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More and more package/PCB system designs are requiring thermal analysis. Power dissipation is a critical issue in package/PCB systems design which requires careful consideration of the thermal and electrical domains. To better understand thermal analysis, we can take the heat conduction in solids as an example and use the duality of the two domains. Figure 1 and table 1 give the fundamental and basic relationships between the electrical and thermal domains.
Figure 1. Fundamental relationships between the electrical domain and thermal domain
oC or K
Amperes or Coulombs/s
Power or Heat Flux
PD or Q
Watts or Joules/s
oC/W or K/W
Farads or Coulombs/V
Table 1. Basic relationships between the electrical domain and thermal domain
There are some differences between the electrical and thermal domains such as:
Thermal conduction takes place when a temperature gradient exists in a solid or stationary fluid medium. Heat convection and radiation are more complex thermal transport mechanisms than conduction. Thermal convection occurs while a solid surface is in contact with a fluid material at a different temperature. Thermal radiation is the emission of electromagnetic radiation from all matter with a temperature greater than absolute zero. Figure 2 shows the three thermal transport working diagrams. The descriptive equations of one dimensional applications for all above thermal transport mechanisms can be expressed as shown in table 2.
Figure 2. Three thermal transport mechanism diagram
Q = (T1-T2)/(Δx/kA) = kAΔT/Δx
Q = hcA(Ts-Tf) = hcAΔT
Q = hrA(Th-Tc) = εσA(Th4-Tc4)
Table 2. Equations for different thermal transfer modes
Q is heat transferred per unit time (J/s)
k is thermal conductivity (W/(K.m))
A is the sectional area of the object (m2)
ΔT is temperature difference
Δx is the thickness of the material
hc is convective heat transfer coefficient
hr is radiative heat transfer coefficient
T1 is initial temperature in one side
T2 is the temperature in the other side
Ts is temperature of the solid surface (oC)
Tf is the average temperature of the fluid (oC)
Th is hot side temperature (K)
Tc is cold side temperature (K)
ε is emissivity of the object (for a black body) (0~1)
σ is Stefan-Boltzmann constant=5.6703*10-8 (W/(m2K4))
Sigrity PowerDC is a proven electrical and thermal technology that has been used in the design, analysis, and sign-off of real-world packages and PCBs for many years. The integrated electrical/thermal co-simulation helps users easily confirm the design has met specified voltage and temperature thresholds, without having to spend significant effort sorting out the impacts which are difficult to judge. With this technology, you can get accurate design margins and lower manufacturing cost for your designs. The following figure shows the method used in PowerDC for electrical/thermal co-simulation:
Figure 3. PowerDC Electrical/Thermal Co-Simulation Scheme Diagram
Besides E/T co-simulation, PowerDC provides other thermal related functionality such as:
With these technologies and capabilities, you can easily and quickly evaluate the heat flow and thermal radiation both graphically and numerically for your package or printed circuit board designs.
Figure 4. Package thermal model extraction
Figure 5. Package thermal stress analysis example
Figure 6. Multi-board thermal analysis
Figure 7. Chip-package thermal co-simulation with Voltus-PowerDC
Join us at Semi-Therm 34th Annual Symposium & Exhibit on March 20-21 in booth 306 and learn more about how Cadence® Sigrity PowerDC technology can help you solve your IR drop, current density, and thermal issues in your IC package and PCB designs. We are also presenting a joint paper with Huawei Technologies on “Application of Thermal Network Approach to Electrical-Thermal Co-simulation and Chip-Package-Board Extraction” in the technical session.
We look forward to seeing you at Semi-Therm!