13 March 2008 SKA TDP Antennas Meeting 1 Antenna Cost Modeling For Large Arrays Larry R. D'Addario Jet Propulsion Laboratory operated for NASA by Caltech

13 March 2008 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:

13 March 2008 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.

13 March 2008 SKA TDP Antennas Meeting 4 SKA Optimization Example From: S. Weinreb, SKA Memo No. 77

13 March 2008 SKA TDP Antennas Meeting 5 Antenna Mechanical Cost: Traditional Model Power law formula –C a (A,f ) = C ref (A /A ref )  (f/f ref )  –first principles: Blackman and Schell 1966, IEE Conf. 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).

13 March 2008 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 = k 1 V 2/3 f 1/3 D 8/3 –corrected result: mass = k 2 V 2/3 f 1/3 D 10/3 Deflection in operating wind is usually not a controlling specification. Survival in maximum wind is often more important, leading to mass  D 3. Economies of scale not included. Cost of making an accurate reflector surface can be significant, but only  D 2. In spite of these difficulties, traditional model may be accurate over a limited range of sizes.

13 March 2008 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

13 March 2008 SKA TDP Antennas Meeting 8 Wide-Range Cost vs. Size Model panelized hydroformed printed, steerable printed, fixed Min. wavelength = 3 cm Caution: parameters may be wrong! At large diameters, cost of reflector/BUS dominates Below a few meters, cost of reflector is negligible, fixed costs dominate. Multiple dishes per mount 10λ

13 March 2008 SKA TDP Antennas Meeting 9 CostModel/EffectiveArea vs. Size Dishes Printed Antennas Fixed Pointing Min. wavelength = 3 cm Caution: parameters may be wrong!

13 March 2008 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

13 March 2008 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.

13 March 2008 SKA TDP Antennas Meeting 12 Motor cost vs. size over a wide range

13 March 2008 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.

13 March 2008 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) 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$

13 March 2008 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

13 March 2008 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.

13 March 2008 SKA TDP Antennas Meeting 17 Backup Slides Follow

13 March 2008 SKA TDP Antennas Meeting 18 Examples of Surface Error Budgets D, m12 25 f, GHz (c/20  ) Panel manufacture, mm Alignment, mm Gravity, mm Wind, mm Thermal gradients, mm Total, , mm rss Reference[1][2][3] [1] JPL prototype antenna for DSN array (calculated). [2] Preliminary design for ALMA: T. Anderson, ALMA Memo 253, Sept [3] VLBA antenna: P. Napier et al., Proc IEEE, 82:668ff, 1994.

13 March 2008 SKA TDP Antennas Meeting 19 Model Parameters for Large Arrays Figures of Merit and requirements (fixed) –Frequency range –FOM1 = A tot / T (point source sensitivity) –FOM2 = (A tot / T) 2 (B/A) = NBA tot / T 2 (survey speed) Dimensions (free) –Size of each antenna element, A Number of elements is N = A tot /A –Physical temperature of front end electronics, T phys –Number of simultaneous beams, B Cost models needed for large-array cost optimization –Antenna mechanical C a (A,f ) [this paper] –Antenna-connected electronics C e (B,T phys ) –Others (central electronics, signal transmission, infrastructure, etc.) are less important.

13 March 2008 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 Below a few meters, cost of reflector is negligible, fixed costs dominate. At large diameters, cost of reflector dominates

13 March 2008 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

13 March 2008 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.