A Ku-Band Polarimeter for the Owens Valley Radio Observatory 40-Meter Telescope Citation Karkare, Kirit Sukrit (2011) A Ku-Band Polarimeter for the Owens Valley Radio Observatory 40-Meter Telescope. Senior thesis (Major), California Institute of Technology. doi:10.7907/AX7Y-QF79. https://resolver.caltech.edu/CaltechTHESIS:02132018-113613816 Abstract Blazars are active galactic nuclei - small, extremely luminous objects at the center of galaxies powered by material accreting around a supermassive black hole - which emit relativistic jets of highly energetic plasma along our line of sight. There is no accepted model for jet composition, acceleration, and confinement; observations at different wavelengths will help us understand these emission mechanisms. Since 2007, the 40-Meter Telescope at the Owens Valley Radio Observatory has been monitoring over 1100 blazars every two days. The variability in radio light curves is likely to be correlated with gamma-rays, which we are observing with the Fermi Gamma-Ray Space Telescope. A new Ku-band receiver for the 40-Meter Telescope is in development. It will offer increased sensitivity, MHz spectral resolution from 12-18 GHz, and calculation of Stokes I, Q, and U parameters. In this thesis, I present the design, assembly, and testing of various components in the receiver chain. I evaluate the suitability of a commercial radio frequency over optical link for use in the receiver, describe the fabrication and verification of bandpass filters and sideband separating modules, and present the design and testing of a digital back end spectrometer which uses field-programmable gate array devices. When complete in late 2011 , the new receiver will allow the continuation of the blazar monitoring program with the addition of spectral and polarization information, which will be invaluable in understanding blazar jet emission. Item Type: Thesis (Senior thesis (Major)) Subject Keywords: (Physics and English) Degree Grantor: California Institute of Technology Division: Physics, Mathematics and Astronomy Major Option: Physics Minor Option: English Thesis Availability: Public (worldwide access) Research Advisor(s): Readhead, Anthony C. S. Group: Owens Valley Radio Observatory (OVRO), Astronomy Department Thesis Committee: None, None Defense Date: 3 May 2011 Record Number: CaltechTHESIS:02132018-113613816 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:02132018-113613816 DOI: 10.7907/AX7Y-QF79 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 10708 Collection: CaltechTHESIS Deposited By: Joy Painter Deposited On: 14 Feb 2018 00:52 Last Modified: 14 Nov 2025 19:59 Thesis Files Preview PDF - Final Version See Usage Policy. 8MB Repository Staff Only: item control page

A Ku-Band Polarimeter for the Owens Valley Radio Observatory 40-Meter Telescope Thesis by Kirit Sukrit Karkare In P artial Fulfillment of the Requirements for the Degree of Bachelor of Science California Institute of Technology Pasadena, Cal ifornia 2011 (Submitted May 3, 2011 ) ii © 2011 Kirit Sukrit Karkare All Rights Reserved iii Acknowledgments I am grateful to everyone in the Caltech Radio Astronomy Laboratory for their help during this project . Oliver King, with whom I've worked very closely fo r the last year , has been incredibly willing to explain the gory details of radio la.bwork, and I've learned a. huge a.mount from his guidance. Glenn J ones is the reason I was able to get anythi ng CASPER-related working in the first place, and has been extremely patient with a.II of my questions. ·M atthew Stevenson introduced me to CASPER and set me up to start working two summers ago. Rodrigo Reeves and Kiera.n Cleary have been great labmates. Walter Max-Moerbeck a11d Joey Richards were very helpful in explaining the science behind the instrument. T he staff at the Owens Valley Radio Observato ry were excellent hosts during my several visits. Finally, tha nks to my research advisor, Tony Readhead , fo r giving me the opportunity to spend the last two years with the Caltech Radio Astronomy Laboratory. He has been an amazing teacher and mentor and I could not have asked for a better person to introduce me to radio instrumentation. T his work was supported by the Caltech Summer Undergrad uate Research Fellowship Office and by the Rose Hills Foundation . 'Il:avel to the 2010 CASPER Workshop was provided by the Harvard-Smithsonian Center for Astrophysics . iv Abstract Blazars are active galactic nuclei - small, extremely lumino us obj ect s at the center of gala..xies powered by ma terial accreting around a supermassive black hole - which emit relativistic jets of highly energetic plasma along our line of sight. There is no accepted model for jet composition , acceleration, and confinement ; observations at different wavelengths will help us underst and these emission mechanisms. Since 2007, the 40-Met er Telescope at t he Owens Valley Radio Observa tory has been monitoring over 1100 blaza.rs every two days. T he variability in radio light curves is likely to be correlated with gamma-rays, which we ru·e observing with the Fermi Ga mma-Ray Space Telescope. A new Ku-band receiver for t he 40-Meter Telescope is in development. It will offer increased sensitivity, MHz spectral resolution fr om 12-18 GHz, and calculation of Stokes I, Q, and U parameters. In this thesis, I present the design, assembly, and testing of various components in the receiver chain. I evaluat e the suita bility of a commercial radio frequency over optical link for use in the receiver, describe the fabrication and verification of bandpass filters and sideband separating modu les, and present the design and testing of a digital back end spect romet er which uses field-programmable gat e a rray devices. When complete in late 2011 , the new receiver will allow the continuat ion of the blazar monitoring program wit h t he addition of spectral and polarization info rmation. which will be invalua ble in underst anding blazar jet emission . v Contents Acknowledgme nts iii Abstract iv 1 Introduction 1 1.1 Blazars 1 1.2 Monitoring Program 1 1.3 The OVRO 40-Meter Telescope 2 1.4 Overview 3 Background 4 2.1 Radio Polarimetry 4 2.2 Vect or Network Analysis . 5 2.3 Digital Signal Processing in Radio Astronomy . 7 2.4 Receiver Design . 7 2 3 RF over Optical Link 3.1 4 Results . . . . . . . 8 . . . . . . 8 Bandpass Filters and Sideband Separating Modules 12 4.1 Construction 13 4.2 Results . . . . 15 5 Back End Electronics 16 5.1 Hardware 16 5.2 Software . 17 5.2.1 System Generator and iADCs . 17 5.2.2 PFB and FFT 19 5.2.3 Demodulation Blocks 21 5.2.4 Stokes Blocks .. 21 vi 6 5.2.5 Quantization and Accumulat ion 23 5.2.6 Readout . . . . 24 Integ ration a nd Testing 25 6. 1 ROACH Clocking .. 25 6.2 Integrat ion and P olarization Test ing 25 6.3 ROACH Gain Relat ions . . . . . . . 26 Conclusion 29 Bibliogra phy 30 7 vii List of Figures 1.1 Schematic of an Active Galactic Nucleus. 2 1.2 OVRO 40-Meter Telescope. 3 2.1 Two-port device with its wave quantities. 6 3.1 S 2 1 (insertion loss) of the Optilab syst em. 9 3.2 S 11 (return loss) of the Optilab system. . 9 3.3 Group delay of t he Opt ilab syst em , with and without EDFA. 10 3.4 Compression at 1 GHz. . . 10 3.5 Opt ilab RF over Optical Link setup: VNA. LT -20 t ransmitter, 100 m cable, EDFA amplifier , and LR-30 receiver .. 11 4.1 Local Oscillator schematic. . . 13 4.2 T wo soldered bandpass fil ters. 14 4.3 A surface-mount soldered sideband separating module. . 14 4.4 Spect ral response of a 500-1000 MHz bandpass filter and sideband separating mod ule at wo = 14 GHz (lower sideband in green, upper sideband in blue) . . 15 5.1 Reconfigurable Open Architecture Computing Hardware (ROACH ). 16 5.2 Analog t o Digital Converter ( iADC) .. 17 5.3 ROACH Polarimeter. 18 5.4 Fine spectral response of PFB/ FFT (each of t he 5 bins surrounding 300 MHz is a . . . different color) . . . . 20 5.5 Demodulation block. 21 5.6 Stokes detection block. 22 6.1 The entire signal chain . A noise diode is connected to two 180° hybrids, mixed with a 14 GHz LO , and sent into four sideband separating modules, eight bandpass filters. 6.2 and the ROACH. . . . . 26 Power in horn A, left circular polarization from a noise diode .. 27 viii 6.3 R(QA), Stokes Q from a noise diode. 28 6.4 Gain curves for a simple spectrometer and a dem odula tor. . 28 1 Chapter 1 Introduction 1.1 Blazars Active Galactic Nuclei (AG N) are compact regions at the centers of galaxies that emit much higher radiation than normal across the entire electromagnet ic sp ectrum . They are believed t o derive their power from rotation and accretion disks surrounding a rotating supermassive black hole. Those t hat emit strongly in the radio region are termed radio-loud , and show emission from t wo highly collimated relativistic jets which emerge along the spin axis of the accretion disk and black hole in opposite directions (Figure 1.1 ). Blazars are those AGN in which the jet s are aligned at a small angle t o our line of sight. Small variations in this orientation angle are responsible for their wide range of observational properties, including rapid varia bility, high p olarization. and apparent superluminal features . Despite decades of observations. there is no accepted model fo r the composit ion , acceleration. and confinement of these relativistic jets. Multi-wavelength observations of blazars will allow us to better underst and these important feat ures. 1.2 Monitoring Program Since mid-2007, the 40-Meter Telescope at the Owens Valley Radio Observatory (OVRO) has been monitoring nearly 1200 gamma-ray blazar candidat es at 15 GHz [l ]. These sources from t he Candidate Gamma-Ray Blazar Survey have been sampled a.bout twice per week, giving 3-year light curves which are being cross-correlat ed with gamma-ray light curves (100 MeV t o a few hundred GeV) of t he same sources from the Large Area Telescope on t he Fermi Gamma-Ray Space Telescope. This monitoring program will allow us t o derive t he int rinsic radio and gamma-ray characteristics of the blazar population , including the dependence of variability on redshift and luminosity and the combination of radio properties t hat could predict gamma-ray luminosity. The essential physics behind t he correlation between radio and gamma-ray data is to characterize the time lag bet ween peaks 2 Figure 1.1: Schema tic of an Active Galactic Nucleus. in the light curves from t he two regimes. This will help to constrain the location of the emission mechanisms within the jet . and thus aid in underst anding the jet composit ion . 1.3 The OV RO 4 0-Met er Te lescop e The OVRO 40-Meter Telescope (Figure 1.2). built in 1966. is a n f/ 0.4 parabolic reflect or tha t is actually 130 feet in dian1eter. The present receiver features a Dicke-switcl1ed cryogenic high electron mobility transistor (HEMT) receiver with a noise temperature of 30 K that observes a single band from 13.5 to 16.5 GHz. The two symmetric off-axis feed horns produce t wo Gaussian beams of 15T' FWHM, separated by 12.95' in azimuth. and select left circular polarization. The overall apert ure efficiency is 'f/ A = 0.25. We are building a new pseudo-correlation p olarimeter for this telescope that will give Stokes I. Q, and U measurements with megahertz ~pectr al resolution in twelve 500 MHz bands between 12 and 18 GHz (Ku-band). The new receiver will feature a noise temperature of 20 K. allowing for better-sampled blazar light curves in addition t o the polarization measurements. In addit ion , the use of reprogrammable digital electro nics allows users to t ailor t he back end to their needs. providing flexibility in case future observational requirements change. 3 Figure 1.2: OVRO 40-Met er Telescope. 1.4 Overview In this work. I present the design. assembly, and testing of various components in the receiver cha.in. I first review the necessary background t o underst and radio polarimetry. vector network analysis, and digital signal processing in the context of the new receiver. I then evaluate the suitability of a commercial radio frequency (RF ) over optical link fo r use in t he receiver, describe the fabrication and verification of bandpass fil ters a nd sideband separating modules, and present the design and t esting of a digital back end spectromet er which uses field-programmable gat e array (FPGA) devices t o digitize analog dat a . calculat e polarization information , and output the Stokes paramet ers to an Ethernet connection. 4 Chapter 2 Background 2.1 R adio Polarimetry An astronomical receiver detects electromagnetic radiation , which consists of transverse vibrations of the electromagnetic field. If there is a lasting phase and amplitude relation b etween these vibrations, the wave is polarized. In general, astronomical sources are partially polarized . Polarization can be caused by several mechanisms; in active galaxies, fo r example. synchrotron emission gives rise to almost entirely linear polarization. The Stokes parameters provide a convenient framework in which to describe the polarization of an electromagnetic field. Consider a time-va,rying electric field detected by orthogonal linear components, Ex(t) = ax(t) cos( wt + llx) and Ey(t) = ay (t) cos( wt+ 8y) [2] . Then the Stokes parameters are defined as I (a;(t)) + (a;, (t)) Q ( a~(t) ) - (a;,(t) ) U 2(ax(t)ay(t) cos(5x - 811 )) V 2(ax(t)ay(t) sin(5x - Dy)), where the brackets indicate time averaging. Stokes I represents t he total power detected, while Q, U. and V together specify the polarization state. Since light is often unpolarized, J 2 2: Q2 + U 2 + V 2 [3]. Stokes Q and U together completely specify the linear polarization, and Stokes V represents the circular polarization st ate. The total polarized fraction is p = J Q2 + U 2 + V 2 I I ' t he t otal linear fraction is Pl = JQ 2 + U2 I I. and the circular fraction is Pc= V/ I . T he position angle of t he linear polarization is given by x = ~ arct an (U / Q). Representing the fields as complex voltages, we have E x(t) = ax(t)ei(w t+ox) and Ey(t) = ay(t)ei(wt+S") and thus 5 2 2 Q (! E x( t )i ) - (! E y( t)i ) u 2 (~{Ex(t)E; (t)}) = v 2(8-{Ex(t)E;(t)} ) = -i [(E x(t)E;(t)) - (E; (t)Ey(t) )] . (E x(t)E;(t) ) + (E ;(t )Ey(t)) The new receiver for the 40-Meter Telescope uses an orthomode transducer to detect circular polarization, so transforming to a new orthogonal basis of left and right circular polarization, [ = ~ (x - ifj) and f = ~(x + ifj) , we obtain I (IE1(t)i 2 ) + (!Er(t)i 2 ) Q 2(~ { E1(t) E;( t)}) = U - 2(2l' {E1(t)E;(t )}) = (E1(t)E;(t) ) - (Ei (t)E,.(t)) = (IE1(t)i) (IE,.(t)i) sin(81 - 8r) V (IE1(t)l 2 ) - (IEr( t )l 2 ) . (E1 (t )E;(t)) + (E i(t) Er(t)) = (IE1 (t) i)(! E ,.(t)I) cos(81 - 8,.) Since active gala.'<ies do not emit circular polarization, the receiver does not compute V. 2.2 Vector N e twork Ana lysis One of the most common measuring tasks in RF engineering involves the analysis of circuits. A network analyzer achieves this by generating a sinusoidal test signal that is applied to the device under test (DUT) [4]. Assuming that the DUT is linear. the analyzer measures it response, which is also sinusoidal. A scalar network analyzer measures only the amplitude difference between wave quantities, while a vector network analyzer (VNA) measures both the amplitude and phase of the wave quantities. \Ve first consider a one-port device, and distinguish between the incident wave a and the reflect ed wave b. The incident wave propagates from the analyzer to the DUT , and the reflected wave travels in the opposite direction. The wave quantities have units of VW, so to detect true power we must measure lai 2 and lbl 2 . The reflection coefficient r = %represents the ratio of the incident to reflected wave. In general. r is complex and can be calculated from the complex impedance Z . The standard reference impedance is Zo = 50 fl. The normalized impedance is z = Z/Zo, and can be used to det ermine the reflection coefficient z- 1 z+ l I' = - - . We now consider a two-port device. Besides the reflection at the two ports, we also admit the possibility of tran mission in the forward and reverse direct.ions. In comparison to the reflection coefficient , the scattering parameters (S-parameters, Figure 2.1) S11 , S1 2. S21 , and S22 are defined as the ratios of the respective wave quantities . For forward measurements, we attach a reflection-free 6 b2 Sz, b2 rev Reverse Forward measurement !.! t measurement s, ! a 2<===i OUT Port 2 b1.rev Port 1 Figure 2.1: T wo-port device with its wave quantities. terminat ion r = 0 on port 2, implying that a 2 = 0. \Ve then measure t.he input reflection coefficient S 11 (return loss) on port. 1 and t he forward transmission coeffi cient S 2 1 (insertion loss) between ports 1 and 2: Su b1 I a1 a2 = 0 S 21 b2 I a1 a2 = 0 The same measurement may be done in t he reverse direction , terminating port 1. Then In general, both incident waves can be non- zero (a 1 # 0 and a 2 =f 0). We consider the superposition of the two measurement sit uat ions a 1 = 0 and a2 =f 0 with a 1 =f 0 and a 2 = 0. Then we have We can group the parameters to obtain the S-mat rix and the wave quantities t o obtain the vectors a and b , giving b = Sa: A VNA measures the generally complex S-matrix as a function of frequency. The magnitude of the S-parameter corresponds to the amplitude ratio of t he wave quanti ties, while the phase corresponds to the phase difference bet ween the wave quanti ties. 7 2.3 Digital Signal Processing in Radio Astronomy Radio astronomy instrumentation is highly specialized. Individual instruments can take over five years to design and build , and as a result are often obsolescent even before they are deployed. Additionally, due to the advent of arrays of large numbers of small antennas, a growing trend in radio astronomy is that of high-performance real-time digital signal processing (DSP). New instrumentation must be able to process large amounts of continuous data while performing such operations as spatial correlation and wideband spectroscopy. General computing clusters, which have traditionally been used for this purpose, are not suited for these high-bandwidth calcula tions due to their inherently non-parallel architectures. FPGAs are reconfigurable logic devices in wide commercial use. occupying a place between custom-designed hardware and software. They are much better suited for real-time DSP due to their spatially parallel execution model; scaling on a faster track than Moore's Law, they can offer over 100 times the computing throughput of a microprocessor-based system . The Collaboration for Astronomy Signal Processing and Electronics Research (CASPER) group at UC Berkeley has been developing FPGA-based devices specifically for radio astronomy [5]. By using commercial FPGAs and open-source DSP libraries, CASPER. st ays up t o date with the latest hardware advances, introd uces modularity in instrumentation design, and has developed a large support community for its hardware. Their boards are in use at radio observatories around t he world. 2.4 Receiver Design The new Ku-band receiver for the 40-Met er t elescope was designed by Dr. Oliver King. Two horns, slightly off axis at the prime focus, detect left and right circular polarization. The dual beam structure allows subtraction of atmospheric fl uctu ation and LNA (low noise amplifier) gain drift. These voltages are then combined using broadband 180° hybrids before passing through LNAs provided by Dr. Sandy Weinreb. The RF signals then leave t he cryost at and are transported from the prime focus to the base of t he t elescope using an R.F over Optical link . In the base, the signals are recovered and undergo quad rature mixing to separate the 12-18 GHz signal into 500 MHz subbands. The sub-band signals are then digitized and processed using FPGA-based boards developed by CASPER.. They are correlated to produce beam-differenced total intensity and linear polarization from ea.ch horn with mega.hertz spectral resolution. Finally, the spectra are stored for la ter analysis. 8 Chapter 3 RF over Optical Link The suitability of an RF over Optical Link was analyzed for use in the receiver. The link is intended to route the radio signal at sky frequency from the front end , located at the prime focus of the t elescope, down t he feed legs to the base, where t.he rest of t he electronics reside. This method is advant ageous because optical fib ers offer very low loss - sometimes on the order of 0.1 dB / km whereas traditional coaxial cable can lose up t o 20 dB/100 feet. It is also possible t o multiplex the fo ur RF signals onto one fib er. Therefore, assuming noise figures and phase shifts can be kept low, it is advisable to use optical fib ers to transmit signals overt.he long (100 meters) distance from t he prime focus to the base. We obtained a t est syst em from Optilab , consisting of a transmitter to t ransform an RF signal from DC t o 20 GHz to an optical signal, which is sent over optical fib er unt il it arrives a t a receiver, at which point it is again converted into an RF signal. An amplifier may also be inserted between the transmitter and receiver should the signal levels be too low. 3 .1 R esults T he Optilab RF over Optical link consists of an Optilab LT-20 transmitter , an EDFA optical amplifi er , and an LR-30 receiver. We used a Rohde & Schwarz ZVA-24 VNA t o measure the S-parameters of this system over the range of 10 MHz to 24 GHz. \Ve first looked at the magnitude of S21 and S 11 , insertion loss and return loss respectively. Figure 3.1 shows S2 1 for a wide range of input powers, from 0 t o -50 dBm . Without t he amplifier , the system generally exhibits 35 dB of loss over the 100 meters of cable, and is relatively const ant across the band of interest (12-18 GHz) . Figure 3.2 shows S 11 for an input power of -10 dBm. Less than -10 dB are reflected across t he Ku-band. The group delay of the system is the phase difference b et ween the inse1ted and received waves, arg(S21) - arg(Sn ). We looked at the group delay with a nd without the EDFA amplifier (Figure 3.3) . When a best-fit trend is removed , the residual group delay is less than 0.05 ns across the band . Finally, we measured the 1 dB compression p oint . Although amplifiers maintain constant gain for low-level input signals, they will saturate a t higher power levels and become nonlinear. The 1 dB 9 -30 -40 -50 iD -60 ~ is -70 -80 ...J .5 j -90 - - odBm - - -10dBm -100 - - -2odBm - - -30dBm -110 -40 dBm - - -SOdBm -120 2 4 6 B 10 12 14 16 18 20 22 24 22 24 freqtJency [GHz] Figure 3.1: S21 (insertion loss) of the Optilab system. · 10 -15 iD -20 :!:lo ~ ;:;; -25 t s -30 -' ~ £ -35 -40 -45 2 4 6 B 10 12 14 16 18 20 Frequency [GHz]) Figure 3.2: S 11 (return loss) of the Optilab system. 10 0 ·0.2 I ·0.4 - - withEDFA - - Without EDFA § ·0.6 -o.e -1 -1 .2 ..._,_....__...__.....__ _,__ _...._ __._ _.___ _.__...__ _.__ _.__ __. 2 4 6 8 10 12 14 18 16 20 22 24 Frequency [GHz Figure 3.3: Group delay of the Optilab system , with and without EDFA. -35 .2 .---- - .......- - -- . - -- -.---- - .......----.----~--~ -35 .4 -35 .6 <Xi' ;g. -35.8 ~ (;) :,ij -36 .~ J -36.2 8 ~ -36 .4 "36 .6 -37'----__.._ _ _.....__ _ _,___ ___.._ _ __.__ _ __.__ _ -50 -40 -30 -20 - 10 0 Input Power [dBm] Figure 3.4: Compression at 1 GHz. 10 ~ -36 .6 20 11 Figure 3.5: Optilab RF over Optical Link setup: VNA. LT-20 transmitter. 100 m cable. EDFA amplifier , and LR-30 receiver. compression point is the power level that causes the system t o drop in gain by 1 dB. Compression occurs around 15 dBm (Figure 3.4) at 1 GHz. The RF over Optical link (Figure 3.5) may be considered suitable for use in the new receiver if it exhibits several properties: there must be enough dynamic range for the variety of expected signals, and there must be less than 5° variation in phase across the band. From these measurements, in addition t o others made by Dr. Oliver King, the t ransmission amplitude, noise level. and linearity meet the requirements for the receiver. Other t est s of stability over time have shown that phase is extremely dependent on the t emperat ure of the cable; therefore, a suitable t emperature control system must be construct ed . This is a secondary issue. however. since all four signals are multiplexed onto the same cable and the same variations will be induced in each. 12 Chapter 4 Bandpass Filters and Sideband Separating Modules Once the Ku-band signal is transported from the prime focus to the base of the telescope using the RF over Optical link. it must be converted to baseband and separated into 500 MHz sub-bands in order to be read by the digital backend . Consider an RF time-domain signal x(t ) in the range of 12-18 GHz arriving in the base of the t elescope. It is mixed with a local oscillat or (LO) of a ce1tain frequency wo and divided into two. one wit h a 90° phase shift. We then have two signals. i (t ) = x(t) cos( wot ) and q(t ) = x(t ) sin (wot ). In the spectral domain , this is I (w) X (w) 0 7r [8(w - wo) + 8(w + wo)] Q(iv·) X (w) 0 ~ [8(w - wo ) + 8(w + wo)]. J The signal is composed of the sum and difference of the RF signal and LO frequency. In order to pick out a single sideband for each signal. I and Q arc sent through a 90° hybrid which p erforms the following: I (w) + jQ(w) X (jw ) 0 7r8(1.v· - wo ) jI(w) + Q (w) X (jw) 0 7r8(w + wo) . The signal is now separated into the upper and lower sideband. However. since the sp ectrum has been brought down t o baseband. power will also appear reflected in the frequency axis. Therefore. a signal in the upper sideband will appear faintly in the lower sideband, and vice versa. Finally. the signals are sent through a 500 - 1000 MHz bandpass filter to isolat e the frequencies outside of the sampling range of the back end. In the frequency domain , this is a convolution with the rectangular 13 Sidobr.nd ~ <• 11ar.1Lin!1 mixing Band Vl l'n•quonry 2 D.5 4 14 .0 1 H.O 1 a.o :1 ;, I fi.5 G 1 7.0 Figure 4. 1: Local Oscillator schematic. fun ction II(w): _ (w- 7.50MHz MHz) 500 X (w) 7rb(· _ ) II (w + 750 MHz) . © wo © 500 MHz Upper Sideband X(w) 0 7rb(:..-1 + wo) 0 II Lower Sideband w The signals are now in the range of 500 - 1000 MHz. and can be Nyquist san1pled by the back end running at 1 GHz. The spectrum calculated in the backend electronics is reversed in the frequency axis. By choosing different values of wo, we may pick out various bands to sample. In the new receiver design. LOs of 13.0, 13.5. 14.0, 16.0. 16.5 , and 17.0 GHz cover the entire Ku-band (Figure 4.1). 4 .1 Construction Spare unmounted 500 - 1000 MHz bandpass filters were obtained from the Combined Array for Research in Millimet er-Wave Astronomy (CARMA). The filters were then soldered onto cust om printed circuit boards (PCBs) . connected to RF SMA connectors (Figure 4.2). and tested with a VNA to ascertain that the passband was correct . The filters am passive and require no external power. The sideband separating modules were built from scratch. Capacitors, digital amplifiers, and a 90° hybrid were surface-mount soldered onto custom PCBs designed by Dr . Oliver King. Once the components were placed (Figure 4.3) . the modules were heated in an infrared oven for 7 minutes to secure the pieces to the board . The board requires 5 volt s to power the digital amplifiers. The user controls the gain by connecting t o the board through a Lab.Jack controller and P ython script. Up to 32 dB of gain may be applied by controlling 5 bits from the P ython script. 14 Figure 4.2: Two soldered bandpass filters. Figure 4.3: A surface-mount soldered sideband separating module. 15 Sideband Separation -2 0 .--~~~~~~~~~~~~~~~~~~~-, -25 -30 ~ -35 ~ ., ~ - 40 0.. " -45 :l c. 0 -50 -6fll.s 13.0 13.S 14.0 14.5 15.0 15.5 Frequen cy [G Hz] Figure 4.4: Spectral response of a 500-1000 MHz bandpass fil ter and sideband separating module at wo = 14 GHz (lower sideband in green , upper sideband in blue) . 4 .2 Results To test the setup, a 0-20 GHz signal generator and 14 GHz LO were connected to a Ku-band mixer. The I and Q outputs were then sent into the two inp uts on the sideband separating modules, through t he bandpass filters, and fin ally detected on a spectrum analyzer. We measured the power output of the system by inserting a -40 dBm sinusoidal wave at sky frequency, a nd observing the output power from both the upper and lower sidebands. A script was wri tten in GPIB to automate the testing procedure. The LO at 14 GHz produces t wo sidebands, from l :rn-13.5 GHz and from 14. 5-15.0 GHz. Due to the downconversion, the output power appears in the 500 - 1000 MHz range and not in the 13.0 - 15.0 GHz range. Figure 4.3 shows the results of both sidebands overlaid. T he higher-power signal in each band corresponds t o the intended domain, while the lower-power signal is t he ghosting effect of the opposite sideband . The sideband separation , or difference in power between these signals, is about 10-15 dB. These figures are somewhat low for use in t he receiver. It has recently been discovered t hat the system is starved for power from the LO. When t he LO signal is amplified by 7 dB, image rejection improves to greater than 20 dB across the band. 16 Chapter 5 Back End Electronics 5. 1 H a rdware We use the Reconfigurable Open Architecture Computing Hardware (ROACH, Figure 5.1) FPGA processing boards developed by the CASPER group at UC Berkeley to digitize the analog radiofrequency signal, compute the Stokes parameters. and outpu t spectra to an ethernet connection. The ROACH features a Xilinx Virtex5 FPGA for signal processing and a P owerPC running Linux to control the board (programmining the FPGA. interfacing between external Ethernet devices and software registers) . One may remotely log into the PowerPC through the Ethernet connection to communicate with the ROACH. Two quad data rate SRAMS provide high-speed memory. and one DDR2 SDRAM module provides lower-speed memory for the FPGA. Input is provided by two ZDOK ports, through which two Analog to Digit al Converters (iADCs. Figure 5.2) may be connected. The iADCs are also developed by CASPER and feature two input analog ports in addition to an optional external clock source. The iADCs may sample each of the analog inputs at up to 1 GHz; or, if the two inputs are interleaved . at 2 GHz. Figure 5.1: Reconfigurable Open Architecture Computing Hardware (ROACH). 17 Figure 5.2: Analog t o Digit.al Converter (iADC). 5 .2 Software The ROACH is programmed using a combina tion of MatLab / Simulink and librasies developed by the CASPER group. Simulink is a graphical block diagraming t ool which is powered by a customizable set of block libraries, and is widely used in digit.al signal processing. In practice, one opens libraries developed by Xilinx (specific for the Virtex5 FPGA ) and CASPER (specific for communication with the ROACH and astronomy applications) . drags and drops individual blocks onto a template, connects t he blocks, adjusts block paramet ers, and then compiles the design. Once complete, Mat.Lab outputs a bitfile which can be copied onto the P owerPC , and then programmed onto the FPGA. In this section we walk through the FPGA design (Figure 5.3). 5 .2.1 Syst e m G e nerator a nd iADCs The System Generat or block sets the clock speed of t he FPGA, while the iADC block controls t he parameters of the digitizers attached to the ROACH. In general . the FPGA speed is based on the desired sampling speed . For normal use, the iADC samples two analog signals a t up to 1 GSample/s, and the FPGA runs at one qua rter of the iADC speed. Therefore, for each clock cycle of the FPGA , the iADC feeds four parallel inputs into the FPGA . The sideband separating modules and bandpass filters out put in the 500-1000 MHz range. To Nyquist sample the 500 MHz bandwidth analog signal. we clock the iADCs at 1 GHz and the FPGA at 250 MHz. The band of interest is the 500 MHz above baseband , so the spectrum will be reversed in the frequency a.xis. The iADC inputs consist of combina tions of circular polarizations: A L - BL and AL+ BL into the first ; A n - B n and A n+ B R into the second. 18 Figure 5.3: ROACH Polarimeter. 19 5.2.2 PFB and FFT After digitization , the signal is sent t o the P olyphase Filter Bank (PFB) and Fast Fourier Transform (FFT). These two blocks work in conjunction to t ransform the time-domain signal into a frequencydomain spectrum. The basic Discrete Fourier Transform (DFT ) for an input time-domain signal x(n) is given by N- 1 X (m) = L x(n)e-j2nnm/ N , n =O where X (m) is the mth output frequency component. m = 0. 1, 2, 3, .. ., N - 1 is the output frequency index (the spacing of which is determined by the sam pling rate), n is the time-domain index of t he input samples, j = ;=I, and N is the number of samples in t he input sequence [6] . Unfortunat ely, the DFT is extremely computationally intensive: the number of calculations scales as the square of the length of the input time series. However , the FFT radix-2 algorithm, which reduces various redundant operations, only takes if log 2 N calculations for t he same size DFT. The only caveat is t hat they must be performed with a number of p oints equal to a power of two. The CASPER FFT block may out put 2, 4, 8, 16, 32, 64 ... point spectra, and is only limited by the resources on the FPGA. In most cases, the input frequencies will not fall exactly on one of the FFT bins, and thus power will leak out into the surrounding bins. This effect may be reduced by windowing, a process which reduces the sidelobes of the leakage by multiplying the input sequence by a function of the same size. For a window function w(n) , t he FFT is now N- 1 X w(m) = L w(n) · x(n )e- 2j-;rnm/ N. n =O A st andard window function is the Hamming window , given by w(n) = 0. 54 - 0.46cos ( -2r.n ) N for n = 0, 1, 2. .... N - 1. After digitization by the iADC blocks . the time-domain signals are fed into the PFB block. The PFB further divides the signal into pa rallel 't aps" and applies a finite impulse response filter to t he timestream , followed by multiplication with a Hamming window. More t aps used implies less inter-channel spectral leakage, but more logic is used. Each filter is lined up so that t here is approximately a 3 dB amplit ude decrease when they overlap. They are then fed into the FFT block, which performs the radix-2 algorithm and outputs frequency-domain spectra. We select a 27 = 128-point FFT and a 4-t ap PFB since we do not require extremely high spectral resolution fo r blazar monitoring. When an FFT is performed on real data (as is t he case fo r astronomical sources) , it outputs 20 Linear PFB Response 260 240 ;''\ I \ I \ I \ I ~ 200 .l!l ·c: !§"' 180 I 'O I ·c;, '§ 160 I I \ I :;;;: .S Qi 140 "" I 220 \ I \l :;:: I 0 Q_ 120 100 80 60 290 II I ~ I I 292 294 296 298 300 302 304 306 308 310 Frequency [MHz] Figure 5.4: Fine spectral response of PFB/ FFT (each of the 5 bins surrounding 300 MHz is a different color). a spectrum which is symmetric in positive and negative frequencies. Therefore, in order to save resources and reduce redundant calculations, the FFT block only outputs the positive frequencies . In order to keep the timing correct , there are only two output channels - odd and even positive frequencies. Therefore, every 32 clocks of the FPGA, the PFB / FFT blocks read in 128 time-domain dat a points (due t o the four parallel inputs from the iADC , clocked at four times the FPGA speed) and output 64 frequency-domain points. By clocking the iADC at 1000 MHz, we Nyquist sample up to 500 MHz, resulting in a spectral resolution of 500 MHz = 7. 8 MHz/bin. b. 64 ms The response of the PFB / FFT combination to a sinusoidal signal over several frequency bins is seen in Figure 5.4. Each color corresponds to one of the 5 bins surrounding the 300 MHz bins. As input frequency is varied , power drops t o a bout half of its nominal level as it crosses between bins; this occurs at 290.5 , 297, 303, and 309 .5 MHz. where power levels are about 65+ 65 = 130, a pproximately half of the power contained when the signal is in a single bin. This corresponds to the expect ed 3 dB falloff in between the PFB filter taps. 21 sync_m sync_oul a a+ b ~ b ., c_to_ri con ... ~n_of 18_17rl1 [20. 17}->(18 171 Termina1or l>ITJ convert_o f1 ~ Terminator1 [2017t->[ 1817J oonvert_of2 c_to_ri1 Terminator2 [20 .17}->{1817] 18_17r1o Figure 5.5: Demod ulation block. 5. 2 .3 D e modulatio n Blocks The PFB/ FFT blocks output AL - B L, A L+ B L, AR - B R, and A R+ B R in the frequency domain. The demodulation blocks (Figure 5.5) take these signals and recombine t hem to isolate the left and right circular polarizations for both horns. The left polarizat ion block takes in AL - B L and A L + BL , separates them into their real and imaginary components (clue t o t he FFT), and performs R( A L - B L)+ R (A L +BL) 2?R( AL) ~( AL - 2~( A L) B L)+ ~( A L+ BL) R( A L - B L) - ?R( A L +BL) - 2R (B L) ~( A L - - 2 ~( BL) - B L) - ~( A L+ BL) (5 .1 ) The same process is perfo rmed for right circular polarization. The signals are then recombined into complex A L, B L, A R, and B R. Since t he PFB/ FFT block out puts both odd and even frequencies, in order to keep t iming correct we use one block for even demodulation and one for odd , resulting in four total demodulation blocks . 5.2.4 Stokes Blocks T he Stokes blocks take in the left and right polarizations of each horn and cross-correlate them t o obtain t he Stokes paramet ers (Figure 5.6 ). In t he horn A block, t he following operat ions are performed: 22 sync_m sync_out 2 alO --~-.cu L:_____::_j____ al_pov.-0 all )--,----1-t_::f-~ '"""o powe'2 ..,. Ro •-t• 90PhaseSh1h XMultiplyO qa_ in"(l XMuttiplyl ua_imO XMulliply2 90PhaseShift1 ~~ qa_iml R•~ • m t\' XMultipty3 ua_iml powe(.l Figure 5.6: Stokes detection block. Where Risa 90° phase shift , operating on the separated real and imaginary values of AR: The spectra out of IALl 2 and IARl2 are simply t he the power detected, and the sum of the two gives Stokes I. The cross-correlations of AL and A R give complex spectra for Stokes Q and U. The spectra of interest corresponding to t he expected Stokes Q a11d U from a real source, as calculated in Chapter 2.1 , are computed in addition to other cross-correlat ions; all are stored fo r later analysis. Specifically, Stokes Q corresponds to the real part of QA, and Stokes U corresponds to the imaginary 23 part of UA. Once we separate the inputs into their real and imaginary components, AL 0 A n yields ?R(ALAn) ?R(A L) ?R(A n) - 8' (AL)~( A n) ~( AL AR) ?R ( An)~( A L) + ?R (AL)~( A n ). The same process occurs for horn B. The Stokes blocks outpu t 12 different spectra: However , since we process odd and even frequencies simultaneously, 24 spectra emerge from the Stokes blocks to be interleaved later. 5 .2.5 Quant izat ion and Accumulation Each spectrum is then multiplied by a factor that the user may enter into a software regist er. This digital gain allow the user t o control the height of the sp ectrum, and thus find a balance between low values (yielding large artifacts) and high values (yielding large data files) . Next , the spectra are accumulated. The accumulation syst em is based on the FFT size: since we use a 128-point. FFT , cut in half to 64 channels, and spread out over 2 parallel outputs, we obtain a full spectrum every 64/2 = 32 clocks. There is a minimum sync period required of any CASPER PFB/ FFT system determined by T = PFB taps · LCM(reorder orders)· FFT size . , no. inputs where the reorder orders are characteristic of the FFT size . Our minimum sync period given reorders of size 2 and 5 i;; T = 4 · LCM (2,5) · 128 4 = 1280 clocks. This minimum sync period is an integer multiple of the number of clocks it t akes to read out a full spectrum - here, one sync accumulates 1280/3 2 = 40 spect ra in one period . We may accumulat e spectral periods in integer multiples of the sync period; that is. the user may input an accumulation time of T = 1280n clocks, where n is the number of multiples of 40 spectra to be accumulated. Since the period of a 250 MHz ROACH is 4 ns, the minimum accumulation time is 1280 · 4 ns = 5.1 2 µ s. Accumulation lengths. which must be integer multiples of these, may be set in real-time by the user by writing to a software register. 24 5.2 .6 Readout After accumulation , each spectrum is fed into a block random access memory (BRAM) which is visible from the PowerPC . The spectrum remains on t he BRA.M until a new sequence is received , at which p oint the previous one is overwritten. Based on an interface written by Dr. Glenn Jones, a program to display the spectra was writ ten in Python. Consisting of a graphical user interface (GUI) using the Qt backend, it runs on the host PC and connects remotely to the ROACH. It displays a window with the spectrum which can be scaled along both axes, in addition t o a "waterfall plot " which shows st acked sp ectra in a time series. The software retrieves both the odd and even channels from any BRAM, which must be specified by t he user in the GUI, and interleaves them to form a full 64-point spectrum. Every 100 ms, the GUI retrieves t he lat est spectrum from the BRA.Ms. Therefore, when used in display mode, most spect ra are discarded . An upgrade is in development to retrieve and save each spectrum to disk in real time. 25 Chapter 6 Integration and Testing 6.1 ROACH Clocking Although the back end is intended to run at 250 MHz, compiling a design with many multiplications and FFTs is difficult at this speed. At 200 MHz, however , almost any design will compile as long as there is enough space on the FPGA. It is therefore more efficient t o make sure that t he ROACH output makes sense at a lower speed, and only afterwards bring it up to the desired clock rate. In t his chapter, the ROACH is clocked at 200 MHz and the iAD Cs are clocked at 800 MHz, meaning t hat only 400 MHz are Nyquist sampled. 6.2 Integration and Polarization Testing T he most important item in testing the ROACH is making sure that. given an polarized input , t he software correctly computes the Stokes parameters. To test polarization, the sideband separating modules and bandpass filters are integrated wit h the ROACH t o create a complete signal chain for the base of the telescope (Figure 6.1 ). Test sig,·nals are mixed with t he 14 GHz LO and sent into the sideband separating modules. We see one twelfth of t he total receiver bandwidth using one of the six LOs in total. Since each ROACH samples 500 MHz, i.e. one sideband , only fo ur out of the eight p ossible outputs from the LO are tested. Recall that in a circular basis, the Stokes parameters calculated are given by I (IE1 (t )l 2 ) + (I Er(t)l 2 ) Q (IE1 (t) l)(IE,.(t)I) cos(81 - or) u (IE1(t)l )(IE,.(t) I) sin (J1 - 8r). Before entering the bandpass filters and sideband separating modules, the left and right polarizations from horns A and B enter two 180° hybrid:;. which output the sum and difference of the 26 Figure 6.1: The entire signal chain. A noise diode ii:; connected to two 180° hybrids, mixed with a 14 GHz LO. and sent into four sideband separating mod ules, eight bandpass filters. and the ROACH. signals. For simplicity when testing the roach, we terminate one input on each of the hybrids so that the outputs of A L - B L . A L+ BL , A n - E n, An+ En simplify t o A L, AL , An. A n. To generate an unpolarized signal, Q = U = 0, the inputs must be uncorrelated. We use two Advanced Microwave broadband noise diodes. one for A L and one for An , t o generat e white noise in the range of 0-18 GHz. By virtue of t heir separation t he outpu t spectrum should show only noiselike characteristics in Q and U. Figure 6. 2 shows the spectrum of A L given this noise source. Since the bandpass filter picks out 500 - 1000 MHz and we are only Nyquist. sampling 400 MHz. a portion of the spectrum is zero. The spectrum of An is identical, and the sum of the two gives Stokes I. The spectra for both B L and E n are zero, as expect ed. To generate a linearly polarized signal , it. suffices to route the output of a single noise diode into both A L and A n. We then have Ei = E r . and if the cable lengths are equal, 81 - Dr = 0. which corresponds to a pure Q signal. To change Q into U. a phase delay must be inserted ; this may easily be accomplished by varying the length of cable to any one input. 6.3 ROACH Gain Relations Tot al intensity spectra are calculated as expect ed . For such a signal we expect Q = O; instead, however. the spectrum saturates (Figure 6.3). Before further polarization testing can proceed , the reason for this saturation must be determined . A li kely culprit is the fact that with many the many multiplications necessary fo r calculation of the Stokes parameters. numbers may overflow the hard- 27 70000 r-~~-.-~~---.A~L_P_o_w_e~r~w_i_th~N_o~is_e~D_io_d_e..--~-;=:::r:::=::=::=;i - spectrum 60000 ~ 50000 . ..... ; N n " 40000 ·;;; ~ ~ 30000 ::> 'iij i 20000 10000 0o~~~~l0,.-~--:2~0:--~----:3~ 0~~--:4~0~~-,: 5~ 0 ~~....,,.60,_-~~7~0 Frequency • 1400/64) [MHz! Figure 6.2: Power in horn A, left circular polarization from a noise diode. coded bit widths. After several blocks in the design , numbers that have been growing in bitwidth are recast to lower widths in order t o conserve resources. Vve suspect that some of these recastings choose the wrong bits and therefore discard significant numbers, resulting in an erroneous measurement. To determine where in the design the overflow occurs, several more designs were compiled. The first is a simple spectromet er. After the FFT, power is det ected and immediately accumulated into a spectrum without any further a rithmetic. Since it has had much less time fo r bit growth, it is expected to have the most dynamic range in digital units. The second compiled design is a spectromet er with the demodulation blocks added. Both of these designs also contain a digital gain block before accumulation. In order t o determine the useful ceiling and find the range over which the designs output linearly, power into the ROACH was held consta nt and the gain was allowed to vary from 210 t o 2 18 . Figure 6.3 shows the gain curve for the two designs, plotted just before the spectrum saturated. By det ermining the saturation point as a fun ction of d ept h into the ROACH design , it will be possible to correct the bit overflow errors in the full design and obtain reasonable spectra. 28 l.O lei Q A Real Power with Noise Diode I- spectrum! 0.8 0.2 0·00. c - - -,010,----=20 . ,__ _,J0 "=""'--"" 40~--.,50~--"' 60,_.__ __,,,10· Frequency+ {400/6 4} (MHzJ Figure 6. 3: R(QA )· Stokes Q from a noise diode. Gain Curve Comparison Spectrometer Derrodulator 35 10 12 14 x 10• Figure 6.4: Gain curves for a simple spectrometer and a demodulator. 29 Chapter 7 Conclusion In this thesis, I have presented the design , assembly, and testing of various components of a new Ku-band receiver for the OVRO 40-Meter Telescope. I tested an Optilab RF over Optical link to bring the sky signal into the base of the telescope, and det ermined that apart from phase variations with temperature, its noise figure and S-parameters are suitable for use in t he receiver. I built several 500 - 1000 MHz bandpass filters and sideband separating modules, intended to downconvert the sky signal and separate it into two 500 MHz sidebands. The modules exhibited better t han 20 dB of separation between the upper and lower sidebands from 12-18 GHz. I designed and wrote code to program the Virtex-5 FPGA on a ROACH to calculate the Stokes parameters given the input from the front end of the receiver , although it has not yet successfully compiled at the target speed of 250 MHz. The Stokes I total intensity calculation works correctly. I am now testing the dynamic range of the output given various bitwidths at different points in t he design, in order to remove the saturation errors that appear in polarized spectra . Once the ROACH code is complet e and debugged , I will write software to control and visualize the back end data interactively. I will then replicate the design onto the remaining 11 ROACHes, construct the .5 other local oscillator assemblies, a nd connect t he back a nd to t he front end when the horns, cryostat , and amplifiers are complete. T he new receiver will be on the sky and t aking polari zed spectra of blazars by the end of 2011. 30 Bibliography [l] Richards, J ., et al. 2011 , accepted for publication. [2] King, 0. 2009 , Doct oral Dissertation , Oxford University. [3] Tinbergen , J. , 1996, Cambridge University Press. [4] Riebel, M. , 2005 , Rohde & Schwarz GmbH & Co . KG. [5] Parsons, A. , et al. 2009 , Ast ro2010 Decadal Survey Committee. [6] Lyons, R. , 2004, Prentice Hall .