not survive field environment. Removing floppy disks makesthe impedance match of the 4sl no better than the 4sq or the 4pt.162.3. The Four Point feed and The Four Sleeve feed(a) (b)Figure 2.8: (a) A picture of the 4sl built as a modification of the 4sq. (b)Measured return loss of the 4sl.These two trials, along with some other modifications, are not satisfyingto be used as CHIME feed. Therefore, a new feed needs to be designed.17Chapter 3MethodTo design a wide bandwidth feed for CHIME, the loop is: begin with de-signing a feed; then simulate it with CST; after simulation, the designedfeed is built and measured; measured results are compared to simulated re-sults to verify the simulation; disagreement between measurement and sim-ulation leads to re-simulation of the design until they agree; if agreementbetween measurement and simulation is achieved, a new design is formedbased on performance of the previous design, previous steps are looped untilall CHIME’s feed requirements are satisfied by a particular design.Feed itself can be simulated by Computer Simulation Technology (CST)3 to get its current pattern, beam pattern and impedance spectra. Amongthem, beam pattern can be measured in the anechoic chamber in Universityof Toronto, impedance spectra can be measured by Vector Network Analyzer(VNA) in the UBC lab.Feed installed on focal line can be simulated by Grasp 4 to get the skybeam, which is a reflection of feed illumination on the cylindrical reflector. Aslice through the far-field beam of the telescope can be measured by observingthe signal as a pulsar or bright source transits, and these measurements arecompared to models.3.1 GraspGRASP is a commercial software package which simulates optical beams byapplying the physical theory of diffraction (PTD) and physical optics (PO)to calculate currents when a transmitting antenna illuminates a reflector.The basic simulation procedure is:1. a user sets up geometry of feed and reflector;2. surface of reflector is meshed automatically by Grasp;3https://www.cst.com/4http://www.ticra.com/products/software/grasp183.1. Grasp3. the user imports the beam pattern of feed from CST simulation asillumination to reflector;4. E field and B field are calculated by Grasp at each mesh grid on thereflector’s surface according to the feed illumination pattern;5. induced current on each mesh grid is calculated through PO or PTDfrom field distribution on reflector’s surface; and6. field radiated from the current distribution in step 5 is calculated andadded to the original field.CHIME’s beam to the sky is the far-field limitation of step 6. As anexample, Fig. 3.1 visualizes the above procedure. If there are additionalstructures involved to make the system have multi-reflection path, step 4-5-6 would be looped to include the additional reflections.Figure 3.1: An offset circular dish together with a feed at its focus with onereflection path considered to illustrate Grasp simulation procedure.Grasp will be used to simulate interaction between feed and reflector toget beam on the sky after feed has been designed by CST.193.2. CST3.2 CSTCST has different solvers for electromagnetic analysis under different cases.The one used in CHIME feed design is transient solver 5. The basic principleof transient solver is Finite-Difference Time-Domain (FDTD) [15], whichsolves Maxwell equation in 3D spatial grid step by step in the time domain.3.2.1 CST Simulation OverviewA CST user must construct a three dimensional model of an antenna andmake several operational choices, particularly about the desired accuracyof results, the distance scale of physical interpolation (the mesh scale forcalculations), the size and shape of the volume to be simulated and thefrequency range of interest.CST treats the antenna under study as a transmitter, which is simplytime-reversed from our intended use, and calculates a beam pattern usingthe following steps.1. Generates a closed box whose walls are a few perfect matching layers(PML) to encompass the antenna totally but do not touch it.2. Meshes the entire space, which is closed by PML, according to an-tenna’s material properties and dimensions.3. Feeds an excitation signal in time domain to antenna’s input port, suchas SMA port.4. Starts updating E field, B field, current and charge at all mesh gridsonce a time by following the FDTD algorithm.5. Calculates and stores total energy in the closed box at each time stepand stops calculation if total energy is smaller than some user specifiedvalue.The physical picture of step 4 is: the excitation signal, started from theinput port, propagates along the mesh grids as time goes; signals propagatein space until they reach PML layers and get absorbed because of specialElectromagnetic properties of PML, just like in open space without anyreflection back to structure.In the post process, signals in time domain at the input port are storedand go through FFT to get input impedance in the frequency domain. E5https://www.cst.com/Products/CSTmws/TransientSolver203.2. CSTfield in time domain on the inner surface of PML are stored and go throughFFT to get signal in frequency domain. Then for each frequency channel,E field on PML’s inner surface is integrated and transformed to get far-fieldbeam pattern. E field or B field or current at any mesh knot in the closedspace can be stored for other usage, for example, to get material loss and toview current distribution.3.2.2 Test of our Approach to CST through A DipoleModelThe validity of our approach to CST simulation is checked through dipole,which is the simplest and most widely used antenna. The basics of dipoleis two identical conductive elements, such as two rods, fed in the middle bytransmission line, as shown in Fig. 3.2 (a). What we are interested is thehalf-wavelength dipole whose total length is half of the working frequency’swavelength, ie, L = λ/2.(a) (b)Figure 3.2: (a) A typical dipole with two conductive elements whosetotal length is L. For convenience, origin of the coordinate system is setat the center of dipole, and the z-axis is along the dipole. (b) Currentdistribution in sine form. Image source: http://electronicdesign.com/site-files/electronicdesign.com/files/uploads/2013/07/0613WTDantennas_FIG2.gif.The performance of dipole is well measured, widely accepted and canbe worked out analytically under ideal assumptions or numerically throughMothods of Moments (MoM) using Python or numerically through FDTD,which is realized by CST simulation.All these three approaches to work out the performance of the dipoleare carried out and compared to each other to validate our understanding ofCST.213.2. CSTAnalytical CalculationIn the ideal case, the rods are infinitely small, there is only current parallelto z-axis. The gap between the rods is also infinitely small so that it doesnot affect current distribution. At the end of each rod, the current is zerosince there is just no where for the current to go. At each single frequency,the current distribution should be a sine function, as shown in Fig. 3.2 (b)and Eq. 3.1:I(z) ={I0sin[k( l2 − z)], 0 ≤ z ≤ l2I0sin[k( l2 + z)],− l2 ≤ z < 0,(3.1)where k is the wave number defined by k ≡ 2piλ .Since current distribution is already known under ideal case assumption,the next important parameter of an antenna would be its input impedance.Real part of input impedance is calculated first for simplification. The ideato calculate real input impedance is that: real input impedance representspower radiated off by the antenna through the input port. Since P = I(t)×V (t), power has a non-zero average if the ratio V/I is real. Power has a zeroaverage if the ratio V/I is imaginary therefore imaginary input impedancerepresents power stored near antenna:Prad =|Iin|22 Rin, (3.2)where Prad is radiated power, Iin is current at input port and Rin is realpart of input impedance.To calculate the real part of input impedance, first calculate far fieldaccording to current distribution, as:Eθ ' jηI0e−jkr2pir [cos(pi2 cosθ)sinθ ] (3.3)Hφ ' jI0e−jkr2pir [cos(pi2 cosθ)sinθ ], (3.4)where η is the intrinsic impedance of the vacuum, defined as η ≡√µ0ε0 '377 (Ohm).As a result, the power in the farfield isPrad =" 12Re[E ×H∗]ds = η I204piˆ pi0cos2(pi2 cosθ)sinθ dθ = η|I0|28pi Cin(2pi),(3.5)223.2. CSTwhere Cin(x) = 0.5772 + ln(x)−´ cos(y)y dy.Therefore, the real part of input impedance Rin isRin = 2×PradI20' 73 (Ohm). (3.6)Similarly, to get the imaginary part of input impedance, near field iscalculated from current distribution and then integrated along the surface ofdipole, as shown in Chapter 8 of [16]. The full input impedance for an idealdipole isZin = 73 + 42.5j (Ohm). (3.7)MoM Numerical CalculationMethod of moments (MoM) is generally believed to be a reliable numericalmethod to analyze EM problems, but sometimes it can be very time consum-ing. To apply MoM method to dipole, the basic assumption is that currenton the rods of dipole has only z-component and has no variation on therods’ circumference. Therefore current on the rod surface can be presentedby current in the rod center with equal magnitude.The steps to deploy MoM is:1. apply a voltage Vin to the gap between the two rods;2. with the distance d between the two rods, calculates the E field in thegap simply as Egap = Vind ;3. divide these two rods into small pieces, say N pieces, so that each pieceof rod has the length l = LN . Assume each piece i has its own currentIi constantly distributed along its length;4. calculate the field along the surface of rod generated by these pieces ofcurrents. Field is a function of these currents [I0, I1, ...];5. work out the solution of [I0, I1, ...] so that E field generated by thesecurrents cancels the original E field generated by Vin (As a result,current distribution along the rod is achieved, together with the inputport current Iin. ); and6. with Vin and Iin calculates the input impedance Zin simply as Zin =VinIin .233.2. CSTThe finer the rod is divided, the more accurate the result is. There aresome other small techniques can be applied, such as: current on each smallpiece can be in parabolic or triangular form rather than constant form toimprove the smoothness of currents along the whole dipole. Also, symmetryof dipole can be used to simplify calculation. With this in mind, pythonscripts have been written to calculate current.distribution and input impedance of a half-wavelength dipole.CST CalculationAs mentioned before, to use CST to calculate properties of dipole antenna,a model needs to be set up first, as shown in Fig. 3.3.Figure 3.3: A dipole model set up in CST. The two gray rods are theperfect electrical conductor (PEC) and they are separated by a gap to placean excitation discrete port6, which is the red cone.The parameters to describe this dipole and CST settings are:rN : 2LrN defines the radius of rod. the bigger the rN, the smaller the rodgN : LgN defines the gap between the two rods. The bigger gN, the smallerthe gaplpwv : number of mesh per wavelength, defines the general mesh densitydx : number of mesh lines across the radius of the rod cross section,defines the local mesh densitybodwv : wavelength/bodwv is the nearest distance between PML anddipole antenna243.2. CSTOther parameters can also be manipulated but results are not sensitiveto them, so they are not listed here. In the CST simulation, the bigger thelpwv and dx, the more accurate the result should be. A very important tipis that:no matter what is the object that needs to be analyzed, makesure the simulated result is converged if only CST simulation pa-rameters are refined because there is only one true fact of theobject which does not depend on how it is simulated.Therefore, during the CST simulation procedure, I have refined lpwv, dx,bodwv step by step until the input impedance is converged within 1.5% foreach set of [rN, gN ].Comparison among Analytical Solution, Python MoM and CSTFDTDAfter current distribution and input impedance of dipoles have been ob-tained through these three methods, these results are compared to check ourapproach to CST simulation.Fig. 3.4 shows the three components of dipole’s currents simulated byCST. It agrees with the analytical assumption and MoM assumption that,currents are mainly aligned along the z-axis. Z-component of currents cal-culated from different methods are compared in Fig. 3.5. It is shown thatthey generally agree with each other, the small difference between CST andanalytical calculation is caused by the finite gap and finite radius of rod inthe CST model, while the analytical calculation is assuming an ideal case. Itis not clear here to say which result is more accurate, but it definitely con-firms that CST simulation here repeats classic idea. Confirmation of CST’sability to simulate current is also a confirmation of CST’s ability to simulateantenna’s beam pattern.253.2. CST150 100 50 0 50 100 150location along dipole [mm]020406080100120140magnitude of current components from CST [A]x-component of currenty-component of currentz-component of currentFigure 3.4: Three components of dipole’s currents simulated by CST. Thehalf-wavelength dipole’s frequency is centered at 600 MHz, so its length is250 mm. X-component and Y-component are almost zero, which repeats theclassic picture that currents on dipole mainly allign with the rods.263.2. CST150 100 50 0 50 100 150location along dipole [mm]0.00.20.40.60.81.0magnitude of z-components of current [A]MoM simulationCST simulationanalytical calculationsFigure 3.5: Z-components of current distribution given by MoM simulationCST simulation and analytical calculation are compared. The good agree-ment among them validates my approach to CST to understand dipole’scurrent pattern.Another important parameter of antenna is input impedance and itscomparison among these three approaches is shown in table 3.1. As rN getsbigger, the value given by CST is closer to analytical value, and it shouldbe. When rN gets bigger than 10100, CST is not able to simulate becausethe very small structure requires very small mesh, thus too much memory isneeded. For finite value of rN , the different impedances given by CST andMoM imply 1 % difference in reflected power, which is already the best thatCST can do. I find this level of agreement is good enough to support myapproach to CST considering that MoM has simplified assumptions too.The agreement on both current distribution and input impedance amongCST simulation, MoM method and analytical solution under ideal assump-tion confirms the validity of CST and my understanding of it. Therefore,CST would be used in the future analysis and design.273.2. CSTTable 3.1: Input impedance comparison for half-wavelength dipole for dif-ferent values of rN, while fixing gN=100.rN 1000 5000 10000 10100 20000 ∞ (theory)CST(real, imaginary) (86,54.1) (82,50.8) (80,47.5) (79, 48.9) N/A (73,42.5)MoM(real, imaginary) (83,44.3) (76,42.4) (75,42.0) (75,42.0) (74,41.8) (73,42.5)3.2.3 Plan of UseTo design a CHIME feed, following plans to use CST are made.1. CST Model of 4sq and its variants would be constructed to get theircurrent distributions so that our physical understanding of these feedswould be improved. Beam pattern would be modeled at the sametime and compared to measurement so that validity of models can bechecked.2. The 4sq would be modeled by CST through various efforts until sim-ulated impedance spectra agree with measurement. The ability tosimulate impedance spectra accurately is mandatory before applyingCST to design wide bandwidth feed.3. The believable simulation technique gained from step 2 would be usedto test different ideas of designing until a promising design is found.4. The same technique would be applied again to optimize the designfound in step 3 until CHIME’s specific requirements are satisfied.28Chapter 4Modeling the CurrentPatterns, Beam Shapes andImpedance Spectra of SingleFeed 4sq and its VariantsModeling is to help improve understanding 4sq and its variants so we canget some intuition on how to design a new feed. In addition, the ability tomodel impedance spectra is mandatory to design a new wide band feed.4.1 Visualizing Current Patterns and BeamShapesCST has been used to predict the current pattern and the radiative propertiesof a 4sq antenna, a 4pt and a 4sl.4.1.1 The 4sq and Its Petal board ModelA simplified 4sq petal board model has been built in CST to represent thereal 4sq, as shown in Fig. 4.1 (a). Fig. 4.1 (b) shows the front view of themodel. Frequency range of this model is set to 400 MHz to 800 MHz.294.1. Visualizing Current Patterns and Beam Shapes(a) (b)Figure 4.1: (a) Petal board model of the 4sq. Petal board and ground planeare present but stem boards and baseboard are not included because theyare measured to have almost no influence on the beam pattern. Groundplane is just present in space rather than electrically connected to the 4sqantenna. (b) Front view of the 4sq petal board model. Since balun’s usageis to balance current on the petal board, so the complex, detailed feedingtraces on real petal board are replaced with a symmetric discrete port, asshown in the lower right corner. The coordinate system is set that feed ispointing up to the positive z-axis, and feed is excited in the polarizationparallel to the x-axis.Current PatternTo understand radiating mechanism of the 4sq, current patterns at differentfrequencies are needed. Left of Fig. 4.2 shows the current distribution onpetal board at a phase 7 at 600 MHz 8. At each frequency, current at eachspatial point just varies sinusoidally in time, so it is informative enough tolook at absolute magnitude distribution of the current, as shown in the rightof Fig. 4.2.7“at a phase” means at a point in the time domain.8600 MHz is chosen for representation of a wide band antenna because 600 MHz isthe center frequency of our frequency range and 4sq’s radiating property smoothly variesin frequency.304.1. Visualizing Current Patterns and Beam Shapes(a) Current distribution at a phase at 600 MHz(b) Absolute magnitude distribution of current at 600 MHzFigure 4.2: Current pattern of a 4sq which shows that currents concentrateon edges of the petals.314.1. Visualizing Current Patterns and Beam ShapesIt is shown that when the petal board is fed with x-polarized excitationsignal, currents on the y-axis-aligned inner petal edges are opposite in direc-tion, so they attract each other. Currents on the x-axis-aligned inner petaledges are in the same direction, so they repel each other. Finally, currentscondense along the y-axis-aligned inner edges and the x-axis-aligned outeredges. Moreover, since currents along the two pairs of inner edges are inopposite direction, they cancel each other and do not contribute to radia-tion. Currents on these four x-axis-aligned outer edges are all in the samedirection at any time and these currents form the basis of 4sq’s radiationpattern. Therefore, for each polarization, the basics of the 4sq is a pair offace-to-face bent dipoles, fed by a common input, as shown in Fig. 4.3.Figure 4.3: T dipole model representing the basics of current distributionon the 4sq. Gray parts are the metal to represent structure of T dipoles.Red arrows indicate the path and direction of currents excited by the port.Current patterns at other frequencies show the same idea, except thatratio of currents’ magnitude along inner edges to currents’ magnitude alongouter edges changes with frequency.Beam PatternKeith Vanderlinde has measured the H plane of the 4sq, which can be usedto check whether the previous 4sq petal board model is correct or not. If itis correct, simulation of the petal board model can give us information on E324.1. Visualizing Current Patterns and Beam Shapesplane, which is not measured.To begin with a visual idea, Fig. 4.4 shows the 3D presentation of simu-lated 4sq’s beam pattern at 600 MHz. It can be seen that the beam patternis pretty smooth in the forward direction of the 4sq and there are three sidelobes in the backward direction. Note, this beam pattern is for the x po-larization. Beam’s 2D view is shown in Fig. 4.5. Beam patterns at otherfrequencies are similar to this one except for small differences in directivityand beam width. E plane’s beam width across 400 MHz to 800 MHz is∼ 60◦, while H plane’s beam width across band is ∼ 60◦.Figure 4.4: 3D representation of simulated 4sq’s beam at 600 MHz. Thebeam is smooth and broad in the forward direction.334.1. Visualizing Current Patterns and Beam Shapes(a)(b)Figure 4.5: (a) Simulated E plane of 4sq’s beam, with beam width to be58.3◦. (b) Simulated H plane of 4sq’s beam, with beam width to be 85.8◦344.1. Visualizing Current Patterns and Beam ShapesTo better compare the CST simulation with measurement, beam patternof the 4sq at several frequencies in CHIME band are simulated and fittedto a Gaussian distribution with centroid and 3dB beam width as fittingparameters. The same fitting is done for the measurement of 4sq’s H planeat several frequencies. Beam widths from these two fittings are comparednumerically to check CST’s validity, as shown in Fig. 4.6. We can see thereis a pretty good match between simulation and measurements, confirmingour current understanding of current pattern and beam pattern.Figure 4.6: The 4sq’s H plane beam width comparison between CST simu-lation and measurements. They agree well with each other, confirming 4sq’ssimulation and understanding got from simulated results are believable.Centroids of simulated beams are almost zero because geometry of the4sq petal board model and all CST settings are symmetric. Zero centroid isa confirmation of CST simulation. Centroids of measured beams have offsetscompared to simulations because of practical factors, like asymmetric feed-ing traces in the center of petal board and the asymmetric geometry of theanechoic chamber where beams are measured, which are not included in CST354.1. Visualizing Current Patterns and Beam Shapesmodel. Therefore, centroids between simulation and measurement should bedifferent. Further more, we should not bother to try to put these detailsin CST model, because they can be changed in future CHIME feed candi-date and does not affect our current purpose to understand 4sq’s radiatingmechanism.This centroid disagreement is a very good example that we should under-stand what is the model and be clear what is the expected difference betweenmodel and reality. The truth is that we can never build a model which isexactly the same as the real case.4.1.2 4sq’s Variants and Their Petal Board ModelsThe 4pt and the 4sl, which have been built and tested already throughexperimental trials, are modelled to get their current distribution and beamshape. A grasp of the similarity and difference in EM behavior among the4sq, the 4pt and the 4sl is necessary to decide which path to take in futurefeed design.The Four Point FeedThe geometry of 4pt’s petal board is shown in Fig. 4.7 (a), whose 600MHz current distribution at a phase is shown in Fig. 4.7 (b). It can beenseen that it basically follows the same radiating mechanism as the 4sq, ie,currents condense along edges of petals. Beam pattern of the 4pt at 600MHz is simulated, as shown in Fig. 4.8. Compared with beam patterns ofthe 4sq, 4pt’s beams are basically the same. They are smooth and broad inthe forward direction.364.1. Visualizing Current Patterns and Beam Shapes(a)(b)Figure 4.7: (a) Geometry of the 4pt petal board. (b) Current distributionof the 4pt at 600 MHz at a phase. Currents of the 4pt concentrate on edgesagain like the 4sq.374.1. Visualizing Current Patterns and Beam ShapesFigure 4.8: 3D representation of 4pt’s beam at 600 MHz. E plane’s beamwidth is 55.9◦. H plane’s beam width is 77.7◦.The Four Sleeve FeedAnother variant which has been simulated is the 4sl without disks. Thegeometry of the 4sl’s petal board is shown in Fig. 4.9 (a), whose 600MHzcurrent distribution at a phase is shown in Fig. 4.9 (b). It can been seen thatthe 4sl again basically follows the same radiation mechanism as the 4sq andthe 4pt. Simulated beam pattern of the 4sl is shown in Fig. 4.10. Comparedwith beam pattern from the 4sq and the 4pt, the 4sl beam shares the samecharacteristics.384.1. Visualizing Current Patterns and Beam Shapes(a)(b)Figure 4.9: (a) Geometry of the 4sl petal board. (b) Current distributionof the 4sl at 600 MHz at a phase. Currents of the 4sl concentrate on edgesagain like the 4sq and the 4sl.394.1. Visualizing Current Patterns and Beam ShapesFigure 4.10: 3D representation of 4sl’s beam at 600 MHz. E plane’s beamwidth is 53.7◦. H plane’s beam width is 73.7◦.4.1.3 Comparison of Different FeedsTable 4.1 shows the Half Power Beam Width (HPBW) comparison on bothE plane and H plane among the 4sq, the 4pt and the 4sl at 600 MHz. It canbe seen that beam patterns of these feeds are very similar to each other. Thissmall difference does not make a preference to one feed than another. Thissimilarity is also reasonable since wavelength is 500mm at 600 MHz, whichis 2 or 3 times the size of petal board. So modifications of petal board issmall compare to wavelength and cannot be seen strongly in beam pattern.The conclusion is that: modifications of 4sq’s petal board usually do nothurt the smooth and broad beam pattern and might be applied to have widerbandwidth without penalty.404.2. Input Impedance of Single 4sqTable 4.1: HPBW comparison among the 4sq, 4pt and 4sl.models 4sq 4pt 4slE plane width(degree) 58.3 55.9 53.7H plane width(degree) 85.8 77.7 73.74.2 Input Impedance of Single 4sqInput impedance is a key item that needs to be improved from existing feeds.Right now it is the stage to explore CST to reproduce the return loss of aknown feed, the 4sq. So that CST’s ability to simulate CHIME feed can beverified and used for designing.4.2.1 Petal Board Model and Impedance TransformationIt is already known that the 4sq consists of a radiating petal board followedby balancing transmission lines all the way to SMA ports. In the idealpicture, only the petal board needs to be simulated, then impedance trans-formation theory can be applied to calculate the impedance at SMA portsfrom impedance at petal board. This saves lots of simulation time compar-ing with models which include all components of the 4sq. Therefore, petalboard model is firstly tried together with impedance transformation to getimpedance spectra.Transmission Line TheoryA transmission line is a usually a long uniform structure, such as a cable,to carry radio wave. The length of transmission line is comparable to wave-length so circuit theory cannot be used directly. On the other hand, EMfields on a transmission line usually only vary in one dimension, so there isno need to solve field equations in 3D space. [17].The scheme of a transmission line is shown in Fig. 4.11 (a). It extendsuniformly in the x-axis direction to carry EM wave. An equivalent lumpedelement circuit of a small length ∆x of transmission line is shown in Fig.4.11 (b).414.2. Input Impedance of Single 4sq(a)(b)Figure 4.11: (a) Geometry of a part of a transmis-sion line aligned in the x-axis. (b) Lumped elementmodel for ∆x long transmission line. Image source:http://en.wikibooks.org/wiki/Communication_Systems/Wired_Transmission.Apply Kirchhoff’s law to the lumped circuit:v(x, t)−R∆xi(x, t)− L∆x∂i(x, t)∂t = v(x+ ∆x, t) (4.1a)i(x, t)−G∆xv(x+ ∆x, t)− C∆x∂v(x+ ∆x, t)∂t = i(x+ ∆x, t). (4.1b)Divide Eq. 4.1 by ∆x and take the limit that ∆x→ 0 we get:∂v(x, t)∂x = −Ri(x, t)− L∂i(x, t)∂t (4.2a)∂i(x, t)∂x = −Gv(x, t)− C∂v(x, t)∂t . (4.2b)424.2. Input Impedance of Single 4sqThis is called the telegrapher equation or transmission line equation in thetime domain.In the frequency domain, where EM wave is in sinusoidal steady-statecondition, i(x, t) = i(x)ejωt and v(x, t) = v(x)ejωt, Eq. 4.2 can be rewrittenasdv(x, t)dx = −(R+ jωL)i(x, t) (4.3a)di(x, t)dx = −(G+ jωC)v(x, t). (4.3b)From Eq. 4.3, voltage and current can be solved:d2v(x)dx2 − γ2v(x) = 0 (4.4a)d2i(z)dx2 − γ2i(x) = 0, (4.4b)where γ = α+ jβ =√(R+ jωL)(G+ jωC). The solutions to Eq. 4.4 arev(x) = V +0 e−γx + V −0 eγx (4.5a)i(x) = I+0 e−γx + I−0 eγx, (4.5b)e−γx is the term of wave propagating forward while eγx is the term of wavepropagating backward. γ is the propagation factor of EM wave.Combine Eq. 4.5 and Eq. 4.3:Z0 ≡V +0I+0= −V−0I−0=√R+ jωLG+ jωC . (4.6)The characteristic impedance Z0, determined by internal properties of thetransmission line, equals the ratio of voltage’s magnitude to current’s mag-nitude when EM wave propagates only in one direction.For a lossless transmission line, R = G = 0, then Z0 =√LC is purely realand independent of frequency. Meanwhile γ = jω√LC is purely imaginaryso that wave propagating along the transmission line does not attenuate inmagnitude but only varies in phases.To summarize, voltage and current propagation in a transmission line arev(x) = V +0 e−γx + V −0 eγx (4.7a)i(x) = V+0Z0e−γx − V−0Z0eγx. (4.7b)434.2. Input Impedance of Single 4sqZ0 represents the properties of transmission line itself. There are forwardwave e−γx and backward wave eγx whose magnitude are respectively V +0 andV −0 .The relative magnitudes of V +0 and V −0 are determined by the boundarycondition of a transmission line, ie, the end configuration. For example, Fig.4.12 shows a transmission line ended with a load ZL.Figure 4.12: Load impedance ZL is transformed to Zin by a transmis-sion line with length L and characteristic impedance Z0. Image source:http://www.antenna-theory.com/basics/impedance.phpAt x = 0, apply circuit theory and Eq. 4.7, we getZL =vx=0ix=0= V+0 + V −0V +0 − V −0Z0. (4.8)This givesΓ ≡ V−0V +0= ZL − Z0ZL + Z0, (4.9)where Γ is the reflection coefficient, defined as the ratio of backward waveto forward wave.If length of the transmission line is l, the input impedance Zin isZin ≡vx=−lix=−l= ejγl + Γe−jγlejγl − Γe−jγlZ0 = Z0ZL + jZ0tan(γl)Z0 + jZLtan(γl). (4.10)Eq. 4.10 is the very important impedance transformation equation to trans-form the load impedance to the input impedance of a transmission line. Ifmultiple transmission lines are along the way from load to input, Eq. 4.10should be applied in sequence.444.2. Input Impedance of Single 4sqApplication of Impedance Transformation to CHIME 4sqBased on the impedance transformation theory discussed above, the proce-dure to apply it for 4sq’s input impedance is:1. simulate impedance of a pair of petals at the intersection between thepetal board and stem boards by setting up a CST petal board model;2. calculate shunt impedance at intersection between the petal board andstem boards when look into the transmission line formed by bottomlayers of adjacent stem boards;3. calculate the characteristic impedance of microstrip transmission lines;4. parallelize petal impedance and shunt impedance to get load impedanceof microstrip transmission lines;5. apply Eq. 4.10 step by step, depending on how many stages of mi-crostrips are along baluns, to get Zin at SMA port; and6. parallelize Zin with itself from previous step.For step 1, the model is the same as Fig. 4.1, except that this is theimpedance of a pair of four petals. It needs to be doubled to get impedanceof a pair of two petals; for step 2, the transmission line is short-loaded atbaseboard and a rough estimate of shunt impedance can be made by ananalytical calculation of a parallel plate transmission line; for step 3, char-acteristic impedance of a finite width microstrip is calculated by using em-pirical equations provided by Rogers 9; for step 6, Zin is parallelized withitself because there is another parallel path from petal board to SMA fromin-pair feeding. After step 6, transformed impedance at SMA is comparedto measurement, as shown in Fig. 4.13. There is clearly disagreement.9https://www.rogerscorp.com/documents/783/acm/Design-Data-for-Microstrip-Transmission-Lines-of-TMM-Laminates.pdf454.2. Input Impedance of Single 4sqFigure 4.13: Comparison of 4sq’s return loss between measurement andimpedance transformation method (transformed from simulated impedanceat the petal board).Coupling and ConclusionsEfforts have been made step by step to figure out reasons for the disagreementon 4sq’s return loss between measurement and the impedance transformationmethod.First, it is found that this disagreement is not due to inaccurate estima-tion of shunt impedance, because no matter how I change shunt impedanceand even I exclude it, return loss given by impedance transformation methodis almost the same.Second, validity of Rogers’ empirical equations and CST impedance sim-ulation has been checked by simulation of a single short-loaded microstrip,as shown in Fig. 4.14 (a). Simulated input impedance is compared withimpedance calculated from Rogers equation, as shown in Fig. 4.14 (b). Theirmatch confirms both CST simulation and Rogers’ empirical formula.464.2. Input Impedance of Single 4sq(a)200 400 600 800 1000 1200frequency/MHz0100002000030000400005000060000700008000090000Z_realRogers_calculationcst_simulation(b)Figure 4.14: Input impedance of a single short-ended microstrip transmissionline, given by both simulation and Rogers’ analytical solution. (a) A modelto simulate the input impedance of a short-ended microstrip transmissionline. (b) Real part of input impedance comparison between simulation andempirical equation given by Rogers.474.2. Input Impedance of Single 4sqWith the previous two points in mind, validity of impedance transforma-tion method itself in the context of the 4sq needs to be checked.Therefore, the simplest impedance transformation configuration, which is apetal board fed by one microstrip in the center and a waveguide port feedingthe other end of microstrip to get Zin there, has been set up, as shown inFig. 4.15. Input impedances of this configuration are simulated with lengthof microstrip to be 100 mm, 400 mm and 600 mm respectively. Except fordirect simulation, there are another three ways to get Zin of the 600 mmconfiguration.First, use a 600 mm long microstrip to transform input impedance frompetal board. Second, use a 500 mm long microstrip to transform inputimpedance from the 100 mm configuration. Third, use a 200 mm long mi-crostrip to transform input impedance from the 400 mm configuration. Allthese three transformed Zin are compared with the directly simulated result,as shown in Fig. 4.16.The disagreement shown in Fig. 4.16 (a) and the agreement in Fig.4.16 (c) proves that there is strong coupling between the petal board andmicrostrip, making the part of microstrip close to petal board not an idealtransmission line. Comparison between Fig. 4.16 (b) and Fig. 4.16 (c)shows that the further the microstrip’s part, the less the coupling. Recallthat the analysis of voltage and current distribution on transmission line isbased on the assumption that transmission line is pretty long and isolatedand its EM behaviour is not affected by anything else, it is understandablethat the coupling between petal board and microstrip degrades the validityof applying impedance transformation for the 4sq. Further analysis provesthat there is also strong coupling between stem boards and the baseboard.484.2. Input Impedance of Single 4sq(a)(b)Figure 4.15: (a) Perspective view of a one-stage microstrip feeding the 4sqpetal board. (b) Details on how microstrip feeds the petal board.494.2. Input Impedance of Single 4sqFigure 4.16: (a) Simulated Zin of the 600 mm configuration are compared with (a)impedance transformed from petal board, (b) impedance transformed from the 100 mmconfiguration, (c) impedance transformed from the 400 mm configuration. Left panel isZreal and right panel is Zimag. The conclusion is: there is strong coupling between thepetal board and microstrip.504.2. Input Impedance of Single 4sqThe existence of shunt impedance and in-pair feeding makes any trialto simulate part of the 4sq and to include couplings at the same time notpossible.4.2.2 Full Feed ModelThe impedance spectra given by the petal board model simulation and animpedance transformation are wrong because they ignore multiple couplingsaround. Thereafter, a full 4sq model has been constructed, as shown in Fig.4.17 (a). A full detailed 4sq model cannot be managed by CST, since it costslots of memory to represent the details. Therefore, there are two importantsimplifications in the full feed model.First, the traces on the baseboard are simplified to be clear and sym-metric, as shown in Fig. 4.17 (b). Second, traces of only one polarizationin present. This can be seen in both the baseboard construction and petalboard construction, shown in Fig. 4.17 (c).The first simplification is verified by my previous experiences with CSTthat traces’ length on the base board has little effect on return loss, let alonehow traces are distributed. The second simplification is verified by the returnloss measurement that, no matter the other polarization is short, open orloaded, the return loss of the polarization under test is almost the same. Fig.4.18 shows the return loss comparison between the full feed model simulationand VNA measurement. We can see that they agree pretty well with eachother.(a) (b) (c)Figure 4.17: (a) Perspective view of the full 4sq model. (b) Simplified baseboard of the full 4sq model. (c) Petal board shows that only one polarizationis present.514.2. Input Impedance of Single 4sqFigure 4.18: 4sq’s return loss comparison between the full 4sq model simula-tion and measurement. The agreement between these two proves the validityof full feed model to predict impedance spectra of the 4sq.The full feed model, which has already been proved to be efficient topredict impedance spectra of the 4sq, will be applied for future CHIME feeddesign.52Chapter 5The Cloverleaf Feed5.1 Inspiration and Confirmation of the CloverleafIdeaVarious modifications of the 4sq have been tried to make it wide-band, suchas the 4pt, the 4sl. But they are all not satisfying due to narrow bandwidthor manufacture difficulty. A turning point in our approach occurred duringa design discussion several of us had at the DRAO in which we realized thatthe Vivaldi antennas [18, 19], which are arrays of curved elements, have amuch broader bandwidth than simple straight dipoles do. Recall that thecurrent pattern of the 4sq is just like two straight dipoles facing each other,we realize that a Vivaldi-like 4sq might be broad band. To make the 4sqVivaldi-like, it is straightforward to make its outer edges to be curved. Fromnow on, a Vivaldi-like 4sq is called the cloverleaf antenna.A cloverleaf feed in MOST bandTo test the idea of cloverleaf feed, Duncan Campbell-Wilson added copperstrips by hand to MOST 4sq to make its outer edges curved, as shown inFig. 5.1 (a), its return loss measurement is shown in Fig. 5.1 (b) whenan extra tuning short is added to the stem boards to improve impedancematch. Without the extra tuning short on stem boards, the return loss isnot that small but its shape across band is still broad . This experimentis very encouraging, confirming the cloverleaf feed is broad band, especiallyrecall that this is a first-try handmade feed without any numerical design.Our belief is that a careful numerical design of petal shapes and/or balunswould make the cloverleaf feed wide band without tuning short.535.2. CHIME Cloverleaf Feed(a) (b)Figure 5.1: (a) A cloverleaf prototype hand built from MOST 4sq. Frontview. (b) Measurement of the return loss of MOST cloverleaf feed after atuning short is added to the stem boards. This experiment supports the ideathat a cloverleaf antenna might be very broadband.5.2 CHIME Cloverleaf Feed5.2.1 Further Test of the Full Feed ModelTo test the validity of full feed model for reproducing return loss of thecloverleaf feed, several cloverleaf feeds in CHIME band are built, measuredand simulated.First, we built a cloverleaf prototype by cutting metal sheet to be curvedand balance it with CHIME 4sq baluns, as shown in Fig. 5.2 (a). A fullfeed model of this feed has been constructed in CST and simulation is com-pared to measurement as shown in Fig. 5.2 (b). The very good agreementbetween simulation and measurement reassures full feed model’s validity inthe CHIME feed design.Then, a printed version of the cloverleaf feed is built but its return loss’smeasurement disagrees with the simulation. Later it is found that, the FR4in the gap between petals has non-negligible effect on impedance at the petalboard ports, causing disagreement to simulation which includes no dielectricsin petal board. Recall that current concentrates along 2 pairs of inner petal545.2. CHIME Cloverleaf Feededges, there is strong E field to see RF4 in the gaps and be affected by its di-electric constant. The difference between the cut-out prototype and printedprototype is just like the difference between transmission line filled with airand transmission line filled with FR4. After the FR4 gaps are removed, re-turn loss measurement does agree with simulation.(a) (b)Figure 5.2: (a) A cloverleaf prototype in CHIME band. Front view. (b)Return loss comparison between measurement and simulation of the CHIMEcloverleaf prototype. It confirms the full feed model simualtion technique isapplicable to the cloverleaf feed.5.2.2 Cloverleaf Feed Design and OptimizationAfter further confirmation of full feed model technique, it is now the stageto apply this simulation technique for designing CHIME cloverleaf feed nu-merically.The procedure is as follows:1. use W,R,L to parametrize petal board, as shown in Fig. 5.3;2. while fix baluns to be the 4sq baluns, optimize W,R,L until the small-est return loss across band is found; and3. redesign the 2-stage 4sq baluns to have 3-stage transmission lines, atthe optimal W,R,L found above, as shown in Fig. 5.4.555.2. CHIME Cloverleaf FeedIn step 2, 4sq baluns are used only for manufacture convenience. Once someoptimization result comes from step 2, a corresponding cloverleaf feed can bemade easily to reassure everything is working as what we think, and it is. An-other crucial designing note is that after optimization of petal shape, a newstage transmission line should be introduced in step 3 rather than continueoptimizing the two-stage baluns for lower return loss, because the essence ofstep 2 is an optimization of petal shape to the two-stage transmission linewhich already exists. Any deviation of transmission line’s parameters wouldmake return loss worse except for introducing new freedom. This is exactlyto make further use of the great flexibility of microstrip transmission linescompared to other types of transmission lines. Meanwhile the total length oftransmission lines on stem boards should be kept the same to ensure a quar-ter wavelength separation between petal board and ground plane at centralfrequency 600 MHz.Figure 5.3: The shape of each petal consists of two perpendicular straightlines, two 45 degree circular arcs with radiusR and one half an ellipse. W isthe major axis of the ellipse and L is the length from the intersection of thestraight sides to the outer edge of the ellipse. The shape is illustrated herefor the adopted values of gap, R,L and W .565.2. CHIME Cloverleaf Feed(a) (b)Figure 5.4: Baluns are redesigned to have three-stage transmission lines.Two of them are on stem boards, while the third is on baseboard. (a) A two-stage transmission line on stem boards, which are parametrized by W1, L1and W2, L2. (b) A one-stage transmission line on base board, which isparametrized by W3, L3.Finally, the designed parameters are in table 5.1.Table 5.1: Designed parameters of the cloverleaf feed in CHIME band.parameters W L R W1 L1 W2 L2 W3 L3designed value(mm) 138.5 131.9 20.0 3.5 94.0 2.5 40.0 1.9 45.05.2.3 Realization of the Optimized Cloverleaf Feed DesignAn cloverleaf feed is built according to the designed parameters, as shownin Fig. 5.5 (a). Fig. 5.5 (b) shows that the ports at center of the cloverleaffeed’s petal board have been modified to have simpler and clearer geometry.The cloverleaf feed’s return loss is measured and compared to simulation,shown in Fig. 5.6. There is a pretty good agreement between simulationand measurement. Return loss is smaller than -10dB return loss across theCHIME band, with majority of the band to be smaller than -15dB. Return575.2. CHIME Cloverleaf Feedlosses of the two polarizations are similar to each other because of carefuldesign of traces on the baseboard to reduce coupling and to improve sym-metry.(a) (b)Figure 5.5: (a) Perspective view of the cloverleaf feed built with designedparameters. Note, the FR4 in gaps between the petals are removed but thefar end is kept because it improves mechanical strength of the petal boardquite a lot. (b) Modified port at the center of cloverleaf petal board to makethe connections simpler.Fig. 5.7 shows measurements of both E plane and H plane of this clover-leaf feed, which are done by Jeff Peterson at Carnegie Mellon University.The beam pattern is broad and smooth across the band, with only few sidelobes in the backward direction. It is a confirmation of our understandingof beams in chapter 4 and also a confirmation of this design.Furthermore, the largest dimension on petal board, which is the diagonallength, is 27 cm. Size of the cloverleaf feed is small enough to be placed atany azimuth angle in CHIME array. This cloverleaf feed consists of PCBboards, the same as the 4sq, so it should be strong enough to survive fieldenvironment. The existence of ground plane provides a mirror image of thefeed so that phase centers of beams across the band all locate on the groundplane. The Teflon balun boards, the viaed double-layer petal board and585.2. CHIME Cloverleaf Feed200 300 400 500 600 700 800 900 1000frequency/MHz4035302520151050s11/dBP1:396 P1:823P2:392 P2:832return loss of designed clover antennameasurement of polarization P1measurement of polarization P2simulation of polarization P2Figure 5.6: Return loss comparison between measurement and simulation ofCHIME cloverleaf feed. The agreement between them confirms the validityof simulation and the very wide bandwidth shown in this figure confirms thedesign of the cloverleaf feed.the removal of FR4 in the gap between petals together make the loss of thecloverleaf feed to be the smallest.Up to now, all requirements of the CHIME feed, especially a very widebandwidth, are satisfied by this cloverleaf design. So it is confirmed to bethe final and will be mass produced and deployed on the CHIME pathfinder.595.2. CHIME Cloverleaf Feed(a)(b)Figure 5.7: Measurement of co-polar beam pattern of the designed cloverleaf.They are smooth and broad across band, as required by CHIME. (a) E planemeasurement of designed CHIME cloverleaf feed. (b) H plane measurementof designed CHIME cloverleaf feed60Chapter 6Manufacture and Deploymentof The Cloverleaf FeedsThe cloverleaf feed whose design has been expressed in the previous chapterhas been built, measured and confirmed to be the CHIME feed. Therefore,it is mass produced and deployed on CHIME pathfinder to take sky data.6.1 Specifications of the Designed Cloverleaf FeedFollowings are the specifications of designed cloverleaf.• Parameters of microstrip traces and petal shape are displayed in Table5.1.• Additional structural specifications needed to manufacture the wholecloverleaf feed are shown in Fig. 6.1. All units are in mm.• The FR4 in gaps between petals on the petal board are removed butthe very out end are left, as can be seen in Fig. 5.5 (a) and Fig. 6.1(c).• 1 oz rolled copper is printed on both sides of FR4-supported petalboard.• Petal board is viaed.• Baluns’ dielectric material is chosen to be Arlon DiClad 880, which islow-loss, cheap, with dielectric constant around 2.2.• The thickness of balun boards is 1.57±0.13 mm.The FR4 in very out end of gaps are left to make petal board stronger. Rolledcopper rather than electro-deposited copper is chosen because the former isless lossy, more smooth on the surface and the prices of these two do notdiffer too much.616.1. Specifications of the Designed Cloverleaf Feed100.077.490.015.317.95.018.01.6 4.0(a) (b)141.2240.023.6 3.02.0 4.091.0269.54.0(c)Figure 6.1: Manufacture dimensions of the designed cloverleaf feed. (a)Dimensions of baseboard. (b) Dimensions of 4 stem boards. Stem A hastwo traces, while stem C has none. This is set by the geometry for in-pairfeeding. (c) Dimensions of petal board.626.2. Manufacture Process6.2 Manufacture ProcessTo get mass production of cloverleaf feeds, I exported geometries of thecloverleaf feed from CST in dxf files. With great help from Richard Lam,dxf files were transformed to Gerber files, which are the standard formatfor manufacture companies. 132 sets of petals were ordered from CanadianCircuits and 132 sets of baluns were ordered from Enigma. These two com-panies are different because different substrates are needed for balun boardsand petal boards. Enigma helped to penalize stem boards and baseboardstogether to reduce material waste. The panel is shown in Fig. 6.2. The costof boards for each feed is around 120 dollars. This number will be reducedto 80 dollars for full CHIME because 1280 feeds instead of 132 feeds will beordered. We assembled 128 feeds from PCB boards by using a jig, as shownin Fig. 6.3. It takes around 2 minutes to assemble a feed from PCB boards.Each feed was tested in the lab with the VNA to see whether it is workingproperly. Table 6.1 illustrates how we tested each feed. All the cloverleaffeeds passed the test successfully and were deployed as feed array on thefocal lines of CHIME pathfinder, as shown in Fig. 6.4.Table 6.1: Details on The Cloverleaf Feeds’ Acceptance Test.test setup VNA is calibrated and the same configuration is applied for everyfeed under testtest procedure mount a feed to a 1.5 m high pole, where feed’s orientation can bechanged ;connect the 2 outputs of 2 polarizations to the 2 ports of VNA;measure S11 and S22 in the frequency range [400MHz, 800MHz];make a judgment on whether the feed pass the test by visualization.pass criteria 10 S11 and S22 were less than -2dB, in the range [400MHz, 450MHz];S11 and S22 were less than -5dB, in the range [450MHz, 500MHz];S11 and S22 wre less than -10dB, in the range [450MHz, 650MHz];S11 and S22 were smaller than -15dB around 600MHz;S11 and S22 exhibited interaction with the room environment asdemonstrated by significant changes with feed’s orientation10feed passes the test if an orientation can be found in which S11 and S22 satisfy allthe criteria listed in the right side.636.2. Manufacture Process(a) Top view of panelized boards (b) Bottom view of panelized boardsFigure 6.2: Panelization of base boards and stem boards to reduce materialwaste.646.2. Manufacture ProcessFigure 6.3: A jig for assembling the cloverleaf feeds.Figure 6.4: The cloverleaf feeds installed on CHIME pathfinder as feed array.656.3. Sky Data Taken from Deployed Cloverleaf Feeds6.3 Sky Data Taken from Deployed CloverleafFeedsTo have an preliminary test the cloverleaf feed’s performance on the reflector,the pulse from the pulsar PSR B0329+54 was measured, as shown in Fig.6.5. The cloverleaf feeds on the reflector sees that the arriving time of thesignal varies with frequency due to dispersion of galactic matter. It is a proofthat the cloverleaf feeds are working properly across the band.Figure 6.5: One pulse measurement of the pulsar B0329+54 from the clover-leaf feed on the CHIME pathfinder. The phase range of X-axis correspondsto the period of the pulsar, which is 0.7 s. The measured arriving time ofsignal depends on frequency. This is a sign of galactic matter’s dispersionand a sign of good performance of the cloverleaf feed cross band.To measure the shape of reflector beams, holography has been appliedbetween CHIME pathfinder and the 26m Telescope at DRAO for a Cas A11 transit. The 26m telescope was tracking Cas A during the period whendata were taken. Observed data displayed in Fig. 6.6 agrees with severalcommon senses, which are: signal should have fringes in the time domainbecause there is East-West baseline between CHIME pathfinder and the26m Telescope; the fringe should be finer for a higher frequency and width11http://en.wikipedia.org/wiki/Cassiopeia_A.666.3. Sky Data Taken from Deployed Cloverleaf Feedsof reflector beams should be finer for a higher frequency. Moreover, shape ofreflector beams, as indicated by red dots, exhibit a generally normal shape,which can be fitted by a Gaussian distribution in the main lobe. Therefore,the cloverleaf feeds are working well.To have an idea of what the reflector beam would look like on the full sky,a Grasp model has been constructed in which pathfinder’s reflector is fed bythe beam pattern of a cloverleaf feed. The simulated co-polar beam on thefull sky is shown in Fig. 6.7 (a). Since cylindrical reflector is aligned north-south, it is reasonable to see the beam elongated in north-south direction.Reflector beams’ widths in the slice of CasA transit are compared betweenmeasurement and simulation, as shown in Fig. 6.7 (b). The agreement thereis a confirmation of my simulation and also a confirmation of our preliminaryunderstanding of our beams.676.3. Sky Data Taken from Deployed Cloverleaf Feeds(a)(b)Figure 6.6: Cross correlations between DRAO’s 26m Telescope and CHIMEpathfinder when Cas A transited through CHIME pathfinder’s field of view.Both reflectors are fed with the cloverleaf feeds. x-axis is linearly mapped totime. Its spans 3600 s. (a) cross correlation at 527 MHz. (b) cross correlationat 780 MHz. The fringes are clear as shown by the data points. Shape ofreflector beams are generally good, as indicated by red dots. Comparisonbetween (a) and (b) shows that the width of reflector beams and spacing offringes depend on frequency. Image Credit: Mateus Fandino.686.3. Sky Data Taken from Deployed Cloverleaf Feeds(a)(b)Figure 6.7: (a) Grasp simulated co-polar reflector beam at 600 MHz. (b)Simulated beam widths in the slice of CasA transit are compared to measure-ments for north-south polarization and east-west polarization of the clover-leaf feed.69Chapter 7ConclusionThe cloverleaf antenna designed in this thesis meets all the feed requirementsof CHIME, especially the very wide bandwidth requirement.Because of the very good performance of the cloverleaf antenna, CHIMEfeed becomes finalized as a fixed element in the whole experiment. Thisremoves large uncertainty of CHIME and smooths the whole procedure.CHIME’s foreground removal strategy, which once was based on an over-simplified assumption of feed’s beam pattern, can be evaluated realisticallysince CHIME’s feeds and all properties related with them are now real data.Because impedance spectra of the cloverleaf feed as the CHIME feed areknown and fixed, an effective approach to lower system temperature nowbecomes clear: redesign LNA to have minimal noise at the cloverleaf feed’simpedance spectra. The performance of reflector can be studied directly interms of beams to the sky because the feed, as an input to reflector beams, iswell understood, good enough and finalized. For example, centroids of reflec-tor beams are measured to wander east-west across band. The mechanism ofwandering is not understood yet. But we have made sure wandering comesfrom reflector rather than feeds because 180 degree azimuthal rotation offeed does not result in a 180 degree phase change in the centroid spectrum.Without cloverleaf feeds, feeds with bad performance have to be installed,making CHIME pathfinder to be less useful. For example, feeds with narrowbandwidth harm the system behavior across the band so that dispersion ofgalactic matter might not be seen from pulsar measurement. Feeds withlarge size exclude the configuration of feed array in which each element isazimuthally rotated 45 degree so that we loose the chance to analyze thebehavior of pathfinder whose reflector beams between two polarizations arethe same. Feeds which introduce high system temperature reduce SNR,making CHIME pathfinder’s sky mapping more time consuming or even notpossible.In conclusion, the successful design of the cloverleaf feed is a real progressfor CHIME.Moreover, the idea and design procedure of cloverleaf feeds can be easilytuned to other bandwidth for other usage. Actually, designing a similar70Chapter 7. Conclusioncloverleaf feed for MOST is already on the task list.The next step is to use Grasp to analyze the interaction between feed andreflector to get reflector beams on the sky. It has been confirmed already byboth simulation and measurement that widths of reflector beams oscillatewith frequency with 30 MHz ripples because there is an extra bounce ofbeams between reflector and focal line. Slices of beams have been measuredby using pulsar and other bright radio sources. It needs intensive effortto integrate measured beam slices to simulated 3D beams based on theiraccuracy level.Cross talk between element in the deployed feed array is another topicneeds future analysis.71Bibliography[1] Kevin Bandura, Graeme E Addison, Mandana Amiri, J Richard Bond,Duncan Campbell-Wilson, Liam Connor, Jean-Francois Cliche, GregDavis, Meiling Deng, Nolan Denman, et al. Canadian hydrogen in-tensity mapping experiment (chime) pathfinder. In SPIE AstronomicalTelescopes+ Instrumentation, pages 914522–914522. International Soci-ety for Optics and Photonics, 2014.[2] Adam G. Riess et al. Observational evidence from supernovae for anaccelerating universe and a cosmological constant. Astron. J., 1998.[3] Saul Perlmutter, G Aldering, G Goldhaber, RA Knop, P Nugent,PG Castro, S Deustua, S Fabbro, A Goobar, DE Groom, et al. Measure-ments of Ω and Λ from 42 high-redshift supernovae. The AstrophysicalJournal, 517(2):565, 1999.[4] P. J. E. Peebles and Bharat Ratra. The cosmological constant and darkenergy. Reivews of Modern Physics, 2003.[5] Steen Hannestad and Edvard Mörtsell. Probing the dark side: Con-straints on the dark energy equation of state from cmb, large scalestructure, and type ia supernovae. Phys. Rev. D, 66:063508, Sep 2002.[6] Adam G Riess, Louis-Gregory Strolger, Stefano Casertano, Henry CFerguson, Bahram Mobasher, Ben Gold, Peter J Challis, Alexei V Fil-ippenko, Saurabh Jha, Weidong Li, et al. New hubble space telescopediscoveries of type ia supernovae at zâĽě 1: narrowing constraints onthe early behavior of dark energy. The Astrophysical Journal, 659(1):98,2007.[7] J. Richard Shaw. All-sky interferometry with spherical harmonic transittelescope. The Astrophysical Journal, 2014.[8] Gregory Davis. A two element interferometer prototype for the canadianhydrogen intensity mapping experiment. Master’s thesis, University ofBritish Columbia, 2009.72Bibliography[9] J.R. Nealy C.G. Buxton, W.L. Stutzman. Analysis of a new widebandprinted antenna element (the foursquare) using fdtd techniques. URSINational Radio Science Meeting, 1998.[10] Seong-Youp Suh, Warren Stutzman, William Davis, Alan Waltho, KirkSkeba, and Jeffrey Schiffer. A novel low-profile, dual-polarization, multi-band base-station antenna element-the fourpoint antenna. In Vehicu-lar Technology Conference, 2004. VTC2004-Fall. 2004 IEEE 60th, vol-ume 1, pages 225–229. IEEE, 2004.[11] SS Suh, WL Stutzman, WA Davis, Alan Waltho, and J Schiffer. Anovel printed dual polarized broadband antenna, the fourclover antenna.Proceeding of the international symposyum on antenna and Progation,ISAP 2004, Sendai, Japan, pages 77–80, 2004.[12] Seong-Youp Suh, Warren Stutzman, William Davis, Alan Waltho, andJeffrey Schiffer. A generalized crossed dipole antenna, the fourtear an-tenna. In Antennas and Propagation Society International Symposium,2004. IEEE, volume 3, pages 2915–2918. IEEE, 2004.[13] Martin Leung. A Wideband Feed for A Cylindrical Radio Telescope.PhD thesis, University of Sydney, 2008.[14] J.G. Robertson. The most and other raido telescopes. Aust. J. Phys.,44:729, 1991.[15] Stephen D. Gedney. Introduction to the Finite-Difference Time-DomainMethod for Electromagnetics. Synthesis Lectures on ComputationalElectromagnetics. Morgan and Claypool, 2011.[16] Constantine A. Balanis. Antenna Theory: Analysis and Design. JohnWiley And Sons, Inc., Hoboken, 2005.[17] David M. Pozar. Microwave Engineering. John Wiley And Sons, Inc,2005.[18] Yunqiang Yang, Y Wang, and Aly E Fathy. Design of compact vivaldiantenna arrays for uwb see through wall applications. Progress In Elec-tromagnetics Research, 82:401–418, 2008.[19] Ehud Gazit. Improved design of the vivaldi antenna. In IEE ProceedingsH (Microwaves, Antennas and Propagation), volume 135, pages 89–92.IET, 1988.73Appendix74The Cloverleaf Antenna: A CompactWide-bandwidth Dual-polarization Feed for CHIMEMeiling Denga and Ducan Campbell-Wilsonb for the CHIME collaborationaDepartment of Physics and Astronomy, The University of British Columbia, Email: mdeng@phas.ubc.cabSchool of Physics, The University of Sydney, Email: dcw@physics.usyd.edu.auAbstract—We have developed a compact, wide-bandwidth,dual-polarization cloverleaf-shaped antenna to feed the CHIMEradio telescope. The antenna has been tuned using CST tohave smaller than -10dB s11 for over an octave of bandwidth,covering the full CHIME band from 400MHz to 800MHz and thisperformance has been confirmed by measurement. The antennasare made of conventional low loss circuit boards and can bemass produced economically, which is important because CHIMErequires 1280 feeds. They are compact enough to be placed 30cmapart in a linear array at any azimuthal rotation.Keywords: antenna, dual polarization, wide bandwidth, radiotelescopeI. INTRODUCTIONWe have built a novel, cloverleaf shaped compact dual-polarization feed for the Canadian Hydrogen Intensity-Mapping Experiment [1]. CHIME is a radio telescope designedto measure Baryon Acoustic Oscillations (BAO) by measuringthe intensity of neutral hydrogen over half the sky through theredshift range 0.8  z  2.5. At these redshifts the 21cm lineof neutral hydrogen appears in the frequency range 400MHzto 800MHz. CHIME has no moving parts; it consists of fiveparallel cylindrical parabolic reflectors, each 20m wide, 100mlong and f/0.25. Feeds are spaced 30cm apart along each focalline. Signals are amplified and brought to a single customdigital correlator.The full instrument requires 1280 dual polarization feedswith an acceptable beam pattern, low material loss and s11lower than -10dB from 400MHz to 800MHz. With this manyfeeds, it is important that uniform, reliable feeds can bemanufactured economically. Other solutions considered asCHIME feeds are the four-square antenna [2] [3] developedfor the Molonglo Telescope [4] , the four-point antenna [5] andthe four-point antenna with tuning plate [6]. All these feedsgenerate an approximately circular beam suitable for feedingdeep paraboloidal reflectors. The performance of these feedsdiffers mostly in their matching bandwidth.II. RADIATION MECHANISMOur feeds are a modification of four-square antennas de-veloped for the Molonglo Observatory. The petals, stem andbase are all made from printed circuits boards (PCB). Tobroaden the bandwidth, we have modified the petals to havecurved outer edges as shown at left in Figure 1, eliminatingthe depedence on a single dimension. The curves are smoothand each petal is symmetric. CST simulated current patternis shown at right in Figure 1 for one linear polarization at600MHz. The currents near the gaps between petals run inopposing directions so they cancel, and do not contribute tothe radiation pattern. For this polarization, farfield radiation Fig. 1. At left, the shape of each petal consists of two perpendicular straightlines, two 45 degree circular arcs with radius R and one half an ellipse. W isthe major axis of the ellipse and L is the length from the intersection of thestraight sides to the outer edge of the ellipse. The shape is illustrated here forthe adopted values of gap, R,L, and W . Each of the four tabs shown at thecentre is connected to one side of a vertical microstrip transmission line andin each case the full width of the adjacent petal is connected to the other lead.At right, CST simulated currents for one linear polarization at 600MHz areshown. Note the small asymmetry in the curent distribution near the centrebecasue of the tab geometry.arises from the coherent currents running along the curvedouter edges of the top and bottom pair of petals. For each linearpolarization, two differential signals, each from a pair of petals,are combined through tuned baluns to form one single-endedoutput. Thus each single polarization signal involves currentsin all four petals. This is called in-pair feeding. Full baluns,from both polarizations, consist of four identical microstriptransmission lines along four vertical support boards(stem) anda horizontal base board. Both of the single-ended outputs areon the base board. Each transmission line is varied in severalabrupt steps, and the lengths and characteristic impedancesof the transmission line segments are tuneable. We havedemonstrated that electrical losses in conventional circuit boardmaterials generate unacceptable noise levels for astronomicalinstrumentation. Teflon-based PCB is used everywherethere isa transmission line.III. TUNING THE ANTENNA PERFORMANCEIn order to tune the antenna parameters to produce ac-ceptable performance we have constructed a full CST modelof a cloverleaf antenna(only one polarization present). Toverify the procedure, we first built two different cloverleafantennas with arbitrarily chosen shapes, measured their s11and compared these measurements to CST simulations. Thecomparison proves our CST simulation is reliable.978-1-4799-2225-3/14/$31.00 c2014 Crown.75Measurements show that coupling between two polariza-tions and coupling between adjacent antennas do not affects11. Therefore, we proceeded to iterate the cloverleaf designusing CST following the plan listed below.We initially fixed the parameters of the transmission linesto a design chosen for ease of manufacture: the transmissionline has two characteristic impedances, one on the verticalsupport board and the other on the horizontal baseboard.We set the initial petal parameters to be (R,W,L) =80, 140, 150)mm and altered R,W, and L successively, tolearn which parameters have the most impact on the antenna’ss11. Altering R has very little impact, and we fixed it toR = 20mm, the peak of a very shallow performance curve.We used the optimization algorithm implemented in CST toexplore s11 in (W,L) space. Varying W and L simultaneouslyuntil CST finds the smallest s11 across the band. Optimizationwas still running after two days and we manually stopped it.We found that for these transmission lines and for R =20mm, s11 has strong dependence on W and L. However,all s11 curves pass through an apparent fixed point at approx-imately f = 580MHz, S11 = 12dB. From this result andfrom a manual exploration of transmission line impedance weconcluded that this optimization step is essentially minimizings11 by matching the petal shape to the fixed balun parameters.We introduced an additional degree of freedom by dividingthe vertical portion of the transmission line from one segmentto two segments with different impedances. From amongmore than 60 sets of parameters returned by CST, we picked(W,L) = (138.5, 131.9)mm which has the smallest s11 acrossthe band although it does not meet our specifications andexplore transmission line properties. We held total lengthof vertical transmission line fixed to ensure 14 separationbetween radiating petals and reflective ground plane, andvaried characteristic impedances and the step location.With the upper trace width 3.5mm, length 92mm and lowertrace width 2.5mm, length 40mm, the result is dramatic. Thefixed point is removed and the s11 is below -15dB acrossthe band except for near 400MHz, where we just meet ourrequirement of -10dB.We stopped our tuning procedure at this point. Althougha solution has been found which exceeds our requirements,the system has not been optimized. Petal shape parametersand transmission line parameters have been varied separatelybut the full space of these parameters has not been explored.We can use this in future work to add additional performancecriteria to the design procedure.IV. RESULTSFour petals of the chosen shape are built into one pieceof double-sided PCB with FR4 as substrate to save cost. Viasconnect the two copper surfaces to reduce material loss inFR4. The circuit boards are slotted to remove FR4 in thegaps between petals because leaving FR4 in the gaps has aserious effect on both antenna impedance and material losses.Note that the resulting petal size and shape are compatiblewith 45 degree aimuthal rotation in an array. The s11 of anassembled feed is shown in Fig. 2 for both polarizations andin comparison with simulations. According to simulation, thebeam pattern is smooth in both the E-plane and the H-plane.HPBW varies within several degrees across the band. The sixPCB pieces of the cloverleaf antenna are soldered togetherusing a mechanical jig. A photo of eight antennas in a linearFig. 2. The measured s11 spectrum for both linear polarizations is plottedalong with the CST simulation. Note the similarity between two polarzations.This design exceeds the requirement of S11  10dB over the full bandfrom 400 to 800 MHz.Fig. 3. A linear array of eight cloverleaf antennas installed at the focal line ofthe CHIME Pathfinder at the Dominion Radio Astrophysical Observatory inPenticton, BC, Canada. The picture is taken through the wire mesh reflectivesurface (mesh spacing 19 mm) illustrating a photonsview of the antennas andground plane. Notice that each feed has an image-feed in the ground plane,12 away at the passband centre frequency. Notice also the four slots cut toremove dielectric material from the gaps between the petals.array installed on the CHIME pathfinder is shown in Fig.3.V. ACKNOWLEDGEMENTSCHIME is funded by the four partner institutions, grantsfrom NSERC and the Canada Foundation for Innovation. MDacknowledges support from MITACS. DCW acknowledgessupport from Sydney University for this work.REFERENCES[1] CHIME is a partnership between UBC, McGill, UToronto and theDRAO. http://chime.physics.ubc.ca[2] Martin Leung (2008), “A Wideband Feed for a Cylindrical RadioTelescope” , Ph.D thesis, University of Sydney[3] C. Buxton;W. Stutzman;and J. Nealy, “Implementation of the Foursquareantenna in broadband arrays”, URSI National Radio Science meeting,July 1999. (Paper 99-12)[4] J.G. Robertson, “The MOST and Other Radio Telescopes”, Aust. J.Phys. 1991, 44, 729[5] Seong-Youp Suh; Stutzman, W.L.; Davis, W.A., “Low-profile, dual-polarized broadband antennas”, Antennas and Propagation Society In-ternational Symposium, 2003.[6] Seong-Youp Suh; Stutzman, W.L.; Davis, W.A.; Waltho, A.E.; Skeba,K.W.; Schiffer, J.L., “Bandwidth improvement for crossed-dipole typeantennas using a tuning plate”, Antennas and Propagation Society In-ternational Symposium, 2005.76

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