here to go to our main page on transmission lines
here to go to our main page on transmission line loss
here to go to our Why 50 ohms? page
New for October 2007!
He's information on minimizing loss of transmission lines, which
is expressed as the attenuation factor in units of dB/length or
Nepers/length. Of course, once you deviate from 50 ohms, you'll
need to add transformers to get back to 50 ohms because it is the
widely accepted standard for everything. OK, 75 ohms is also a standard,
but it is not used as much as 50 ohms.
Coax transmission lines exhibit
a well-known minimum in attenuation versus line impedance. At zero
ohms the loss/length is infinity, the same is true at infinity ohms.
Air coax has its minimum attenuation
at 77 ohms. It is believed that this phenomenon is what caused the
75 ohm impedance standard for cables. The plot below is for air-coax,
outer conductor D=0.049 inches, copper conductors, at a frequency
of 10 GHz. Minimum loss is a little more than 0.5 dB for a foot
of this cable (which you can't buy anywhere, no one makes air coax
Remember, the minimum attenuation
feature is also a function of the coax dielectric constant. For
PTFE-filled cables, the minimum attenuation is nearly at 50 ohms
(52 ohms by our calculation, which you can verify when you download
our coax calculator Excel file!).
So, what's the story with microstrip
and stripline? Is there a sweet spot on the impedance/attenuation
function? We'll spoil the ending, the answer is "no!"
The equations for microstrip
are quite complicated, we'll avoid them and rely on Agilent's ADS
software to look into this. We used a well-known microstrip media,
10 mil alumina circuit with gold conductors, at 10 GHz.
The minimum attenuation is at
Z0=0 ohms. Not only is this a useless impedance, but it seems strange
that there is a finite loss under these conditions (shouldn't it
be either zero or infinity?) What's going on here? Recall the loss
per length calculation, resistance/length appears in the numerator,
while characteristic impedance is in the denominator. Both are decreased
as the line width increases, but not exactly proportionately.
You could build up a closed
form equation for microstrip loss/length as a function of line width,
then take the limit as W goes to infinity and you'd come up with
the non-zero value of attenuation at Z0=0. If anyone has the time,
send us the math and we'll post it!
We used ADS to calculate the
attenuation factor of a PTFE stripline board with copper conductor
and popular geometry.
Stripline has the same result,
loss is minimum as Z0=0. Although the curves would change if you
played with parameters such as metal conductivity, dielectric constant,
and geometry, trust us, the attenuation factor always decreases
when impedance is reduced. This is a Microwaves101 Rule