Max Current
5.6 Thermal Runaway with Constant Current
The IPC 2152 recommendation for the maximum current that should be used in a 13 mil diameter through-hole via is less than 3 A. This is the same estimate as for a 20 mil wide trace. Of course, it depends on the local thermal environment of the via, but it is safe to assume the maximum current handling for a 13 mil via is 3 A. If more current is required in an application, such as when transporting a 10 A current, assume 3 A per via, which would require 4 vias in parallel between any power trace transitioning from one layer to another, which would carry the full 10 A.
5.6 Thermal Runaway with Constant Current
There are generally two types of power sources: constant voltage and constant current.
In a constant voltage supply, the output voltage is controlled with internal feedback to keep the output voltage constant regardless of the load. This means that even if the current draw changes due to a changing load resistance, the output voltage will stay the same.
This is the most common type of power supply. AC to DC converters are generally constant voltage supplies. A low drop out (LDO) regulator is a constant voltage supply. A battery is basically a constant voltage supply.
The output impedance of an ideal, constant voltage supply is very low. No matter the current, the output voltage change is nearly 0 V:
output
V ~ 0
Z 0
I I
= = =
The second type of power supply is a constant current supply. In this type of supply, the output voltage is continually adjusted by internal feedback circuitry to keep the current coming out of the supply and through the external load constant. If the load resistance decreases, the output voltage decreases to keep the current through the load
constant. If the load resistance increases, the output voltage increases to keep the output current constant.
Of course, there are limits to the max voltage that can be used with a constant current supply. If the load resistance increases so much that the supply can’t provide a high-enough voltage to keep the current constant, the supply switches to constant voltage (CV) mode. But, if the current can be provided with an output voltage below the max voltage setting, the supply stays in the constant current (CC) mode.
The output impedance of an ideal constant current supply is surprisingly very high:
output
V V
Z I ~ 0
= = =
When PCB traces are driven by a constant current supply, as was done in the experiments measuring the temperature rise of traces, there is a potential behavior that can arise which can result in the temperature of a trace increasing on its own, high enough to smoke, melt, and potentially act like a fuse and open. This effect is called thermal runaway.
The resistivity of copper is temperature dependent. The higher the temperature of the copper, the higher its resistivity. The figure of merit that describes this property is the temperature coefficient of resistance, . For copper, it is about 0.4%/degC.
If the copper temperature rises, because the ambient temperature rises by 10 degC, the resistance of a copper interconnect will increase by 0.4%/degC x 10 degC = 4%.
The resistance of a copper trace, which includes the temperature dependence, is:
( )
R=R 10 + T
5.6 Thermal Runaway with Constant Current 135
Where:
R = the resistance at any temperature above ambient R0 = the resistance at ambient temperature
= the temperature coefficient of resistance of copper
T = the temperature above ambient
If a constant current supply is used to drive a current through the copper trace, as the temperature rises, the resistance increases but the current would be the same. The same current through a higher resistance means the power dissipation increases, which increases the trace temperature.
The increased temperature further increases the resistance, and the power consumption increases even more. If the current is over a threshold, the temperature will continue to rise indefinitely until the wire gets so hot as to melt, fuse, and open up: a thermal runaway.
This condition can be illustrated by adding the temperature dependence of the resistance to the above analysis:
( )
2 2 2 2
0 0 0
T I R I R 1 T I R I R T
= = + = +
After a little algebra, the temperature rise over ambient is:
2 0 2
0
T I R
1 I R
=
−
This says that when the current increases, as I2 R0 approaches , the denominator gets smaller and the temperature difference explodes. At this point, the temperature will rapidly increase. This is thermal runaway.
The condition for the current required to instigate a thermal runaway is when the denominator explodes, or,
2 0
0
1 I R 0 or I 1
− = = R
Small features of the thermal environment of the board that affects the thermal resistance can have a large impact on the temperature rise and the current when thermal runaway begins.
This behavior is easy to observe. When a constant current supply is used to drive a fixed current through a copper trace, the voltage across the trace is directly related to the instantaneous resistance:
V= I R
Since I is held constant by the power supply, the voltage is a direct measure of the resistance. As the temperature increases, so will the resistance and the measured voltage across the trace.
To measure the thermal runaway effect, the 6 mil trace was driven by a constant current power supply while the voltage across the trace was measured with a scope. This experimental set up is shown in Figure 5.5.
5.6 Thermal Runaway with Constant Current 137
Figure 5.5 Measurement system to apply a constant current to a 1-inch ling trace and measure the voltage across it with a 10x scope probe.
Below a current threshold, the resistance of the trace did not change as the current changed. The interconnect did not heat up and the resistance was constant.
When enough current was passed through the trace to heat it above ambient, the temperature rose to a higher equilibrium value, but then remained constant. When the wire was touched, the
temperature momentarily dropped, the resistance dropped, and the voltage across the trace decreased. Figure 5.6 shows an example of the measured voltage across the 6 mil wide trace with 3 A DC, constant current. The trace was hot to the touch.
Figure 5.6 Measured voltage across the trace with 3 A constant DC current. The voltage was stable for 80 seconds and the wire was touched, decreasing its temperature, its
resistance, and the measured voltage.
Even a current of 3.5 A through the 6 mil wide trace, while making the trace hot to the touch, did not start a thermal runaway. However, when the current was raised to 3.9 A, the thermal runaway condition was met. The temperature increased continuously until the trace got red hot, smoked, melted, and then fused open. Figure 5.7 shows the measured voltage that is proportional to the resistance which is proportional to the trace’s temperature and the trace’s power dissipation under constant current.
5.6 Thermal Runaway with Constant Current 139
Figure 5.7 A DC current of 3.9 A through the 6 mil wide trace initiates thermal runaway and the temperature increases for almost 3 minutes before it fuses open.
This is a danger in constant current circuits with conductors having a positive temperature coefficient of resistance. If the current is above a threshold value related to the thermal resistance to the environment, it is possible for the temperature to increase on its own to a catastrophic end.
This behavior is not possible with a constant voltage supply. In this case, as the temperature of the trace increases and the resistance increases at constant voltage, the current will actually decrease and the power consumption will decrease. The power consumption self- limits at constant voltage.
While it is possible to melt a trace using a constant voltage supply by raising the voltage so the current through the traces exceeds 4 A, it may require small increases to the output voltage. As the trace heats up, it will decrease the current and the power consumption and self- limit the temperature rise.
Watch this video and I will show the maximum current through a narrow trace and demonstrate thermal
runaway.