loss due to substrate conductivity
Updated March 30,
here to go to our main page on microstrip
here to go to our page on microstrip loss
here to our main page on transmission line loss
New for April 2007! Loss
due to substrate conductivity in microstrip was never really a problem
for engineers... until we started considering making stuff using
silicon as a dielectric! This is an important topic for the
Silicon is a semiconductor, as
opposed to a semi-insulator that GaAs is, or an insulator like alumina.
Silicon comes in many flavors, its bulk resistivity can be less
than 1 ohm-cm, to as high as 10,000 ohm-cm in special cases.
We don't have a neat, closed
form equation for this. So we used Sonnet
to analyze the problem. Note that EDA software such as ADS has no
way to account for substrate conductivity in their microstrip model.
But Sonnet cranks through 100 GHz of analysis on this problem in
ten seconds on a $400 Dell Dimension 4700, it's truly EM analysis
This page is obviously under
construction, but here's three plots for a 1mm line at various resistivities:
Here's 1000 ohm cm, or 0.1 Siemens/m.
This is a damn good transmission line, almost lossless, but 1000
ohm-cm silicon is hard to come by!
Here's the result at 100 ohm
cm. Now we have loss on the order of 0.5 dB/mm.
Here's the result at 10 ohm-cm
(10 S/m). Now the loss is going to kill you!
Time for a Microwaves101
rule of thumb!
In order to use silicon as a substrate, you need resistivity at
least 100 ohm-cm or the loss is going to eat your lunch.