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Rule of thumb: Aspect ratio for 50Ω microstrip

20 May 2016  | Eric Bogatin

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All 50Ω microstrip lines in FR4 have the same aspect ratio. Using a 2D field solver, we can explore what this ratio is for a specific value of Dk (dielectric constant) and conductor thickness.

Spoiler summary: The ratio of the line width to the dielectric thickness of a 50Ω microstrip in FR4 is about 2:1. This is a simple to remember, easy to use consistency check for your designs.

Most single-ended controlled-impedance interconnects are designed for a characteristic impedance of 50Ω. The historical reason for the use of 50Ω is related to the minimum attenuation in a coax cable and was driven by the early days of radar applications.

And even today, the use of 50Ω lines in printed circuit boards is a reasonable compromise between manufacturability, power dissipation, crosstalk control, and compatibility with driver technology.

Of course, the characteristic impedance of a line is completely independent of its length. We control the impedance of a line by specifying the cross-sectional geometry, and by materials selection. That's why 2D field solvers are so successful in designing the stack-up for transmission lines.

Based on the results from a 2D field solver, we can develop an easy to remember rule of thumb to guide our designs, and use as an important & quick consistency check of any other calculation.

It is only the aspect ratio and the Dk of the material that affects the characteristic impedance of a transmission line. The first order terms are the line width and dielectric thickness. The trace thickness is a second order term.

If we increase the width of a trace, its characteristic impedance should decrease. If we increase the dielectric thickness, the characteristic impedance should increase. If we do both, but keep the ratio constant, the characteristic impedance should stay about the same.

This suggests that all 50Ω microstrip lines on FR4 substrate should have the same aspect ratio. Using a field solver, this aspect ratio is found to be about 2:1.

Thus, rule of thumb #27 is:

For a 50Ω microstrip in FR4, the ratio of line width to dielectric thickness is 2:1. This is independent of the actual width or dielectric thickness.

Just how good is this rule of thumb? We can explore it using a 2D field solver. The perfect tool for this analysis is the Polar Instruments SI9000. We can set up a stack-up, fix a few parameters, and calculate the other parameters that result in a 50Ω line. I used the surface microstrip geometry shown in figure 1.

Figure 1: Microstrip cross section used in this analysis.

In this example, I set the Dk to 4.0 and the conductor thickness to half-ounce copper (0.6 mils). Then I swept the dielectric thickness from 2 mils to 20 mils and calculated the line width needed for a 50Ω single-ended impedance. I used no etch-back in the line. I exported the results to Excel and plotted the aspect ratio for each dielectric thickness that resulted in 50Ω characteristic impedance. This is shown in figure 2.

Figure 2: Calculations from the Polar Instruments SI9000 2D field solver for the case of a constant 50Ω microstrip. This shows the ratio of line width to dielectric thickness is about 2:1 for a 50Ω FR4 microstrip.

When the Dk is 4.0 and the trace is half-ounce copper, it is remarkable that the aspect ratio of a 50Ω line is so close to 2:1. This is a very easy to remember rule of thumb.

Of course, if the Dk were higher, or the conductor thicker, the aspect ratio would change. But it's still very close to 2:1 – close enough for a rule of thumb. Also shown in figure 2 is the aspect ratio for a higher Dk and thicker lines.

The next time your fab vendor comes back to you with a 50Ω microstrip design in FR4 with an aspect ratio of 1:1, consider finding another fab vendor.

About the author
Eric Bogatin is Signal Integrity Evangelist at Teledyne LeCroy.

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