Trace width of a Printed Circuit Board (PCB) is a basic yet very crucial parameter which needs to be defined while designing a PCB. Calculation of trace width is important for both power and signal boards. This parameter defines the current carrying capacity of a PCB. Before going into the details of trace width, it is important to look at the factors which limit the flow of current through a conductor. Any conductor with a specific (cross sectional) area ‘A’ carrying the electrical current ‘I’ offers an electrical resistance of ‘R’ towards the flow of current. The electrical resistance results in the loss of electrical energy into the heat dissipation which depends on the square of the current flowing through the conductor (hence these losses are known as I2R losses). With the rising current, the heat dissipation also increases and beyond a certain point excessive heat results in failure of the current carrying conductor. To reduce the heat dissipation (I2R losses) in the conductor the resistance needs to be decreased. Electrical resistance of a conductor is inversely proportional to the area ‘A’ and directly proportional to the length ‘L’ of the conductor.
‘ρ’ is the electrical resistivity of the conductor material under consideration. For copper, the resistivity is 1.7x10-8 (ohm-m). If the length needs to remain constant, area can be increased to reduce the electrical resistance. Or in other words, increasing the area of the conductor increases its current carrying capacity (by reducing the heat losses or I2R losses).
This methodology of increasing current carrying capacity through increase in area now can be extended towards PCBs as well. ‘Traces’ on a PCB (sometimes also referred to as tracks) are the copper electrical connections responsible for carrying the electrical current. Due to the two-dimensional nature of a PCB circuit, the ‘width’ of traces is used to define the maximum amperage of a PCB board rather than the cross-sectional area (as height becomes a constant after choosing a thickness of copper). The formula for calculating the trace width is derived from following mathematical expression below (published in IPC-2221 standard):
I= Maximum current (A)
dT= increase in temperature above ambient (°C)
A= cross-sectional area (mils2)
‘k’ is constant which depend on the position of traces on the board
k (for internal traces) = 0.024
k (for external traces) = 0.048
Reason for different values of k is that the traces on the outer side of the PCB have a better chance of heat dissipation through the process of convection as compared to the internal layers. As a result of that, heat starts to accumulate on the internal layers. Higher value of ‘k’ for the internal layer means wider trace width which helps dissipate the accumulated heat. However, if the circuit is placed inside complete vacuum, the outer layers cannot lose heat through the process of convection. So, while designing PCBs in a vacuum, same value of ‘ k ’ needs to be chosen for internal and external layers i. e. 0.024.
The exponents of ‘dT’ and ‘A’ are a result of physical constants of copper such as resistivity of copper and temperature coefficient of copper. Area of trace (mil2) can be calculated by rearranging (2) as shown below:
With a chosen thickness ‘T’ (mils), the trace width ‘w’ (mils) can be calculated:
Figure below depicts the (for a contact thickness of 1oz or 35 um) current capacity against the calculated trace width for different changes in temperature from ambient.
Although the formula in the equation (4) does not have a mathematical limit, its accuracy keeps decreasing with higher values of current and trace width. For values of current higher than 35 A for outer traces 17.5A for internal traces or trace width higher than 400 mil, this formula will result in significant error value. Additionally, the mathematical formula to calculate the trace width does not keep into account some other factors such as count of components, vias and pads in the circuit. And finally, factors like dust are also taken into account in large scale production of PCBs. This mathematical formula also assumes that the components do not cause any hindrance in heat dissipation. That’s why an additional buffer is added to the calculated value to avoid complexities arising from external factors.
It is also important to maintain proper spacing between the traces to avoid any transient short circuit condition in power circuit boards or signal interference in signal boards. A general rule is to maintain spacing between two parallel running traces which is three times the trace width. Location of power, ground and signal traces on the board is also important. It is recommended to strategically place the power traces and not have the power traces go from one component to the other in a complex daisy chain configuration. In nutshell, calculation of proper trace width according to the expected current requirements of your board is an important step for the continuous operation of a PCB within safe operating temperature range.
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