[SI-LIST] Re: Zo vs Zin

  • From: "Beal, Weston" <weston_beal@xxxxxxxxxxx>
  • To: si-list@xxxxxxxxxxxxx
  • Date: Mon, 17 Mar 2003 13:47:48 -0800

Jayaprakash,

This RF equation uses frequency, and as Arpad stated earlier, this assumes a 
sine wave.  What is the sine wave frequency of your square wave?  Maybe you 
could evaluate this equation at all the frequency that have significant 
strength in your signal.

Regards,
Weston


-----Original Message-----
From: Jayaprakash Balachandran [mailto:edpc108@xxxxxxxxx]
Sent: Monday, March 17, 2003 12:53 PM
To: arpad.muranyi@xxxxxxxxx; si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] Re: Zo vs Zin



Thanks Muranyi and others who participated in this
thread. According to the text books, input impedance 
of the transmission line is given by expression, 


Zin  =      Zo[ZL + jZotan(vl)]
            ------------------
            [Zo + jZLtan(vl)]


  v = propagation constant 
    = ((R+jwL)(G+jwC))^0.5
  
  w = 2*pi*f

Zin = Zo when there is no reflection, as pointed by
others.  

My question arised while I was trying to analyze
current drawn from a square wave generator driving an 
arbitrary Transmission line. (Square wave generator of
zero internal impedance is assumed). 

Going by the fundamental defination of Zo and Zin, 
 
I expect, in the first time step, Square wave
generator will see an impedance of Zo and from next
step it will see Zin (given by the above expression)
due to reflections from far end. 

(However the forward and reflected waves still see an
impedance of Zo. )

Here what I mean by time step is the time  taken by
the wave to reach the load end when driven from Source
end and viceversa. or simply transmission line delay. 

A quick ADS simulation, plotting Vin/I (I is the
current drawn from the source), confirmed Impedance
seen by the source is Zo only for first time step. 

Thanks and regards,
Jayaprakash. 




















  




 --- "Muranyi, Arpad" <arpad.muranyi@xxxxxxxxx> wrote:
> 
> Even though this is a standard topic and a well
> understood phenomena,
> there is a lot of confusion out there.  I believe
> that the confusion
> is caused by people not making it clear what kind of
> "Impedance" they
> are talking about.
> 
> When you read a book that is RF (analog) oriented,
> chances are you will
> get a different language on impedance compared with
> when you are reading
> a book on signal integrity (digital) dealing mostly
> with time domain =
> work.
> 
> Remember, RF people think in sinusoidal steady state
> most of the time,
> where the signal is transmitted with a carrier
> frequency that doesn't
> change much.  In such a world you can count on the
> various geometric
> shapes of T-lines (and stubs) giving you impedance
> transformers, opens,
> shorts, and what have you, based on standing waves
> in the line, etc.
> And these will be "frequency dependent" of course,
> since the 1/4 or 1/2
> wave length responses of the T-line will obviously
> depend on the
> carrier frequency to length relationship.
> 
> On the other hand, in the digital world we have a
> wide band signaling
> most of the time.  (A data line can have signals
> having frequencies
> anywhere from 0 to Max_clock_f).  How can you tune
> an impedance
> transformer to a signal if you don't know what its
> frequency is?
> So in this world people refer to the characteristic
> impedance most
> of the time, which, as others already pointed out,
> describe the line
> without considering the waves going back and forth
> in it.  The frequency
> dependence of this kind of impedance is mostly based
> on the losses in
> the line, etc., and do not include the various
> cancellation effects
> of standing waves, etc.
> 
> The confusion that makes our discussions so
> interesting and lively
> some times comes from these two camps using their
> own jargons
> disregarding that the other camp may hear or
> interpret the same
> words completely differently.  This is a very
> effective way to
> mystify the subject.
> 
> I would encourage everyone to be clear in describing
> what their
> background and assumptions are so that everyone can
> get the most
> out of what they are presenting.
> 
> Arpad Muranyi
> Intel Corporation
>
=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=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D
> 
> 
> 
> 
> 
> 
> 
> 
> -----Original Message-----
> From: Zhou, Xingling (Mick)
> [mailto:xlzhou@xxxxxxxxx]
> Sent: Thursday, March 13, 2003 8:49 AM
> To: 'Om.Mandhana@xxxxxxxxxxxx'
> Cc: edpc108@xxxxxxxxx; si-list@xxxxxxxxxxxxx
> Subject: [SI-LIST] Re: Zo vs Zin
> 
> 
> 
> The  exact relation of Z_in with Z0, Z_load and
> position of the load is =
> a
> standard topic in transmission line theory. It can
> be found in any books
> about transmission line theory such as Pozar's. =20
> 
> -----Original Message-----
> From: Om Mandhana [mailto:Om.Mandhana@xxxxxxxxxxxx]
> Sent: Thursday, March 13, 2003 10:53 AM
> Cc: edpc108@xxxxxxxxx; si-list@xxxxxxxxxxxxx
> Subject: [SI-LIST] Re: Zo vs Zin
> 
> 
> 
> Assuming the voltage and current amplitudes of the
> traveling wave as
> (V0+, I0+) in the +z-direction and (V0-,I0-) in the
> -z-direction,
> the characteristic impedance ZO is equal to the
> ratio of the voltage
> amplitude to the current amplitude for each of the
> traveling waves
> individually (with an additional minus sign in case
> of the -z =
> propogating
> wave).
> 
> Thus, the characteristic impedance
> ZO =3D V0+/I0+ =3D -(V0-)/I0-.
> 
> The input impedance, Zin(z) is the ratio of the
> total voltage, (incident =
> and
> reflected),
> V(z) to the total current, I(z) at point z on the
> line.
> 
> Thus, the input impedance
> Zin(z) =3D V(z)/I(z).
> 
> The characteristic impedance is not equal to the
> input impdeance, unless =
> one
> of the
> two waves is absent.
> 
> 
> "Clewell, Craig" wrote:
> 
> > Jayaprakash,
> >
> > Zc is the ratio of voltage to current traveling in
> one direction on a
> > T-line.  Remember that a T-line has at least 2
> modes of signal flow.  =
> When
> > there are no reflections from the far end of the
> T-line Zin =3D Zc =
> because
> > there is only one mode of signal flow.  When you
> have reflections on =
> the
> > line the relation Zin =3D Zc breaks down.
> >
> > Craig
> >
> > -----Original Message-----
> > From: Jayaprakash Balachandran
> [mailto:edpc108@xxxxxxxxx]
> > Sent: Wednesday, March 12, 2003 9:14 AM
> > To: si-list@xxxxxxxxxxxxx
> > Subject: [SI-LIST] Zo vs Zin
> >
> > Dear SIers,
> >
> >    What is the difference between characteristic
> > impedance and input impedance in a transmission
> line?
> >
> > Thanks in advance,
> > Jayaprakash.
>
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=====
Balachandran Jayaprakash                             
Celestijnenlaan,                                                   
3/61, 3001, Heverlee,                                           
Leuven, Belgium.                                                  
Mobile: +32-472-630120

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