1 / 22

Antenna Cost Modeling For Large Arrays

Antenna Cost Modeling For Large Arrays. Larry R. D'Addario Jet Propulsion Laboratory operated for NASA by Caltech. Outline. Cost modeling for large arrays definitions motivation Antenna mechanical cost over a wide range of sizes traditional model improved model

nova
Download Presentation

Antenna Cost Modeling For Large Arrays

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Antenna Cost ModelingFor Large Arrays Larry R. D'Addario Jet Propulsion Laboratory operated for NASA by Caltech SKA TDP Antennas Meeting

  2. Outline • Cost modeling for large arrays • definitions • motivation • Antenna mechanical cost over a wide range of sizes • traditional model • improved model • Suggestions for further work This is an updated version of an URSI 2007 (Ottawa) talk, available at: http://www.astro.caltech.edu/USNC-URSI-J/Ottawa_presentations/ SKA TDP Antennas Meeting

  3. Cost Modeling • Cost modeling is different from costing: • No design exists yet, but tradeoffs should be understood and optimization undertaken before a design is selected. • Model == parameterized cost • some parameters fixed, especially performance measures • other parameters free, preferably over a wide range • Model should show parameter dependence accurately, but may give a poor absolute cost estimate for any fixed set of parameters. • Empirical: fit formula to known costs of full systems • First principles: use market data for basic costs (labor rates, raw material prices); derive system cost by analysis. SKA TDP Antennas Meeting

  4. SKA Optimization Example From: S. Weinreb, SKA Memo No. 77 SKA TDP Antennas Meeting

  5. Antenna Mechanical Cost: Traditional Model • Power law formula • Ca(A,f ) = Cref (A/Aref)(f/fref) • first principles: Blackman and Schell 1966, IEEConf. • cost, including labor, proportional to mass of raw materials • deflection at a fixed wind speed proportional to 1/f, indep. of A • NRE neglected • theoretical  = 4/3 (2 = 8/3  2.7) * • theoretical  = 1/3 • empirical: JPL study, Wallace 1979 • exponent   1.27 (2 = 2.55) • Valid only in limited circumstances • large antennas, where material cost dominates • fixed technology of construction * The calculation in the original paper contains errors. A correct analysis by the same reasoning yields 2 = 10/3. The incorrect result is widely known due to its quotation in the textbook Antenna Theory by Collin and Zucker (1969). SKA TDP Antennas Meeting

  6. Theoretical Dependence • Blacksmith and Schell: deflection of outer edge of dish in given wind is made independent of size. Cost assumed proportional to mass of material. • published result: mass = k1 V2/3f 1/3D8/3 • corrected result: mass = k2V2/3f1/3D10/3 • Deflection in operating wind is usually not a controlling specification. Survival in maximum wind is often more important, leading to mass  D3. • Economies of scale not included. • Cost of making an accurate reflector surface can be significant, but only  D2. • In spite of these difficulties, traditional model may be accurate over a limited range of sizes. SKA TDP Antennas Meeting

  7. Antenna Mechanical Cost: Improved Models • Cover a wide size range, sub-wavelength to ~100m. • Let construction technology vary with size: • 100m to ~10m: panelized reflectors • ~10m to ~10λ: single-piece reflectors • hydroformed metal • composite • 10s of cm to λ: printed (or horn or Vivaldi) • sub-wavelength: printed antennas, not steerable • Use separate models for major elements: • Reflector (including backup structure, if any) • Mount and drive • Separate NRE from replication cost SKA TDP Antennas Meeting

  8. Wide-Range Cost vs. Size Model Min. wavelength = 3 cm Caution: parameters may be wrong! panelized Multiple dishes per mount hydroformed At large diameters, cost of reflector/BUS dominates Below a few meters, cost of reflector is negligible, fixed costs dominate. 10λ printed, steerable printed, fixed SKA TDP Antennas Meeting

  9. CostModel/EffectiveArea vs. Size Min. wavelength = 3 cm Caution: parameters may be wrong! Printed Antennas Dishes Fixed Pointing SKA TDP Antennas Meeting

  10. List of Model Parameters par.a(1)=214; %PCB cost $0.14/in^2 = $214/m^2. par.a(2)=1000; %NRE for PCB par.a(3)=1.385e6; %Hydroforming factory: $1.385M fixed par.a(4)=3.64e6/12^3; %Hydroforming mold: $3.64M for 12m dia par.a(5)=30000/12^2; %Hydroforming reflector: $30k for 12m dia par.a(6)=2.2e5/12^3; %Drives,mount,foundation: $220k for 12m dia par.a(7)=2.5; %Panelized reflector exponent par.a(8)=2.5e5/12^par.a(7); %Panelized reflector: $250k for 12m dia par.a(9)=142000; %Panelized NRE, const, 142k$ for 12m dia. par.a(10)=0.60; %Aperture efficiency, hydroformed & panelized par.a(11)=pi/180*63; %Max off-boresight angle for non-steerable par.a(12)=pi/180*82.6; %Max zenith angle for steerable par.a(13)=1; %Min size of steerable mount, m. par.a(14)=15000; %Base cost of mount: mountCost = a14 + a6*d^3. % Antenna size breakpoints by effective area par.b(1)=(lambda./(1+cos(par.a(11)))).^2 .* sin(par.a(11)); %Max non-steerable par.b(2)=pi/4*0.3^2*par.a(10); %Minimum hydroformed = 0.3m par.b(3)=pi/4*12^2*par.a(10); %Maximum hydroformed = 12m SKA TDP Antennas Meeting

  11. Why Traditional Model Does Not Work • Structural analysis is flawed • Cost of complex components is not proportional to mass of materials. • Accurate surface panels • Motors, encoders, gearboxes, bearings • Assembly labor (as opposed to raw machining) • Testing • For steerable reflectors: • At large sizes, cost of reflector dominates • At small sizes, cost of reflector is negligible • Substantially different technologies are optimum in different size ranges. SKA TDP Antennas Meeting

  12. Motor cost vs. size over a wide range SKA TDP Antennas Meeting

  13. Why Empirical Modeling Does Not Work • Little reliable data exists • Variations in accounting methods • What is included in the reported costs? • How was responsibility divided? • How was NRE handled? • Variations in specifications • Frequency limit • Transportable vs. fixed • Operating environment, reliability • Mass production has not been attempted at most sizes • ATA is providing the first experience: N=34+, d=6m • VLA is next largest example, N=28, ~30 years ago. SKA TDP Antennas Meeting

  14. Case Study: Cost of 12m Antennas • 2004 survey of manufacturers commissioned by JPL • Identical specs provided to all, including • 0.3 mm rms surface • 44 m/sec survival wind, 13 m/sec operating wind • 18 arcsec blind pointing, non-repeatable error • quantity 100 • 7 responses; estimates ranged from 217k$ to 1653k$ (7.6:1). • 2005 study for SKA (R. Schultz, SKA Memo 63) • More thorough design, intended for mass production • 0.3 mm rms required only at night • lower operating wind speed • quantity > 1000 • Unit cost estimate 200.9k$, incl. overhead and profit, excl. NRE • Actual cost of 1 each antenna purchased by JPL • Approximately 750k$, including NRE • ALMA antenna, quantity 25, .02 mm rms: 6.76M$ SKA TDP Antennas Meeting

  15. Lessons: Using Estimated Costs • Cost estimates, even by experienced manufacturers, are not reliable because • No commitment is made if a firm bid is not required • Insufficient engineering effort is expended in the absence of payment • To obtain believable estimates, either • require firm bids and show that funds exist, or • pay for the estimation work SKA TDP Antennas Meeting

  16. Further Work • Refine model parameters • Consider additional technologies • Dense arrays of non-printed antennas (e.g., Vivaldi) • Asymmetrical reflectors (e.g., cylinders) • Wire-based antennas • Study cost vs. maximum frequency • For dishes, need separate models for reflector and backup structure • At some high frequency breakpoint, must change materials to avoid von Hoerner's thermal limit • from aluminum/steel to low-tempco and more expensive CFRP or similar • At some low frequency breakpoint, mesh reflectors, wire antennas, and simpler supporting structures become attractive. SKA TDP Antennas Meeting

  17. Backup Slides Follow SKA TDP Antennas Meeting

  18. Examples of Surface Error Budgets [1] JPL prototype antenna for DSN array (calculated). [2] Preliminary design for ALMA: T. Anderson, ALMA Memo 253, Sept 1997. [3] VLBA antenna: P. Napier et al., Proc IEEE, 82:668ff, 1994. SKA TDP Antennas Meeting

  19. Model Parameters for Large Arrays • Figures of Merit and requirements (fixed) • Frequency range • FOM1 = Atot / T (point source sensitivity) • FOM2 = (Atot / T)2(B/A) = NBAtot / T2 (survey speed) • Dimensions (free) • Size of each antenna element, A • Number of elements is N = Atot /A • Physical temperature of front end electronics, Tphys • Number of simultaneous beams, B • Cost models needed for large-array cost optimization • Antenna mechanical Ca(A,f ) [this paper] • Antenna-connected electronics Ce(B,Tphys) • Others (central electronics, signal transmission, infrastructure, etc.) are less important. SKA TDP Antennas Meeting

  20. Old vs. Size Model (July 2007 paper) • Disclaimers: • Not all technologies considered • Parameter values may be wrong At large diameters, cost of reflector dominates At large diameters, cost of reflector dominates Below a few meters, cost of reflector is negligible, fixed costs dominate. SKA TDP Antennas Meeting

  21. Per-antenna Electronics • Includes feed, LNA, downconverter/LO (if any), channelizer, digitizer • Not all are necessarily located at antenna, but must be duplicated for each antenna. • Includes all support hardware, e.g. cryocooler (if used). • Cost is dominated by integration: packaging, interconnections, power supplies, assembly labor – not by the semiconductor devices. • Not subject to Moore's Law • Improved by more design effort, more custom-engineered parts • For single dishes or small arrays, this "NRE" is not justified; it makes sense for large arrays • Designing for mass production; economies of scale SKA TDP Antennas Meeting

  22. Electronics Cost Trends • Improvements • Wider bandwidth feeds and LNAs require fewer to cover a given frequency range. • Lower noise at room temperature increases frequency at which cryocooling is cost effective. • Higher integration levels produce smaller packages, fewer interconnections, and require less power. • RF in to optical fiber out on a single chip or multi-chip module • Mixed signal chips, including substantial DSP with analog processing • Many channels per chip or module • Limitations • Multi-beam antennas require more electronics. • for phased array feeds, complex signal processing is added • For arrays with steerable reflectors, gain from integration is limited because hardware is geographically dispersed. • Custom ICs are cost effective only if large numbers are needed. SKA TDP Antennas Meeting

More Related