When designing electronic circuits you need to take into account the temperature of the components, if there is too much heat they will fail, if they run hot their lifetime is reduced. I once did reliability calculations for a friend to show how how much a temperature of 95 degrees Celsius reduced the lifetime of a complete electronic system, the notional "Mean Time To Failure" (MTTR) reduces exponentially as temperature goes up, the Arrhenius expression gives an indication of this, but it is not the complete story.
A common rule of thumb is that for every 10°C increase in temperature, the failure rate of a component doubles, but this is conservative as it does not take into account all the reasons for failure of electronic systems. but even so, clearly going from 25 degrees to 55 degrees causes failure at least 2^3 or 8 times quicker.
Temperatures above 50 degrees should be avoided, 50 is about the maximum you can put your finger on (for about 5 seconds) without too much "ouch". A modern thermal imager is a useful tool. It is only accurate if the emmissivity of what is being looked at it is not too extreme.
The traditional way to calculate the temperatures is to use thermal resistance figures and add these up - the same way you add resistors in series. For semiconductors (the most sensitive of our components I think, at least for rapid failure, some capacitors do dry out at elevated temperatures) you want the temperature inside the transistor or diode to be kept below the manufacturers maximum and you increase lifetime if you can get well below it. The manufacturer hopefully publishes the thermal resistance from the semiconductor junction to the case. If this is all that is used them you can calculate what temperature the junction is if the case is at a certain value and the device is dissipating so many watts of power. Thermal resistances are the most convenient to work with, some datasheets give the data in different ways, derating curves or values, you can convert these to thermal resistances or, at worst, use data for the same physical package using a datasheet for a similar device
For example: the datasheet for the IRF510 states thermal resistance ratings as;
Junction-to-ambient RthJA as 62 degrees C per watt (this is for when no heatsink is used)
Junction-to-case RthJC of 3.5 degrees/watt. (used when the case is not just in air)
Case-to-(Heat)sink, flat greased surface RthCS of 0.5 degrees per watt
(Note you can grease the interface, insert mica washers for electrical insulation but good heat transfer or use thermal pads, all have values well under a half a degree per watt)
An example heatsink costing £3 to £4 and two inches high, an inch and half wide and half an inch deep has a specified natural (non fan assisted) thermal resistance of 9 degrees C per watt (FEC1892328). For around a tenner you can get 3 or 4 degrees per watt heatsinks. Bigger is expensive.
The device has a maximum junction temperature of 175 degrees C (though I'd prefer to opt for 125)
The temperature rise above ambient is simply the power times the thermal resistance
Thus if the device is running at 10 Watts and we assume an ambient temperature of 25 degrees we have;
Pd * (Rjc + Rcs + Rsa) + Ta = Tj
= 10 * (3.5 + 0.5 + 9 ) + 25 = 155 ignoring dissipation from case directly to air.
Fairly hot! and if the heatsink is inside a case that is poorly ventilated the "ambient" can easily be tens of degrees above 25. A fan or bigger heatsink is needed.
Big heat sinks are expensive, Harry Lythall (SM0VPO) has good rules of thumb on his website suggesting that if you take the square area of aluminium exposed to air then the thermal resistance of home made heat sinks is roughly
Taken from http://sm0vpo.altervista.org/begin/heat-0.htm
We assumed constant power being dissipated in the example above, so you'd have to use the maximum power as the worst case, if the device was being switched and was only "on" 10% of the time then you could guesstimate that the effective power was a tenth of the peak, but only if the cycle time was fast.
If the device is passing an SSB modulated carrier then a "duty cycle of 30% might be appropriate, which drops to 15% if you only transmit half the time. This assumes you don't talk for too long before saying "over". A large transmitter heatsink and case does have significant thermal mass which helps.
The ARRL says; (ignoring the ratio of receive to transmit times)
Conversational SSB with no speech processing, uses a 20% duty cycle which includes voice characteristics and syllabic duty factor.
Conversational SSB with heavy speech processing, uses a 50% duty cycle which includes voice characteristics and syllabic duty factor.
Conversational CW, uses a 40% duty cycle
Voice FM, RTTY, FT8 use a 100% duty cycle.
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What we don't know from the simple "heat resistance" model are the time constants involved,
How quick do things heat up and cool down?
I never learnt this at University, never saw it discussed in my textbooks and when I asked a couple of mechanical engineering university lecturers about it, they didn't know either, Other than a cursory mention of thermal mass and their specific capacities. I put the calculation to one side as the one time I needed it I did a crude calculation and actually measured a time graph of the temperature rise, close enough in my specific case. I always thought that I must get back to that and research how to do it "properly".
Then along came a Youtube video by "FesZ", Riccardo Tinivella entitled "Static and Transient Thermal Models", you can find it at https://youtu.be/BGi_n28D8ro?si=CAK3EodXQ0U-wn-K
For the simple static cases of above, FesZ uses resistors and adds a voltage source to model ambient temperature and a current source to represent the source of energy (heat). Voltage is an analogy for temperature and the amps represents watts in the current source.
Even this "model" is useful if there are several sources of heat, the "circuit" then has parallel and series resistance between the several current sources and the one voltage source. You can see what each device case temperature gets to. LTspice does the calculation for you.
For the single device described above I made three models.
First I modelled the equation above and then added the case to air dissipation (R8), I then adjusted the given 62 degrees/watt to twice this value, reasoning that only half the case is exposed to the air and half connected to the heatsink.
So junction temperatures ranged from 155, 133 and 143 degrees for 10 Watts of dissipation, 100% of the time.
If we had two IRF510s, each dissipating 5 watts then the circuit, and corresponding temperatures would be as below; the junctions are now at just under 120 degrees. The heatsinks are a bit hot however.
If we replace the heat sink with something around 5 degrees/watt then the temperatures drop to
; with Heat sink of 5 degrees/wattV(heatsink_temp3): 70V(junction_temp3): 88V(device_case_temp4): 73V(ambient_temp3): 25V(device_case_temp3): 73V(junction_temp4): 88
Still a bit hot, try to get your heatsink down to 50, and keep an eye on junction temperature.
For an SSB transmitter that is transmitting uncompressed, unprocessed speech we can use 30% of peak power. Simply setting the current to 3 Amps (1.5A per device) gives us a thermal model for 10W PEP/3W average. The 3.5 degrees/watt heatsink is at 35 degrees and the junctions are at 40.
To really see the changes of temperature when pulses of power are applied, the dynamic changes of temperature requires knowing the heat capacity, the thermal masses of the devices, this is rarely given in the datasheets but FesZ shows devices that summarize the data and this is enough to model and produce graphs of temperature against time.
Some transistors have thermal models that are either a Pi network of series resistors and capacitors to ground or a ladder network of parallel RC pairs in series. Inserting this in the thermal models and using a pulse or changing current source allows plotting the peak temperature against time. You could even apply a .WAV file of speech to the current source. See FesZ video for a good example.
Two problems remain, sometimes the data is missing or given in an alternative form. and secondly the environment around the heatsink matters a lot. A heatsink contained within a small case or fed an airflow from a fan changes the figures dramatically. This is why heatsinks are often mounted outside the case but you must allow clear space above and below the heatsink so that convection can take place and the heated air rises away from the heatsink and ambient temperature air is drawn in.
You could use thermal data from a similar device in the same case/package. Better than nothing, but design conservatively.
As regards fans, there are graphs for some heatsink datasheets that give improved thermal resistance values for various flow rates. Again, assuming the fan is fed cool ambient air and pushes the hot air away.
The volume of a heatsink for a given flow condition can be obtained by using the following equation:
Volume(heatsink) = volumetric resistance (Cm3 °C/W)/thermal resistance θSA (°C/W)
An approximate range of volumetric resistance is given in the following table: (TI datasheet SLVA462)
(LFM) (Cm3 °C/W)
200 150 - 250
500 80 - 150
1000 50 - 80
The next important criterion for the performance of a heatsink is the width. It is linearly proportional to the performance of the heatsink in the direction perpendicular to the airflow. Considering an example, an increase in the width of a heatsink by a factor of two, three, or four increase the heat dissipation capability by a factor of two, three, or four.
Similarly, the square root of the fin length used is approximately proportional to the performance of the heatsink in the direction parallel to the airflow. In case of an increase in the length of the heatsink by a factor of two, three, or four only increases the heat dissipation capability by a factor of 1.4, 1.7, or 2.
If the board has sufficient space, it is always beneficial to increase the width of a heatsink rather than the length of the heatsink.
The full calculation for the combined thermal resistance of a fan and heatsink is so complex you are better to use an online calculator or apply some simple rules of thumb.
A (over)simple rule of thumb is that a fan will decrease the thermal resistance of a heatsink by a factor of two to four. But there are a lot of "it depends" things to think about.
The maths behind some of it is described at https://www.heatsinkcalculator.com/blog/heat-sink-design-optimization-for-forced-convection/ if you enjoy working with hyperbolic Tan functions and Reynold numbers then knock yourself out...
The same website covers using PCB as a heatsink, which is often overlooked but is important particularly when using surface mount components. (https://www.heatsinkcalculator.com/blog/how-to-calculate-the-thermal-resistance-of-a-pcb/) these uses Bessel functions, wild maths...
A much more sophisticated approach is to use proper thermal modelling software that uses "fine white elephants" to quote an in-phrase we used to confuse students with. FEM, (Finite Element Method) analysis breaks down a 3D shape into small sections and uses boundary conditions to create matrices to be solved by numerical methods. Often used for calculating and visually displaying mechanical stress or electromagnetic field strengths, it can also solve dynamic (and static) thermal flow problems.
FreeCAD has an FEM workbench although I have not yet gone down that rabbit hole, curiouser and curiouser...
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