Total Cost, $K - SKA

Cost Equation for the SKASander Weinreb, Caltech/JPL, sweinreb@caltech.eduLarry D’Addario, NRAO and SETI Institute, ldaddario@astro.berkeley.eduJuly 21, 20011. General form of spreadsheet2. Performance and cost parameters3. Results: Cost vs antenna diameter and other parameters4. Front-end model (Modified July 21, 2001)5. Signal processing modelAppendix A - Notes on Signal Processing Costs for SKA (Added July 21,2001)Appendix B - Cost Dependence When Field of View is Maintained (Added July 21, 2001(Full Excel Spreadsheet is available as a file on SKA web sites: SKAcostEq1.xls)CostEQ2.doc Created on 7/21/2001 9:35 AM Page 1 of 18

SKA Cost Equation Spread SheetRows are for input or computed parameterssuch as cost coefficients or performanceparametersColumns are for varying antenna diametersSheets are for varying major parameters suchas cryogenic temperature or era of electronicscosts.Output of the program is the total cost and costof each subsystem. The Aeff/Tsys isconstrained at 20,000 by computing the numberof antennas needed for each station.Parameters – There are 14 performanceparameters and 19 cost parameters listed on thenext pageModels – Details are in the equations in thespreadsheet. Antenna cost is 0.1*D^3 K$.CostEQ2.doc Created on 7/21/2001 9:35 AM Page 2 of 18

SKA Cost Equation Input ParametersUnits: K$US(2001), meters, GHzParam Array Performance ParametersDefaultValue Param Array Cost Parameters Default ValueNs Number of stations in array 100 Cso Fixed cost per station, land, civil, 300M Specified Figure of Merit, M = A/Tsys 20,000 Ka Antenna cost coefficient, 0.10B Processed total continuum bandwidth 4.0 X Antenna cost exponent 3.0Nl Number of spectral line channels 16,000 Ccl Cooling cost per antenna 20.0D Physical diameter of element (meters) 10.0 Cfd Average dual-polariz feed cost 2.0Ef Aperature efficiency 0.70 Cln Average LNA + mixer cost 0.8Tant Antenna noise temperature, Tant = 10 14 Clo LO cost 3.0Kln Lna noise coefficient dependant upon 0.40 Cifo Fixed IF cost per polarization 1.0Tphy Physical temperature of LNA 15 Kif Dual IF cost per GHz of bandwidt 0.2F Frequency for system temperature spe 10 a1 _Digitization coefficient 2.00Nbn Number of frequency bands 3 e _Digitization exponent 2.00Kch _Number of separately digitized chann 4 a2 _Digitization constant 0.50Le _Average distance, element to station 0.50 d _Tracking coefficient (per GHz) 0.72Nbeam_Beams per station 4 f _Tracking constant 0.10Kproc _Processing cost coefficient (per 0.48Kmem _Memory cost (per word)2.10E-04kct _Corner turner cost coefficient (p 1.00E-03Kcor _Correlator cost coef (per baselin 0.024Kchip Price per large FPGA chip 0.14Color code:Purple: correction of error since previous version.Blue: change to value or formula since previous version.Red: variable whose value changes across this sheetGreen: variable whose value is different from previous sheetBold type: input parameter; normal type means value is calculated.CostEQ2.doc Created on 7/21/2001 9:35 AM Page 3 of 18

SKA Cost Breakdown by Subsystem vs Antenna DiameterAeff/Tsys = 20,000, Aeff=360,000, Tsys=18K, BW=4GHz, 15K CryogenicsAntenna Cost = 0.1D^3 K$, 2001 Electronics Cost = $54K per Element2,000,000Fixed CostsCivil Station1,500,000Signal TransmissionElectronicsCentral ProcessingAntennaTotal Cost, $K1,000,000Antenna500,000Electronics0Signal TransmissionCentral ProcessingFixed CostsCivil Station5 8 10 12 15 20 30Antenna Diameter, MetersCostEQ2.doc Created on 7/21/2001 9:35 AM Page 5 of 18

SKA Cost Breakdown by Subsystem vs Antenna DiameterAeff/Tsys = 20,000, Aeff=360,000, Tsys=18K, BW=4GHz, 15K CryogenicsAntenna Cost = 0.1D^3 K$, 2010Electronics Cost = $15K per Element2,000,000Fixed CostsCivil Station1,500,000Signal TransmissionElectronicsCentral ProcessingAntennaTotal Cost, $K1,000,000500,000Antenna0ElectronicsSignal TransmissionCentral ProcessingFixed CostsCivil Station5 8 10 12 15 20 30Antenna Diameter, MetersCostEQ2.doc Created on 7/21/2001 9:35 AM Page 6 of 18

SKA Cost vs Antenna DiameterCompares Current and Projected (2010) Electronics CostsAll for 15K cryogenics, 4 GHz BW, 100 Stations, A/T = 20,000Antenna Cost = 0.1D^3 $K$2,000,000$100,000Total Cost, $K(US2001)$1,500,000$1,000,000$500,000$10,000$1,000$100Antenna Unit Cost,$K$0$105.0 10.0 15.0 20.0 25.0 30.0Element Diameter, Meters$54K Electronics $15K Electronics Antenna CostCostEQ2.doc Created on 7/21/2001 9:35 AM Page 7 of 18

SKA Cost vs Processed Bandwidth forTwo Antenna DiametersAll for 15K Cryogenics$2,000,000Cost, $K (US2001)$1,500,000$1,000,000$500,000$00.0 2.0 4.0 6.0 8.0Processed Bandwidth, GHz6551 x 10m Antenna 2912 x 15m AntennaCostEQ2.doc Created on 7/21/2001 9:35 AM Page 8 of 18

SKA Cost vs Number of Stations forTwo Processed BandwidthsAll for 15K Cryogenics, 10m antennas. A/T = 20,000$2,500,00080Cost, $K (US2001)$2,000,000$1,500,000$1,000,000$500,000604020Antennas per Station$00 100 200 300 400Number of Stations01 GHz Bandwidth 4 GHz Bandwidth Antennas per StationCostEQ2.doc Created on 7/21/2001 9:35 AM Page 9 of 18

Front-End Cost and Performance ModelCooler Type PhysicalTempCoolerCost, K$Noise @10 GHzNoise @50 GHzNoise @F GHzNone 300 1 40 200 4*F+16Peltier 180 3 24 120 2.4*F+10Pulse or Klemenko 60 6 10 50 1.0*F+4Gifford-McMann 15 20 4 20 0.4*F+1Total Front-End Cost, FE$FE$ = Cooler$ + 3(Bands)*2(Polarizations)* LNA$LNA$ = $0.8K*(Fmax/10)^.3i.e. FE$ = $11.9K for Pulse Cooling with Fmax = 20 GHzTotal Electronics Cost, EL$, per AntennaEL$ = FE$+ 3*Feed$+LO$+IF$+Fixed$Feed$ = $1K, LO$ = $5K, IF$ = 2*(0.5 + 2*BW), Fixed$ = $1Ki.e. EL$ = 11.9 + 3*1 + 5 + 2*4.5 +1 = $29.9KTotal System Noise, TsysTsys = Tlna + [10 + 4* (F/10)] F>1 GHz, Not Including Antenna LossesCostEQ2.doc Created on 7/21/2001 9:35 AM Page 10 of 18

Signal Processing Cost Model• EACH ANTENNA1. DigitizationC d = [k d (B/N ch ) e + c d ] N ch (exponent e is approximately 2)Cost per channel increases faster than bandwidth => more channels• Presently expensive -- total for array is more than the correlator!2. Tracking• Primarily delay and phase tracking of sources• Per antenna per beam -- multi beaming is probably needed to mitigate small FOV ofstation beam.• All-digital implementation assumed• EACH STATION1. Summation to form phased-array, per beam• Multi-beaming probably needed due to small station beam2. Transmission to central processing facility• available bandwidth shared among beams.• CENTRAL PROCESSING (CORRELATION)1. Per antenna section• filter bank for L spectral channels• cost grows as B log(L) if minimum-memory FFTs are used2. Interconnection section• can dominate cost for large N• natural architecture grows as B N 3• clever architecture grows as B N log(N)3. Cross correlation section• grows as B L N 2 (note L dependence, even for FX architectureCostEQ2.doc Created on 7/21/2001 9:35 AM Page 11 of 18

Appendix A - Notes on Signal Processing Costs for SKAL. D’Addario 2001-Jul-04; revised Jul-07, Jul-12ANTENNA-ELEMENT SIGNAL PROCESSING COSTS1. DigitizationIn present technology, this is an expensive element of the overall signal processing. Weestimate about 10k$ per element for 4 GHz bandwidth, which becomes 45M$ for 4500 elements(100 stations of 45 elements each). This is about equal to the cost of the central signal processing(correlator) and 3% of the total cost of the array, based on our current estimates for one reasonablecase.The cost of digitization rises faster than the bandwidth of each separately-digitized channel,and appears to go approximately as the square over the range 10 to 1000 MHz for presentlyavailable commercial devices. Therefore, it is advantageous to break up the total bandwidth priorto digitization into as many channels as practical, provided that performance does not suffer. In ourcost estimates, we have usually used at least 4 channels (to allow for 2 polarizations at 2independent sky frequencies) and kept the channel bandwidth at 1 GHz or less.2. TrackingFor each signal channel of each antenna element, it is necessary to provide for time-varyingadjustment of the delay and phase so as to track a desired direction on the sky. In our costestimates, we assume that this is accomplished digitally. The cost of computation and control forthis purpose appears to be negligible (

CORRELATOR COST DEPENDENCIESWe assume that it's important to cross-correlate the signals from all stations, over the fullbandwidth of each. The cost of this is proportional to the total bandwidth, regardless of whetherthat bandwidth represents a single channel on the sky or several independent channels (beams).There is a weak dependence on the number of channels, but this is insignificant if that number issmall compared with the final number of subchannels into which the total bandwidth will beanalyzed.The central processing separates naturally into a per-station part and a per-baseline partwhose costs are proportional to B N and BN 2 , respectively. Each cost term has additional factorsthat depend on the architecture and on the spectral resolution, as well as a coefficient that dependson the implementation technology. For the large-N case, the baseline term dominates the stationterm. For sufficiently large N, the baseline electronics will not fit into a single chip, nor a singlecircuit board or small set of boards, and therefore it must be partitioned into some number K ofseparate pacakages, each of which accomplishes 1/K of the processing. There are several ways todo the partitioning [1], and this determines the top-level architecture of the system. We concentratehere on the so-called ``FX'' architecture, where the bandwidth B from each antenna is partitioned byfrequency into segments of bandwidth B/K and each element of the baseline part processes onesuch segment for all antennas.The available technology determines how much processing can be fit into one package, andthus how many packages K are required and how small each bandwidth segment B/K must be. Weset K = t B N 2 /2, where t is a technology-dependent coefficient that gets smaller as circuitrybecomes denser and/or faster.The segmentation is done in the station part, which we assume to consist of one package perantenna. Therefore, C=N K interconnections are needed between different packages in order to getthe signals from the station part to the baseline part. Substituting, we see that C = t B N 3 /2.Because of this N 3 dependence, for sufficiently large N the cost can easily be dominated by theinterconnections, even if t is small. This situation can be substantially improved by imposing anadditional device between the station part and the baseline part whose purpose is to re-order thedata; it is called a “corner turner'' [2]. Then the number of interconnections is reduced from N K toN+K, where N are needed from the station part to the corner turner, and K from the corner turner tothe baseline part. Unfortunately, the corner turner itself is potentially a very large machine whoseobvious implementation involves N K internal interconnections and data storage proportional toNK, hence its size grows as N 3 . But a much more efficient implementation exists [2][3] thatreduces it to a size proportional to N 2 log N, in a manner similar to the FFT's reduction of thenumber of operations in a discrete Fourier transform of size L from L 2 to L log L.In addition, a new architecture for the baseline part [4] allows it to be organized so that notall K segments need to be connected directly to the corner turner. This allows the corner turnersize to be grow only as N log N.13

It may be desired to analyze the bandwidth into many more than K subchannels, sayL>>K, for spectroscopy. Then each of the K segments processes L/K subchannels. It is oftensuggested that the FX architecture allows L to be increased arbitrarily at negligible additional cost.In the station part, filter banks based on the FFT can be used so that the cost increases only aslog(L); then, unless L is extreme, the cost of the station part remains small compared to theinterconnections and baseline part. The interconnection cost is independent of L for a given B andN. In the baseline part, the computation rate (for cross multiplication and accumulation) is alsoindependent of L, since the data rate of each subchannel goes as 1/L. However, L separateaccumulators are needed per baseline, so storage requirements increase as L. Depending on thecost of storage compared with computation, this may be important. Usually it is not possible totake advantage of the low cost per bit of large RAM because efficient use of the computationalhardware requires many multiply-add operations to be done in parallel at high speed, leading tomany short memories rather than few large ones, and requiring them to be integrated on the samechip with the computational elements. This can cause the accumulator storage to be the dominantcost, so that the overall cost is nearly proportional to L. The dependence is then nearly the same asin the XF architecture, where the costs of both computation and storage are proportional to L.Indeed, this would make the absolute cost of the XF architecture smaller because the individualmultipliers and accumulators are considerably less complex.All of this is summarized in the chart on the last page of this document.REFERENCES[1] L. D'Addario, ``Correlators: General design considerations.'' ATA Memo No. 24, 2001-Mar-13.[2] L. Urry, ``A corner turner architecture.'' ATA Memo No. 14, 2000-Nov-17.[3] L. D'Addario, ``Generalization of the memoryless corner turner to the non-square case.'' ATAMemo No. 22, 2001-Mar-16.(All of the above are temporarily available viahttp://astron.berkeley.edu/ral/ATAImagerDocs.html .)[4] L. Urry, this conference.JUSTIFICATIONS OF COST COEFFICIENTSa1,ea2digitizer cost parameters, fit to prices of commercial ADC chipsdigitizer cost constant: guess at costs of downconversion, anti-alias filtering, circuit board,$500. This can't be too far off.14

d,etracking coef, const: One XV300E should do 2 channels at 100 MHz, costs $144; based onpreliminary design for ATA. So 722$/GHz. Constant term, $100, is just a guess tocover packaging and power.Kproc Xilinx XV300E, 3072slices/1929perFFT1024inPlace -> 1.5 radix4 butterflys=3 radix2,$144/3= $48 ea., @100 MHz -> 480 $/butterfly/GHzKmem Xilinx XV300E:144$/(2mem)*(32b/word)/(131072b block RAM)/100MHz = 0.0001758 k$/word/GHzwhere half of chip cost is allocated to memoryKcorr Xilinx XV300E: 3072slices/51perMAC = 60 MACs, 100 MHz each, $144/chip144$/(2comp)/60MAC/100MHz = .0120 k$/MAC/GHzwhere half of chip cost is allocated to computationKinfr Total chip cost/$144 -> chip count. 16 chips/board, $160 for board, rack, power.Check: Total central processing for B=0.2, Ns=350, Nl=2048 is 5.6M$ -- ATA caseB=16, Ns= 64, Nl=8192 is 58.7M$ -- ALMA caseThe ATA result is about 4x higher than the independent cost estimate (hardware only) made for theproposal. That proposal used future FPGA prices that are indeed about 4x lower per unitperformance than the present prices used here; with this correction, the agreement is excellent. TheALMA result is also about 4x higher than its presently projected actual cost, but its architecture isquite different than assumed here.15

Correlator Cost Model:FX ArchitectureFiltering Interconnection CorrelationComputation α B N log L β B N log N αB N 2 / 2Storage χ B N L (control only) δ B L N 2 / 2Where:B is the total processed bandwidthN is the number of stationsL is the number of spectral channelsGreek symbols are cost coefficients, dependent on technology.Correlation does not include cross-polarized products.16

Appendix B - Cost Dependence When Field of View is MaintainedLRD, 2001-Jul-12The analyses presented at the conference considered the cost dependence on variousparameters, including antenna size, front end cooling temperature, and electronics costs,while keeping the number of stations constant. This required varying the number ofantennas per station in order to have enough collecting area to meet the A e /T sysrequirement. Formally, the number of phased array beams was kept constant at 4. Butthe cost would be nearly unaffected if the number of beams were larger, provided that theprocessed bandwidth B is shared among all the beams.Here we consider relaxing that restriction.If the antennas are clustered into stations at N s each, and if they are close-packed withina station, then each station beam is about 1/ N s the size of the primary antenna (element)beam in solid angle. So if we still want to image the whole primary beam, we will needN s phased-array beams. I put this into the spreadsheet to look at the dependence on N s .Rather than sharing B among the beams, I fixed the bandwidth/beam b, making thetotal bandwidth B = 2 b N s (2 for polarization). Naturally this can lead to very large Band high cost for transmission and central processing, so I considered values of bonly from 0.1 to 0.5 GHz.The result is given in the accompanying figure. It can be seen that a shallow minimum inthe total cost occurs at N s = 200. Above this, the slow increase in total cost is caused byrapid increase in central processing (correlation) cost, which reaches 33% of the total at400 antennas per station and 500 MHz bandwidth. Below the minimum, the correlatorcost continues to decrease (in spite of the larger number of beams required), but the totalcost is strongly affected by the processing required at each station to form many beams,including both digitization (assumed separate for each beam) and tracking.17

SKA Cost vs Number of Stations forBeam-filled case, 0.1 and 0.5 GHz/beamAll for 15K Cryogenics, 12m antennas, 4550 total, A/T = 20,000$3,500,000100Cost, $K (US2001)$3,000,000$2,500,000$2,000,000$1,500,000$1,000,000$500,00080604020Ants/stn == beams$000 100 200 300 400Number of Stations0.1 GHz/beam 0.5 GHz/beam Antennas per Station18

SKA Cost Estimates July 21, 2001File: skacosteq1.xlsUnits K$US(2001), meters, GHzAntenna Diameter, Meters 10,0Parameter Array Parmeters ValueC Total array cost, fixed costs, elements, processing 1.270.322Cat Total antenna cost, Ne*Ns*Ca 691.538Celt Total electronics cost, Ne*Ns*Ce 412.710Cpt Total processing cost includiing station sum 65.275Ctr Signal transmission costs 20.800Csot Total civil costs at stations, Ns*Cso 30.000Co Fixed cost per array - design + central civil 50.000Cs Total station cost, elements + combining electronics 11.345Cm Total element cost, antenna + receivers + processing 160Cp Central Signal processing costs 65.002Ns Number of stations in array 100Ne Number of elements per station 69Deq Equivalent single-antenna diameter of station 83N Total number of elements, N = Ns*Ne 6.915A Effective area of array, A=N*Ae 380.000M Specified Figure of Merit, M = A/Tsys 20.000M Computed Figure of Merit, M = A/Tsys 20.000Tsys System noise temperature at frequency, F 19B Processed total continuum bandwidth 4,0Nl Number of spectral line channels 16.000R Antenna/Electronics ratio, Ca/Ce 1,68Ropt Minimum cost ratio, Ropt = 1 / (X / 2 -1) 2,0Antenna ParametersD Physical diameter of element (meters) 10,0Ap Physical area of element, Ap = 0.785*D^2 79Ef Aperature efficiency 0,70Ae Effective area of element, Ae=Ap*Ef 55Tant Antenna noise temperature, Tant = 10 +4*(F/10) 14Cs Cost per station, Cs =Cso + Ne*(Ca+Ce) 11.342Cso Fixed cost per station, land, civil, bunker, cables 300Ca Cost per antenna, Ca = Ka*D^X 100Ka Antenna cost coefficient, 0,10X Antenna cost exponent 3,0Csm Antenna cost per square meter physical area,K$/m^2 1,274Receiver ParametersTsys Tsys = Tln +Tant 19Tln Tln = Kln*F+K1 5Kln Lna noise coefficient dependant upon cooler 0,40Tphy Physical temperature of LNA 15F Frequency for system temperature specification 10Ce Electronics cost per antenna, Goal 59,7Ce Ce = Ccl +Nbn*(Cfd +2* Cln) +Clo+Cif +Cpe 59,7Ccl Cooling cost per antenna 20,0Nbn Number of frequency bands 3Cfd Average dual-polariz feed cost 2,0Cln Average LNA + mixer cost 0,8Clo LO cost 3,0Cif Dual IF cost, Cif =2* (Cifo+Kif*B/2) 3,6Cifo Fixed IF cost per polarization 1,0Kif Dual IF cost per GHz of bandwidth 0,2Signal Transmission ParametersCtr Cost of transmission, Ctr =Ns*(Clk + Ls*Cfb) 20.800Clk Fiber transceiver cost, Clk = Klk*B 8,00Klk Tranceiver cost per GHz 2,00Ls Average station to control center distance, km 100Cfb Fiber installed cost, per fiber per km 2Signal Processing Parameters(FX architecture assumed for correlator)(Bandwidth shared among beams)Cdig Digitization Cdig = (a1*(B/Kch)^e+a2) * Kch 10,00a1 _Digitization coefficient 2,00e _Digitization exponent 2,00a2 _Digitization constant 0,50Kch _Number of separately digitized channels 4Ctre Transmission, el to stn ctr (Klk*B + Le*Cfb) 9,00Le _Average distance, element to station center 0,50Ctrack Tracking, elements Ctrack = (d*B + f*Nbeams) 3,28d _Tracking coefficient (per GHz) 0,72f _Tracking constant 0,10Nbeams _Beams per station 4Cpe Element processing cost = Cdig+Ctre+Ctrack 22,28Csum Beam summation cost, c*B*(Ne-1) 2,726c _Summation coefficient 0,010Cps Station processing cost = Cpe*Ne + Csum 1.543Cfilt Filtering cost Cfilt = (Kproc+Kmem)*log2(Nl)*B*Ns 2.682,4Kproc _Processing cost coefficient (per GHz) 0,48Kmem _Memory cost (per word) 1,76E-04Cci Correlator interconnections Cci=Cct + 2*Klk*Ns*B 1.603Cct Cost of corner turner Cct = kct*B*Ns *log2(Ns) 2,7kct _Corner turner cost coefficient (per connection) 1,00E-03Ccor Cross correlation cost = (Kcor+Kmem*Nl) *B*Ns*Ns/2 56.496Kcor _Correlator cost coef (per baseline-GHz) 0,012Kchip Price per large FPGA chip 0,144Nchip Large chip count = (Cfilt+Cci+Ccor)/Kchip 422.091Cinfr Correlator infrastructure, $10/large chip 4.221Cpc Central processing cost = Cfilt+Cci+Ccor +Cinfr 65.002Cp Total signal processing cost = Cps*Ns+Cpc 219.349

Color code:Purple: correction of error since previous version.Blue: change to value or formula since previous version.Red: variable whose value changes across this sheetGreen: variable whose value is different from previous sheetBold type: input parameter; normal type means value is calculated.

SKA Cost Equation Input ParametersUnits: K$US(2001), meters, GHzParam Array Performance ParametersDefaultValue Param Array Cost Parameters Default ValueNs Number of stations in array 100 Cso Fixed cost per station, land, civil 300M Specified Figure of Merit, M = A/Tsys 20.000 Ka Antenna cost coefficient, 0,10B Processed total continuum bandwidth 4,0 X Antenna cost exponent 3,0Nl Number of spectral line channels 16.000 Ccl Cooling cost per antenna 20,0D Physical diameter of element (meters 10,0 Cfd Average dual-polariz feed cost 2,0Ef Aperature efficiency 0,70 Cln Average LNA + mixer cost 0,8Tant Antenna noise temperature, Tant = 10 14 Clo LO cost 3,0Kln Lna noise coefficient dependant upon 0,40 Cifo Fixed IF cost per polarization 1,0Tphy Physical temperature of LNA 15 Kif Dual IF cost per GHz of bandwidt 0,2F Frequency for system temperature sp 10 a1 _Digitization coefficient 2,00Nbn Number of frequency bands 3 e _Digitization exponent 2,00Kch _Number of separately digitized chan 4 a2 _Digitization constant 0,50Le _Average distance, element to station 0,50 d _Tracking coefficient (per GHz) 0,72Nbeam_Beams per station 4 f _Tracking constant 0,10Kproc _Processing cost coefficient (pe 0,48Kmem _Memory cost (per word)2,10E-04kct _Corner turner cost coefficient (p 1,00E-03Kcor _Correlator cost coef (per baseli 0,024Kchip Price per large FPGA chip 0,14Color code: Klk Fiber Tranceiver per GHz 2Purple: correction of error since previous version.Blue: change to value or formula since previous version.Red: variable whose value changes across this sheetGreen: variable whose value is different from previous sheetBold type: input parameter; normal type means value is calculated.

SKA Cost Estimates July 21, 2001File: skacosteq1.xlsUnits K$US(2001), meters, GHzAntenna Diameter, Meters 5,0 8,0 10,0 12,0 15,0 20,0 30,0Parameter Array Parmeters Value Value Value Value Value Value ValueC Total array cost, fixed costs, elements, processing 2.163.512 1.364.319 1.270.322 1.282.439 1.386.654 1.652.120 2.286.299Cat Total antenna cost, Ne*Ns*Ca 345.769 553.230 691.538 829.845 1.037.307 1.383.076 2.074.613Celt Total electronics cost, Ne*Ns*Ce 1.650.839 644.859 412.710 286.604 183.427 103.177 45.857Cpt Total processing cost includiing station sum 66.104 65.430 65.275 65.190 65.121 65.067 65.029Ctr Signal transmission costs 20.800 20.800 20.800 20.800 20.800 20.800 20.800Csot Total civil costs at stations, Ns*Cso 30.000 30.000 30.000 30.000 30.000 30.000 30.000Co Fixed cost per array - design + central civil 50.000 50.000 50.000 50.000 50.000 50.000 50.000Cs Total station cost, elements + combining electronics 20.277 12.285 11.345 11.466 12.509 15.163 21.505Cm Total element cost, antenna + receivers + processing 72 111 160 232 397 860 2760Cp Central Signal processing costs 65.002 65.002 65.002 65.002 65.002 65.002 65.002Ns Number of stations in array 100 100 100 100 100 100 100Ne Number of elements per station 277 108 69 48 31 17 8Deq Equivalent single-antenna diameter of station 83 83 83 83 83 83 83N Total number of elements, N = Ns*Ne 27.662 10.805 6.915 4.802 3.074 1.729 768A Effective area of array, A=N*Ae 380.000 380.000 380.000 380.000 380.000 380.000 380.000M Specified Figure of Merit, M = A/Tsys 20.000 20.000 20.000 20.000 20.000 20.000 20.000M Computed Figure of Merit, M = A/Tsys 20.000 20.000 20.000 20.000 20.000 20.000 20.000Tsys System noise temperature at frequency, F 19 19 19 19 19 19 19B Processed total continuum bandwidth 4,0 4,0 4,0 4,0 4,0 4,0 4,0Nl Number of spectral line channels 16.000 16.000 16.000 16.000 16.000 16.000 16.000R Antenna/Electronics ratio, Ca/Ce 0,21 0,86 1,68 2,90 5,66 13,40 45,24Ropt Minimum cost ratio, Ropt = 1 / (X / 2 -1) 2,0 2,0 2,0 2,0 2,0 2,0 2,0Antenna ParametersD Physical diameter of element (meters) 5,0 8,0 10,0 12,0 15,0 20,0 30,0Ap Physical area of element, Ap = 0.785*D^2 20 50 79 113 177 314 707Ef Aperature efficiency 0,70 0,70 0,70 0,70 0,70 0,70 0,70Ae Effective area of element, Ae=Ap*Ef 14 35 55 79 124 220 495Tant Antenna noise temperature, Tant = 10 +4*(F/10) 14 14 14 14 14 14 14Cs Cost per station, Cs =Cso + Ne*(Ca+Ce) 20.266 12.281 11.342 11.464 12.507 15.163 21.505Cso Fixed cost per station, land, civil, bunker, cables 300 300 300 300 300 300 300Ca Cost per antenna, Ca = Ka*D^X 13 51 100 173 338 800 2.700Ka Antenna cost coefficient, 0,10 0,10 0,10 0,10 0,10 0,10 0,10X Antenna cost exponent 3,0 3,0 3,0 3,0 3,0 3,0 3,0Csm Antenna cost per square meter physical area,K$/m^2 0,637 1,019 1,274 1,529 1,911 2,548 3,822Receiver ParametersTsys Tsys = Tln +Tant 19 19 19 19 19 19 19Tln Tln = Kln*F+1 5 5 5 5 5 5 5Kln Lna noise coefficient dependant upon cooler 0,40 0,40 0,40 0,40 0,40 0,40 0,40Tphy Physical temperature of LNA 15 15 15 15 15 15 15F Frequency for system temperature specification 10 10 10 10 10 10 10Ce Electronics cost per antenna, Goal 59,7 59,7 59,7 59,7 59,7 59,7 59,7Ce Ce = Ccl +Nbn*(Cfd +2* Cln) +Clo+Cif +Cpe 59,7 59,7 59,7 59,7 59,7 59,7 59,7Ccl Cooling cost per antenna 20,0 20,0 20,0 20,0 20,0 20,0 20,0Nbn Number of frequency bands 3 3 3 3 3 3 3Cfd Average dual-polariz feed cost 2,0 2,0 2,0 2,0 2,0 2,0 2,0Cln Average LNA + mixer cost 0,8 0,8 0,8 0,8 0,8 0,8 0,8Clo LO cost 3,0 3,0 3,0 3,0 3,0 3,0 3,0Cif Dual IF cost, Cif =2* (Cifo+Kif*B/2) 3,6 3,6 3,6 3,6 3,6 3,6 3,6Cifo Fixed IF cost per polarization 1,0 1,0 1,0 1,0 1,0 1,0 1,0Kif Dual IF cost per GHz of bandwidth 0,2 0,2 0,2 0,2 0,2 0,2 0,2Signal Transmission ParametersCtr Cost of transmission, Ctr =2*Ns*(Ne*Clk + Ls*Cfb) 20.800 20.800 20.800 20.800 20.800 20.800 20.800Clk Fiber transceiver cost, Clk = Klk*B 8,00 8,00 8,00 8,00 8,00 8,00 8,00Klk Tranceiver cost per GHz 2,00 2,00 2,00 2,00 2,00 2,00 2,00Ls Average station to control center distance, km 100 100 100 100 100 100 100Cfb Fiber installed cost, per fiber per km 2 2 2 2 2 2 2Signal Processing Parameters(FX architecture assumed for correlator)(Bandwidth shared among beams)Cdig Digitization Cdig = (a1*(B/Kch)^e+a2) * Kch 10,00 10,00 10,00 10,00 10,00 10,00 10,00a1 _Digitization coefficient 2,00 2,00 2,00 2,00 2,00 2,00 2,00e _Digitization exponent 2,00 2,00 2,00 2,00 2,00 2,00 2,00a2 _Digitization constant 0,50 0,50 0,50 0,50 0,50 0,50 0,50Kch _Number of separately digitized channels 4 4 4 4 4 4 4Ctre Transmission, el to stn ctr (Klk*B + Le*Cfb) 9,00 9,00 9,00 9,00 9,00 9,00 9,00Le _Average distance, element to station center 0,50 0,50 0,50 0,50 0,50 0,50 0,50Ctrack Tracking, elements Ctrack = (d*B + f*Nbeams) 3,28 3,28 3,28 3,28 3,28 3,28 3,28d _Tracking coefficient (per GHz) 0,72 0,72 0,72 0,72 0,72 0,72 0,72f _Tracking constant 0,10 0,10 0,10 0,10 0,10 0,10 0,10Nbeams _Beams per station 4 4 4 4 4 4 4Cpe Element processing cost = Cdig+Ctre+Ctrack 22,28 22,28 22,28 22,28 22,28 22,28 22,28Csum Beam summation cost, c*B*(Ne-1) 11,025 4,282 2,726 1,881 1,189 0,652 0,267c _Summation coefficient 0,010 0,010 0,010 0,010 0,010 0,010 0,010Cps Station processing cost = Cpe*Ne + Csum 6.174 2.412 1.543 1.072 686 386 171Cfilt Filtering cost Cfilt = (Kproc+Kmem)*log2(Nl)*B*Ns 2.682,4 2.682,4 2.682,4 2.682,4 2.682,4 2.682,4 2.682,4Kproc _Processing cost coefficient (per GHz) 0,48 0,48 0,48 0,48 0,48 0,48 0,48Kmem _Memory cost (per word) 1,76E-04 1,76E-04 1,76E-04 1,76E-04 1,76E-04 1,76E-04 1,76E-04Cci Correlator interconnections Cci=Cct + 2*Klk*Ns*B 1.603 1.603 1.603 1.603 1.603 1.603 1.603Cct Cost of corner turner Cct = kct*B*Ns ^2*log2(Ns) 2,7 2,7 2,7 2,7 2,7 2,7 2,7kct _Corner turner cost coefficient (per connection) 1,00E-03 1,00E-03 1,00E-03 1,00E-03 1,00E-03 1,00E-03 1,00E-03Ccor Cross correlation cost = (Kcor+Kmem*Nl) *B*Ns*Ns/2 56.496 56.496 56.496 56.496 56.496 56.496 56.496Kcor _Correlator cost coef (per baseline-GHz) 0,012 0,012 0,012 0,012 0,012 0,012 0,012Kchip Price per large FPGA chip 0,144 0,144 0,144 0,144 0,144 0,144 0,144Nchip Large chip count = (Cfilt+Cci+Ccor)/Kchip 422.091 422.091 422.091 422.091 422.091 422.091 422.091Cinfr Correlator infrastructure, $10/large chip 4.221 4.221 4.221 4.221 4.221 4.221 4.221Cpc Central processing cost = Cfilt+Cci+Ccor +Cinfr 65.002 65.002 65.002 65.002 65.002 65.002 65.002Cp Total signal processing cost = Cps*Ns+Cpc 682.403 306.172 219.349 172.186 133.599 103.586 82.148

Color code:Purple: correction of error since previous version.Blue: change to value or formula since previous version.Red: variable whose value changes across this sheetGreen: variable whose value is different from previous sheetBold type: input parameter; normal type means value is calculated.

SKA Cost Breakdown by Subsystem vs Antenna DiameterAeff/Tsys = 20,000, Aeff=360,000, Tsys=18K, BW=4GHz, 15K Cryogenics2.000.000 Antenna Cost = 0.1D^3 K$, 2001 Electronics Cost = $54K per Element1.500.000Fixed CostsSignal TransmissionElectronicsCivil StationCentral ProcessingAntennaTotal Cost, $K1.000.000Antenna500.000Electronics0Signal TransmissionCentral ProcessingCivil StationFixed Costs5 8 10 12 15 20 30Antenna Diameter, Meters

SKA Cost Estimates July 21, 2001File: skacosteq1.xlsUnits K$US(2001), meters, GHzAntenna Diameter, Meters 5,0 8,0 10,0 12,0 15,0 20,0 30,0Parameter Array Parmeters Value Value Value Value Value Value ValueC Total array cost, fixed costs, elements, processing 2.539.097 1.709.110 1.650.843 1.712.295 1.901.543 2.320.499 3.274.894Cat Total antenna cost, Ne*Ns*Ca 509.554 815.287 1.019.108 1.222.930 1.528.662 2.038.217 3.057.325Celt Total electronics cost, Ne*Ns*Ce 1.862.115 727.389 465.529 323.284 206.902 116.382 51.725Cpt Total processing cost includiing station sum 66.629 65.635 65.406 65.281 65.179 65.100 65.043Ctr Signal transmission costs 20.800 20.800 20.800 20.800 20.800 20.800 20.800Csot Total civil costs at stations, Ns*Cso 30.000 30.000 30.000 30.000 30.000 30.000 30.000Co Fixed cost per array - design + central civil 50.000 50.000 50.000 50.000 50.000 50.000 50.000Cs Total station cost, elements + combining electronics 24.033 15.733 15.150 15.765 17.657 21.847 31.391Cm Total element cost, antenna + receivers + processing 58 97 146 218 383 846 2746Cp Central Signal processing costs 65.002 65.002 65.002 65.002 65.002 65.002 65.002Ns Number of stations in array 100 100 100 100 100 100 100Ne Number of elements per station 408 159 102 71 45 25 11Deq Equivalent single-antenna diameter of station 101 101 101 101 101 101 101N Total number of elements, N = Ns*Ne 40.764 15.924 10.191 7.077 4.529 2.548 1.132A Effective area of array, A=N*Ae 560.000 560.000 560.000 560.000 560.000 560.000 560.000M Specified Figure of Merit, M = A/Tsys 20.000 20.000 20.000 20.000 20.000 20.000 20.000M Computed Figure of Merit, M = A/Tsys 20.000 20.000 20.000 20.000 20.000 20.000 20.000Tsys System noise temperature at frequency, F 28 28 28 28 28 28 28B Processed total continuum bandwidth 4,0 4,0 4,0 4,0 4,0 4,0 4,0Nl Number of spectral line channels 16.000 16.000 16.000 16.000 16.000 16.000 16.000R Antenna/Electronics ratio, Ca/Ce 0,27 1,12 2,19 3,78 7,39 17,51 59,11Ropt Minimum cost ratio, Ropt = 1 / (X / 2 -1) 2,0 2,0 2,0 2,0 2,0 2,0 2,0Antenna ParametersD Physical diameter of element (meters) 5,0 8,0 10,0 12,0 15,0 20,0 30,0Ap Physical area of element, Ap = 0.785*D^2 20 50 79 113 177 314 707Ef Aperature efficiency 0,70 0,70 0,70 0,70 0,70 0,70 0,70Ae Effective area of element, Ae=Ap*Ef 14 35 55 79 124 220 495Tant Antenna noise temperature, Tant = 10 +4*(F/10) 14 14 14 14 14 14 14Cs Cost per station, Cs =Cso + Ne*(Ca+Ce) 24.017 15.727 15.146 15.762 17.656 21.846 31.391Cso Fixed cost per station, land, civil, bunker, cables 300 300 300 300 300 300 300Ca Cost per antenna, Ca = Ka*D^X 13 51 100 173 338 800 2.700Ka Antenna cost coefficient, 0,10 0,10 0,10 0,10 0,10 0,10 0,10X Antenna cost exponent 3,0 3,0 3,0 3,0 3,0 3,0 3,0Csm Antenna cost per square meter physical area,K$/m^2 0,637 1,019 1,274 1,529 1,911 2,548 3,822Receiver ParametersTsys Tsys = Tln +Tant 28 28 28 28 28 28 28Tln Tln = Kln*F+4 14 14 14 14 14 14 14Kln Lna noise coefficient dependant upon cooler 1,00 1,00 1,00 1,00 1,00 1,00 1,00Tphy Physical temperature of LNA 60 60 60 60 60 60 60F Frequency for system temperature specification 10 10 10 10 10 10 10Ce Electronics cost per antenna 45,7 45,7 45,7 45,7 45,7 45,7 45,7Ce Ce = Ccl +Nbn*(Cfd +2* Cln) +Clo+Cif +Cpe 45,7 45,7 45,7 45,7 45,7 45,7 45,7Ccl Cooling cost per antenna 6,0 6,0 6,0 6,0 6,0 6,0 6,0Nbn Number of frequency bands 3 3 3 3 3 3 3Cfd Average dual-polariz feed cost 2,0 2,0 2,0 2,0 2,0 2,0 2,0Cln Average LNA + mixer cost 0,8 0,8 0,8 0,8 0,8 0,8 0,8Clo LO cost 3,0 3,0 3,0 3,0 3,0 3,0 3,0Cif Dual IF cost, Cif =2* (Cifo+Kif*B/2) 3,6 3,6 3,6 3,6 3,6 3,6 3,6Cifo Fixed IF cost per polarization 1,0 1,0 1,0 1,0 1,0 1,0 1,0Kif Dual IF cost per GHz of bandwidth 0,2 0,2 0,2 0,2 0,2 0,2 0,2Signal Transmission ParametersCtr Cost of transmission, Ctr =2*Ns*(Ne*Clk + Ls*Cfb) 20.800 20.800 20.800 20.800 20.800 20.800 20.800Clk Fiber transceiver cost, Clk = Klk*B 8,00 8,00 8,00 8,00 8,00 8,00 8,00Klk Tranceiver cost per GHz 2,00 2,00 2,00 2,00 2,00 2,00 2,00Ls Average station to control center distance, km 100 100 100 100 100 100 100Cfb Fiber installed cost, per fiber per km 2 2 2 2 2 2 2Signal Processing Parameters(FX architecture assumed for correlator)(Bandwidth shared among beams)Cdig Digitization Cdig = (a1*(B/Kch)^e+a2) * Kch 10,00 10,00 10,00 10,00 10,00 10,00 10,00a1 _Digitization coefficient 2,00 2,00 2,00 2,00 2,00 2,00 2,00e _Digitization exponent 2,00 2,00 2,00 2,00 2,00 2,00 2,00a2 _Digitization constant 0,50 0,50 0,50 0,50 0,50 0,50 0,50Kch _Number of separately digitized channels 4 4 4 4 4 4 4Ctre Transmission, el to stn ctr (Klk*B + Le*Cfb) 9,00 9,00 9,00 9,00 9,00 9,00 9,00Le _Average distance, element to station center 0,50 0,50 0,50 0,50 0,50 0,50 0,50Ctrack Tracking, elements Ctrack = (d*B + f*Nbeams) 3,28 3,28 3,28 3,28 3,28 3,28 3,28d _Tracking coefficient (per GHz) 0,72 0,72 0,72 0,72 0,72 0,72 0,72f _Tracking constant 0,10 0,10 0,10 0,10 0,10 0,10 0,10Nbeams _Beams per station 4 4 4 4 4 4 4Cpe Element processing cost = Cdig+Ctre+Ctrack 22,28 22,28 22,28 22,28 22,28 22,28 22,28Csum Beam summation cost, c*B*(Ne-1) 16,266 6,329 4,036 2,791 1,772 0,979 0,413c _Summation coefficient 0,010 0,010 0,010 0,010 0,010 0,010 0,010Cps Station processing cost = Cpe*Ne + Csum 9.099 3.554 2.275 1.580 1.011 569 253Cfilt Filtering cost Cfilt = (Kproc+Kmem)*log2(Nl)*B*Ns 2.682,4 2.682,4 2.682,4 2.682,4 2.682,4 2.682,4 2.682,4Kproc _Processing cost coefficient (per GHz) 0,48 0,48 0,48 0,48 0,48 0,48 0,48Kmem _Memory cost (per word) 1,76E-04 1,76E-04 1,76E-04 1,76E-04 1,76E-04 1,76E-04 1,76E-04Cci Correlator interconnections Cci=Cct + 2*Klk*Ns*B 1.603 1.603 1.603 1.603 1.603 1.603 1.603Cct Cost of corner turner Cct = kct*B*Ns ^2*log2(Ns) 2,7 2,7 2,7 2,7 2,7 2,7 2,7kct _Corner turner cost coefficient (per connection) 1,00E-03 1,00E-03 1,00E-03 1,00E-03 1,00E-03 1,00E-03 1,00E-03Ccor Cross correlation cost = (Kcor+Kmem*Nl) *B*Ns*Ns/2 56.496 56.496 56.496 56.496 56.496 56.496 56.496Kcor _Correlator cost coef (per baseline-GHz) 0,012 0,012 0,012 0,012 0,012 0,012 0,012Kchip Price per large FPGA chip 0,144 0,144 0,144 0,144 0,144 0,144 0,144Nchip Large chip count = (Cfilt+Cci+Ccor)/Kchip 422.091 422.091 422.091 422.091 422.091 422.091 422.091Cinfr Correlator infrastructure, $10/large chip 4.221 4.221 4.221 4.221 4.221 4.221 4.221Cpc Central processing cost = Cfilt+Cci+Ccor +Cinfr 65.002 65.002 65.002 65.002 65.002 65.002 65.002Cp Total signal processing cost = Cps*Ns+Cpc 974.858 420.412 292.463 222.960 166.094 121.864 90.272

Color code:Purple: correction of error since previous version.Blue: change to value or formula since previous version.Red: variable whose value changes across this sheetGreen: variable whose value is different from previous sheetBold type: input parameter; normal type means value is calculated.

SKA Cost Estimates July 21, 2001File: skacosteq1.xlsUnits K$US(2001), meters, GHzAntenna Diameter, Meters 5,0 8,0 10,0 12,0 15,0 20,0 30,0Parameter Array Parmeters Value Value Value Value Value Value ValueC Total array cost, fixed costs, elements, processing 4.024.666 2.729.583 2.659.177 2.780.539 3.118.067 3.846.468 5.489.853Cat Total antenna cost, Ne*Ns*Ca 873.521 1.397.634 1.747.043 2.096.451 2.620.564 3.494.086 5.241.128Celt Total electronics cost, Ne*Ns*Ce 2.982.551 1.165.059 745.638 517.804 331.395 186.409 82.849Cpt Total processing cost includiing station sum 67.793 66.090 65.697 65.483 65.309 65.173 65.076Ctr Signal transmission costs 20.800 20.800 20.800 20.800 20.800 20.800 20.800Csot Total civil costs at stations, Ns*Cso 30.000 30.000 30.000 30.000 30.000 30.000 30.000Co Fixed cost per array - design + central civil 50.000 50.000 50.000 50.000 50.000 50.000 50.000Cs Total station cost, elements + combining electronics 38.889 25.938 25.234 26.447 29.823 37.107 53.541Cm Total element cost, antenna + receivers + processing 55 94 143 215 380 843 2743Cp Central Signal processing costs 65.002 65.002 65.002 65.002 65.002 65.002 65.002Ns Number of stations in array 100 100 100 100 100 100 100Ne Number of elements per station 699 273 175 121 78 44 19Deq Equivalent single-antenna diameter of station 132 132 132 132 132 132 132N Total number of elements, N = Ns*Ne 69.882 27.298 17.470 12.132 7.765 4.368 1.941A Effective area of array, A=N*Ae 960.000 960.000 960.000 960.000 960.000 960.000 960.000M Specified Figure of Merit, M = A/Tsys 20.000 20.000 20.000 20.000 20.000 20.000 20.000M Computed Figure of Merit, M = A/Tsys 20.000 20.000 20.000 20.000 20.000 20.000 20.000Tsys System noise temperature at frequency, F 48 48 48 48 48 48 48B Processed total continuum bandwidth 4,0 4,0 4,0 4,0 4,0 4,0 4,0Nl Number of spectral line channels 16.000 16.000 16.000 16.000 16.000 16.000 16.000R Antenna/Electronics ratio, Ca/Ce 0,29 1,20 2,34 4,05 7,91 18,74 63,26Ropt Minimum cost ratio, Ropt = 1 / (X / 2 -1) 2,0 2,0 2,0 2,0 2,0 2,0 2,0Antenna ParametersD Physical diameter of element (meters) 5,0 8,0 10,0 12,0 15,0 20,0 30,0Ap Physical area of element, Ap = 0.785*D^2 20 50 79 113 177 314 707Ef Aperature efficiency 0,70 0,70 0,70 0,70 0,70 0,70 0,70Ae Effective area of element, Ae=Ap*Ef 14 35 55 79 124 220 495Tant Antenna noise temperature, Tant = 10 +4*(F/10) 14 14 14 14 14 14 14Cs Cost per station, Cs =Cso + Ne*(Ca+Ce) 38.861 25.927 25.227 26.443 29.820 37.105 53.540Cso Fixed cost per station, land, civil, bunker, cables 300 300 300 300 300 300 300Ca Cost per antenna, Ca = Ka*D^X 13 51 100 173 338 800 2.700Ka Antenna cost coefficient, 0,10 0,10 0,10 0,10 0,10 0,10 0,10X Antenna cost exponent 3,0 3,0 3,0 3,0 3,0 3,0 3,0Csm Antenna cost per square meter physical area,K$/m^2 0,637 1,019 1,274 1,529 1,911 2,548 3,822Receiver ParametersTsys Tsys = Tln +Tant 48 48 48 48 48 48 48Tln Tln = Kln*F+10 34 34 34 34 34 34 34Kln Lna noise coefficient dependant upon cooler 2,40 2,40 2,40 2,40 2,40 2,40 2,40Tphy Physical temperature of LNA 180 180 180 180 180 180 180F Frequency for system temperature specification 10 10 10 10 10 10 10Ce Electronics cost per antenna, Goal 42,7 42,7 42,7 42,7 42,7 42,7 42,7Ce Ce = Ccl +Nbn*(Cfd +2* Cln) +Clo+Cif +Cpe 42,7 42,7 42,7 42,7 42,7 42,7 42,7Ccl Cooling cost per antenna 3,0 3,0 3,0 3,0 3,0 3,0 3,0Nbn Number of frequency bands 3 3 3 3 3 3 3Cfd Average dual-polariz feed cost 2,0 2,0 2,0 2,0 2,0 2,0 2,0Cln Average LNA + mixer cost 0,8 0,8 0,8 0,8 0,8 0,8 0,8Clo LO cost 3,0 3,0 3,0 3,0 3,0 3,0 3,0Cif Dual IF cost, Cif =2* (Cifo+Kif*B/2) 3,6 3,6 3,6 3,6 3,6 3,6 3,6Cifo Fixed IF cost per polarization 1,0 1,0 1,0 1,0 1,0 1,0 1,0Kif Dual IF cost per GHz of bandwidth 0,2 0,2 0,2 0,2 0,2 0,2 0,2Signal Transmission ParametersCtr Cost of transmission, Ctr =2*Ns*(Ne*Clk + Ls*Cfb) 20.800 20.800 20.800 20.800 20.800 20.800 20.800Clk Fiber transceiver cost, Clk = Klk*B 8,00 8,00 8,00 8,00 8,00 8,00 8,00Klk Tranceiver cost per GHz 2,00 2,00 2,00 2,00 2,00 2,00 2,00Ls Average station to control center distance, km 100 100 100 100 100 100 100Cfb Fiber installed cost, per fiber per km 2 2 2 2 2 2 2Signal Processing Parameters(FX architecture assumed for correlator)(Bandwidth shared among beams)Cdig Digitization Cdig = (a1*(B/Kch)^e+a2) * Kch 10,00 10,00 10,00 10,00 10,00 10,00 10,00a1 _Digitization coefficient 2,00 2,00 2,00 2,00 2,00 2,00 2,00e _Digitization exponent 2,00 2,00 2,00 2,00 2,00 2,00 2,00a2 _Digitization constant 0,50 0,50 0,50 0,50 0,50 0,50 0,50Kch _Number of separately digitized channels 4 4 4 4 4 4 4Ctre Transmission, el to stn ctr (Klk*B + Le*Cfb) 9,00 9,00 9,00 9,00 9,00 9,00 9,00Le _Average distance, element to station center 0,50 0,50 0,50 0,50 0,50 0,50 0,50Ctrack Tracking, elements Ctrack = (d*B + f*Nbeams) 3,28 3,28 3,28 3,28 3,28 3,28 3,28d _Tracking coefficient (per GHz) 0,72 0,72 0,72 0,72 0,72 0,72 0,72f _Tracking constant 0,10 0,10 0,10 0,10 0,10 0,10 0,10Nbeams _Beams per station 4 4 4 4 4 4 4Cpe Element processing cost = Cdig+Ctre+Ctrack 22,28 22,28 22,28 22,28 22,28 22,28 22,28Csum Beam summation cost, c*B*(Ne-1) 27,913 10,879 6,948 4,813 3,066 1,707 0,736c _Summation coefficient 0,010 0,010 0,010 0,010 0,010 0,010 0,010Cps Station processing cost = Cpe*Ne + Csum 15.598 6.093 3.899 2.708 1.733 975 433Cfilt Filtering cost Cfilt = (Kproc+Kmem)*log2(Nl)*B*Ns 2.682,4 2.682,4 2.682,4 2.682,4 2.682,4 2.682,4 2.682,4Kproc _Processing cost coefficient (per GHz) 0,48 0,48 0,48 0,48 0,48 0,48 0,48Kmem _Memory cost (per word) 1,76E-04 1,76E-04 1,76E-04 1,76E-04 1,76E-04 1,76E-04 1,76E-04Cci Correlator interconnections Cci=Cct + 2*Klk*Ns*B 1.603 1.603 1.603 1.603 1.603 1.603 1.603Cct Cost of corner turner Cct = kct*B*Ns ^2*log2(Ns) 2,7 2,7 2,7 2,7 2,7 2,7 2,7kct _Corner turner cost coefficient (per connection) 1,00E-03 1,00E-03 1,00E-03 1,00E-03 1,00E-03 1,00E-03 1,00E-03Ccor Cross correlation cost = (Kcor+Kmem*Nl) *B*Ns*Ns/2 56.496 56.496 56.496 56.496 56.496 56.496 56.496Kcor _Correlator cost coef (per baseline-GHz) 0,012 0,012 0,012 0,012 0,012 0,012 0,012Kchip Price per large FPGA chip 0,144 0,144 0,144 0,144 0,144 0,144 0,144Nchip Large chip count = (Cfilt+Cci+Ccor)/Kchip 422.091 422.091 422.091 422.091 422.091 422.091 422.091Cinfr Correlator infrastructure, $10/large chip 4.221 4.221 4.221 4.221 4.221 4.221 4.221Cpc Central processing cost = Cfilt+Cci+Ccor +Cinfr 65.002 65.002 65.002 65.002 65.002 65.002 65.002Cp Total signal processing cost = Cps*Ns+Cpc 1.624.758 674.279 454.938 335.790 238.305 162.483 108.325

Color code:Purple: correction of error since previous version.Blue: change to value or formula since previous version.Red: variable whose value changes across this sheetGreen: variable whose value is different from previous sheetBold type: input parameter; normal type means value is calculated.

SKA Cost vs Antenna Diameter for 3 Cooling TemperaturesAeff/Tsys = 20,000, Aeff=360,000, Tsys=18K, BW=4GHz,Antenna Cost = 0.1D^3 K$, 2001 Electronics Cost = $54K per Element$3.000.00030.000Cost, $K (US2001)$2.500.000$2.000.000$1.500.000$1.000.000$500.00025.00020.00015.00010.0005.000Number of Antennas$05,0 10,0 15,0 20,0 25,0 30,0Element Diameter, Meters15K Cryogenics 60K Cryogenics 180K Cryogenics# Antennas, 15K # Antennas, 60K # Antennas, 180K0

SKA Cost Estimates July 21, 2001File: skacosteq1.xlsUnits K$US(2001), meters, GHzAntenna Diameter, Meters 10,0 10,0 10,0 10,0 15,0 15,0 15,0 15,0Parameter Array Parmeters Value Value Value Value Value Value Value ValueC Total array cost, fixed costs, elements, processing 1.104.173 1.152.641 1.270.322 1.588.670 1.285.394 1.316.074 1.386.654 1.564.696Cat Total antenna cost, Ne*Ns*Ca 691.538 691.538 691.538 691.538 1.037.307 1.037.307 1.037.307 1.037.307Celt Total electronics cost, Ne*Ns*Ce 296.116 328.066 412.710 664.983 131.607 145.807 183.427 295.548Cpt Total processing cost includiing station sum 16.319 32.637 65.275 130.549 16.280 32.560 65.121 130.242Ctr Signal transmission costs 20.200 20.400 20.800 21.600 20.200 20.400 20.800 21.600Csot Total civil costs at stations, Ns*Cso 30.000 30.000 30.000 30.000 30.000 30.000 30.000 30.000Co Fixed cost per array - design + central civil 50.000 50.000 50.000 50.000 50.000 50.000 50.000 50.000Cs Total station cost, elements + combining electronics 10.177 10.497 11.345 13.871 11.989 12.132 12.509 13.631Cm Total element cost, antenna + receivers + processing 143 147 160 196 380 385 397 434Cp Central Signal processing costs 16.250 32.501 65.002 130.004 16.250 32.501 65.002 130.004Ns Number of stations in array 100 100 100 100 100 100 100 100Ne Number of elements per station 69 69 69 69 31 31 31 31Deq Equivalent single-antenna diameter of station 83 83 83 83 83 83 83 83N Total number of elements, N = Ns*Ne 6.915 6.915 6.915 6.915 3.074 3.074 3.074 3.074A Effective area of array, A=N*Ae 380.000 380.000 380.000 380.000 380.000 380.000 380.000 380.000M Specified Figure of Merit, M = A/Tsys 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000M Computed Figure of Merit, M = A/Tsys 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000Tsys System noise temperature at frequency, F 19 19 19 19 19 19 19 19B Processed total continuum bandwidth 1,0 2,0 4,0 8,0 1,0 2,0 4,0 8,0Nl Number of spectral line channels 16.000 16.000 16.000 16.000 16.000 16.000 16.000 16.000R Antenna/Electronics ratio, Ca/Ce 2,34 2,11 1,68 1,04 7,88 7,11 5,66 3,51Ropt Minimum cost ratio, Ropt = 1 / (X / 2 -1) 2,0 2,0 2,0 2,0 2,0 2,0 2,0 2,0Antenna ParametersD Physical diameter of element (meters) 10,0 10,0 10,0 10,0 15,0 15,0 15,0 15,0Ap Physical area of element, Ap = 0.785*D^2 79 79 79 79 177 177 177 177Ef Aperature efficiency 0,70 0,70 0,70 0,70 0,70 0,70 0,70 0,70Ae Effective area of element, Ae=Ap*Ef 55 55 55 55 124 124 124 124Tant Antenna noise temperature, Tant = 10 +4*(F/10) 14 14 14 14 14 14 14 14Cs Cost per station, Cs =Cso + Ne*(Ca+Ce) 10.177 10.496 11.342 13.865 11.989 12.131 12.507 13.629Cso Fixed cost per station, land, civil, bunker, cables 300 300 300 300 300 300 300 300Ca Cost per antenna, Ca = Ka*D^X 100 100 100 100 338 338 338 338Ka Antenna cost coefficient, 0,10 0,10 0,10 0,10 0,10 0,10 0,10 0,10X Antenna cost exponent 3,0 3,0 3,0 3,0 3,0 3,0 3,0 3,0Csm Antenna cost per square meter physical area,K$/m^2 1,274 1,274 1,274 1,274 1,911 1,911 1,911 1,911Receiver ParametersTsys Tsys = Tln +Tant 19 19 19 19 19 19 19 19Tln Tln = Kln*F+1 5 5 5 5 5 5 5 5Kln Lna noise coefficient dependant upon cooler 0,40 0,40 0,40 0,40 0,40 0,40 0,40 0,40Tphy Physical temperature of LNA 15 15 15 15 15 15 15 15F Frequency for system temperature specification 10 10 10 10 10 10 10 10Ce Electronics cost per antenna, Goal 42,8 47,4 59,7 96,2 42,8 47,4 59,7 96,2Ce Ce = Ccl +Nbn*(Cfd +2* Cln) +Clo+Cif +Cpe 42,8 47,4 59,7 96,2 42,8 47,4 59,7 96,2Ccl Cooling cost per antenna 20,0 20,0 20,0 20,0 20,0 20,0 20,0 20,0Nbn Number of frequency bands 3 3 3 3 3 3 3 3Cfd Average dual-polariz feed cost 2,0 2,0 2,0 2,0 2,0 2,0 2,0 2,0Cln Average LNA + mixer cost 0,8 0,8 0,8 0,8 0,8 0,8 0,8 0,8Clo LO cost 3,0 3,0 3,0 3,0 3,0 3,0 3,0 3,0Cif Dual IF cost, Cif =2* (Cifo+Kif*B/2) 2,4 2,8 3,6 5,2 2,4 2,8 3,6 5,2Cifo Fixed IF cost per polarization 1,0 1,0 1,0 1,0 1,0 1,0 1,0 1,0Kif Dual IF cost per GHz of bandwidth 0,2 0,2 0,2 0,2 0,2 0,2 0,2 0,2Signal Transmission ParametersCtr Cost of transmission, Ctr =2*Ns*(Ne*Clk + Ls*Cfb) 20.200 20.400 20.800 21.600 20.200 20.400 20.800 21.600Clk Fiber transceiver cost, Clk = Klk*B 2,00 4,00 8,00 16,00 2,00 4,00 8,00 16,00Klk Tranceiver cost per GHz 2,00 2,00 2,00 2,00 2,00 2,00 2,00 2,00Ls Average station to control center distance, km 100 100 100 100 100 100 100 100Cfb Fiber installed cost, per fiber per km 2 2 2 2 2 2 2 2Signal Processing Parameters(FX architecture assumed for correlator)(Bandwidth shared among beams)Cdig Digitization Cdig = (a1*(B/Kch)^e+a2) * Kch 2,50 4,00 10,00 34,00 2,50 4,00 10,00 34,00a1 _Digitization coefficient 2,00 2,00 2,00 2,00 2,00 2,00 2,00 2,00e _Digitization exponent 2,00 2,00 2,00 2,00 2,00 2,00 2,00 2,00a2 _Digitization constant 0,50 0,50 0,50 0,50 0,50 0,50 0,50 0,50Kch _Number of separately digitized channels 4 4 4 4 4 4 4 4Ctre Transmission, el to stn ctr (Klk*B + Le*Cfb) 3,00 5,00 9,00 17,00 3,00 5,00 9,00 17,00Le _Average distance, element to station center 0,50 0,50 0,50 0,50 0,50 0,50 0,50 0,50Ctrack Tracking, elements Ctrack = (d*B + f*Nbeams) 1,12 1,84 3,28 6,16 1,12 1,84 3,28 6,16d _Tracking coefficient (per GHz) 0,72 0,72 0,72 0,72 0,72 0,72 0,72 0,72f _Tracking constant 0,10 0,10 0,10 0,10 0,10 0,10 0,10 0,10Nbeams _Beams per station 4 4 4 4 4 4 4 4Cpe Element processing cost = Cdig+Ctre+Ctrack 6,62 10,84 22,28 57,16 6,62 10,84 22,28 57,16Csum Beam summation cost, c*B*(Ne-1) 0,682 1,363 2,726 5,452 0,297 0,595 1,189 2,379c _Summation coefficient 0,010 0,010 0,010 0,010 0,010 0,010 0,010 0,010Cps Station processing cost = Cpe*Ne + Csum 458 751 1.543 3.958 204 334 686 1.759Cfilt Filtering cost Cfilt = (Kproc+Kmem)*log2(Nl)*B*Ns 670,6 1.341,2 2.682,4 5.364,8 670,6 1.341,2 2.682,4 5.364,8Kproc _Processing cost coefficient (per GHz) 0,48 0,48 0,48 0,48 0,48 0,48 0,48 0,48Kmem _Memory cost (per word) 1,76E-04 1,76E-04 1,76E-04 1,76E-04 1,76E-04 1,76E-04 1,76E-04 1,76E-04Cci Correlator interconnections Cci=Cct + 2*Klk*Ns*B 401 801 1.603 3.205 401 801 1.603 3.205Cct Cost of corner turner Cct = kct*B*Ns ^2*log2(Ns) 0,7 1,3 2,7 5,3 0,7 1,3 2,7 5,3kct _Corner turner cost coefficient (per connection) 1,00E-03 1,00E-03 1,00E-03 1,00E-03 1,00E-03 1,00E-03 1,00E-03 1,00E-03Ccor Cross correlation cost = (Kcor+Kmem*Nl) *B*Ns*Ns/2 14.124 28.248 56.496 112.992 14.124 28.248 56.496 112.992Kcor _Correlator cost coef (per baseline-GHz) 0,012 0,012 0,012 0,012 0,012 0,012 0,012 0,012Kchip Price per large FPGA chip 0,144 0,144 0,144 0,144 0,144 0,144 0,144 0,144Nchip Large chip count = (Cfilt+Cci+Ccor)/Kchip 105.523 211.045 422.091 844.182 105.523 211.045 422.091 844.182Cinfr Correlator infrastructure, $10/large chip 1.055 2.110 4.221 8.442 1.055 2.110 4.221 8.442Cpc Central processing cost = Cfilt+Cci+Ccor +Cinfr 16.250 32.501 65.002 130.004 16.250 32.501 65.002 130.004Cp Total signal processing cost = Cps*Ns+Cpc 62.098 107.600 219.349 525.832 36.627 65.877 133.599 305.923

Color code:Purple: correction of error since previous version.Blue: change to value or formula since previous version.Red: variable whose value changes across this sheetGreen: variable whose value is different from previous sheetBold type: input parameter; normal type means value is calculated.

SKA Cost vs Processed Bandwidth forTwo Antenna DiametersAll for 15K Cryogenics$2.000.000Cost, $K (US2001)$1.500.000$1.000.000$500.000$00,0 2,0 4,0 6,0 8,0Processed Bandwidth, GHz6551 x 10m Antenna 2912 x 15m Antenna

SKA Cost Estimates July 21, 2001File: skacosteq1.xlsUnits K$US(2001), meters, GHzAntenna Diameter, Meters 10,0 10,0 10,0 10,0 10,0 10,0 10,0 10,0Parameter Array Parmeters Value Value Value Value Value Value Value ValueC Total array cost, fixed costs, elements, processing 1.067.172 1.104.173 1.200.832 1.484.780 1.197.318 1.270.322 1.506.960 2.342.751Cat Total antenna cost, Ne*Ns*Ca 691.538 691.538 691.538 691.538 691.538 691.538 691.538 691.538Celt Total electronics cost, Ne*Ns*Ce 296.116 296.116 296.116 296.116 412.710 412.710 412.710 412.710Cpt Total processing cost includiing station sum 4.418 16.319 62.778 246.326 17.671 65.275 251.112 985.304Ctr Signal transmission costs 10.100 20.200 40.400 80.800 10.400 20.800 41.600 83.200Csot Total civil costs at stations, Ns*Cso 15.000 30.000 60.000 120.000 15.000 30.000 60.000 120.000Co Fixed cost per array - design + central civil 50.000 50.000 50.000 50.000 50.000 50.000 50.000 50.000Cs Total station cost, elements + combining electronics 20.054 10.177 5.239 2.769 22.390 11.345 5.823 3.061Cm Total element cost, antenna + receivers + processing 143 143 143 143 160 160 160 160Cp Central Signal processing costs 4.349 16.250 62.711 246.261 17.396 65.002 250.843 985.043Ns Number of stations in array 50 100 200 400 50 100 200 400Ne Number of elements per station 138 69 35 17 138 69 35 17Deq Equivalent single-antenna diameter of station 118 83 59 42 118 83 59 42N Total number of elements, N = Ns*Ne 6.915 6.915 6.915 6.915 6.915 6.915 6.915 6.915A Effective area of array, A=N*Ae 380.000 380.000 380.000 380.000 380.000 380.000 380.000 380.000M Specified Figure of Merit, M = A/Tsys 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000M Computed Figure of Merit, M = A/Tsys 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000Tsys System noise temperature at frequency, F 19 19 19 19 19 19 19 19B Processed total continuum bandwidth 1,0 1,0 1,0 1,0 4,0 4,0 4,0 4,0Nl Number of spectral line channels 16.000 16.000 16.000 16.000 16.000 16.000 16.000 16.000R Antenna/Electronics ratio, Ca/Ce 2,34 2,34 2,34 2,34 1,68 1,68 1,68 1,68Ropt Minimum cost ratio, Ropt = 1 / (X / 2 -1) 2,0 2,0 2,0 2,0 2,0 2,0 2,0 2,0Antenna ParametersD Physical diameter of element (meters) 10,0 10,0 10,0 10,0 10,0 10,0 10,0 10,0Ap Physical area of element, Ap = 0.785*D^2 79 79 79 79 79 79 79 79Ef Aperature efficiency 0,70 0,70 0,70 0,70 0,70 0,70 0,70 0,70Ae Effective area of element, Ae=Ap*Ef 55 55 55 55 55 55 55 55Tant Antenna noise temperature, Tant = 10 +4*(F/10) 14 14 14 14 14 14 14 14Cs Cost per station, Cs =Cso + Ne*(Ca+Ce) 20.053 10.177 5.238 2.769 22.385 11.342 5.821 3.061Cso Fixed cost per station, land, civil, bunker, cables 300 300 300 300 300 300 300 300Ca Cost per antenna, Ca = Ka*D^X 100 100 100 100 100 100 100 100Ka Antenna cost coefficient, 0,10 0,10 0,10 0,10 0,10 0,10 0,10 0,10X Antenna cost exponent 3,0 3,0 3,0 3,0 3,0 3,0 3,0 3,0Csm Antenna cost per square meter physical area,K$/m^2 1,274 1,274 1,274 1,274 1,274 1,274 1,274 1,274Receiver ParametersTsys Tsys = Tln +Tant 19 19 19 19 19 19 19 19Tln Tln = Kln*F+1 5 5 5 5 5 5 5 5Kln Lna noise coefficient dependant upon cooler 0,40 0,40 0,40 0,40 0,40 0,40 0,40 0,40Tphy Physical temperature of LNA 15 15 15 15 15 15 15 15F Frequency for system temperature specification 10 10 10 10 10 10 10 10Ce Electronics cost per antenna, Goal 42,8 42,8 42,8 42,8 59,7 59,7 59,7 59,7Ce Ce = Ccl +Nbn*(Cfd +2* Cln) +Clo+Cif +Cpe 42,8 42,8 42,8 42,8 59,7 59,7 59,7 59,7Ccl Cooling cost per antenna 20,0 20,0 20,0 20,0 20,0 20,0 20,0 20,0Nbn Number of frequency bands 3 3 3 3 3 3 3 3Cfd Average dual-polariz feed cost 2,0 2,0 2,0 2,0 2,0 2,0 2,0 2,0Cln Average LNA + mixer cost 0,8 0,8 0,8 0,8 0,8 0,8 0,8 0,8Clo LO cost 3,0 3,0 3,0 3,0 3,0 3,0 3,0 3,0Cif Dual IF cost, Cif =2* (Cifo+Kif*B/2) 2,4 2,4 2,4 2,4 3,6 3,6 3,6 3,6Cifo Fixed IF cost per polarization 1,0 1,0 1,0 1,0 1,0 1,0 1,0 1,0Kif Dual IF cost per GHz of bandwidth 0,2 0,2 0,2 0,2 0,2 0,2 0,2 0,2Signal Transmission ParametersCtr Cost of transmission, Ctr =2*Ns*(Ne*Clk + Ls*Cfb) 10.100 20.200 40.400 80.800 10.400 20.800 41.600 83.200Clk Fiber transceiver cost, Clk = Klk*B 2,00 2,00 2,00 2,00 8,00 8,00 8,00 8,00Klk Tranceiver cost per GHz 2,00 2,00 2,00 2,00 2,00 2,00 2,00 2,00Ls Average station to control center distance, km 100 100 100 100 100 100 100 100Cfb Fiber installed cost, per fiber per km 2 2 2 2 2 2 2 2Signal Processing Parameters(FX architecture assumed for correlator)(Bandwidth shared among beams)Cdig Digitization Cdig = (a1*(B/Kch)^e+a2) * Kch 2,50 2,50 2,50 2,50 10,00 10,00 10,00 10,00a1 _Digitization coefficient 2,00 2,00 2,00 2,00 2,00 2,00 2,00 2,00e _Digitization exponent 2,00 2,00 2,00 2,00 2,00 2,00 2,00 2,00a2 _Digitization constant 0,50 0,50 0,50 0,50 0,50 0,50 0,50 0,50Kch _Number of separately digitized channels 4 4 4 4 4 4 4 4Ctre Transmission, el to stn ctr (Klk*B + Le*Cfb) 3,00 3,00 3,00 3,00 9,00 9,00 9,00 9,00Le _Average distance, element to station center 0,50 0,50 0,50 0,50 0,50 0,50 0,50 0,50Ctrack Tracking, elements Ctrack = (d*B + f*Nbeams) 1,12 1,12 1,12 1,12 3,28 3,28 3,28 3,28d _Tracking coefficient (per GHz) 0,72 0,72 0,72 0,72 0,72 0,72 0,72 0,72f _Tracking constant 0,10 0,10 0,10 0,10 0,10 0,10 0,10 0,10Nbeams _Beams per station 4 4 4 4 4 4 4 4Cpe Element processing cost = Cdig+Ctre+Ctrack 6,62 6,62 6,62 6,62 22,28 22,28 22,28 22,28Csum Beam summation cost, c*B*(Ne-1) 1,373 0,682 0,336 0,163 5,492 2,726 1,343 0,652c _Summation coefficient 0,010 0,010 0,010 0,010 0,010 0,010 0,010 0,010Cps Station processing cost = Cpe*Ne + Csum 917 458 229 115 3.087 1.543 772 386Cfilt Filtering cost Cfilt = (Kproc+Kmem)*log2(Nl)*B*Ns 335,3 670,6 1.341,2 2.682,4 1.341,2 2.682,4 5.364,8 10.729,7Kproc _Processing cost coefficient (per GHz) 0,48 0,48 0,48 0,48 0,48 0,48 0,48 0,48Kmem _Memory cost (per word) 1,76E-04 1,76E-04 1,76E-04 1,76E-04 1,76E-04 1,76E-04 1,76E-04 1,76E-04Cci Correlator interconnections Cci=Cct + 2*Klk*Ns*B 200 401 802 1.603 801 1.603 3.206 6.414Cct Cost of corner turner Cct = kct*B*Ns ^2*log2(Ns) 0,3 0,7 1,5 3,5 1,1 2,7 6,1 13,8kct _Corner turner cost coefficient (per connection) 1,00E-03 1,00E-03 1,00E-03 1,00E-03 1,00E-03 1,00E-03 1,00E-03 1,00E-03Ccor Cross correlation cost = (Kcor+Kmem*Nl) *B*Ns*Ns/2 3.531 14.124 56.496 225.984 14.124 56.496 225.984 903.936Kcor _Correlator cost coef (per baseline-GHz) 0,012 0,012 0,012 0,012 0,012 0,012 0,012 0,012Kchip Price per large FPGA chip 0,144 0,144 0,144 0,144 0,144 0,144 0,144 0,144Nchip Large chip count = (Cfilt+Cci+Ccor)/Kchip 28.240 105.523 407.213 1.599.096 112.961 422.091 1.628.854 6.396.385Cinfr Correlator infrastructure, $10/large chip 282 1.055 4.072 15.991 1.130 4.221 16.289 63.964Cpc Central processing cost = Cfilt+Cci+Ccor +Cinfr 4.349 16.250 62.711 246.261 17.396 65.002 250.843 985.043Cp Total signal processing cost = Cps*Ns+Cpc 50.197 62.098 108.558 292.106 171.745 219.349 405.187 1.139.379

Color code:Purple: correction of error since previous version.Blue: change to value or formula since previous version.Red: variable whose value changes across this sheetGreen: variable whose value is different from previous sheetBold type: input parameter; normal type means value is calculated.

SKA Cost vs Number of Stations for Two Processed BandwidthsAll for 15K Cryogenics, 10m antennas. A/T = 20,000$2.500.00080Cost, $K (US2001)$2.000.000$1.500.000$1.000.000$500.000604020Antennas per Station$00 100 200 300 400Number of Stations01 GHz Bandwidth 4 GHz Bandwidth Antennas per Station

SKA Cost Estimates July 21, 2001File: skacosteq1.xlsUnits K$US(2001), meters, GHzAntenna Diameter, Meters 5,0 8,0 10,0 12,0 15,0 20,0 30,0Parameter Array Parmeters Value Value Value Value Value Value ValueC Total array cost, fixed costs, elements, processing 882.635 836.916 916.797 1.023.367 1.204.861 1.530.433 2.207.545Cat Total antenna cost, Ne*Ns*Ca 345.769 553.230 691.538 829.845 1.037.307 1.383.076 2.074.613Celt Total electronics cost, Ne*Ns*Ce 414.923 162.079 103.731 72.035 46.103 25.933 11.526Cpt Total processing cost includiing station sum 21.844 21.506 21.429 21.386 21.352 21.325 21.306Ctr Signal transmission costs 20.100 20.100 20.100 20.100 20.100 20.100 20.100Csot Total civil costs at stations, Ns*Cso 30.000 30.000 30.000 30.000 30.000 30.000 30.000Co Fixed cost per array - design + central civil 50.000 50.000 50.000 50.000 50.000 50.000 50.000Cs Total station cost, elements + combining electronics 7.863 7.436 8.242 9.311 11.129 14.387 21.160Cm Total element cost, antenna + receivers + processing 27 66 115 188 352 815 2715Cp Central Signal processing costs 21.292 21.292 21.292 21.292 21.292 21.292 21.292Ns Number of stations in array 100 100 100 100 100 100 100Ne Number of elements per station 277 108 69 48 31 17 8Deq Equivalent single-antenna diameter of station 83 83 83 83 83 83 83N Total number of elements, N = Ns*Ne 27.662 10.805 6.915 4.802 3.074 1.729 768A Effective area of array, A=N*Ae 380.000 380.000 380.000 380.000 380.000 380.000 380.000M Specified Figure of Merit, M = A/Tsys 20.000 20.000 20.000 20.000 20.000 20.000 20.000M Computed Figure of Merit, M = A/Tsys 20.000 20.000 20.000 20.000 20.000 20.000 20.000Tsys System noise temperature at frequency, F 19 19 19 19 19 19 19B Processed total continuum bandwidth 4,0 4,0 4,0 4,0 4,0 4,0 4,0Nl Number of spectral line channels 16.000 16.000 16.000 16.000 16.000 16.000 16.000R Antenna/Electronics ratio, Ca/Ce 0,84 3,45 6,75 11,66 22,77 53,98 182,19Ropt Minimum cost ratio, Ropt = 1 / (X / 2 -1) 2,0 2,0 2,0 2,0 2,0 2,0 2,0Antenna ParametersD Physical diameter of element (meters) 5,0 8,0 10,0 12,0 15,0 20,0 30,0Ap Physical area of element, Ap = 0.785*D^2 20 50 79 113 177 314 707Ef Aperature efficiency 0,70 0,70 0,70 0,70 0,70 0,70 0,70Ae Effective area of element, Ae=Ap*Ef 14 35 55 79 124 220 495Tant Antenna noise temperature, Tant = 10 +4*(F/10) 14 14 14 14 14 14 14Cs Cost per station, Cs =Cso + Ne*(Ca+Ce) 7.857 7.434 8.240 9.310 11.129 14.387 21.160Cso Fixed cost per station, land, civil, bunker, cables 300 300 300 300 300 300 300Ca Cost per antenna, Ca = Ka*D^X 13 51 100 173 338 800 2.700Ka Antenna cost coefficient, 0,10 0,10 0,10 0,10 0,10 0,10 0,10X Antenna cost exponent 3,0 3,0 3,0 3,0 3,0 3,0 3,0Csm Antenna cost per square meter physical area,K$/m^2 0,637 1,019 1,274 1,529 1,911 2,548 3,822Receiver ParametersTsys Tsys = Tln +Tant 19 19 19 19 19 19 19Tln Tln = Kln*F+1 5 5 5 5 5 5 5Kln Lna noise coefficient dependant upon cooler 0,40 0,40 0,40 0,40 0,40 0,40 0,40Tphy Physical temperature of LNA 15 15 15 15 15 15 15F Frequency for system temperature specification 10 10 10 10 10 10 10Ce Electronics cost per antenna, Goal 15,0 15,0 15,0 15,0 15,0 15,0 15,0Ce Ce = Ccl +Nbn*(Cfd +2* Cln) +Clo+Cif +Cpe 14,8 14,8 14,8 14,8 14,8 14,8 14,8Ccl Cooling cost per antenna 4,0 4,0 4,0 4,0 4,0 4,0 4,0Nbn Number of frequency bands 3 3 3 3 3 3 3Cfd Average dual-polariz feed cost 0,5 0,5 0,5 0,5 0,5 0,5 0,5Cln Average LNA + mixer cost 0,5 0,5 0,5 0,5 0,5 0,5 0,5Clo LO cost 0,0 0,0 0,0 0,0 0,0 0,0 0,0Cif Dual IF cost, Cif =2* (Cifo+Kif*B/2) 1,4 1,4 1,4 1,4 1,4 1,4 1,4Cifo Fixed IF cost per polarization 0,3 0,3 0,3 0,3 0,3 0,3 0,3Kif Dual IF cost per GHz of bandwidth 0,1 0,1 0,1 0,1 0,1 0,1 0,1Signal Transmission ParametersCtr Cost of transmission, Ctr =2*Ns*(Ne*Clk + Ls*Cfb) 20.100 20.100 20.100 20.100 20.100 20.100 20.100Clk Fiber transceiver cost, Clk = Klk*B 1,00 1,00 1,00 1,00 1,00 1,00 1,00Klk Tranceiver cost per GHz 0,25 0,25 0,25 0,25 0,25 0,25 0,25Ls Average station to control center distance, km 100 100 100 100 100 100 100Cfb Fiber installed cost, per fiber per km 2 2 2 2 2 2 2Signal Processing Parameters(FX architecture assumed for correlator)(Bandwidth shared among beams)Cdig Digitization Cdig = (a1*(B/Kch)^e+a2) * Kch 2,00 2,00 2,00 2,00 2,00 2,00 2,00a1 _Digitization coefficient 0,40 0,40 0,40 0,40 0,40 0,40 0,40e _Digitization exponent 2,00 2,00 2,00 2,00 2,00 2,00 2,00a2 _Digitization constant 0,10 0,10 0,10 0,10 0,10 0,10 0,10Kch _Number of separately digitized channels 4 4 4 4 4 4 4Ctre Transmission, el to stn ctr (Klk*B + Le*Cfb) 2,00 2,00 2,00 2,00 2,00 2,00 2,00Le _Average distance, element to station center 0,50 0,50 0,50 0,50 0,50 0,50 0,50Ctrack Tracking, elements Ctrack = (d*B + f*Nbeams) 0,92 0,92 0,92 0,92 0,92 0,92 0,92d _Tracking coefficient (per GHz) 0,18 0,18 0,18 0,18 0,18 0,18 0,18f _Tracking constant 0,05 0,05 0,05 0,05 0,05 0,05 0,05Nbeams _Beams per station 4 4 4 4 4 4 4Cpe Element processing cost = Cdig+Ctre+Ctrack 4,92 4,92 4,92 4,92 4,92 4,92 4,92Csum Beam summation cost, c*B*(Ne-1) 5,512 2,141 1,363 0,940 0,595 0,326 0,134c _Summation coefficient 0,005 0,005 0,005 0,005 0,005 0,005 0,005Cps Station processing cost = Cpe*Ne + Csum 1.366 534 342 237 152 85 38Cfilt Filtering cost Cfilt = (Kproc+Kmem)*log2(Nl)*B*Ns 1.341,0 1.341,0 1.341,0 1.341,0 1.341,0 1.341,0 1.341,0Kproc _Processing cost coefficient (per GHz) 0,24 0,24 0,24 0,24 0,24 0,24 0,24Kmem _Memory cost (per word) 5,00E-05 5,00E-05 5,00E-05 5,00E-05 5,00E-05 5,00E-05 5,00E-05Cci Correlator interconnections Cci=Cct + 2*Klk*Ns*B 203 203 203 203 203 203 203Cct Cost of corner turner Cct = kct*B*Ns ^2*log2(Ns) 2,7 2,7 2,7 2,7 2,7 2,7 2,7kct _Corner turner cost coefficient (per connection) 1,00E-03 1,00E-03 1,00E-03 1,00E-03 1,00E-03 1,00E-03 1,00E-03Ccor Cross correlation cost = (Kcor+Kmem*Nl) *B*Ns*Ns/2 16.200 16.200 16.200 16.200 16.200 16.200 16.200Kcor _Correlator cost coef (per baseline-GHz) 0,010 0,010 0,010 0,010 0,010 0,010 0,010Kchip Price per large FPGA chip 0,050 0,050 0,050 0,050 0,050 0,050 0,050Nchip Large chip count = (Cfilt+Cci+Ccor)/Kchip 354.873 354.873 354.873 354.873 354.873 354.873 354.873Cinfr Correlator infrastructure, $10/large chip 3.549 3.549 3.549 3.549 3.549 3.549 3.549Cpc Central processing cost = Cfilt+Cci+Ccor +Cinfr 21.292 21.292 21.292 21.292 21.292 21.292 21.292Cp Total signal processing cost = Cps*Ns+Cpc 157.938 74.668 55.452 45.014 36.473 29.831 25.086

Color code:Purple: correction of error since previous version.Blue: change to value or formula since previous version.Red: variable whose value changes across this sheetGreen: variable whose value is different from previous sheetBold type: input parameter; normal type means value is calculated.

SKA Cost vs Antenna DiameterCompares Current and Projected (2010) Electronics CostsAll for 15K cryogenics, 4 GHz BW, 100 Stations, A/T = 20,000Antenna Cost = 0.1D^3 $K$2.000.000$100.000$1.500.000$10.000Total Cost, $K(US2001)$1.000.000$500.000$1.000$100Antenna UnitCost, $K$0$105,0 10,0 15,0 20,0 25,0 30,0Element Diameter, Meters$54K Electronics $15K Electronics Antenna Cost

SKA Cost Breakdown by Subsystem vs Antenna DiameterAeff/Tsys = 20,000, Aeff=360,000, Tsys=18K, BW=4GHz, 15K Cryogenics2.000.000 Antenna Cost = 0.1D^3 K$, 2010Electronics Cost = $15K per Element1.500.000Fixed CostsSignal TransmissionElectronicsCivil StationCentral ProcessingAntennaTotal Cost, $K1.000.000500.000Antenna0ElectronicsSignal TransmissionCentral ProcessingCivil StationFixed Costs5 8 10 12 15 20 30Antenna Diameter, Meters

SKA Cost Estimates July 21, 2001File: skacosteq1.xlsUnits K$US(2001), meters, GHzAntenna Diameter, Meters 12,0 12,0 12,0 12,0 12,0 12,0 12,0 12,0Parameter Array Parmeters Value Value Value Value Value Value Value ValueC Total array cost, fixed costs, elements, processing 1.925.363 1.562.279 1.447.036 1.522.012 3.638.425 2.551.656 2.187.368 2.363.413Cat Total antenna cost, Ne*Ns*Ca 829.845 829.845 829.845 829.845 829.845 829.845 829.845 829.845Celt Total electronics cost, Ne*Ns*Ce 990.372 583.549 380.138 278.432 2.584.454 1.380.590 778.658 477.692Cpt Total processing cost includiing station sum 29.745 48.084 85.453 160.535 148.726 240.421 427.264 802.676Ctr Signal transmission costs 10.400 20.800 41.600 83.200 10.400 20.800 41.600 83.200Csot Total civil costs at stations, Ns*Cso 15.000 30.000 60.000 120.000 15.000 30.000 60.000 120.000Co Fixed cost per array - design + central civil 50.000 50.000 50.000 50.000 50.000 50.000 50.000 50.000Cs Total station cost, elements + combining electronics 36.723 14.438 6.351 3.071 68.677 22.427 8.348 3.570Cm Total element cost, antenna + receivers + processing 379 294 252 231 711 460 335 272Cp Central Signal processing costs 28.832 47.632 85.232 160.429 144.161 238.162 426.159 802.147Ns Number of stations in array 50 100 200 400 50 100 200 400Ne Number of elements per station 96 48 24 12 96 48 24 12Deq Equivalent single-antenna diameter of station 118 83 59 42 118 83 59 42N Total number of elements, N = Ns*Ne 4.802 4.802 4.802 4.802 4.802 4.802 4.802 4.802A Effective area of array, A=N*Ae 380.000 380.000 380.000 380.000 380.000 380.000 380.000 380.000M Specified Figure of Merit, M = A/Tsys 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000M Computed Figure of Merit, M = A/Tsys 20.000 20.000 20.000 20.000 20.000 20.000 20.000 20.000Tsys System noise temperature at frequency, F 19 19 19 19 19 19 19 19B Processed total continuum bandwidth 19,2 9,6 4,8 2,4 96,0 48,0 24,0 12,0Nl Number of spectral line channels 4.096 4.096 4.096 4.096 4.096 4.096 4.096 4.096R Antenna/Electronics ratio, Ca/Ce 0,84 1,42 2,18 2,98 0,32 0,60 1,07 1,74Ropt Minimum cost ratio, Ropt = 1 / (X / 2 -1) 2,0 2,0 2,0 2,0 2,0 2,0 2,0 2,0Antenna ParametersD Physical diameter of element (meters) 12,0 12,0 12,0 12,0 12,0 12,0 12,0 12,0Ap Physical area of element, Ap = 0.785*D^2 113 113 113 113 113 113 113 113Ef Aperature efficiency 0,70 0,70 0,70 0,70 0,70 0,70 0,70 0,70Ae Effective area of element, Ae=Ap*Ef 79 79 79 79 79 79 79 79Tant Antenna noise temperature, Tant = 10 +4*(F/10) 14 14 14 14 14 14 14 14Cs Cost per station, Cs =Cso + Ne*(Ca+Ce) 36.704 14.434 6.350 3.071 68.586 22.404 8.343 3.569Cso Fixed cost per station, land, civil, bunker, cables 300 300 300 300 300 300 300 300Ca Cost per antenna, Ca = Ka*D^X 173 173 173 173 173 173 173 173Ka Antenna cost coefficient, 0,10 0,10 0,10 0,10 0,10 0,10 0,10 0,10X Antenna cost exponent 3,0 3,0 3,0 3,0 3,0 3,0 3,0 3,0Csm Antenna cost per square meter physical area,K$/m^2 1,529 1,529 1,529 1,529 1,529 1,529 1,529 1,529Receiver ParametersTsys Tsys = Tln +Tant 19 19 19 19 19 19 19 19Tln Tln = Kln*F+1 5 5 5 5 5 5 5 5Kln Lna noise coefficient dependant upon cooler 0,40 0,40 0,40 0,40 0,40 0,40 0,40 0,40Tphy Physical temperature of LNA 15 15 15 15 15 15 15 15F Frequency for system temperature specification 10 10 10 10 10 10 10 10Ce Electronics cost per antenna, Goal 206,2 121,5 79,2 58,0 538,2 287,5 162,1 99,5Ce Ce = Ccl +Nbn*(Cfd +2* Cln) +Clo+Cif +Cpe 206,2 121,5 79,2 58,0 538,2 287,5 162,1 99,5Ccl Cooling cost per antenna 20,0 20,0 20,0 20,0 20,0 20,0 20,0 20,0Nbn Number of frequency bands 3 3 3 3 3 3 3 3Cfd Average dual-polariz feed cost 2,0 2,0 2,0 2,0 2,0 2,0 2,0 2,0Cln Average LNA + mixer cost 0,8 0,8 0,8 0,8 0,8 0,8 0,8 0,8Clo LO cost 3,0 3,0 3,0 3,0 3,0 3,0 3,0 3,0Cif Dual IF cost, Cif =2* (Cifo+Kif*B/2) 9,7 5,8 3,9 3,0 40,4 21,2 11,6 6,8Cifo Fixed IF cost per polarization 1,0 1,0 1,0 1,0 1,0 1,0 1,0 1,0Kif Dual IF cost per GHz of bandwidth 0,2 0,2 0,2 0,2 0,2 0,2 0,2 0,2Signal Transmission ParametersCtr Cost of transmission, Ctr =2*Ns*(Ne*Clk + Ls*Cfb) 10.400 20.800 41.600 83.200 10.400 20.800 41.600 83.200Clk Fiber transceiver cost, Clk = Klk*B 8,00 8,00 8,00 8,00 8,00 8,00 8,00 8,00Klk Tranceiver cost per GHz 2,00 2,00 2,00 2,00 2,00 2,00 2,00 2,00Ls Average station to control center distance, km 100 100 100 100 100 100 100 100Cfb Fiber installed cost, per fiber per km 2 2 2 2 2 2 2 2Signal Processing Parameters(FX architecture assumed for correlator)(Bandwidth shared among beams)Cdig Digitization Cdig = (a1*(B/Kch)^e+a2) * Kch 99,89 49,94 24,97 12,49 192,09 96,05 48,02 24,01a1 _Digitization coefficient 2,00 2,00 2,00 2,00 2,00 2,00 2,00 2,00e _Digitization exponent 2,00 2,00 2,00 2,00 2,00 2,00 2,00 2,00a2 _Digitization constant 0,50 0,50 0,50 0,50 0,50 0,50 0,50 0,50Kch _Number of separately digitized channels 192,093823 96,0469113 48,0234557 24,0117278 192,093823 96,0469113 48,0234557 24,0117278Ctre Transmission, el to stn ctr (Klk*B + Le*Cfb) 39,42 20,21 10,60 5,80 193,09 97,05 49,02 25,01Le _Average distance, element to station center 0,50 0,50 0,50 0,50 0,50 0,50 0,50 0,50Ctrack Tracking, elements Ctrack = (d*B + f*Nbeams) 23,44 11,72 5,86 2,93 78,76 39,38 19,69 9,84d _Tracking coefficient (per GHz) 0,72 0,72 0,72 0,72 0,72 0,72 0,72 0,72f _Tracking constant 0,10 0,10 0,10 0,10 0,10 0,10 0,10 0,10Nbeams _Beams per station 96 48 24 12 96 48 24 12Cpe Element processing cost = Cdig+Ctre+Ctrack 162,74 81,87 41,44 21,22 463,95 232,47 116,74 58,87Csum Beam summation cost, c*B*(Ne-1) 18,258 4,516 1,105 0,264 91,290 22,582 5,526 1,321c _Summation coefficient 0,010 0,010 0,010 0,010 0,010 0,010 0,010 0,010Cps Station processing cost = Cpe*Ne + Csum 15.649 3.936 996 255 44.652 11.187 2.809 708Cfilt Filtering cost Cfilt = (Kproc+Kmem)*log2(Nl)*B*Ns 5.534,3 5.534,3 5.534,3 5.534,3 27.671,6 27.671,6 27.671,6 27.671,6Kproc _Processing cost coefficient (per GHz) 0,48 0,48 0,48 0,48 0,48 0,48 0,48 0,48Kmem _Memory cost (per word) 1,76E-04 1,76E-04 1,76E-04 1,76E-04 1,76E-04 1,76E-04 1,76E-04 1,76E-04Cci Correlator interconnections Cci=Cct + 2*Klk*Ns*B 3.847 3.848 3.849 3.850 19.236 19.241 19.246 19.251Cct Cost of corner turner Cct = kct*B*Ns ^2*log2(Ns) 5,4 6,4 7,3 8,3 27,1 31,9 36,7 41,5kct _Corner turner cost coefficient (per connection) 1,00E-03 1,00E-03 1,00E-03 1,00E-03 1,00E-03 1,00E-03 1,00E-03 1,00E-03Ccor Cross correlation cost = (Kcor+Kmem*Nl) *B*Ns*Ns/2 17.578 35.157 70.314 140.627 87.892 175.784 351.569 703.137Kcor _Correlator cost coef (per baseline-GHz) 0,012 0,012 0,012 0,012 0,012 0,012 0,012 0,012Kchip Price per large FPGA chip 0,144 0,144 0,144 0,144 0,144 0,144 0,144 0,144Nchip Large chip count = (Cfilt+Cci+Ccor)/Kchip 187.223 309.302 553.453 1.041.750 936.113 1.546.508 2.767.266 5.208.748Cinfr Correlator infrastructure, $10/large chip 1.872 3.093 5.535 10.417 9.361 15.465 27.673 52.087Cpc Central processing cost = Cfilt+Cci+Ccor +Cinfr 28.832 47.632 85.232 160.429 144.161 238.162 426.159 802.147Cp Total signal processing cost = Cps*Ns+Cpc 811.293 441.259 284.442 262.431 2.376.755 1.356.836 987.873 1.085.381

Color code:Purple: correction of error since previous version.Blue: change to value or formula since previous version.Red: variable whose value changes across this sheetGreen: variable whose value is different from previous sheetBold type: input parameter; normal type means value is calculated.

SKA Cost vs Number of Stations forBeam-filled case, 0.1 and 0.5 GHz/beamAll for 15K Cryogenics, 12m antennas, 4550 total, A/T = 20,000$3.500.000100Cost, $K (US2001)$3.000.000$2.500.000$2.000.000$1.500.000$1.000.000$500.00080604020Ants/stn == beams$000 100 200 300 400Number of Stations0.1 GHz/beam 0.5 GHz/beam Antennas per Station