EDITS: 6/11/19 - Fixed broken links; Updated calculations for LM7805
Thermal Calculations
The biggie! In theory, the design should run without generating high temperatures but I want to be sure. I have calculated power dissipation and temperature rises for key components both at ambient and with a heatsink attached. I’m aware that ambient really reflects the ‘enclosure’ temperature, mitigated by passive ventilation (vents) and active ventilation (fan), but I selected 25 degrees C in these but tested values at 75 degrees C as well. I’m provisioning a thermistor to measure the ambient temperature so if I find it’s getting close (or exceeding) 75 C I can take action, e.g. get bigger heatsink if space allows or install a fan.
I set up a number of scenarios to calculate against:
Scenario 1: Load pulling 3A at 1V, 0.333Ohms
Scenario 2: Load pulling 3A at 15V, 5Ohms
Scenario 3: Load pulling 0.5A at 15V, 30Ohms
Scenario 4: Load pulling 1.5A at 15V, 10Ohms
Scenario 5: Load pulling 0.5A at 1V, 2Ohms
Ambient is set at 25C and the following heatsink choices were selected to give a range of thermal resistances:
Heatsink 1, Rha = 26C/W
Heatsink 2, Rha = 21C/W
Heatsink 3, Rha = 15C/W
Heatsink 4, Rha = 8.6C/W
Heatsink 5, Rha = 10.21C/W. This was an interesting catalogue item - a ceramic heatsink that sticks on and is very small dimension. Frankly, I don't trust it (the same Rha is given for all sizes it comes in) but I'm using the value anyway.
When calculating Pdiss, the formula used is
Pdiss = (Vin - Vout) * I
When calculating junction temperature, the formulas are
No heatsink: (Pdiss * Junction-to-Ambient resistance) + Ambient
Heatsink: (Pdiss * (Junction-to-Case resistance + heatsink resistance)) + Ambient
In these calculations I haven't taken account of thermal resistance of paste etc. I think if that made a difference, it is running too hot anyway. All parameters have come from data sheets or from simulation results from LTSpice as the scenario is executed. I've used BOLD to indicate a temperature the design can work with, and thus whether or not a heatsink is required.
Low Voltage Supply, LM7805, TO-220
The information and table below have been replaced with that following: these calculations do not take account of the current draw for the Arduino and thus are incorrect; the Rjc value is also incorrect.
Virtual junction temperature, Tjmax = 125C
Junction-to-Ambient Resistance, Rja = 19C/W
Junction-to-Case Resistance, Rjc = 17C/W
| Parameter | Scenario 1 | Scenario 2 | Scenario 3 | Scenario 4 | Scenario 5 |
|---|---|---|---|---|---|
| Vin | 23.8V | 23.8V | 23.8V | 23.8V | 23.8V |
| Vout | 5.03V | 5.06V | 5.06V | 5.06V | 5.06V |
| I | 0.011A | 0.012A | 0.011A | 0.014A | 0.014A |
| Pdiss | 0.207W | 0.225W | 0.206W | 0.262W | 0.262W |
| No heatsink, temp with Rja | 28.92C | 29.27C | 28.92C | 29.98C | 29.98C |
| Heatsink 1, temp with Rjc and Rha | 33.88C | 34.67C | 33.86C | 36.28C | 36.28C |
I haven't added calculations for other heatsinks as they don't help. Counter-intuitively, the heatsink makes it worse because the Junction-to-Case resistance is so high that adding on the heatsink resistance makes it worse. In any case, this part will not be problematic at these voltages/currents.
CORRECT CALCULATIONS
Virtual junction temperature, Tjmax = 125C
Junction-to-Ambient Resistance, Rja = 19C/W
Junction-to-Case Resistance, Rjc = 3C/W
| Parameter | Scenario 1 | Scenario 2 | Scenario 3 | Scenario 4 | Scenario 5 |
|---|---|---|---|---|---|
| Vin | 23.8V | 23.8V | 23.8V | 23.8V | 23.8V |
| Vout | 5.03V | 5.06V | 5.06V | 5.06V | 5.06V |
| I | 0.235A | 0.235A | 0.235A | 0.235A | 0.235A |
| Pdiss | 4.412W | 4.404W | 4.404W | 4.404W | 4.404W |
| No heatsink, temp with Rja | 108.83C | 108.67C | 108.67C | 108.67C | 108.67C |
| Heatsink 1, temp with Rjc and Rha | 152.95C | 152.71C | 152.71C | 152.71C | 152.71C |
| Heatsink 2, temp with Rjc and Rha | 130.89C | 130.69C | 130.69C | 130.69C | 130.69C |
| Heatsink 3, temp with Rjc and Rha | 104.42C | 104.27C | 104.27C | 104.27C | 104.27C |
| Heatsink 4, temp with Rjc and Rha | 76.18C | 76.09C | 76.09C | 76.09C | 76.09C |
| Heatsink 5, temp with Rjc and Rha | 83.28C | 83.18C | 83.18C | 83.18C | 83.18C |
Heatsink 4 would work although the temperature is higher than I would want - there's also no room for a heatsink of that size on the PCB. Instead, the part has been swapped for a DC-DC Switching Regulator which is a lot more efficient and should cause no thermal issues.
Current Source, LT3092, SOT223
Junction Temperature, Tjmax = 125C
Junction-to-Ambient Resistance, Rja = 24C/W
Junction-to-Case Resistance, Rjc = 15C/W
| Parameter | Scenario 1 | Scenario 2 | Scenario 3 | Scenario 4 | Scenario 5 |
|---|---|---|---|---|---|
| Vin | 23.80V | 23.80V | 23.80V | 23.80V | 23.80V |
| Vout | 1.40V | 15.32V | 15.32V | 15.32V | 1.28V |
| I | 0.001A | 0.001A | 0.001A | 0.001A | 0.001A |
| Pdiss | 0.03W | 0.01W | 0.01W | 0.01W | 0.03W |
| No heatsink, temp with Rja | 25.75C | 25.28C | 25.28C | 25.28C | 25.76C |
I haven't calculated with a heatsink as this part won't be problematic at these voltages/current.
Linear Regulator, LT3081, TO-220
Junction Temperature, Tjmax = 125C
Junction-to-Ambient Resistance, Rja = 40C/W
Junction-to-Case Resistance, Rjc = 3C/W
| Parameter | Scenario 1 | Scenario 2 | Scenario 3 | Scenario 4 | Scenario 5 |
|---|---|---|---|---|---|
| Vin | 2.93V | 16.21V | 15.72V | 17.18V | 2.90V |
| Vout | 1.04V | 15.19V | 15.47V | 15.38V | 1V |
| I | 1.53A | 1.47A | 0.26A | 0.78A | 0.26A |
| Pdiss | 2.89W | 1.5W | 0.07W | 1.41W | 0.49W |
| No heatsink, temp with Rja | 140.67C | 84.98C | 27.6C | 81.38C | 44.46C |
| Heatsink 1, Temp with Rjc and Rha | 108.86C | 68.48C | 26.89C | 65.87C | 39.11C |
| Heatsink 2, Temp with Rjc and Rha | 94.40C | 60.99C | 26.56C | 58.83C | 36.67C |
| Heatsink 3, Temp with Rjc and Rha | 77.05C | 51.99C | 26.17C | 50.37C | 33.76C |
| Heatsink 4, Temp with RjC and Rha | 58.84C | 42.39C | 25.75C | 41.25C | 30.64C |
I didn't calculate with Heatsink 5. For most scenarios, the LT3081 will run well within their Tjmax but scenario 1 clearly looks like it could be a problem without a heatsink. Even with Heatsink 3, that's a bit hotter than I'd like so I'm settling on Heatsink 4.
NPN MOSFET (Switching Regulator), IRF3205PBFIRF3205PBF, TO-220
Junction Temperature, Tjmax = 175C
Junction-to-Ambient Resistance, Rja = 62C/W
Junction-to-Case Resistance, 0.75C/W
Case-to-Sink, flat, greased resistance = 0.5C/W
Pdiss is calculated at 0.164W at full load - see the calculations for the LTC1624 on YAPS Part Four - Design - Calcuations (ii).
With no heatsink, temperature with Rja = 35.19C. I haven't calculated with heatsinks here as it isn't necessary.
Schottky Diode (Switching Regulator), MBRS340T3G, SMC
Junction Temperature, Tjmax = 150C
Junction-to-Lead Resistance, Rjl = 11C/W
Pdiss is calculated at 1.469W under short circuit - see the calculations for the LTC1624 on YAPS Part Four - Design - Calcuations (ii).
With no heatsink, temperature with Rjl = 41.16C. I haven't calculated with heatsinks here as it isn't necessary.
Bridge Rectifier, GBU603GBU603, SIP
Junction Temperature, Tjmax = 150C
Junction-to-Ambient Resistance, Rja = 7C/W
Junction-to-Case Resistance, Roc = 2C/W
Forward Voltage = 0.9V (per diode)
The data sheet specifies Rja and Rjc with an aluminium heatsink attached of dimensions 6.5x3.5x0.15 cms.
| Parameter | Scenario 1 | Scenario 2 | Scenario 3 | Scenario 4 | Scenario 5 |
|---|---|---|---|---|---|
| Forward Voltage, 2 diodes | 1.8V | 1.8V | 1.8V | 1.8V | 1.8V |
| I | 3A | 3A | 0.5A | 1.5A | 0.5A |
| Pdiss | 5.4W | 5.4W | 0.9W | 2.7W | 0.9W |
| Heatsink 4, Temp with Rha | 82.24 | 82.24 | 34.54 | 53.62 | 34.54 |
Not much point in doing calculations with this as the thermal resistance characteristics assume a heatsink of a certain size in place. Heatsink 4 matches that size pretty much although scenario 1 and scenario 2 are potentially problematic in terms of raising ambient inside the enclosure. I will use that and monitor via the thermistor what is happening - there is room on the PCB to get a bigger one if necessary.