-
- News
- Books
Featured Books
- design007 Magazine
Latest Issues
Current IssueLevel Up Your Design Skills
This month, our contributors discuss the PCB design classes available at IPC APEX EXPO 2024. As they explain, these courses cover everything from the basics of design through avoiding over-constraining high-speed boards, and so much more!
Opportunities and Challenges
In this issue, our expert contributors discuss the many opportunities and challenges in the PCB design community, and what can be done to grow the numbers of PCB designers—and design instructors.
Embedded Design Techniques
Our expert contributors provide the knowledge this month that designers need to be aware of to make intelligent, educated decisions about embedded design. Many design and manufacturing hurdles can trip up designers who are new to this technology.
- Articles
- Columns
Search Console
- Links
- Events
||| MENU - design007 Magazine
Trace Currents and Temperature, Part 2: Empirical Results
March 6, 2013 |Estimated reading time: 10 minutes
This column originally appeared in the December 2012 issue of The PCB Design Magazine.
The first part of this series (available here) ended with two models for analysis, Equations 6 and 7, repeated here as Equations 1 and 2. Equations 1 and 2 have been modified slightly from those in Part 1 by the inclusion of a proportionality constant, k. Recall that the difference between Equations 1 and 2 is the inclusion of form factor in the latter, by breaking the area term into its width and thickness components.
I = k*ΔTβ1 * Aβ2 [Eq. 1]
I = k* ΔTβ1 * Wβ2 * Thβ3 [Eq. 2]
Where I = current
ΔT = change in temperature
A = area
W = trace width
Th = trace thickness
Empirical Testing
I have tested this model with three sets of data. The first is the original IPC data we all know and love. Most of us know it by IPC-2221, “Generic Standard on Printed Circuit Board Design.” Its curves were also published as IPC-D-275. Mike Jouppi has spent considerable time and effort in reviewing this data and resurrecting significant aspects of its history [1]. Perhaps most notable was the following:
- The data were first published in 1955 under NBS Report 4283. It was known that there were some variables that needed further study, so the original charts were labeled “Tentative.”
- Further studies were never funded.
- The original charts were redrawn and republished many times through the years, and the word “Tentative” was dropped somewhere along the way.
- Although the original tables included curves for both external and internal traces, data were taken only for external traces. The data for internal traces were derived simply by derating the data for external traces by 50%.
There are several shortcomings to this original data. One in particular is the lack of information contained within the charts reflecting the form factor of the traces under study.
A second set of empirical data was found in an article by Friar and McClurg, published in Design News back in 1968 [2]. There are two reasons to include this data in an analysis. First, there are not many sources of published data to choose from! Second, the data purport to analyze the relationship including the form factor of the traces. This data will be referred to in this column as the Design News data or simply by the initials DN.
Finally, IPC has recently published a new (fully revised) standard, IPC-2152 “Standard for Determining Current Carrying Capacity in Printed Circuit Board Design (August 2009).” Jouppi, among others, was very instrumental in creating this new standard. The main body of the standard has a Figure (5-1) which is representative of all traces. Well over 100 charts are included in the Appendix for readers who want to fine tune the results in varying ways. This standard purports to take form factor into consideration (something that can be derived from the charts in the Appendix).
Empirical results will be shown for these three data sources.
Procedure for Analysis
While original, detailed data is difficult to come by; charts are readily available for all three sources. Therefore, it is possible to read data points off the charts. Statistical regression analysis can be used with these data points to estimate and derive the underlying relationships and equations. This would have been somewhat difficult a generation ago, but modern spreadsheets now provide very powerful statistical analysis capabilities that allow us to do things like this easily.
There is the underlying question of whether the charts can be read with enough precision to proceed. While there will certainly be errors in reading the data points, there are three compelling factors that allow us to proceed:
- Errors will be relatively minor.
- More importantly, errors should be randomly distributed, and therefore will not add any bias into the results.
- The magnitude of the errors can be inferred from various statistical measures, in particular the standard errors (and R2 values) of the analyses.
These topics are beyond the scope of this column, but people with a statistical background will recognize what is said here and be comfortable with the approach.
Empirical Results
The empirical results for the three data sources are shown in Equations 3 through 8.
Looking first at the results that do not consider form factor, Equations 3, 5, and 7, two things are apparent. First, the exponents for the terms are pretty close for each source. They are not exact, but considering all the variables involved, they are very close. This means we can have a fairly high degree of confidence in the shape of the curves. By that I mean that the curves from each data source seem to have roughly the same slopes and curvatures.
On the other hand, the proportionality factors (the “k’s” in the equations) are, at least in some cases, remarkably different, especially for the DN data. The proportionality factor defines the location of the curves (as opposed to the shape of the curves). The result is that we can have confidence in the shape of the curves, but not as much in the location of the curves.
When we look at form factor information (Equations 4, 6, and 8), we see several things. First, Equations 3 and 4 for the original IPC data are virtually identical. That is, there is no form factor information whatsoever. This is not unexpected, since independent data for form factor was not collected. And this fact is readily apparent in the result.
In the DN data, however, there is a significant difference in the shapes of the curves involving form factor. Thus, the DN data implies form factor is very important. There is also an anomaly in the DN data. The data for 1-oz and 5-oz traces follow almost identical curves (Equation 6), but the 2-oz curves (Equation 6a) have a significantly different proportionality constant. There is no obvious explanation for this, but I suspect it reflects a lack of control over the test procedures for 2-oz traces. More on that later.
The results for the current IPC data seem to follow in between the other two results. The differences between Equations 7 and 8 seem to suggest that including form factor makes a difference in the results, but the difference is not as pronounced as in the DN case.
Potential Reasons for Differences
There are differences in the test procedures in the three cases. But not all the differences are reported or known. Some of the differences are shown in Table 1.
Table 1. Some differences in test procedures in the three data sources.
The test boards were hung vertically in the original IPC study, but placed horizontally in the DN study. I believe the current IPC test procedure follows the early study’s procedure. Mike Jouppi has shown that it can take up to five minutes for a trace to stabilize after a change in current [3]. Reportedly the early study procedure only allowed the temperature to stabilize for 30 seconds. The time is not reported in the DN study. Interestingly, the DN data is more conservative [4] than the early IPC data, consistent with a longer stabilization time for the DN data. The stabilization time for the current IPC data is not reported, but I am told there was “sufficient time” for the temperature to stabilize.
Perhaps the most significant difference in test procedure is the method in which the trace temperature measurement is made. The IPC studies infer the temperature by the change in resistance. Refer back to Part 1 of this series for a discussion of the thermal coefficient of resistivity (i.e., how resistance changes with temperature). The DN study reportedly infers the change in resistance using an infrared microscope.
Figure 1. Differences in temperature measurement.
Both approaches are legitimate ways to measure temperature, but they sometimes may measure different things. The change in resistance approach measures the average temperature across the entire cross-sectional area and length of the trace, while the infrared microscope measures the temperature at a precise spot along the surface of the trace. One might argue that the infrared approach might result in higher overall measurements than the change in resistance approach. This would also be consistent with the fact that the DN results are more conservative [4] than the PC results.
Finally, each temperature measurement approach has its own inherent parameters that must be controlled or calibrated. The change in temperature approach requires a fairly precise knowledge of the thermal coefficient of resistivity for the trace material. This parameter is highly dependent on the particular alloy of copper used. On the other hand, the infrared approach is highly dependent on the reflectivity of the surface of the material being tested. Typically infrared microscopes must be calibrated before each measurement. Errors in adjusting for the reflectivity can significantly impact the results. One might speculate that this might be one reason why the 2-oz DN results are so different from the 1-oz and 5-oz results.
Rationality of the Results
Here is an interesting exercise. Take the results for the form factor equations (Equations 6 and 8), rearrange terms, approximately square both sides (e.g., (W.57)2 is approximately W), and recognize that A = W * Th, and that R ≈ 1/A. The last line in the table shows the results.
Table 2. An interesting exercise.
The IPC data suggests that the change in temperature is directly proportional to i2R (i.e., heating only). The DN results suggest that the change in temperature is directly proportional to i2R and inversely proportional to the square root of the width (i.e., heating and cooling). The DN results are more consistent with our form factor model introduced in Part 1 of this series.
What is the Truth?
So what is the truth here? Which equations are correct? Those of us in engineering always want to know what the answer is! Well, here’s my take: Beats the heck out of me!
Here are some considerations:
- The DN data fit the form factor model better. That is comforting.
- We will see in Part 3 that the DN data also fit the fusing current models better, although there will be some qualifications to that statement when we make it.
- The current IPC data were taken under probably the best controlled conditions ever, by responsible researchers, with the most resources devoted to this type of investigation. They ought to be the most reliable.
- Perhaps most importantly, the original IPC data have passed the test of time for over 55 years!
Bottom line: There are many factors that impact the trace temperature relationships. While we can be pretty comfortable with the shape of the relationship, the location of the curves (i.e., the proportionality constant) depends on so many things that there may not be a universal truth. As uncomfortable as that sounds, that may be the practical reality.
Calculator
UltraCAD has released a calculator based on Equations 3 through 8 that can be used to make trace temperature calculations [5]. Five different data sources can be used for evaluation, the current IPC-2152 data for internal or external traces in air and for traces in a vacuum, the original IPC data (from IPC-D-275) or the Design News data. The user can enter any three of four parameters (width, thickness, current, and temperature change) and the calculator will calculate the fourth. The calculator also has provision for including the skin effect, if that is a consideration [6].
Figure 2. UltraCAD’s PCB Trace Calculator.
In Part 3 of this series we will look at fusing current, the amount of current necessary to just melt a trace.
References
- “Current Carrying Capacity in Printed Circuits, Past, Present, and Future,” presented at IPC Printed Circuits Expo, March 25, 2003.
- “Printed Circuits and High Currents,” Friar, Michael E. and McClurg, Roger H., Design News, Vol. 23, December 6, 1968, pp. 102 - 107.
- “Thermal Characterization of Electrical Conductors in Multi-Layer Printed Wiring Boards in Space Environments,” Michael R. Jouppi, staff engineer, Lockheed Martin, Denver, Colorado.
- “Conservative” in this context means that a given change in temperature is associated with a smaller current with the DN data than with IPC data.
- Available for download at www.ultracad.com. Click on menu item “Calculators.”
- See my column series on skin effect here.
Douglas Brooks has an MS/EE from Stanford University and a Ph.D. from the University of Washington. He has spent most of his career in the electronics industry in positions of engineering, marketing, general management, and as CEO of several companies. He has owned UltraCAD Design Inc. since 1992. He is the author of numerous articles in several disciplines, and has written articles and given seminars all over the world on signal integrity issues since founding UltraCAD. His book, Printed Circuit Board Design and Signal Integrity Issues was published by Prentice Hall in 2003. Visit his website at www.ultracad.com.