here to go to our page on conductivity
here to go to our page on transmission line losses
Why are there
two conductors on this high power line?
Additional explanations of skin
depth and its effects on microwave circuits can be found here:
sheet resistance (first read about "DC"
sheet resistance here)
sheet resistance examples
Skin depth is one of the most
fundamental issues in microwave engineering, but it also affects
lower frequencies, even 60 cycle AC power. The skin
depth equation is as relevant to microwave engineering as Newton's
law (F=mA) is to physics.
This is one of the best discussions
of skin depth effects anywhere, including the entire searchable
microwave paper collection of the IEEE.
We know, because we did the search! Along with this discussion we
offer a download that calculates
equivalent RF sheet resistance for metals that have up to three
different layers. If you are a thin film vendor and would like to
sponsor this outstanding page and beat your competitors to the punch,
By the way, we use the metric
system for this discussion, and in the download. Why? because there
are no popular units of bulk resistivity in the English system.
Regarding skin depths and thin film thicknesses, if you want to
convert from microns to micro-inches exactly, divide microns by
0.0254. There are approximately 40 micro-inches in one micron, that's
close enough when you are dealing with plating.
Here is a clickable index for
this web page:
of skin depth - a timeless story
- what is it?
that power line...
of skin depth - a timeless story
The topic of skin depth is a
misunderstood one, but we are going to end that right here and now.
Every time microwave engineers encounter a new frequency band or
a new metalization scheme, there is some question over RF losses
in transmission lines such as microstrip. Often "experts"
start in on the discussion, and it goes like this...
"Hey Bert, the gain on
that new design stinks, what's the problem? Did you change anything
from the last design?"
"Nothing major, Ernie.
Except we did go to a new thin film vendor... outsourced to Pakistan.
There was a language barrier, don't know if they were able to
understand the plating specification. The assemblers love it,
they say the gold plating is 'hard as a rock'!"
"Oh jeez, sounds like
a skin depth problem. We're just process people, we don't know
nothing about RF. Go get the Wally, the old fart who saved that
low frequency X-band job for us 20 years ago!"
Later when Wally shows up for
work around 10:30 AM, and is interrupted from his daily manicure
with a pocket knife...
"Oh Great One, can you
tell us if we have a problem with the deep mystery of skin depth?"
"While you are filling
my coffee cup, let me scratch up one of your parts with my disgusting
but still very cool Microwaves101 pocketknife... yes, here's the
problem, it's nickel plating!"
"Yes, we knew about that
when it was in process, but we fixed it by tripling the gold plating
requirement. There's 300 microinches of gold there, it's gotta
be low loss!"
"You don' unnerstand...
it don't matter if there's more gold there than in Priscilla Presley's
wedding ring! You're in a pickle and that there gold ain't gonna
fix it no how! If you whippersnappers would get off that newfangled
E-M software baloney and learn you some fundamentals, maybe our
stock price would rise enough so I could afford to retire, dagnabbit!
I gotta go, it's time for my nap now!"
The same conversation is heard
many times around the country each year, and thousands of man-hours
are wasted, often with expensive design-of-experiments where egghead
test engineers try to measure the effects of different plating schemes,
or worse, EM freaks try to model the effects using electromagnetic
analysis software. By reading this web page the heartbreak of skin
depth need not affect anyone's pay raise ever again, even if you
are "just a process guy".
- what is it?
Skin depth is a measure of how
far electrical conduction takes place in a conductor, and is a function
of frequency. At DC (0 Hz) the entire conductor is used, no matter
how thick it is. As you double the cross-sectional area of a wire,
the DC resistance per unit length decreases by half, as you'd expect
according to Ohm's law. At RF frequencies, the effect that conductor
thickness has on its conductance is nonlinear (actually, a negative
exponential.) There is a limitation on the conductance that you
can achieve, and increasing the thickness of precious metals to
reduce losses RF can be a waste of money if you don't know what
you are doing.
One common misconception about
skin depth is which surface of a conductor is carrying the RF current.
It is always (mostly*) the surface nearest the media in which the
EM wave propagates. Illustrated below in a cross-section of microstrip,
the RF currents are highest in the lower surface of the microstrip
line. That is why the first metal is most important to conductivity
in a microstrip multi-metal stack-up. Please note that for waveguide,
the opposite is true; it doesn't matter what you underplate with,
the surface plating is what counts.
* There are some fields on
the top of microstrip line, but at much lower intensity.
We propose to analyze this in April 2009 and create a page on
the topic. Here's a page on microstrip
loss which helps explain the concept.
The well-known equation is for
skin depth given below. Note that skin depth
is a function of only three variables, frequency (f ), resistivity
and relative permeability (R).
Bulk resistivity is a measure
of how resistive a material is. It is the reciprocal of bulk conductivity.
Click here to look up your favorite
metals' conductivities. And click
here to try out our skin-depth calculator.
Believe it or not, conductors
can become thinner at higher frequencies with little impact on circuit
loss, because the skin depth shrinks with frequency. Although the
sheet resistance of metalization always increases with frequency,
the RF loss per wavelength can actually decrease. Thus 150 microinches
of gold on alumina thin-films at X-band can be thinned to half that
for millimeterwave applications to save money without compromising
performance. A branchline
coupler at Q-band will have less loss in dB than one designed
for L-band! Millimeterwaves are so cool...
It's time for some Microwaves101
Rules of Thumb!
of thumb: always plan on providing at least five skin depths
of low-loss conductor. This will keep more than 99% of your
electrons happy and provide good performance without wasting
of thumb: when using copper-clad boards, you usually won't
have to give skin depth another thought, because you will
have at least 700 microinches of copper (1/2 ounce) on both
sides, which is five skin depths down to 330 MHz.
that power line...
Most engineering problems only
consider skin depth at microwave frequencies. Let's look at a wider
Notice that when
you plot different conductors this way, they don't look much different.
At 60 Hertz, no matter what the conductor, the skin depth is about
1 centimeter. That means that a power line 10 centimeters in diameter
will satisfy the "five skin depths" rule (radius is 5
centimeters). Bigger than that and you are wasting copper. So to
decrease losses on long high-tension runs, power companies sometimes
hang double, and even triple wires for each power phase.
But wait! There's
more to that power line than meets the eye. This information came
from Jeff, in November 2010. Thank you sir!
There may be some small
savings on resistance due to skin depth but considering there
is no electric field between the adjacent lines (in the same phase),
this would not justify the added expense. The reason for using
multiple cables on a single phase is to increase the equivalent
radius (aka GMR, geometric mean radius) of the cable. This in
turn both raises the distributed capacitance and increases the
breakdown voltage (the sharper the edge, the lower the breakdown
voltage). Thus, two small, cheap cables are electrically the same
as a thick, expensive cable.
Where skin depth does help
in 60 Hz power transmission is in cable strength. Rather than
make the cables out of pure aluminum, a steel core is added for
strength. Since steel has a non-unity relative permeability, this
has a significant effect on skin depth. The 60 Hz power guide
is kept mainly in the aluminum outer cladding while the core provides
the physical backing for the cable.
Long ago, there
was great debate about whether power should be distributed as direct
or alternating current. Read
about it here!