13 March 2008 SKA TDP Antennas Meeting 1 Antenna Cost Modeling For Large Arrays Larry R. D'Addario...

13 March 2008 SKA TDP Antennas Meeting 1

Antenna Cost ModelingFor Large Arrays

Larry R. D'AddarioJet 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

• 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/


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 Optimization ExampleSKA Cost vs Antenna Diameter and FPA Beams (J)

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 3 6 9 12 15 18 21 24

Antenna Diameter, m

Arr

ay C

ost

, M$

J=1J=4J=16J=100

for Arrays with Constant Survey Sensitivity

From: S. Weinreb, SKA Memo No. 77


Antenna Mechanical Cost: Traditional Model• Power law formula

– Ca(A,f ) = Cref (A /Aref) (f/fref) – 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).


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 V 2/3 f 1/3 D 8/3

– corrected result: mass = k2 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 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.


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


Wide-Range Cost vs. Size Model

10-2

10-1

100

101

102

10-2

10-1

100

101

102

103

104

105

106

107

108

Effective Diameter, m

Con

stru

ctio

n C

ost E

stim

ate,

US

$(20

06)

270k$ (d/12m)2.7

MODEL: unit cost

unit cost best estimates

MODEL: non-recurring cost

panelized

hydroformed

printed, steerable

printed, fixed

Min. wavelength = 3 cmCaution: 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


10-2

10-1

100

101

102

102

103

104

105

Effective diameter, m

Re

pro

du

ctio

n C

ost

pe

r U

nit

Effe

ctiv

e A

rea

, US

$(2

00

6)/

m2

CostModel/EffectiveArea vs. Size

DishesPrintedAntennas

FixedPointing

Min. wavelength = 3 cmCaution: parameters may be wrong!


List of Model Parameterspar.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 fixedpar.a(4)=3.64e6/12^3; %Hydroforming mold: $3.64M for 12m diapar.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 exponentpar.a(8)=2.5e5/12^par.a(7); %Panelized reflector: $250k for 12m diapar.a(9)=142000; %Panelized NRE, const, 142k$ for 12m dia.

par.a(10)=0.60; %Aperture efficiency, hydroformed & panelizedpar.a(11)=pi/180*63; %Max off-boresight angle for non-steerablepar.a(12)=pi/180*82.6; %Max zenith angle for steerablepar.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 areapar.b(1)=(lambda./(1+cos(par.a(11)))).^2 .* sin(par.a(11)); %Max non-steerablepar.b(2)=pi/4*0.3^2*par.a(10); %Minimum hydroformed = 0.3mpar.b(3)=pi/4*12^2*par.a(10); %Maximum hydroformed = 12m


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.


Motor cost vs. size over a wide range

10-2

10-1

100

101

102

101

102

103

104

105

Rated output power, kW

Uni

t pr

ice,

US

$Cost of Brushless DC Servo Motors

Glentek quotation, 100ea

Baldor online list price

model: 100$ (P/1kW)0.5


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.


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$, including NRE• ALMA antenna, quantity 25, .02 mm rms: 6.76M$


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


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.


Backup Slides Follow


Examples of Surface Error Budgets

D, m 12 12 25

f, GHz (c/20) 66 600 54

Panel manufacture, mm 0.10 .018 0.16

Alignment, mm 0.10 .012 0.13

Gravity, mm .12 .007

0.20Wind, mm .01 .006

Thermal gradients, mm .02 .008

Total, , mm rss 0.19 .025 0.28

Reference [1] [2] [3]

[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.


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.


Old vs. Size Model (July 2007 paper)

10-2

10-1

100

101

102

10-2

100

102

104

106

108

Equivalent Diameter, m

Con

stru

ctio

n C

ost

Est

imat

e, U

S$(

2006

)

unit cost best estimates

non-recurring cost model

260k$ (d/12m)2.7

unit cost modelprinted, fixed

printed, steerable

hydroformed

panelized

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


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


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.

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