Signal and Power Integrity (PCB/IC Packaging) Blogs

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

Electrical Domain			Thermal Domain
Variable	Symbol	Units	Variable	Symbol	Units
Voltage	V	Volts	Temperature	T	oC or K
Current	I	Amperes or Coulombs/s	Power or Heat Flux	PD or Q	Watts or Joules/s
Resistance	R	Ohms	Thermal resistance	RThetaAB	oC/W or K/W
Capacitance	C	Farads or Coulombs/V	Thermal capacitance	CTheta	Joules/ oC
ΔVAB=VA-VB=I*RAB			ΔTAB=TA-TB=PD* RThetaAB

Table 1. Basic relationships between the electrical domain and thermal domain

There are some differences between the electrical and thermal domains such as:

• In the electrical domain, the current is constrained to flow within specific circuit elements, but in the thermal domain heat flow emanates from the heat source in three dimensions by any or all of the three thermal transport mechanisms: conduction, convection and radiation.
• Thermal coupling between elements is more prominent and difficult to isolate than electrical coupling.
• Measurement tools are different. For thermal analysis, infrared cameras and thermocouples replace oscilloscopes and voltage probes.

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

Transfer Mode	Heat transferred
Conduction	Q = (T1-T2)/(Δx/kA) = kAΔT/Δx
Convection	Q = hcA(Ts-Tf) = hcAΔT
Radiation	Q = hrA(Th-Tc) = εσA(Th4-Tc4)

Table 2. Equations for different thermal transfer modes

Where:

            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

            h_c is convective heat transfer coefficient

            h_r is radiative heat transfer coefficient

            T₁ is initial temperature in one side

            T₂ is the temperature in the other side   

            T_s is temperature of the solid surface (^oC)

T_f is the average temperature of the fluid (^oC)

            T_h is hot side temperature (K)

T_c 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:

• Thermal model extraction (Figure 4)
• Thermal stress analysis (Figure 5)
• Multi-board analysis (Figure 6)
• Chip-package-board co-simulation (Figure 7)

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 34^th 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!