Basic for heat sink calculation
We know all of this difficult to do completely without a mathematical formula. But I will not talk about black body, Stefan’s law, or derivative, or even the absolute temperature of -273 ° C. I’ll just offer this final simplified formula, whereby the rest of this article should be easier to digest:
P = (T1 – T2) / Rth
or
Rth = (T1 – T2) / P
where :
P = power in Watts (W)
T1 – T2 = temperature difference in degrees Celsius (° C)
Rth = Thermal resistance, ° C / W
Note the similarity of this formula with another famous formula you need to know (if you do not already know, learn it now):
I = (U1 – U2) / R
where :
I = current in amperes (A)
U1 – U2 = potential difference in volts (V)
R = resistance in Ohms
We will have to go through subtraction and division. Admit that there are worse.
Heat sink Calculation method
To begin, we agree that the thermal resistance, which we call now Rth, can be represented in the same way that the electrical resistance used in electronic assemblies. This allows you to navigate easily, even with a diagram of usual type:
The heat dissipated by the component gaining the environment via several ways:
- the junction box of the component to the component, radiation and conduction;
- the housing component to the surrounding air by radiation and convection;
- the housing component of the radiator by conduction;
- the radiator to the surrounding air by radiation and convection.
The junction of the inner component is the component whose temperature must not exceed a certain limit the risk of being destroyed. The limit value is specified by the manufacturer of the component, it is about 90 ° C for germanium and components from 150 to 200 ° C for silicon components. Note that the calculation methods used for electrical resistors are applied to the thermal resistance, with respect to the in series or in parallel.
Thermal equilibrium of the component
To talk about things, take the example of a transistor. The latter receives a power that depends on the voltage applied between its collector and emitter, and the current through the collector. Refer to this power received PC (power consumption). Because of this received power Pc, the transistor will dissipate some energy, which we call Pd (power dissipation). The transistor tends to thermal equilibrium when the power dissipated equals the power consumed, ie when Pd = Pc. If now we call the junction temperature Tj and Ta the ambient temperature, we can write the power dissipation Pd is equal to (Tj – Ta) / Rth. You can also write this:
Tj = Pd * Rth = Ta
We realize and recognize that the junction temperature of the transistor depends at the same time the total thermal resistance, ambient temperature, and of course the power dissipated in the transistor. Based on this observation, we realize that it is possible to calculate the cooling system according to the power terminal and the maximum allowable power dissipation. Next : Calculation of the Heat sink , Example heat sink calculation .
