THERMAL CALCULATORS GUIDELINES
Thermal```
In the paper, the authors discuss three methods to move heat away from the source: 1. Conduction 2. Convection 3. Radiation
Can you elaborate on these three methods of heat transfer based on the paper? Please organize your answer with clear headings and bullet points for each method.### Heat Transfer Methods
The paper "Thermal Design Consideration for Surface Mount Layouts" by Charles Mauney of Texas Instruments outlines three primary methods of heat transfer: conduction, convection, and radiation.
Conduction¶
Conduction is the process by which heat moves through a material, typically from copper to FR4 and so on within a Printed Circuit Board (PCB). This method is crucial because it allows heat to spread out to the required surface area for dissipation. Some materials, such as copper, conduct heat more effectively than others, like FR4. The thermal conductivity factor (K) quantifies a material's ability to conduct heat, measured in Watts per meter-Kelvin (W/m°K) or Watts per meter-Celsius (W/m°C). A lower thermal impedance (theta) is desired, as it indicates a smaller temperature rise per Watt of dissipated heat.
TABLE 1 THERMAL CONDUCTIVITY FACTORS Materials K (W/m°K) K (W/in°C) Copper 355 9 Aluminum 175 4.44 FR4 0.25 0.0064 Solder 63/67 39 1 Air 0.0275 0.0007
Key formulas for conduction include:
* General Conduction Formula: theta = L / (K * A_CS)
* K: Thermal Conductivity Factor
* L: Thermal path length
* A_CS: Cross-sectional area where heat is applied
* Lateral Conduction Heat Flow Formula: theta = L / (K * W * t) = L / (K * A_CS)
* L: Path length of heat flow
* W: Width
* t: Thickness
* W * t = A_CS: Cross-sectional area of heat flow
* Perpendicular Conduction Heat Flow Formulas: theta = t / (K * W * L) = t / (K * A_CS)
* t: Path of heat flow (through the thickness of the material)
* W * L = A_CS: Cross-sectional area where heat is applied
* Heat Flow Through a Via Formula: theta_Cu-Vio = L / (K * A_CS) = L / (K * pi * ((D_0^2 - D_1^2) / 4))
* L: Length of the via
* pi * ((D_0^2 - D_1^2) / 4): Cross-sectional area
* Solder Filled Via Formula: theta_Soller-via = L / (K * A_CS) = L / (K * pi * (D_1^2 / 4))
* Conduction Through Solder Mask Formula: theta_Solder-Mask = L / (K * A_CS)
Important concepts for conduction: * Shorter Thermal Path: A shorter thermal path results in a lower theta, meaning it's more efficient to conduct heat through the thickness of a plane rather than along its length. * Larger Connection Area: A larger connection (area/perimeter) between the IC and PCB leads to a lower theta. Increasing the perimeter of the power pad increases the cross-sectional thermal conduction area, thus lowering the PCB's thermal impedance and keeping the PCB and IC cooler. * Thick Copper and Thin FR4 Layers: Using thick copper layers maximizes heat flow along the copper sheet, while minimizing FR4 thickness, if possible, maximizes heat flow through it. * Multiple Vias: Employing multiple vias significantly lowers the thermal impedance through the PCB. Solder and copper vias greatly enhance the thermal performance of FR4.
Convection¶
Convection is the method of moving heat from the surface of a material to the surrounding air. The temperature rise due to convection is directly proportional to the power dissipated and inversely proportional to both the surface area and the heat transfer coefficient (h). The heat transfer coefficient h is influenced by air speed and temperature difference.
Key formulas for convection include:
* Temperature Rise through Convection: dT = P / (h * A) = 133 * (P / A)
* P: Power in Watts
* h: Heat transfer coefficient (e.g., 0.0075 W/(in^2-C) for no air flow)
* A: Surface area in in.^2
* Theta for Convection: Theta_Surface-area = 1 / (A * h) = (133 (°C-in^2/W)) / A(in^2)
* Minimum PCB Surface Area: A = P / (h * dT) = 133 * (P / dT)
* Junction Temperature: T_J = T_AMB + dT_PCB-Conv + dT_PCB-Cond + dT_JC_IC
A crucial concept in convection is that it depends on the temperature difference (delta T) and area, not the material itself. While copper is a better conductor than FR4, both materials have the same heat dissipation factor for convection.
Thermal Radiation¶
Thermal radiation is the transfer of heat from one surface to another. This process is governed by the Stefan-Boltzmann Law of Radiation.
The formula for thermal radiation is:
* H = e * sigma * A * (T_1^4 - T_2^4)
* e: Emissivity (ranging from 0 to 1)
* sigma: Stefan-Boltzmann constant (5.67 x 10^-8 J/(sm^2K^4))
* A: Surface area
* T_1 and T_2: Kelvin temperatures of the two surfaces
The heat transfer contribution from thermal radiation is often neglected in analysis due to its complexity but can be considered a safety margin in thermal design. It is approximately half the amount of heat transferred by convection, assuming the radiating surface temperature is greater than the ambient temperature.