Frequency - Reactance Nomograph
The frequency - reactance nomograph (chart) below was built on the Visio grid for accuracy, and since it is in vector format, the size can be increased or decreased without affecting the resolution. Clicking on the chart will allow you to download the file in .GIF format, which can be resized, but is not truly rescalable. It is 967x706 pixels and prints out nicely as a wall chart. The image to the right shows a full-size version of the right edge. Why not make the Visio file available? Right now it has a lot of extra stuff embedded in it that was used to make it accurate, and the .VSD file is almost 2 MB. It took many hours to create.
Accuracy of the chart can be easily verified with the standard capacitive reactance and inductive reactance formulas.
What is the inductive reactance of a 1 nH inductor at 1 GHz?
XL= 2π f L = 2π · 109 ·10-9
= 2π = 6.28 Ω
If you look at the small full nomograph, you will see that the bottom axis line is 1 Ω, and the second up from the bottom is 10 Ω. Follow the angled red 1 nH line to where it crosses the 1 GHz vertical line. Now, since the bottom line is 1 Ω and the next one up is 2 Ω. Note that the red line lies between the sixth and seventh lines. On a log scale, you will recognize that the intersection occurs at around 6.3 Ω - close enough for visual inspection.
The log-log format for the chart is used traditionally because it allows many decades (cycles) to be plotted in a relatively small area. If the black primary logarithmic scale was used on only one axis (either frequency or resistance), the component value lines (capacitor or inductor) would trace out parabolic curves that would make the log lines for the component values (blue and red) nearly impossible to draw accurately.