Transcript Antenna Cost Modeling For Large Arrays

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
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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/
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SKA TDP Antennas Meeting
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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.
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SKA TDP Antennas Meeting
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SKA Optimization Example
SKA Cost vs Antenna Diameter and FPA Beams (J)
for Arrays with Constant Survey Sensitivity
2000
J=1
J=4
J=16
J=100
1800
Array Cost, M$
1600
1400
1200
1000
800
600
400
200
0
0
3
6
9
12
15
18
21
24
Antenna Diameter, m
From: S. Weinreb, SKA Memo No. 77
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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).
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SKA TDP Antennas Meeting
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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.
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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
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Wide-Range Cost vs. Size Model
10
8
Min. wavelength = 3 cm
Construction Cost Estimate, US$(2006)
10
10
10
10
10
10
10
10
10
7
panelized
Caution: parameters may be wrong!
6
5
Multiple dishes
per mount
hydroformed
At large diameters,
cost of reflector/BUS
dominates
4
3
Below a few meters, cost
of reflector is negligible,
fixed costs dominate.
10λ
2
printed,
steerable
1
0
2.7
270k$ (d/12m)
MODEL: unit cost
unit cost best estimates
MODEL: non-recurring cost
-1
printed, fixed
-2
10 -2
10
10
-1
10
0
10
1
10
2
Effective Diameter, m
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CostModel/EffectiveArea vs. Size
Reproduction Cost per Unit Effective Area, US$(2006)/m2
10
5
Min. wavelength = 3 cm
Caution: parameters may be wrong!
10
10
4
3
Printed
Antennas
Dishes
Fixed
Pointing
2
10 -2
10
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-1
0
10
Effective diameter, m
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1
10
2
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List of Model Parameters
par.a(1)=214;
par.a(2)=1000;
%PCB cost $0.14/in^2 = $214/m^2.
%NRE for PCB
par.a(3)=1.385e6;
par.a(4)=3.64e6/12^3;
par.a(5)=30000/12^2;
%Hydroforming factory: $1.385M fixed
%Hydroforming mold: $3.64M for 12m dia
%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;
par.a(8)=2.5e5/12^par.a(7);
par.a(9)=142000;
%Panelized reflector exponent
%Panelized reflector: $250k for 12m dia
%Panelized NRE, const, 142k$ for 12m dia.
par.a(10)=0.60;
par.a(11)=pi/180*63;
par.a(12)=pi/180*82.6;
par.a(13)=1;
par.a(14)=15000;
%Aperture efficiency, hydroformed & panelized
%Max off-boresight angle for non-steerable
%Max zenith angle for steerable
%Min size of steerable mount, m.
%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
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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.
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Motor cost vs. size over a wide range
Cost of Brushless DC Servo Motors
5
10
Glentek quotation, 100ea
Baldor online list price
model: 100$ (P/1kW)0.5
4
Unit price, US$
10
3
10
2
10
1
10
-2
10
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10
0
10
Rated output power, kW
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2
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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.
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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$
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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
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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.
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SKA TDP Antennas Meeting
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Backup Slides Follow
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Examples of Surface Error Budgets
D, m
12
f, GHz (c/20)
12
66
25
600
54
Panel manufacture, mm
0.10
.018
0.16
Alignment, mm
0.10
.012
0.13
Gravity, mm
.12
.007
Wind, mm
.01
.006
Thermal gradients, mm
.02
.008
0.19
.025
Total, , mm rss
Reference
[1]
[2]
0.20
0.28
[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.
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SKA TDP Antennas Meeting
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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.
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SKA TDP Antennas Meeting
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Old vs. Size Model (July 2007 paper)
8
Construction Cost Estimate, US$(2006)
10
Disclaimers:
• Not all technologies considered
• Parameter values may be wrong
panelized
6
10
hydroformed
At large diameters,
cost of reflector
dominates
4
10
Below a few meters, cost
of reflector is negligible,
fixed costs dominate.
2
10
printed, steerable
unit cost best estimates
non-recurring cost model
0
10
260k$ (d/12m)2.7
unit cost model
printed, fixed
-2
10
-2
10
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0
10
Equivalent Diameter, m
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2
10
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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
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SKA TDP Antennas Meeting
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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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SKA TDP Antennas Meeting
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