## How to calculate the temperature rise of a PCB and its components

Heat generating electronic components mounted to print circuit boards (PCB) often times rely on the PCB to help dissipate heat to keep the component operating below its maximum temperature limit. Many semi-conductor components are constructed with an exposed metal pad that is directly attached to the PCB to create a low thermal resistance path between the junction of the component and PCB. In this situation the PCB acts as heat sink that conducts heat away from the component and dissipates it to the environment from its large surface area.

Estimating the junction temperature of surface mounted components requires some simplifications to allow the use of manageable calculations that can be carried out using a spreadsheet. The calculation procedure and associated simplifications and assumptions are explained in the following sections.

# PCB Effective Thermal Conductivity

Because of the discontinuous distribution of conductor material used to create traces, ground planes, vias and electrical connection points the thermal conductivity of the PCB is non uniform. To conduct the thermal calculations required to determine the board and component temperatures a single effective thermal conductivity of the PCB is required. A widely used method for calculating an effective PCB thermal conductivity is to use a weighted volume approach. The weighted volume effective thermal conductivity is given by equation 1

1

where:

2

is the total conductor volume

is the total dielectric volume

is the thermal conductivity of the conductor

is the thermal conductivity of the dielectric

Often times it may be difficult to determine the values of V_{c} and V_{d}. A reasonable estimate of the conductor volume for modern PCBs is between 10% and 20%.

# PCB Effective Convection Coefficient

Heat loss from the surface of the PCB takes place due to radiation and convection to the ambient. The following calculations to determine the temperature rise of the PCB components utilize an effective convection coefficient h_{eff} that is a sum of the average convection coefficient due to convection and that due to radiation. The correlations used to calculate the convection coefficients from a flat plate due to radiation and convection will be used.

Equations 11 through 18 in the blog post How to design a flat plate heat sink can be used to determine the effective convection coefficient for a PCB oriented vertically that is cooled via natural convection and radiation.

For horizontally oriented PCBs reference equations 1 through 7 in the blog post Performance of a LED flat plate heat sink in multiple orientations to determine the natural convection coefficient. This is added to the radiation convection coefficient which is independent of orientation to determine the overall effective convection coefficient h_{eff}.

# PCB Temperature Distribution

A PCB from a heat transfer perceptive is a convection cooled flat plate with heat sources distributed across the surface of the plate as shown in figure 1. A method for calculating the temperature distribution across a flat plate that can be implemented using a spreadsheet or common mathematics software is the modified Bessel function method.

Figure 1. PCB with heat generating components

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