What is the aspect ratio for 50Ω microstrip?:
Rule of Thumb #27
Eric Bogatin - May 04, 2016
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.
Remember: before you start using rules of thumb, be sure to read the Rule of Thumb #0: Using
rules of thumb wisely.
Previous: Rule of Thumb #26: The ringing period of reflections
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.
Also see:
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Bogatin's Rules of Thumb
How much is impedance affected by an adjacent trace?: Rule of Thumb #25
PCB’s top ground plane and its effect on a microstrip line’s characteristic impedance
Getting EMC design right – First time, Part 3: High-speed signals & Impedance
Additional information on this and other signal integrity topics can be found at the Signal Integrity
Academy, www.beTheSignal.com.