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

["Chris Padilla \(cpad\)" <cpad@xxxxxxxxx>]

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

-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx]
On Behalf Of Muranyi, Arpad
Sent: Monday, April 09, 2007 3:26 PM
To: si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] Re: impedance and Characteristic impedanece

One of my favorite questions may illustrate the impedance question below
(or confuse people even more)...

Imagine an ideal voltage-controlled-current-source in parallel with a
resistor.  The resistor has a value of 1 Ohm and the output current of
the source is -1 times the voltage across the parallel combination of
the current source and resistor.  (The negative sign is there because I
am assuming that the current flow is positive when the current goes into
the + terminal and comes out of the - terminal of the source as well as
the resistor).

The HSPICE netlist is:

R1  node  0  R=3D3D1
G1  node  0  CUR=3D3D'-1*V(node,0)'

What is the impedance of this circuit when you look into it (Z11)?

Arpad
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