[SI-LIST] Re: impedance and Characteristic impedanece
- From: "Mark Woods" <mark.woods@xxxxxxxxxx>
- To: <si-list@xxxxxxxxxxxxx>
- Date: Mon, 21 May 2007 13:18:07 -0800
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-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx] On
Behalf Of agathon
Sent: Tuesday, April 10, 2007 10:23 PM
To: arpad.muranyi@xxxxxxxxx; cpad@xxxxxxxxx
Cc: si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] Re: impedance and Characteristic impedanece
A-yup.
And don't forget about the ...
1. Matching by reciprocal impedances, whereby a reactive load (like 50 ohms
w/ parasitic C) can be matched to an ideal resistive Tline for all
frequencies. C, or L, is cancelled. No lie.
2. Matching impedances of all propagating modes (typically seen here are
even and odd for stripline/microstrip).
I count 3 methods for original problem solution:
A) Isrc // 1 ohm = -Vn amps // 1ohm => (Thevenin Vn & -1ohm) // 1 ohm =>
Zin = -1//1 = infinity, since Vn src impedance = 0.
B) -V // 1 ohm. Zvccs = V / I = V / -V = -1. Zvccs // 1 = -1 // 1 =
infinite.
C) KCL as just described (C. Padilla). But direction of currents is
everything: Isrc into VCCS, Iresistor out to neg. VCCS terminal.
The key to get around the non-intuitive stuff is: the VCCS current is
isolated from the load and only reacts to V on the load, even though it's
directly connected to the load. The VCCS current leaves the node and SO
DOES the resistor current because there's a Vcontrol = V voltage that isn't
explicit, across R.
-Agathon
On 4/10/07, Muranyi, Arpad <arpad.muranyi@xxxxxxxxx> wrote:
>
> 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
>
>
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
>
>
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
> =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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