FreeLists / si-list / [SI-LIST] Re: impedance and Characteristic impedanece

["Muranyi, Arpad" <arpad.muranyi@xxxxxxxxx>]

Thanks for all the great replies!  I enjoyed
reading them.  There are many ways to skin the
cat, right?  Another analysis would be to make
a Thevenin equivalent of the circuit in which
the Thevenin source generates the same voltage
on one side of the resistor that exists on
the other side, i.e. the current through the
resistor is always zero.

Now, regarding how this relates to the original
topic of T-line impedance:

The resistor in this "trick question" corresponds
to the characteristic impedance of the T-line.

The source (current for Norton, or voltage for
Thevenin) corresponds to the reflected wave in
the T-line (with zero delay).  So the apparent
impedance (which I also like to call "electrical
impedance") can be calculated by looking at what
the circuit does, i.e. taking all voltage and
current relationships into account.  I find this
example a good way to illustrate what goes on
in a T-line without having to go into Maxwell's
wave equations.  To extend this example for
T-lines, all you have to do is add in some
delays (or phase if you do it in the frequency
domain), and you got it...

By the way, you can turn a capacitor into an
inductor with an op-amp, configured as a NIC,
often used for making inductors on the die.
Same thing as in the above discussion, right?
You have a physical device, a capacitor, which
looks completely different in the circuit.

We could call all of this "electrical illusions"...

The lesson from this, which is a big pet peeve
of mine (and I have commented on this before
in this list), is that when we talk about
impedance, we must be clear which one we are
talking about.  RF engineers tend to talk about
the electrical impedance as it is seen at a certain
frequency, taking into account all of the reflection
and standing wave effects, etc..., not mentioning
this underlying assumption most of the time.
Board layout guys or time domain thinkers tend
to talk about the characteristic impedance (most
often not mentioning that assumption either).

Imagine what happens when you put these two types
of guys into the same conversation...  Or imagine
what happens when a newbie takes two T-line basics
classes, one from each of these guys.  Mass confusion,
total nightmare, which I have had the "pleasure" of
experiencing way too many times...

I hope this thread helped to clarify a few basics...

Arpad
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=3D=3D=3D

-----Original Message-----
From: Chris Padilla (cpad) [mailto:cpad@xxxxxxxxx]=20
Sent: Tuesday, April 10, 2007 9:01 AM
To: Muranyi, Arpad; si-list@xxxxxxxxxxxxx
Subject: RE: [SI-LIST] Re: impedance and Characteristic impedanece

The main thing to notice in this simple circuit is the DEPENDENT SOURCE.
The amps supplied by the current source depend on the voltage developed
across the resistor.  I'm sure too many folks glossed over that very
important detail because it appears to be such a simple, "by inspection"
circuit.  In reality it is simple if you just note that small but very
important detail!

I'll generalize the circuit a tad more:

Let the current source be Alpha*v.  Note that Alpha is in dimensions of
amps per volt.
Let the voltage across the current source and the resistor be v.
Let the resistor be R.

Now, look into this circuit to figure out the input impedance.  In
sophomore circuits class, we did this by "hooking on" an arbitray V
source with a labeled driving i.  Figure out V/i and you have Zin.

As my circuit theory professor would say:  Now thrash around a bit!

I did a Kirchoff's Current Law at the top node of the resistor to get: i
=3D Alpha*v + v/R.  Note that v =3D V.

I find that V/i =3D R/(1 + R*Alpha).  Plug in R =3D 1, and Alpha =3D -1 =
and
sure enough, V/i =3D 1/0. =20

Note that Polarity is VERY important here!!

Chris
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