[SI-LIST] Re: impedance and Characteristic impedance
- From: "Eric Bogatin" <eric@xxxxxxxxxxxxxxx>
- To: <james.f.peterson@xxxxxxxxxxxxx>, "'si-list'" <si-list@xxxxxxxxxxxxx>
- Date: Wed, 21 Mar 2007 08:31:56 -0500
Jim and others-
I think the resolution to this seeming paradox:
"How can the impedance for a transmission line be so independent of
frequency when normal circuit impedance is so extremely dependent on
frequency?"
is two fold. First, we use the term impedance in three different ways, all
different and often used incorrectly, interchangeably in the industry. This
confuses our intuition.
When we refer to the impedance the signal sees each step along the way as it
travels down a transmission line, we really should use the term, the
instantaneous impedance. If the transmission line has a constant cross
section, the instantaneous impedance the signal sees is constant each step
of the way. ("Be the signal", and ask, what do you see each step of the
way.)
If the transmission line is uniform, then everywhere along the line, the
instantaneous impedance is the same. It is as though the entire line has one
value of instantaneous impedance. There is one instantaneous impedance that
characterizes the line. We call this the characteristic impedance.
When you look into the front of a line, you see another impedance between
the signal and return path. If you look for a time short compared to the
round trip time delay of the line, you see an impedance equal to the
characteristic impedance. If you look for a very long time, you might see an
open, depending on the termination at the far end.
What is the input impedance of the line? Is it 50 Ohms, for example, or
open? The answer is, it is time dependent. The input impedance changes with
time and at some instants, can be anywhere in between 50 ohms and an open.
If the input impedance, in the time domain changes dramatically, we would
expect to see dramatic changes in impedance in the frequency domain.
In the frequency domain, we are sensitive to the input impedance of the
line- the total, integrated impedance due to the entire line. Depending on
the termination, we can measure almost any value between open and short as
we sweep frequency.
There is a second order factor which Tom is alluding to below. The
instantaneous impedance is slightly frequency dependent. It will vary
slightly as the current re-distributes in the cross section due to skin
depths, which will change the inductance per length of the signal and return
path. This will cause the characteristic impedance to start hi at low
frequency and drop off with higher frequency. The total change is typically
on the order of 10%, and varies with the thickness of the conductors.
There is a smaller effect due to the frequency variation to the dielectric
constant of the material as well.
If you want a more detailed description, and want to really understand what
we mean by characteristic impedance and the impedance of a transmission
line, you might take a look at the online lecture OLL-115 Intro to
characteristic impedance, on my web site. www.bethesignal.com . You can use
coupon code BTS115 to view this lecture for free.
You should also check my book, Signal Integrity- Simplified. This
explanation is in print in the chapter on transmission lines. I also have a
few papers on my web site you can download that discuss this question. They
are free to download.
For info on the frequency dependence of characteristic impedance, see my
column in the upcoming, April issue of PCD&M.
This and all the essential principles of signal integrity are covered in
detail in my class coming up in April 19.
Hope to see you there.
--eric
**************************************
Dr. Eric Bogatin, President
Bogatin Enterprises, LLC
Setting the Standard for Signal Integrity Training
26235 w 110th terr
Olathe, KS 66061
v: 913-393-1305
f: 913-393-0929
c:913-424-4333
e:eric@xxxxxxxxxxxxxxx
www.BeTheSignal.com
****************************************
-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx] On
Behalf Of Peterson, James F (EHCOE)
Sent: Wednesday, March 21, 2007 6:20 AM
To: si-list
Cc: tom@xxxxxxxxxxxxx; nagaup1@xxxxxxxxx
Subject: [SI-LIST] Re: impedance and Characteristic impedance
If I read Raj's question correctly, he is asking a question many of us
have asked :
How can the impedance for a transmission line be so independent of
frequency when normal circuit impedance is so extremely dependent on
frequency?
If you look into the telegrapher's equations you will see the derivation
of t-line impedances...this shows a logical, yet hard to understand,
trail to our familiar equation for the Z of a t-line.
Jim Peterson
Honeywell
-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx]
On Behalf Of Tom Dagostino
Sent: Wednesday, March 21, 2007 12:34 AM
To: nagaup1@xxxxxxxxx; 'si-list'
Subject: [SI-LIST] Re: impedance and Characteristic impedance
Zo =3D3D SQRT(2PiFL/2PiFC). Yes there are terms for resistance and =3D
conductance
too but for this we can ignore them. The frequency dependence drops out
=3D
so
Z0 =3D3D SQRT(L/C). L and C can be functions of frequency but that is =
=3D
minor
compared to their magnitudes for most frequencies in most applications.
Tom Dagostino
Teraspeed(R) Labs
13610 SW Harness Lane
Beaverton, OR 97008
503-430-1065
tom@xxxxxxxxxxxxx=3D20
www.teraspeed.com=3D20
Teraspeed Consulting Group LLC
121 North River Drive
Narragansett, RI 02882
401-284-1827
-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx]
=3D
On
Behalf Of nagaraj
Sent: Tuesday, March 20, 2007 9:04 PM
To: si-list
Subject: [SI-LIST] impedance and Characteristic impedance
When I say impedance, it depends on the
capacitance and inductance. So, these two components depend on frequency
=3D
(wL
and 1/wC, where w=3D3D 2xpixF).
When I say characteristic impedance, it too
has capacitance and inductance involved. So when I say I maintain 50 ohm
characteristic impedance on my board... there may be lot of frequencies
involved in the design resulting in different characteristic impedance.
=3D
then
how the board is said as a 50 ohm impedance controlled..? =3D20
=3D20
=3D20
Thanks and regards,
Raj.
=3D20
________________________________________________________________________
_=3D
___
________
The fish are biting.=3D20
Get more visitors on your site using Yahoo! Search Marketing.
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