[SI-LIST] Re: Open Termination
- From: Sitar Moniker <si_monkey2@xxxxxxxxx>
- To: Larry.Smith@xxxxxxx, weston_beal@xxxxxxxxxxx
- Date: Fri, 17 Sep 2004 09:30:07 -0700 (PDT)
Thanks for the nice explnation from Kraus. Your last para addressed my concerns
about open termination to some extent. There you mentioned:
" ... the voltage doubles, sends an
equal and opposite current backwards down the line and the
superposition of the forward and reverse currents adds to zero as it
must at the open circuit."
Did you mean the equal and opposite current travels back on the microstrip
signal line? or the ground plane (return path)?
When the current is equal and opposite, the net is zero. What do we mean by a
zero current travelling?
Larry Smith <Larry.Smith@xxxxxxx> wrote:
There have been some good intuitive explanations on this thread
concerning the behavior of open circuited transmission lines, the
ratios of V/I and E/H resulting in the impedance of transmission lines
and free space respectively, and an antenna transformer between the
two. The field cell concepts presented by Kraus in his
ELECTROMAGNETICS book can be used to tie the these concepts nicely
together.
Kraus has many examples of "curvilinear squares" combined in parallel
and series to give intuitive insight into inductance, capacitance and
impedance. For example, a square cross section of free space with
infinite length is a field cell and has impedance of
sqrt(u0/e0)=377Ohms. We can envision a pair of flat strips of
parallel conductors on top and bottom of the free space square cross
section proceeding off into infinity. If there was no fringing around
this square, it would be a wave guide or transmission line with 377
Ohms. Twin lead transmission line has 300 Ohms of impedance because
the number of curvilinear squares in series divided by the number of
curvilinear squares in parallel results in a little more than one
square of free space.
If the strips were 10 times as wide as the height between them (10
squares of free space in parallel), it would have 37.7 Ohms
impedance. Actually, it only has to be about 9 times wider than high
because there is about a half a square of fringing on each side of the
structure to make 10 squares in parallel. If a material such as FR4
with eR=4 is placed between the plates, it has impedance about half of
37.7 Ohms calculated from the formula
Z=sqrt(u0/(e0*eR)/#squards_in_parallel. These are field cell concepts
presented by Kraus.
If the the top strip is over an infinite ground plane and is 2 times
wider than the height above the ground plane and has FR4 dielectric,
we have an approximately 50 Ohm transmission line. There are two
377/sqrt(4)=188 ohm squares under the strip plus 2 more for fringing
giving 188/(2+2) or about 50 Ohm transmission line.
I hope you can see where I am going with this. The 50 Ohm micro strip
line could morph into structure twice as wide with about 7 squares of
377 Ohm free space dielectric and still be 50 Ohms. Then it could
angle up higher and higher above the ground plane and increase in
impedance because there are fewer squares in parallel. Let the width
of the structure expand out until there is 1 square of free space
between the top and bottom conductors. This is a transformer from 50
to 377 Ohms. I think they call it a horn antenna.
If the transformer (antenna) works well, there will be no reflection,
the voltage will not double at the end of the line and energy will go
off into free space. If however the micro strip abruptly stops and
there is poor impedance matching to free space (poor radiation
efficiency), then the energy stops, the voltage doubles, sends an
equal and opposite current backwards down the line and the
superposition of the forward and reverse currents adds to zero as it
must at the open circuit.
regards,
Larry Smith
Sun Microsystems
"Beal, Weston" wrote:
>
> Sitar,
>
> Another important point that might make Geoff's wonderful explanation make
> more sense (or less) is to think of an antenna as an impedance transformer.
> An antenna transforms the V/I impedance of the transmission line at the
> driving point of the antenna into a free space intrinsic impedance of E and H
> fields. The intrinsic impedance of the medium (dieletric in most cases) is
> just the ratio of E to H that the medium supports. It is independent of
> geometries because it assumes that the fields are completely enclosed in the
> medium. On the other hand, the impedance of a transmission line depends on
> the geometry of the metal and dieletric because these cause different
> distributions of the current and voltage on the metal conductors.
>
> Regards,
> Weston
>
> -----Original Message-----
> From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx] On
> Behalf Of Geoff Stokes
> Sent: Wednesday, September 15, 2004 9:42 AM
> To: 'si_monkey2@xxxxxxxxx'
> Cc: si-list@xxxxxxxxxxxxx
> Subject: [SI-LIST] Re: Open Termination
>
> Sitar
>
> Forgive me but I need to avoid spending too much time on this. The microstrip
> metal has a surface current which is linked, by the electromagnetic equations
> of Maxwell, to the field immediately adjacent to it. Microstrip's fundamental
> mode is "quasi-TEM" - it approximates Transverse ElectroMagnetic (TEM). TEM
> is a wave where there is no field component in the direction of propagation.
> Also the electric field is perpendicular to the metal surface and the
> magnetic field is everywhere perpendicular to the electric. However the field
> is not uniform. That may imply that E/H is varying (I'm not sure). The
> transmission line is a wave guide. However, the theory says that any wave
> motion can be described by a linear superposition of plane waves in various
> directions. For each component Ei and Hi, Ei/Hi = 377 ohms. Perhaps not for
> the total. Does it matter? The current travels in the direction of
> propagation on the underside of the signal trace, and in the reverse directi!
on
> on the top side of the ground plane. V/I = 50 ohms or whatever, nothing to do
> with the wave impedance of free space.
>
> But at the open circuit, the current tapers down to nearly zero (sum of
> incident and reflected wave current). What's left flows in the fringing
> capacitance. The fringing capacitance is difficult to find, but the order of
> magnitude will be somewhere near the capacitance per unit length times the
> microstrip h. That's a small fraction of 1 pF usually. To find it, you have
> two choices:
>
> 1. Measure it on a network analyser or TDR analyser.
>
> 2. Measure it in simulation.
>
> Both cases require a de-embedding calculation.
>
> Geoff
>
> > -----Original Message-----
> > From: Sitar Moniker [mailto:si_monkey2@xxxxxxxxx]
> > Sent: 15 September 2004 17:24
> > To: Geoff Stokes
> > Cc: si-list@xxxxxxxxxxxxx
> > Subject: [SI-LIST] Re: Open Termination
> >
> >
> > Thank you, Geoff. To be specific, let us consider a microstrip line
> > the load end of which is left open. There are two impedances. One is
> > the impedance of the line (V/I) and the other, beyond the point where
> > the line ends, is the impedance of free space (E/H) . The 377 Ohms I
> > mentioned earlier corresponds to this (E/H). Am I right so far?
> >
> > If the open termination is modelled with fringing capacitance and
> > possibly radiation loss, what is the magnitude of this impedance so we
> > could approximate it with infinity?
> >
> > V and I on the line are due to propagating E and H waves.
> > Then, what is the equivalent of a (V/I)=50 Ohms in terms of
> > corresponding (E/H)? What is the equivalent of (E/H)=377 Ohms in terms
> > of (V/I)?
> >
> > If ideal open circuit approx (Vi=Vr) is good especially at lower
> > frequencies, why do we routinely use it at higher frequencies as well?
> > Is there a somewhat realistic model for open termination?
> >
> > Geoff Stokes wrote:
> > Sitar
> >
> > In addition to your modern engineering books, you also need a
> > classical book on electricity and magnetism or microwave/rf
> > engineering.
> > This will show
> > that:
> >
> > 1. Impedance of a wave in free medium (e.g. air) is not the impedance
> > of a transmission line. One is E/H, the other is V/I.
> > 2. Open termination is not infinite impedance and is sometimes
> > modelled with fringing capacitance and possibly radiation loss.
> > 3. For the ideal open circuit (which does not exactly exist as I just
> > said, but sometimes it's good enough for an approximate analysis,
> > especially at lower frequencies), the incident wave voltage, Vi
> > amplitude is equal to the reflected wave amplitude, and in phase with
> > it. So the total at the open is 2Vi. At some other point on the line,
> > the phases are different, and so you will plot a standing wave.
> >
> > Good luck
> > Geoff
> >
> > > -----Original Message-----
> > > From: Sitar Moniker [mailto:si_monkey2@xxxxxxxxx]
> > > Sent: 14 September 2004 22:48
> > > To: si-list@xxxxxxxxxxxxx
> > > Subject: [SI-LIST] Open Termination
> > >
> > >
> > > In SI and HSDD books, they assume that open termination offers
> > > infinite impedance. My understanding is open end line is exposed to
> > > air which has about 377 ohms.
> > >
> > > 1) How do you get infinite impedance for unterminated line?
> > >
> > > 2) Is there any intuitive way to show that voltage at the open end
> > > doubles- other than using math: ref. coeft. = +1?
> > >
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