# [SI-LIST] Re: Concept of Voltage

• From: Albert Ruehli <albert.ruehli@xxxxxxxxx>
• To: Vinu Arumugham <vinu@xxxxxxxxx>
• Date: Tue, 19 Jul 2011 16:12:02 -0400

```All,
The discussion is actually very interesting an obviously much thought has
gone into the process.
We have to distinguish between the 3D world and the 2D world which is
an approximation to the 3D world.   As I mentioned before, the 3D world
is clearly defined.  In a PEEC model, we have the "Spice" ground
"connected to"  infinity and infinity has the zero potential, no noise
voltage at all.   Any other finite point is not ground.  This makes sense
since now we can get a ground noise voltage as the difference in potential.
The Spice solver has no problem with this, since we have a single reference
node.
In the 2D world, or quasi 3D world the majority of this discussion is
is much more tricky.    A 2D structure has by definition (at least
theoretically)
the same cross-section in lets say, y and z .  So, the x directions extends,
in
principle to infinity which creates a problem with the zero potential.
Fortunately, Spice circuits solvers are ok with this problem as we know
as long as we have a single ground node in our Spice.   For example,
in a differential mode TL we can have two floating input nodes as a port
with the current, as Yuriy states. We send a current into one of the nodes
and we take the same current out of the other node of the port.   Now,
Spice is ok with this since we have some capacitances etc to the ground
or reference node.  We should note that in Spice we do not write an
equation for the ground node.  So, if we have a TL we can ground
the nodes at each end and we get away with it even if we know that
there is a delay etc. between the two ends.   Also, floating nodes are
ok in Spice as long as we have some internal connection or elements to
the nodes.
I have to admit these quasi 3D solutions work better than what I originally
anticipated.

Albert

On Tue, Jul 19, 2011 at 1:43 PM, Vinu Arumugham <vinu@xxxxxxxxx> wrote:

> Yuriy,
> "Considering use of multiport models in a SPICE circuit simulator, the only
> possible and legitimate use of the local reference terminal is to connect
> it
> to a common reference node (global ground)."
>
> Connecting both local references to global ground seems like a
> non-physical connection. We know that in the real world, the voltage
> difference between the local references is defined  at DC and non-zero.
> But in the circuit you are forcing it to zero  for DC and all
> frequencies (gA=gB=0).  It seems Shawn's circuit with only gA tied to
> global ground is better. I of course agree that voltage on gB measured
> w.r.t to global ground is undefined at high frequencies. Could you
> please explain why gA=gB=0 the only legitimate use of the model?
>
> Thanks,
> Vinu
>
> Yuriy Shlepnev wrote:
> > Shawn,
> >
> > You have described a perfect example of what should never be done with
> > multiports described with S-parameters (or equivalent t-line models). It
> is
> > typical model misuse (garbage in - garbage out).
> > Formally, each single port in a multiport has 2 terminals (or nodes) -
> > signal and local reference. There is no information on the potentials of
> > each terminal - only information on the difference of potentials or
> voltage.
> > Moreover, as I pointed earlier, the voltage may be defined not as the
> > difference of potentials (or line integral of electric field), but as a
> > projection of the electric field on the electric field of a wave-guiding
> > eigen-mode. Current flowing out of the reference terminal must be exactly
> > opposite to the current flowing into signal terminal. Again, current may
> be
> > defined either locally or as a projection of magnetic field on the
> > eigen-mode field. The projection definition must be used even for MTL
> with
> > quasi-TEM modes at high frequencies.
> >
> > The only possible way to use a port is to connect it to another port that
> is
> > defined identically. Lumped components can be connected to local or
> lumped
> > ports defined in electromagnetic analysis. Wave-ports can be connected
> only
> > with the identically defined wave ports. An exception is quasi-TEM
> > transmission lines at lower frequencies. Such ports can be connected with
> > the lumped or local ports as long as the cross section stays much smaller
> > than the wavelength (due to similarity of the voltage definition for MTL
> and
> > lumped element). In cases when distance between strips becomes comparable
> > with the wave-length, connection of a quasi-TEM t-line port with a lumped
> > port becomes ambiguous and erroneous.
> >
> > Considering use of multiport models in a SPICE circuit simulator, the
> only
> > possible and legitimate use of the local reference terminal is to connect
> it
> > to a common reference node (global ground). The signal terminal must be
> > connected to a signal terminal of the identically defined port. In case
> of
> > lumped port, the lumped element must be connected between the signal
> > terminal and the global reference node. If a lumped element contains more
> > than two nodes, there must be a separate lumped port (possibly with
> common
> > reference) constructed to connect each signal node of the lumped element.
> > There are no restrictions in the circuit analysis as long as one follows
> the
> > port construction and connection rules and build or collect a sufficient
> > number of multiport models for each interconnect component. Not only
> > quasi-TEM, but optical or substrate integrated waveguides for instance
> can
> > be analyzed with a SPICE solver without any problems.
> >
> > Best regards,
> > Yuriy
> >
> > Yuriy Shlepnev
> > www.simberian.com
> >
> > -----Original Message-----
> > From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx]
> On
> > Behalf Of Shawn Hermite
> > Sent: Monday, July 18, 2011 5:32 PM
> > To: si-list@xxxxxxxxxxxxx
> > Subject: [SI-LIST] Re: Concept of Voltage
> >
> > Hi,
> >
> > For those of you with full faith in the traditional definition of
> voltage,
> > I'd invite you to conduct the following simulation-based experiment:
> > - Collect a 2-port S-parameter from either measurement or simulation of a
> > physical transmission-line structure. It can be PCB trace or co-ax cable;
> > - Let's label the following nodes: (1) sA: the signal node on the left
> side,
> > (2) gA: the reference node on the left side, (3) sB: the signal node on
> the
> > right side, and (4) gB: the reference node on the right side.
> > - By definition, the 2-port S-parameters use two voltage variables:
> > vA=phi(sA)-phi(gA) and vB=phi(sB)-phi(gB). Here phi(.) is the potential
> > function w.r.t. infinite, i.e., phi(infinity)=0.
> > - With a simple mathematical transformation, we can convert the 2-port
> > S-parameter block into a 4-port block, making use of the potential
> variables
> > at the nodes.
> > - In your favorite circuit simulator, HSPICE or ADS ..., you apply an AC
> > voltage source between nodes sA and gA (and possibly a source
> termination),
> > and gA is tied to GND. You need put a termination resistor between sB and
> > gB. But, gB is not tied with GND. The rationale is: the circuit has only
> one
> > true GND.
> > - Run you AC simulation, with any reasonable frequency band. Plot voltage
> at
> > gB, which is phi(gB). It is likely NOT ZERO. Wah lah! you have just
> > extracted the "ground bounce" effect at the receiver.
> >
> > Again, thanks for bearing with my hung-ups on the trivial concept.
> >
> > Regards,
> >
> > Shawn
> >
> > On Mon, Jul 18, 2011 at 12:26 PM, Luciano Boglione
> > <l.boglione@xxxxxxxx>wrote:
> >
> >
> >> Yuri, Shawn,
> >>
> >> Basic questions are always interesting. May I bring up a couple of
> >> additional points to mull over:
> >>
> >> - the definition of voltage should be unique, the integral of E over a
> >> path l. Whether the field is conservative or not, depends on the
> >> field, not on the definition.
> >> - the fact that the field is always conservative locally seems a
> >> logical assumption to make; however, it may butt heads with the
> >> necessary condition for a field to be conservative (dEz/dy=dEy/dz;
> >> dEx/dz=dEz/dx; dEy/dx=dEx/dy where the derivative d/dx, etc. are
> >> partial)
> >> - the modes in a guided propagation structure are determined by the
> >> transversal (x,y) section of the structure (since its cross section is
> >> considered "constant" in order to handle it analytically). The
> >> propagation that occurs in the orthogonal z direction is uniquely
> >> described by a wave equation (e.g. V1*exp(k*z)+V2*exp(-k*z) with k
> >> complex for a sinusoidal field over time, exp(jwt)) independently of
> >> the cross section of the waveguide (e.g. coax cable, waveguide, etc.).
> >> If one can calculate/determine the cross section integral at z=0 and
> >> z=L (say start and end of the structure), the constants V1 and V2
> >> should also be determinable uniquely for each mode.
> >> - when the structure supports DC (lowest cutoff frequency is 0Hz), TEM
> >> modes (strictly speaking) are not part of the mode solution, although
> >> the above procedure (field is split into transverse and longitudinal
> >> components) still applies. In particular, the E field should not be
> >> conservative - although, some approximations can be made to tweak the
> >> solution and use a quasi-TEM approximation... memory may not help me
> >> here, but I believe a lot of more precise information can be found in
> >> Collins, Foundation for Microwave Engineering, McGraw Hill.
> >>
> >> Regards,
> >> Luciano
> >>
> >>
> >> ----- Original Message -----
> >> From: "Yuriy Shlepnev" [shlepnev@xxxxxxxxxxxxx]
> >> Sent: 07/18/2011 08:44 AM MST
> >> To: "'Shawn Hermite'" <shawn.hermite@xxxxxxxxx>;
> >> <si-list@xxxxxxxxxxxxx>
> >> Subject: [SI-LIST] Re: Concept of Voltage
> >>
> >>
> >>
> >> Shawn,
> >> There are two possible definitions of voltage.
> >>
> >> The first one is classical with the integral of electric field between
> >> two points - that definition assumes that the field is conservative
> >> (no difference in voltage value if the integration path is changes).
> >> This definition can be applied to lumped elements or TEM transmission
> >> lines only in case if distance between the integration (measurement)
> >> points is much smaller than the wavelength (locally the field is
> >> always conservative). It pairs with the current definition through a
> >> surface integral over a conductor cross-section (or port cross-section).
> >>
> >> The second definition is specific to waveguiding structures (or
> >> transmission
> >> lines) in microwave theory. Electric field in a cross-section of a
> >> waveguide (or MTL) can be expressed as a sum of eigen-waves with some
> >> coefficients.
> >> Those coefficients are treated as the voltages in the theory of
> >>
> > multiports.
> >
> >> Technically voltages is this case are Fourier coefficients with the
> >> base functions defined by a set of eigen-modes (each wave has its own
> >>
> > voltage).
> >
> >> Currents in the multiport theory are introduced in a similar way
> >> through the projections of magnetic field on the magnetic fields of
> >> the eigen-waves.
> >> There are no restrictions on the size of cross-section with such
> >> definition of voltage and current. Both wave-guide ports and local or
> >> lumped ports can be used to define a multiport. This allows to build
> >> multi-port models to combine distributed and lumped structures.
> >> Circuit theory can be used to analyze connections of such multiports
> >> without any restrictions as soon as the voltages and currents are
> defined
> >>
> > identically for the connected ports.
> >
> >> Considering multi-conductor transmission lines, if it is analyzed with
> >> a static field solver, the electric field is conservative by
> >> definition and voltage can be uniquely defined in the model. Though,
> >> the model breaks if the distance between strips or reference
> >> conductors becomes comparable with the wavelength. In case of
> >> electromagnetic analysis of multi-conductor line, the voltage can be
> >> defined following the first definition only in case if cross-section
> >> size is much smaller than the wavelength. Such solution will be
> >> identical to the obtained with the static field solver. See more on
> >> estimations of frequency boundaries in I.V. Lindell: On the quasi-TEM
> >> modes in inhomogeneous multiconductor transmission lines, IEEE
> >> Transactions on MTT, vol.29, no.8, pp.812-817, 1981 or Electromagnetic
> >> waveguides and transmission lines By Frank Olyslager. In case if
> >> cross-section becomes comparable with the wave-length, the second or
> >> projection definition of voltage can be used to turn MTL into a
> >> multiport. Note that the current definition through the a conductor
> >> cross-section integral stays valid up to higher frequencies than the
> >> conservative voltage definition. This fact can be used to define
> >> voltage through the current and power transmitted by wave.
> >>
> >> Finally, at high frequencies only power of propagating waves is
> >>
> > measurable.
> >
> >> That is why waves and scattering parameters are used for interconnect
> >> analysis at microwave frequencies. See more on definitions of
> >> multiports and S-parameters in presentation #2010_01 at
> >> http://www.simberian.com/TechnicalPresentations.php (tutorial
> >> materials from DesignCon2010).
> >>
> >> Best regards,
> >> Yuriy
> >>
> >> Yuriy Shlepnev
> >> www.simberian.com
> >>
> >>
> >>
> >> -----Original Message-----
> >> From: si-list-bounce@xxxxxxxxxxxxx
> >> [mailto:si-list-bounce@xxxxxxxxxxxxx]
> >> On
> >> Behalf Of Shawn Hermite
> >> Sent: Sunday, July 17, 2011 11:06 PM
> >> To: si-list@xxxxxxxxxxxxx
> >> Subject: [SI-LIST] Concept of Voltage
> >>
> >> To SI experts, especially those used Maxwell's equations in their books:
> >> The concept of voltage has been deeply engrained in our minds. It's
> >> the foundation of the circuit theory and electrical engineering at
> large.
> >> Recently, when collecting materials for a presentation advocating the
> >> importance of signal integrity, I realized that the concept of voltage
> >> is based on the assumption of the electric field being conservative.
> >> The general differential form of Maxwell's equations (the Faraday's
> >> Law part in
> >> particular) contains the dB/dt term that ruins the validity of curl
> >> {E} = 0.
> >>
> >> There are two categories of arguments:
> >> (1) With the integral form of the Faraday's Law, we can treat the
> >> time-varying magnetic flux term as an electromotive-force (like
> >> battery), hence fix the KVL, the general idea of voltage is still
> >> being the line integral of the electric field between two points.
> >> (2) Switching to the frequency-domain, the surface integral of the
> >> B-field is related to the characteristic dimension of the system (D)
> >> and the operating frequency. It goes with some hand-waving arguments,
> >> and the claim is that the unfriendly term is nearly zero when D <<
> >> wavelength. This argument also goes hand-in-hand with validity of
> >> lumped vs. distributed element modeling.
> >>
> >> I have also observed that in a multi-conductor transmission-line (MTL)
> >> system where the TEM mode is propagating, the E-filed is conservative
> >> on each cross-section, thus voltage is well defined between a signal
> >> conductor and the common-reference conductor.  Here, the general
> >> electrodynamic Maxwell's equations are all satisfied. The MTL theory
> >> explains why RF/microwave testing has to be done using co-ax cables.
> >> It also makes sense why 'port' (instead of circuit node) voltage is
> >> used in constructing S-parameters.
> >>
> >> If the second explanation holds true, I am really worried about what
> >> the frequency limit is before we get into trouble with freely applying
> >> knowledge developed with DC or low-frequency circuits.
> >>
> >> Any way, looking for a better answer or proof on the validity of the
> >> concept of voltage.
> >>
> >> Thanks
> >>
> >>
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