# [SI-LIST] Re: Concept of Voltage

• From: Vinu Arumugham <vinu@xxxxxxxxx>
• To: Yuriy Shlepnev <shlepnev@xxxxxxxxxxxxx>
• Date: Tue, 19 Jul 2011 10:43:34 -0700

```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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