[SI-LIST] Re: R: Transmission line impedance
- From: "Chockalingam Selvaraj" <chockalingam_selvaraj@xxxxxxxxxxxx>
- To: <si-list@xxxxxxxxxxxxx>
- Date: Wed, 20 Dec 2006 16:01:38 +0530
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Hello everyone,
Please find inline the compiled text (Thanks to Google :-) )
=20
=20
Cheers,
CK
Chockalingam.S
MindTree Consulting Pvt. Ltd.
India
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Why 50 Ohms?
(Originally published in EDN Magazine <http://www.ednmag.com> , =
September
2000)
Q: Why do most engineers use 50W pc-board transmission lines (sometimes =
to
the extent of this value becoming a default for pc-board layout)? Why =
not 60
or 70W ?-Tim Canales
A: Given a fixed trace width, three factors heavily influence =
pc-board-trace
impedance decisions. First, the near-field EMI from a pc-board trace is
proportional to the height of the trace above the nearest reference =
plane;
less height means less radiation. Second, crosstalk varies dramatically =
with
trace height; cutting the height in half reduces crosstalk by a factor =
of
almost four. Third, lower heights generate lower impedances, which are =
less
susceptible to capacitive loading.
All three factors reward designers who place their traces as close as
possible to the nearest reference plane. What stops you from pressing =
the
trace height all the way down to zero is the fact that most chips cannot
comfortably drive impedances less than about 50W. (Exceptions to this =
rule
include Rambus, which drives 27W, and the old National BTL family, which
drives 17W).
It is not always best to use 50W. For example, an old NMOS 8080 =
processor
operating at 100 kHz doesn't have EMI, crosstalk, or capacitive-loading
problems, and it can't drive 50W anyway. For this processor, because =
very
high-impedance lines minimize the operating power, you should use the
thinnest, highest-impedance lines you can make.=20
Purely mechanical considerations also apply. For example, in dense,
multilayer boards with highly compressed interlayer spaces, the tiny
lithography that 70W traces require becomes difficult to fabricate. In =
such
cases, you might have to go with 50W traces, which permit a wider trace
width, to get a manufacturable board.=20
What about coaxial-cable impedances? In the RF world, the considerations =
are
unlike the pc-board problem, yet the RF industry has converged on a =
similar
range of impedances for coaxial cables. According to IEC publication 78
(1967), 75W is a popular coaxial impedance standard because you can =
easily
match it to several popular antenna configurations. It also defines a =
solid
polyethylene-based 50W cable because, given a fixed outer-shield =
diameter and
a fixed dielectric constant of about 2.2 (the value for solid =
polyethylene),
50W minimizes the skin-effect losses.
You can prove the optimality of 50W coaxial cable from basic physics. =
The
skin-effect loss, L , (in decibels per unit length) of the cable is
proportional to the total skin-effect resistance, R , (per unit length)
divided by the characteristic impedance, Z 0 , of the cable. The total
skin-effect resistance, R , is the sum of the shield resistance and =
center
conductor resistances. The series skin-effect resistance of the coaxial
shield, at high frequencies, varies inversely with its diameter d 2 . =
The
series skin-effect resistance of the coaxial inner conductor, at high
frequencies, varies inversely with its diameter d 1 . The total series
resistance, R , therefore varies proportionally to (1/d 2 +1/d 1 ). =
Combining
these facts and given fixed values of d 2 and the relative electric
permittivity of the dielectric insulation, E R , you can minimize the =
skin-
effect loss, L , starting with the following equation:
=20
In any elementary textbook on electromagnetic fields and waves, you can =
find
the following formula for Z 0 as a function of d 2 , d 1 , and E R :
=20
Substituting Equation 2 into Equation 1 , multiplying numerator and
denominator by d 2 , and rearranging terms:=20
=20
Equation 3 separates out the constant terms /60)*(1/d 2 )) from the
operative terms ((1+d 2 /d 1 )/ln(d 2 /d 1 )) that control the position =
of
the minimum. Close examination of Equation 3 reveals that the position =
of the
minima is a function only of the ratio d 2 /d 1 and not of either E R or =
the
absolute diameter d 2 .
A plot of the operative terms from L , as a function of the argument d 2 =
/d 1
, shows a minimum at d 2 /d 1 =3D3.5911. Assuming a solid polyethylene
insulation with a dielectric constant of 2.25 corresponding to a =
relative
speed of 66% of the speed of light, the value d 2 /d 1 =3D3.5911 used in
Equation 2 gives you a characteristic impedance of 51.1W. A long time =
ago,
radio engineers decided to simply round off this optimal value of
coaxial-cable impedance to a more convenient value of 50W. It turns out =
that
the minimum in L is fairly broad and flat, so as long as you stay near =
50W,
it doesn't much matter which impedance value you use. For example, if =
you
produce a 75W cable with the same outer-shield diameter and dielectric, =
the
skin-effect loss increases by only about 12%. Different dielectrics used =
with
the optimal d 2 /d 1 ratio generate slightly different optimal =
impedances.
There are probably lots of stories about how 50 Ohms came to be. The one =
I am
most familiar goes like this. In the early days of microwaves - around =
World
War II, impedances were chosen depending on the application. For maximum
power handling, somewhere between 30 and 44 Ohms was used. On the other =
hand,
lowest attenuation for an air filled line was around 93 Ohms. In those =
days,
there were no flexible cables, at least for higher frequencies, only =
rigid
tubes with air dielectric. Semi-rigid cable came about in the early =
50's,
while real microwave flex cable was approximately 10 years later.
Somewhere along the way it was decided to standardize on a given =
impedance so
that economy and convenience could be brought into the equation. In the =
US,
50 Ohms was chosen as a compromise. There was a group known as JAN, =
which
stood for Joint Army and Navy who took on these matters. They later =
became
DESC, for Defense Electronic Supply Center, where the MIL specs evolved.
Europe chose 60 Ohms. In reality, in the US, since most of the "tubes" =
were
actually existing materials consisting of standard rods and water pipes, =
51.5
Ohms was quite common. It was amazing to see and use adapter/converters =
to go
from 50 to 51.5 Ohms. Eventually, 50 won out, and special tubing was =
created
(or maybe the plumbers allowed their pipes to change dimension =
slightly).
Further along, the Europeans were forced to change because of the =
influence
of companies such as Hewlett-Packard which dominated the world scene. 75 =
Ohms
is the telecommunications standard, because in a dielectric filled line,
somewhere around 77 Ohms gives the lowest loss. (Cable TV) 93 Ohms is =
still
used for short runs such as the connection between computers and their
monitors because of low capacitance per foot which would reduce the =
loading
on circuits and allow longer cable runs.
-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx] =
On
Behalf Of gianguida@xxxxxxxx
Sent: Wednesday, December 20, 2006 2:33 PM
To: cygnul@xxxxxxxxx;=20
Subject: [SI-LIST] R: Transmission line impedance=20
=20
Dear Sam,=20
obviously there is nothing special in 50 ohm or 60ohm or whatevere value
SI theory and practice are based upon Maxwell equation and its =
semplified
form Trasmission line equation
that simply works for any impedance value ....
=20
Giancarlo
=20
=20
-----Messaggio originale-----
Da: si-list-bounce@xxxxxxxxxxxxx per conto di Sam Pete
Inviato: mer 20/12/2006 7.27
A: si-list@xxxxxxxxxxxxx
Oggetto: [SI-LIST] Transmission line impedance =20
=20
Hi Friends,
=20
Whenever we refer to SI books or application notes, the impedance of =
the
transmission line is mentioned as 50-ohms or 60-ohms. What is the =
speciffic
reason behind this value? why can't it be something different than this? =
OR
Why this 50-ohms conceptualized from the driver's perspective? =
(evolution of
transmission line theory for Digital Design)
Please flood me some info on this.
=20
Regards,
Sam
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