here to go to our page on skin depth
here to go to our page on RF sheet resistance
here to go to our main page on microstrip
here to go to our page on microstrip loss
New for December 2010!
We are finally going to tackle this subject. Come back later please,
we're still working on this! Check out this unrelated topic,
A Rough Justice!
Surface roughness is often the
answer to the question "where did all this loss come from?",
it can be a problem for thin-film
networks and printed wiring
boards alike. When we are discussing roughness, it is typically
in the context on microstrip circuits. Roughness is a double-edged
sword for sure, the rougher the interface between the metal and
the substrate, the better the adhesion, but the higher the attenuation.
A common mistake that new engineers
make when they first hear about surface roughness increasing conductor
loss, is that it's the a problem on the top surface of the metal
in microstrip (the surface you can see). But as we all come to know,
its the surface that you can't see that matters most.
Let's go out to the Microwaves101
laboratory, and listen in as Wally encounters Pasquale working on
his latest design:
Wally: What in tarnation
are you doing there, son?
Pasquale: I'm trying to
polish the metal on the top of my filter, and the gold is smearing
Wally: Where did you get
the notion to do something foolish like that?
Pasquale: Well, my X-band
filter has twice as much loss as the simulator said it would,
and Evita said it was because of surface roughness of the metal,
and she's usually right. Funny, the metal didn't look rough under
the microscope until I tried to polish it with the brillo pad!
Wally: Well, she's always
been right to look at I reckon! Say, where did you get the alumina
for that filter?
Pasquale: Eew, don't say
that about Evita, she's older than my mom and her jewelry is so
clangy! She must be pushing forty! But check out my new ascot...
The alumina came from right here, it was a free sample, and it
says 93% pure, unpolished. Is that good or what?
Wally: It seems any fool
can design a filter these days with that newfangled software.
But it seems that this fool can't build one! Let me set you straight...
but first, who the Hell is Ed Hardy and why are you wearing his
Surface roughness has a big effect
on metal loss. When roughness becomes on the order of skin depth,
attenuation of transmission lines increase. It's semi-predictable,
however, there is no exact calculation of the effect, and surface
roughness by itself is not easy to quantify into a single number.
Although an RMS value is typically used, the geometry of the roughness
is rarely regular or random. Indeed, the roughness could give way
to anisotropic attenuation,
as polishing marks may be more pronounced in the x-axis than the
Recall that the surface conductivity
(or RF resistivity) of a metal film is a function of frequency,
as conduction decreases exponentially from the surface into the
film. Let's make a table of the incremental conductivity versus
at the surface, conductivity
at one skin depth, it is decreased
at two skin depths, 13.5%
at three skin depths, 5.0%
at four, 1.8%
at five, 0.7%
So if you have five skin depths
of metal, you have pretty much captured all of the conduction you
can. Until you mess up the surface.
The roughness of the conductor
interferes with conduction. But it isn't as simple as integrating
the conductivity of remaining, "non-rough" metal. RF currents
seem to find a way up and down the hills and valleys. It's possible
is to observe the attenuation of like structures of various roughness
(roughni?), and come up with an empirical formula for the increase
The most often quoted reference
on increased attenuation in microstrip due to surface roughness
is E. O. Hammerstad and F. Bekkadal, A Microstrip Handbook, ELAB
Report, STF 44 A74169, University of Trondheim, Norway, 1975,
pp 98-110. They provided
an empirical formula for the increase in alpha-c (attenuation constant
due to conductor loss), for microstrip, that came from curve fitting:
where alpha-c' is the attenuation
due to conductivity, after it is increased by roughness, and
delta is the RMS roughness.
It is scary that we have to point
this out, but the units for tan-1 should be in radians,
not degrees... You'll notice that the equation can only increase
alpha-c by a maximum factor of two, even if the roughness is greater
than the skin depth.
We don't have that reference
(yet!), but we'll guess that this was valid when the total thickness
of the metal was many skin depths.
We plotted the function below:
And here are some numerical values
for those readers that are too lazy to try out the calculation:
When RMS roughness is approximately
equal to skin depth, conductor loss is increased by 60%. When roughness
is much more than skin depth, conductor loss is 2X what is could
be under ideal conditions (100% increase).
Surface roughness of typical
Some entries are from Foundations
for Microstrip Circuit Design by Terry Edwards, a Wiley book.