SMA Technical Memorandum #111

To: Marty Levine

From: Ken McCracken

Date: July 28, 1997

Subject: Preliminary Digital Correlator Thermal Analysis

Ref:
1) Thermal Resistance Testing of the Haystack VLSI Correlator Chip SMA Tech Memo #110
2) SMA Specification 40165010000, Control Building Correlator Room Thermal Spec.

Introduction

A preliminary thermal analysis of the digital correlator rack/crate/PCB is documented in the following memo. Detailed thermal information is available from the reference document on the thermal resistances of the Haystack VLSI Correlator Chip. Only general information is known about the majority of the remaining components. The main emphasis of this effort will be to demonstrate the effective cooling of the correlator chips with the assumption that the extraordinary cooling they require will result in satisfactory thermal performance of the remaining components.

Requirements

Most semiconductor chips are fairly reliable up to a junction temperature of 125°C. It is a well documented fact that electronic component life increases with reduced operating temperatures. Therefore, as a rule of thumb, to create a robust thermal design the operating junction temperatures should be derated to a maximum well below this temperature; approximately 85°C. However, this correlating computer design employs custom chips (Haystack VLSI Correlator Chips) that are available in a one-time fixed quantity, the instrument is expected to have a 30 year life, and the environmental site at 14000 feet altitude presents difficult maintenance issues and additional unknowns that will not easily be tested for. For these reasons, the thermal design goal for the digital correlator chip will be to keep the operating junction temperatures below 70°C.

Analysis

The thermal analysis begins at the largest system level and works down to the smallest system. In this way, rack boundary conditions lead to crate air temperatures which then lead to component junction temperature predictions. Since this is a preliminary analysis conservative assumptions will be used throughout.

Rack / Crate Analysis

The digital correlator room is planned to contain (9) nine Schroff 19 inch wide x 72 inch high electronics racks. The thermal design is based on air-cooling of the electronics within the racks. The eight antenna system will be comprised of (12) twelve crates of correlator electronics. A power supply will be required for each crate yielding a total of (12) twelve power supplies. This will mean the digital correlator room will have six electronics racks with two correlator crates each and three electronics racks with four power supplies each. Figure One shows the proposed system of nine electronics racks and their contents.

Figure One

Table One lists the assumed power dissipation of each component in the digital correlator racks down to the PCB level. The PCB power dissipation listed is based on 52 Mhz operation. Each correlator chip is assumed to dissipate 3.13 W. The power supply power dissipation is based on an assumed 70% efficiency.

Table One - Power Dissipation Summary

Figure One shows two different electronic rack configurations. One configuration will contain two digital crates and the second rack configuration will contain four power supplies. The Control Building thermal specification requires 900 acfm per rack delivered at 5°C (±2°C). The cooling air will blow straight up through each rack from floor inlet ducts to return ducts in the ceiling. Since the control building resides on Mauna Kea all air properties will be calculated for 14,000 feet altitude. The air properties for 14,000 feet altitude are listed in Appendix A. From calorimetry the air temperature rise equation is:

Power Dissipated (W) = Mass Flow (kg/sec) Specific Heat (J/kgK) Temperature Rise (°C)

or

Temperature Rise = Power Dissipated / (Mass Flow * Specific Heat)

Power Supply Crate/Rack

Since there has been no mechanical definition of the digital power supplies, the only item that can be estimated is the maximum air temperature of the power supply rack. Calculate the average air temperature rise through the power supply rack.

Air Temp Rise = 3428 W/[(900 cfm)(.732 kg/cu m)(1 m/3.28 ft)³(1 min/60 sec)(1006.7 J/kgK)]

Air Temp Rise = 10.95°C

Maximum Power Supply Rack Air Temperature = 7°C + 11°C = 18°C

Correlator Crate/Rack

Calculate the average air temperature rise through the digital correlator crate racks:

Air Temp Rise = 4000 W/[(900 cfm)(.732 kg/cu m)(1 m/3.28 ft)³(1 min/60 sec)(1006.7 J/kgK)]

Air Temp Rise through Correlator Crate Rack = 12.8°C

This temperature rise is an average air temperature rise through the rack. However, the digital crate’s receiver PCB with daughter board has not been mechanically defined so a realistic estimation of airflow through both sections of the crate is not possible. The airflow will be estimated for this analysis by assuming that the board pitch and thickness is the same for both the correlator PCBs and the receiver PCBs. The only difference will be since the correlator PCBs are deeper they will be assumed to receive proportionally more airflow. Estimate the airflow in the correlator and receiver board sections.

Each section has (8) slots which are .95 in wide

Total Area for Airflow = (26.75 in)(.95 in )(8 slots) = 203.3 sq in

Airflow through correlator section = (17.25/26.75)(900 cfm) = 580.4 cfm

Airflow through receiver section = (9.5/26.75)(900 cfm) = 319.6 cfm

Calculate the air temperature rise through each crate section. For the correlator board section:

Air Temp Rise = 1000 W/[(580 cfm)(.732 kg/cu m)(1 m/3.28ft)³(1min/60 sec)(1006.7 J/kgK)]

Air Temp Rise through Correlator Section of one Crate = 5.0°C

For the receiver board section:

Air Temp Rise = 800 W/[(319 cfm)(.732 kg/cu m)(1m/3.28ft)³(1 min/60 sec)(1006.7 J/kgK)]

Air Temp Rise through Receiver Section of one Crate = 7.2°C

Receiver Board Analysis

Since little is known about the receiver board, this will be the end of the preliminary analysis of it. Assuming two stacked crates and a maximum rack inlet air temperature of 7°C (5°C ±2°C), the maximum air temperature over the top part of the top crate’s receiver boards will be:

Maximum Air Temp Receiver Board Section = 7°C + 7.2°C + 7.2°C = 21.4°C

Using standard electronic components capable of operating at up to 125°C junction temperatures reliably, this worse case ambient temperature at 14,000 feet altitude should be acceptable. However, the receiver board components should still be evaluated thermally once the mechanical definition and parts list is known.

Correlator Board Analysis

Again, assuming two stacked crates and a maximum rack inlet air temperature of 7°C (5°C ±2°C), the maximum air temperature over the top part of the top crate’s correlator boards will be:

Maximum Air Temp Correlator Board Section = 7°C + 5°C + 5°C = 17°C

The junction temperature of the correlator chips will be calculated from the following equation:

Tjunction = Rj/a * Power Diss + Maximum Ambient Temperature

The correlator chip Rj/a values will be obtained from reference one. All the Rj/a values in the Thermal resistance Testing memo are based on knowing the power dissipation and air velocity boundary conditions. Therefore, from the area assumed in the Rack/Crate Analysis section calculate an estimated air velocity over the correlator boards.

Air Velocity over Corr. PCBs = (580 cfm / 8 slots)/[(.95 in)(17.25 in)(1 sq ft/144 sq in)]

Air Velocity over Corr. PCBs = 637.1 ft/min

Since this average air velocity is calculated at the actual operating environment of 14,000 feet altitude, an equivalent sea level velocity must be calculated to use any data in the Thermal Resistance Testing memo. It has been found that the heat transfer relationship between sea level and altitude is based on having the same mass flow at both sea level and altitude. And since the mass flow over a board is simply the density times the velocity times the cross-sectional area, a relationship can be calculated based on the two changing values, the air density and velocity.

Mass flow = (Density)(Velocity)(Area)

Matching sea level and altitude mass flows yields:

(Dens s.l.)(Vel s.l.)(Area) = (Dens alt.)(Vel alt.)(Area)

Since the area is constant and solving for Vel s.l yields:

Vel s.l. = Vel alt. (Dens alt./Dens s.l.)

And substituting density values from Appendix A (14,000 feet and 25°C) yields the following equation:

Vel s.l. = Vel alt. [(.695 kg/cu m)/(1.17 kg/cu m)

Vel s.l. = Vel alt. * .594

Now, substitute the calculated air velocity and determine an equivalent sea level velocity to use in conjunction with the Thermal Resistance Testing memo.

Vel s.l. equiv = (637.1 ft/min)(.594) = 378.4 ft/min

Knowing this velocity, the thermal resistance of the Haystack VLSI correlator chip can be determined from the Thermal Resistance Testing of the Haystack VLSI Correlator Chip memo. From Figure Two of that memo, the resistance junction to ambient (Rj/a) can be read off as about 12.8°C/W with a 3.4 W chip power dissipation and 378 ft/min air velocity. Figure One of the Thermal Resistance Testing memo shows the behavior of the correlator chip with varying power dissipation at 400 lfpm. Applying a least-squares fit to the data yields the following equation for Rj/a as a function of power dissipation:

Rj/a = -1.839 * (Power Diss) + 18.705 (with 400 lfpm at sea level)

It can be assumed that the correlator chip will behave the same way with power dissipation for the slightly lower air velocity, Vel s.l. equiv. = 378.4 ft/min. Applying this equation to the one value read off Figure Two of the Thermal Resistance Testing memo yields the following equation:

Rj/a = -1.839 * (Power Diss) + 19.053 (with 378 lfpm at sea level)

For a worse case (conservative) analysis, the maximum air temperature of the correlator section will be used as an air boundary condition for components at the top of the top crate. Since correlator chips populate the correlator PCB all the way to the top edge this is a fairly reasonable approximation. Table Two lists the estimated junction temperatures based on power dissipation. Note, the maximum crate air temperature used was 17°C for all cases (it was based on the 3.13 W individual chip power dissipation case).

Table Two - Correlator Chip Thermal Data vs. Power Dissipation

A more conservative analysis would impose an additional 10-20% factor on the correlator chip’s Temperature Rise junction to ambient to account for local air flow blockages, adjacent components with high power dissipations, and additional factors beyond the scope of this analysis. This would put a range on the correlator chip maximum junction temperature of 62.8°C to 66.9°C (at 3.13 W dissipation). And, since this is meant to be a preliminary analysis to identify the order of magnitude of the junction temperature, this condition will be imposed on the results to be conservative.

Conclusion

From Table Two, the predicted maximum junction temperature of the Haystack VLSI Correlator chip at 3.13 W dissipation is 63°C to 67°C. Many assumptions form the basis of this prediction; chip and rack power dissipations, local air velocity estimations, rack airflow meeting the specification, the racks and crates assembled as described, etc... When detailed mechanical information is available about the receiver PCBs and daughter boards, a more accurate prediction of the entire digital crate can be made. However, the self-imposed requirement of maximum junction temperatures of less than 70°C for the Haystack VLSI Correlator Chips has been met. Also, when the power supply crates are defined, a detailed thermal analysis should be performed.

Appendix A

Air property data from /home/ken/cprograms/air2.c.
This program gives air properties for air between 200 K and 400 K
at both sea level and 14000 feet altitude.

What is the Air Temperature (K)?258.15 (-15.0 C)

Air Temperature (K) = 258.15 at sea level
Air Density (kg/cu m) = 1.35667
Air Specific Heat (kJ/kg K) = 1.00616
Air Conductivity (W/m K) = 0.022952
Air Kin. Visc. (sq m/sec) = 1.21653e-05
Air Prandlt No. = 0.717881

Air Properties at 14000 feet altitude and 258.15 (K)
Air Density (kg/cu m) = 0.802915
Air Density from ideal gas law (kg/cu m) = 0.802575
Air Specific Heat (kJ/kg K) = 1.00616
Air Conductivity (W/m K) = 0.022952
Air Kin. Visc. (sq m/sec) = 2.05556e-05
Air Prandlt No. = 0.723515

This program gives air properties for air between 200 K and 400 K
at both sea level and 14000 feet altitude.

What is the Air Temperature (K)?271.65 (-1.5 C)

Air Temperature (K) = 271.65 at sea level
Air Density (kg/cu m) = 1.29368
Air Specific Heat (kJ/kg K) = 1.00643
Air Conductivity (W/m K) = 0.024032
Air Kin. Visc. (sq m/sec) = 1.33668e-05
Air Prandlt No. = 0.714371

Air Properties at 14000 feet altitude and 271.65 (K)
Air Density (kg/cu m) = 0.763013
Air Density from ideal gas law (kg/cu m) = 0.762717
Air Specific Heat (kJ/kg K) = 1.00643
Air Conductivity (W/m K) = 0.024032
Air Kin. Visc. (sq m/sec) = 2.26634e-05
Air Prandlt No. = 0.724188

This program gives air properties for air between 200 K and 400 K

at both sea level and 14000 feet altitude.

What is the Air Temperature (K)?275.65 (2.5 C)

Air Temperature (K) = 275.65 at sea level

Air Density (kg/cu m) = 1.27502

Air Specific Heat (kJ/kg K) = 1.00651

Air Conductivity (W/m K) = 0.024352

Air Kin. Visc. (sq m/sec) = 1.37228e-05

Air Prandlt No. = 0.713331

Air Properties at 14000 feet altitude and 275.65 (K)

Air Density (kg/cu m) = 0.751941

Air Density from ideal gas law (kg/cu m) = 0.751657

Air Specific Heat (kJ/kg K) = 1.00651

Air Conductivity (W/m K) = 0.024352

Air Kin. Visc. (sq m/sec) = 2.32689e-05

Air Prandlt No. = 0.723178

This program gives air properties for air between 200 K and 400 K

at both sea level and 14000 feet altitude.

What is the Air Temperature (K)?278.15 (5.0 C)

Air Temperature (K) = 278.15 at sea level

Air Density (kg/cu m) = 1.26335

Air Specific Heat (kJ/kg K) = 1.00656

Air Conductivity (W/m K) = 0.024552

Air Kin. Visc. (sq m/sec) = 1.39453e-05

Air Prandlt No. = 0.712681

Air Properties at 14000 feet altitude and 278.15 (K)

Air Density (kg/cu m) = 0.745182

Air Density from ideal gas law (kg/cu m) = 0.744905

Air Specific Heat (kJ/kg K) = 1.00656

Air Conductivity (W/m K) = 0.024552

Air Kin. Visc. (sq m/sec) = 2.36424e-05

Air Prandlt No. = 0.722284

This program gives air properties for air between 200 K and 400 K

at both sea level and 14000 feet altitude.

What is the Air Temperature (K)?279.65 (6.5 C)

Air Temperature (K) = 279.65 at sea level

Air Density (kg/cu m) = 1.25635

Air Specific Heat (kJ/kg K) = 1.00659

Air Conductivity (W/m K) = 0.024672

Air Kin. Visc. (sq m/sec) = 1.40788e-05

Air Prandlt No. = 0.712291

Air Properties at 14000 feet altitude and 279.65 (K)

Air Density (kg/cu m) = 0.741185

Air Density from ideal gas law (kg/cu m) = 0.740912

Air Specific Heat (kJ/kg K) = 1.00659

Air Conductivity (W/m K) = 0.024672

Air Kin. Visc. (sq m/sec) = 2.38645e-05

Air Prandlt No. = 0.721653

This program gives air properties for air between 200 K and 400 K

at both sea level and 14000 feet altitude.

What is the Air Temperature (K)?290.25 (17.1 C)

Air Temperature (K) = 290.25 at sea level

Air Density (kg/cu m) = 1.20689

Air Specific Heat (kJ/kg K) = 1.0068

Air Conductivity (W/m K) = 0.02552

Air Kin. Visc. (sq m/sec) = 1.50223e-05

Air Prandlt No. = 0.709535

Air Properties at 14000 feet altitude and 290.25 (K)

Air Density (kg/cu m) = 0.714117

Air Density from ideal gas law (kg/cu m) = 0.713871

Air Specific Heat (kJ/kg K) = 1.0068

Air Conductivity (W/m K) = 0.02552

Air Kin. Visc. (sq m/sec) = 2.53884e-05

Air Prandlt No. = 0.715268

This program gives air properties for air between 200 K and 400 K

at both sea level and 14000 feet altitude.

What is the Air Temperature (K)?298.15 (25.0 C)

Air Temperature (K) = 298.15 at sea level

Air Density (kg/cu m) = 1.17003

Air Specific Heat (kJ/kg K) = 1.00696

Air Conductivity (W/m K) = 0.026152

Air Kin. Visc. (sq m/sec) = 1.57253e-05

Air Prandlt No. = 0.707481

Air Properties at 14000 feet altitude and 298.15 (K)

Air Density (kg/cu m) = 0.695195

Air Density from ideal gas law (kg/cu m) = 0.694967

Air Specific Heat (kJ/kg K) = 1.00696

Air Conductivity (W/m K) = 0.026152

Air Kin. Visc. (sq m/sec) = 2.64662e-05

Air Prandlt No. = 0.708446