[SI-LIST] Re: Concept of Voltage
- From: Shawn Hermite <shawn.hermite@xxxxxxxxx>
- To: si-list@xxxxxxxxxxxxx
- Date: Mon, 18 Jul 2011 17:31:44 -0700
Hi,
Thank you all for adding your explanations.
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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