From p289 of the
Schatz book
Ivor Catt (1935- )
posed the question
“When
a voltage step travels down a transmission line at the speed of light guided
by two conductors, where does the
negative charge come from on the bottom
conductor to terminate
the electric field between the conductors?” [20] Figure 6.6
illustrates this
question.
From: Ivor
Catt
Sent: Friday, December 19,
2014 10:52 AM
To: Hans Schantz
Cc: Christopher
Spargo ; Alex Yakovlev ; m.pepper@ee.ucl.ac.uk
; michael.pepper@ucl.ac.uk
Subject: Re: What happened to
Electromagnetic Theory
Dear Hans,
Thank you for your snow job. It is a
shame that you think “The Catt Question” is a “position”.
“As I understand your position - and do
correct me if I misinterpret you - you believe that conventional electromagnetics and current flow cannot explain how a step
signal can propagate along an ideal transmission line at the speed of light
without the current propagating at the speed of light as well.
” This position was Sir Michael Pepper’s, not mine. I only asked a
Question, and did not take a “position”. http://www.ivorcatt.co.uk/cattq.htm
Having published a book, you are in a
key position.
Please ask Sir Michael Pepper to say
that he agrees with you, and has changed his mind from 1993, when he wrote; http://www.ivorcatt.co.uk/2812.htm
“As the wave travels at light velocity,
then charge supplied from outside the system would have to travel at light
velocity as well, which is clearly impossible.”
You will agree that the difference of
opinion between you, publisher of a text book, and Sir Michaekl
Pepper, editor of the top Royal Society journal, has to be resolved.
Ivor Catt
From: Hans Schantz
Sent: Thursday, December
18, 2014 3:02 AM
To: Ivor
Catt
Cc: Christopher
Spargo ; Alex Yakovlev
Subject: Re: What happened to
Electromagnetic Theory
Hello
Ivor,
I've attached a draft chapter and an excerpt of another chapter of my second
edition (revisions in progress) of The Art and Science of Ultrawideband Antennas. The book will be out in the
summer of 2015. I think you might find my material interesting since I, too, focus on much neglected aspects of electromagnetics like the time domain and energy flow,
although I reach different conclusions than you. This chapter covers much of
the material I presented in my talk at Newcastle last month.
As I understand your position - and do correct me if I misinterpret you - you
believe that conventional electromagnetics and
current flow cannot explain how a step signal can propagate along an ideal
transmission line at the speed of light without the current propagating at the
speed of light as well. I've addressed the "Catt Question" on pages
289-290 in the attached. The fields and the energy propagate along the
transmission line at the speed of light (at least for the surrounding medium).
The charge in a typical conductor is vastly greater than the amount of charge
needed to constitute the current. A classical calculation suggests about 14,000
Coulomb/cm3 in copper and an average drift velocity of a few hunderd microns/second following the leading edge of the
wave adequate to account for a 10A current in 14 AWG wire. The comments from McEwan (http://www.ivorcatt.com/2813.htm)
seem spot-on to me. Just as a tsunami can propagate across an ocean in hours
without actually conveying any water over the entire distance, so also can
electromagnetic waves propagate along wires without needing to convey charges
at the speed of light. The fields and the energy propagate at the speed of
light, and in their wake some very modest changes in the charge balance of the
conducting wires give rise to the current. Please help me understand what
aspects of this explanation you find questionable.
Your second question is "Does the dD/dt displacement current at the front edge of the step traveling along at the speed of light guided by two
conductors cause magnetic field? Is that field in the horizontal plane?" (http://www.ivorcatt.co.uk/x22j.pdf)
I believe the answer is yes to both questions. The Chapter 5 excerpt explains
how in the dipole radiation field you have to account for the radial field
component in order to satisfy Gauss' Law. Even transverse waves must have a
little bit of longitudinal component to close the loops. The "horizontal"
magnetic field associated with the dD/dt displacement current makes sense to me. In fact, it's
remarkably similar to Schelkunoff's observation that
signals can couple past shorts in twin lead transmission lines due to magnetic
coupling (see Electromagnetic Fields p. 272). The current through
a physical short generates a dB/dt in the
transmission line loop on the other side of the short that by Lenz's Law
induces a voltage perpetuating the wave on the other side of the short. In a
sense you can think of the dD/dt
displacement current generating the change in magnetic flux right at the
leading edge of the wavefront that in turn advances
the TEM wave on down the line.
I normally parametrize Heaviside step functions using
hyperbolic tangent functions. You'll find my analysis of energy flow around
dipoles being charged or discharged according to this time dependence on pp.
328-332 of the attached. The radiated waveform in each case ends up being the
second derivative of the step function. I also looked at some simple Gaussian
impulses on transmission lines. I've come to the conclusion that energy
reflects off discontinuities in the field impedance in a manner similar to that
in which fields and energy bounce of discontinuities in the impedance of a
medium. You'll find the details in my draft chapter.
I do like your (and your collaborators') ingenious example of treating a
capacitor as a transmission line and your observation that in the limit, the
reflecting waves give rise to the standard exponential voltage rise. But I'm
not sure I follow the argument that a capacitor has no self-inductance. A
transmission line must have inductance in order to convey energy. Without
inductance, H = 0, S = E x H = 0, and there is no power flow. That's the
fundamental physics underlying Heaviside's theory of distortionless
propagation. There must be a balance of electric and magnetic energy for a step
function or any other waveform to propagate without distortion down a
transmission line. Upset the balance, some of the energy slows down, and you
get distortion. With no inductance at all, there's no magnetic field and no
motion of energy. You couldn't charge up a purely inductionless
capacitor since you couldn't get the energy to move into it. In fact, Schelkunoff has a derivation in Electromagnetic
Fields (p. 140-141) showing that for a circular parallel plate
capacitor the equivalent series lumped inductance is L = mu h / (8 pi) where h
is the height or distance between the plates of the capacitor.
In your "Heaviside Signal" article (http://www.ivorcatt.co.uk/x267.pdf)
you identify three "erroneous" beliefs:
1) EM energy is necessarily contrapuntal (by which I assume you mean quadrature, i.e. ninety degree phase relationship between
electric and magnetic fields)
2) E/H does not always equal Sqrt(mu/epsilon)
3) Signals can travel slower than the speed of light.
I agree (1) is erroneous. Quadrature phase is
reactive. You only see it in electromagnetic waves if you have a standing wave
of some kind. The question of the relative phases of E and H causes trouble for
many folks - myself included. Figure 6.9 shows how the
near-fields of a dipole start out ninety degrees out of phase with each other
close to an antenna and converge to being phase synchronous by a half
wavelength or so away. I had to work that out for myself, only to discover
Hertz had already figured it out over a century ago (see Electric Waves
p. 152). We've taken advantage of this phenomenon in our near-field location
systems at Q-Track.
(2) is actually true. E/H can have an arbitrary value
as waves superimpose and interfere, and the superposition is associated with
some of the energy slowing down and changing direction. Section 6.3 develops
and explains this for transient and harmonic waveforms. Equation 6.29 relates
the energy velocity to the impedance.
I believe (3) is false. Signals always propagate at the speed of light. However
the energy velocity may be less than the speed of light and the phase velocity
can be either greater than or less than the speed of light.
There's a great deal on your website, and I may have overlooked something
important. Feel free to point me to anything relevant you think I should
review. You raise very deep and interesting questions, and I look forward to
discussing any or all of these ideas with you further.
I also appreciate your work on the Searle biography of Heaviside. I read the
biography of him back when I was in grad school, and
I look forward to the revised edition Chris has told me might be forthcoming. I
spoke with Prof. Bruce J. Hunt at the University of Texas a few weeks ago. He
wrote an excellent book - The Maxwellians
- describing the work of Lodge, Heaviside, Hertz, and Fitzgerald (principally)
in developing Maxwellian theory into its more modern
form. I asked him about his thoughts on there being much additional Heaviside
material and he pointed me toward Gossick's paper
(attached). Gossick is pessimistic about the
likelihood Heaviside produced much of value in his later years.
Best Regards,
Hans
On 11/18/2014 10:21 AM,
Ivor Catt wrote:
"once I
get home and have a chance to digest your material."
But digesting my material requires months before the penny drops. I know from
bitter experience that discerning fatal flaws in classical theory takes
decades. It did in my case.
It is important to distinguish between analysis of conventional theory and
analysis of my theory.
Conventional theory only requires one fatal flaw to be proven and it then is
undermined. This process has nothing to do with any new Catt theory. In any
case Catt has more than a single theory. Problems for "capacitor self
resonant frequency" is independent of other Catt theory. http://www.ivorcatt.co.uk/cattq.htm
. It took me decades to realise that no relevant professor grasps the waveform
here.
Ivor Catt
-----Original Message----- From: Hans Schantz
Sent: Sunday, November 16, 2014 12:09 PM
To: Ivor Catt
Cc: Christopher Spargo ; Alex Yakovlev
Subject: Re: SP? {Spam?} What happened to
Electromagnetic Theory
I'm currently on travel, flying out of Heathrow tomorrow. I'll take a look and
get back to you in a few days, once I get home and have a chance to digest your
material.
Best,
Hans
On Nov 16, 2014 10:48 AM, Ivor Catt mailto:ivor@ivorcatt.com wrote:
Any chance of interchange on cattq http://www.ivorcatt.co.uk/cattq.htm
or
Second cattq http://www.ivorcatt.co.uk/x22j.pdf
?
Ivor
-----Original Message----- From: Alex Yakovlev
Sent: Saturday, November 15, 2014 11:01 PM
To: Ivor Catt ; Christopher Spargo
Cc: H.schantz@q-track.com
Subject: RE: SP? {Spam?} What happened to
Electromagnetic Theory
Hans,
I thought this is a good moment to introduce you to Ivor
Catt. I am sure
both of you will find many interesting points of interchange for your ideas.
Ivor: Dr Hans Schantz gave
a very stimulating lecture to our NEMIG audience
yesterday, and Chris and I had interesting discussions with Hans, too
http://www.ncl.ac.uk/eee/about/news/item/nemig-seminar-the-time-domain-superposition-and-how-electromagnetics-really-works
We are going to have the video Hans' lecture available
soon on the web.
Kind regards
Alex
________________________________________
From: Ivor Catt [ivor@ivorcatt.com]
Sent: 15 November 2014 21:27
To: Christopher Spargo
Cc: Alex Yakovlev
Subject: SP? {Spam?} What happened to Electromagnetic
Theory
Svetlana, Editor of Electronics World, sat on this article and two more for
2 years. Still not published.
http://www.ivorcatt.co.uk/x7171.htm=
--
Dr. Hans G. Schantz,
CTO
Q-Track Corporation
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Huntsville, AL 35805
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