"Roger" wrote in message
. ..
Richard Clark wrote:
On Thu, 13 Dec 2007 08:40:53 -0800, Roger wrote:


And just for completeness...
The fundamental equations also work when:
- the signal is not sinusoidal, e.g. pulse, step, square, ...
- rather than a load at one end, there is a source at each end
- the sources at each end produce different arbitrary functions
- the arbitrary functions at each end are DC sources
It is highly instructive to compute the forward and reverse
voltage and current (and then power) for a line with the same
DC voltage applied to each end.

...Keith

...Keith


Interesting! The important thing is to get answers that agree with
our experiments.

I have done some computations for DC voltage applied to transmission
lines. The real surprise for me came when I realized that transmission
line impedance could be expressed as a function of capacitance and the
wave velocity. Z0 = 1/cC where c is the velocity of the wave and C is
the capacitance of the transmission line per unit length.


Hi Roger,

This last round has piqued my interest when we dipped into DC. Those
"formulas" would lead us to a DC wave velocity?

73's
Richard Clark, KB7QHC

Hi Richard,

Here are two links to pages that cover the derivation of the formula Zo
= 1/cC and much more.

http://www.speedingedge.com/PDF-File..._Impedance.pdf
http://www.ece.uci.edu/docs/hspice/h...001_2-269.html

Here is the way I proposed to Kevin Schmidt nearly seven years ago after
seeing him use the formula on a web page:

*ASSUME*:
1) An electrical wave travels at the speed of light, c
2) A 'perfect' voltage source without impedance, V
3) A 'perfect' transmission line having no resistance but uniform
capacitance per unit length, C

*CONDITIONS AND SOLUTION*
The perfect voltage source has one terminal connected to the
transmission line prior to beginning the experiment. The experiment
begins by connecting the second terminal to the transmission line. The
voltage source drives an electrical wave down the transmission line at
the speed of light. Because of the limitation of speed, the wave
travels in the shape of a square wave containing all frequencies
required to create a square wave.

The square wave travels down the transmission line at the speed of light
(c). After time (T), the wave has traveled distance cT down the
transmission line, and has charged the distributed capacity CcT of the
line to voltage V over that distance. The total charge Q on the
distributed capacitor is VCcT.

Current (I) is expressed as charge Q per unit time. Therefore the
current into the transmission line can be expressed as

I = Q/T =
VCcT / T = VCc

Impedance (Zo) is the ratio of voltage (V) to current (I). Therefore
the impedance can be expressed as

Zo = V / I =
V / VCc = 1/Cc

We can generalize this by using the velocity of the electrical wave
rather than the speed of light, which allows the formula to be applied
to transmission line with velocities slower than the speed of light.

Of course, only the wave front and wave end of a DC wave can be
measured to have a velocity.

73, Roger, W7WKB

the OBVIOUS error is that the step when the second terminal is connected
DOES NOT travel down the line at c, it travels at some smaller percentage of
c given by the velocity factor of the line.

The second OBVIOUS error is the terminology 'DC wave'. you are measuring
the propagation velocity of a step function. this is a well defined fields
and waves 101 homework problem, not to be confused with the much more common
'sinusoidal stead state' solution that most other arguments on this group
assume but don't understand.

"Dave" wrote in message
news:q7u8j.6941$xd.2942@trndny03...

"Roger" wrote in message
. ..
Richard Clark wrote:
On Thu, 13 Dec 2007 08:40:53 -0800, Roger wrote:


And just for completeness...
The fundamental equations also work when:
- the signal is not sinusoidal, e.g. pulse, step, square, ...
- rather than a load at one end, there is a source at each end
- the sources at each end produce different arbitrary functions
- the arbitrary functions at each end are DC sources
It is highly instructive to compute the forward and reverse
voltage and current (and then power) for a line with the same
DC voltage applied to each end.

...Keith

...Keith


Interesting! The important thing is to get answers that agree with
our experiments.

I have done some computations for DC voltage applied to transmission
lines. The real surprise for me came when I realized that
transmission
line impedance could be expressed as a function of capacitance and the
wave velocity. Z0 = 1/cC where c is the velocity of the wave and C
is
the capacitance of the transmission line per unit length.


Hi Roger,

This last round has piqued my interest when we dipped into DC. Those
"formulas" would lead us to a DC wave velocity?

73's
Richard Clark, KB7QHC

Hi Richard,

Here are two links to pages that cover the derivation of the formula Zo
= 1/cC and much more.

http://www.speedingedge.com/PDF-File..._Impedance.pdf
http://www.ece.uci.edu/docs/hspice/h...001_2-269.html

Here is the way I proposed to Kevin Schmidt nearly seven years ago after
seeing him use the formula on a web page:

*ASSUME*:
1) An electrical wave travels at the speed of light, c
2) A 'perfect' voltage source without impedance, V
3) A 'perfect' transmission line having no resistance but uniform
capacitance per unit length, C

*CONDITIONS AND SOLUTION*
The perfect voltage source has one terminal connected to the
transmission line prior to beginning the experiment. The experiment
begins by connecting the second terminal to the transmission line. The
voltage source drives an electrical wave down the transmission line at
the speed of light. Because of the limitation of speed, the wave
travels in the shape of a square wave containing all frequencies
required to create a square wave.

The square wave travels down the transmission line at the speed of light
(c). After time (T), the wave has traveled distance cT down the
transmission line, and has charged the distributed capacity CcT of the
line to voltage V over that distance. The total charge Q on the
distributed capacitor is VCcT.

Current (I) is expressed as charge Q per unit time. Therefore the
current into the transmission line can be expressed as

I = Q/T =
VCcT / T = VCc

Impedance (Zo) is the ratio of voltage (V) to current (I). Therefore
the impedance can be expressed as

Zo = V / I =
V / VCc = 1/Cc

We can generalize this by using the velocity of the electrical wave
rather than the speed of light, which allows the formula to be applied
to transmission line with velocities slower than the speed of light.

Of course, only the wave front and wave end of a DC wave can be
measured to have a velocity.

73, Roger, W7WKB

the OBVIOUS error is that the step when the second terminal is connected
DOES NOT travel down the line at c, it travels at some smaller percentage
of c given by the velocity factor of the line.

That IS what I said. Think of the velocity as a moving wall, with the
capacitor charged behind the wall, uncharged in front of the moving wall.

The second OBVIOUS error is the terminology 'DC wave'. you are measuring
the propagation velocity of a step function. this is a well defined
fields and waves 101 homework problem, not to be confused with the much
more common 'sinusoidal stead state' solution that most other arguments on
this group assume but don't understand.



Be real. This experiment can be performed, and the DC switched as
frequently as desired. How square the wave front will be depends upon real
world factors.

Go to a transmission line characteristics table and use the formula to
compare Zo, capacity per length, and line velocity. It will amaze you.

73, Roger, W7WKB

On Fri, 14 Dec 2007 05:18:03 -0800, "Roger Sparks"
wrote:

That IS what I said. Think of the velocity as a moving wall, with the
capacitor charged behind the wall, uncharged in front of the moving wall.
....
Be real. This experiment can be performed, and the DC switched as
frequently as desired. How square the wave front will be depends upon real
world factors.

Go to a transmission line characteristics table and use the formula to
compare Zo, capacity per length, and line velocity. It will amaze you.

Hi Roger,

Take a deep breath, exhale, give what's above some more thought in
light of many objections.

Now, tells us just what significance any of this has in relation to
already well established line mechanics? It certainly isn't different
within the confines of its limitations if that is what you are trying
to impress upon the group. I suppose for a mental short-cut it has
some appeal, we get too many theories here based on approximations to
stricter math. One such example is when an equation of approximation
has forgotten the underlying |absolute value| and suddenly an inventor
arrives with a "new" theory that discovers uses for negative
solutions.

Further, there is nothing DC about it at all. DC is either static
(and in spite of Arthur's corruption of the term, that means no
movement whatever) or it is a constant unvarying current. A
succession of distributed capacitors rules unvarying current out (and
if it isn't already obvious, those unmentioned distributed inductors
in one of your links do too) - hence the step, hence the infinity of
waves, and from this, real world dispersion which kills the step
enough to make that varying current apparent enough so as to remove
all doubt.

73's
Richard Clark, KB7QHC

Richard Clark wrote:
On Fri, 14 Dec 2007 05:18:03 -0800, "Roger Sparks"
wrote:

That IS what I said. Think of the velocity as a moving wall, with the
capacitor charged behind the wall, uncharged in front of the moving wall.
....
Be real. This experiment can be performed, and the DC switched as
frequently as desired. How square the wave front will be depends upon real
world factors.

Go to a transmission line characteristics table and use the formula to
compare Zo, capacity per length, and line velocity. It will amaze you.

Hi Roger,

Take a deep breath, exhale, give what's above some more thought in
light of many objections.

Now, tells us just what significance any of this has in relation to
already well established line mechanics? It certainly isn't different
within the confines of its limitations if that is what you are trying
to impress upon the group. I suppose for a mental short-cut it has
some appeal, we get too many theories here based on approximations to
stricter math. One such example is when an equation of approximation
has forgotten the underlying |absolute value| and suddenly an inventor
arrives with a "new" theory that discovers uses for negative
solutions.

Further, there is nothing DC about it at all. DC is either static
(and in spite of Arthur's corruption of the term, that means no
movement whatever) or it is a constant unvarying current. A
succession of distributed capacitors rules unvarying current out (and
if it isn't already obvious, those unmentioned distributed inductors
in one of your links do too) - hence the step, hence the infinity of
waves, and from this, real world dispersion which kills the step
enough to make that varying current apparent enough so as to remove
all doubt.

73's
Richard Clark, KB7QHC

Hi Richard,

The math seems to work, but if you have no use for it, disregard it. On
the other hand, if another perspective of electro magnetics that
conforms to traditional mathematics can provide additional insight, use it.

I am surprised at your criticism in using DC. To me, a square wave is
DC for a short time period. Is the observation that a square wave can
be described as a series of sine waves troubling to you? Perhaps the
observation that a square wave might include waves of a frequency so
high that they would not be confined in a normal transmission line is
surprising or troubling to you?

My goal is to better understand electromagnetic phenomena. You have
given some very astute insight many times in the past and thanks for
that. Negative comment is equally valuable, but sometimes a little
harder to swallow.

73, Roger, W7WKB

On Fri, 14 Dec 2007 09:45:04 -0800, Roger wrote:

Hi Richard,

The math seems to work, but if you have no use for it, disregard it. On
the other hand, if another perspective of electro magnetics that
conforms to traditional mathematics can provide additional insight, use it.

Hi Roger,

This does not answer why TWO mathematics (both traditional) are
needed, especially since one is clearly an approximation of the other,
and yet offers no obvious advantage. I've already spoken to the
hazards of approximations being elevated to proof by well-meaning, but
slightly talented amateurs.

I am surprised at your criticism in using DC. To me, a square wave is
DC for a short time period.

This single statement, alone, is enough to be self-negating. You
could as easily call a car with a standard stick shift an automatic
between the times you use the clutch - but that won't sell cars, will
it?

Is the observation that a square wave can
be described as a series of sine waves troubling to you? Perhaps the
observation that a square wave might include waves of a frequency so
high that they would not be confined in a normal transmission line is
surprising or troubling to you?

DC as sine waves is not a contradiction on the face of it? DC that
consists of waves of a frequency so high that it would not be confined
in a normal transmission line is very surprising, isn't it?

Would it surprise you to find your batteries in their packaging direct
from the store are radiating on the shelf? They are DC, are they not?
If the arguments of your sources works for an infinite line, they must
be equally true for an infinitesimal open line. When your headlights
are on, do they set off radar detectors in cars nearby because of the
high frequencies now associated with DC?

My goal is to better understand electromagnetic phenomena. You have
given some very astute insight many times in the past and thanks for
that. Negative comment is equally valuable, but sometimes a little
harder to swallow.

The pollution of terms such as DC to serve a metaphor that replaces
conventional line mechanics is too shallow glass to attempt to quench
any thirst.

The puzzle here is the insistence on hugging DC, when every element of
all of your links could as easily substitute Stepped Wave and remove
objections. The snake in the wood pile is once having fudged what DC
means, it is only a sideways argument away from rendering the term DC
useless. Is the term Stepped Wave (the convention) anathema for a
leveraging the novel origination (the invention) of DC Wave?

73's
Richard Clark, KB7QHC

Richard Clark wrote:
The puzzle here is the insistence on hugging DC, when every element of
all of your links could as easily substitute Stepped Wave and remove
objections.

How about "continuous wave" for Morse code?
--
73, Cecil http://www.w5dxp.com

Richard Clark wrote:
On Fri, 14 Dec 2007 09:45:04 -0800, Roger wrote:

Hi Richard,

The math seems to work, but if you have no use for it, disregard it. On
the other hand, if another perspective of electro magnetics that
conforms to traditional mathematics can provide additional insight, use it.

Hi Roger,

This does not answer why TWO mathematics (both traditional) are
needed, especially since one is clearly an approximation of the other,
and yet offers no obvious advantage. I've already spoken to the
hazards of approximations being elevated to proof by well-meaning, but
slightly talented amateurs.

The derivation did several things for me. It clearly explains why we do
not have a runaway current when we first connect a voltage to a
transmission line, what transmission line impedance is, that moving
particles can not be the entire explanation for the electromagnetic wave
(because the energy field moves much faster than the electrons), and
puts into place a richer understanding of inductance.

I am surprised at your criticism in using DC. To me, a square wave is
DC for a short time period.

This single statement, alone, is enough to be self-negating. You
could as easily call a car with a standard stick shift an automatic
between the times you use the clutch - but that won't sell cars, will
it?

We could use the concept of a stepped wave, but that would imply the
need for several steps to develop the formula. Only the square wave
front and continued charge maintenance is required, observations that
can be easily verified by experiment.

Is the observation that a square wave can
be described as a series of sine waves troubling to you? Perhaps the
observation that a square wave might include waves of a frequency so
high that they would not be confined in a normal transmission line is
surprising or troubling to you?

DC as sine waves is not a contradiction on the face of it? DC that
consists of waves of a frequency so high that it would not be confined
in a normal transmission line is very surprising, isn't it?


What is your point here? Are implying that the formula is incorrect
because a sine wave was not mentioned in the derivation. I am sure that
all of the sophisticated readers of this news group understand that the
sharp corner of the square wave is composed of ever higher frequency
waves. This leads Cecil to comment that the leading edge of a square
wave could be composed of photons, which is a valid observation. It
also explains your observation that true square waves are not possible
(I am paraphrasing your comments) because of dispersion.

It is interesting to run an FFT on a square wave to see how the
frequencies can be resolved.

Would it surprise you to find your batteries in their packaging direct
from the store are radiating on the shelf? They are DC, are they not?
If the arguments of your sources works for an infinite line, they must
be equally true for an infinitesimal open line. When your headlights
are on, do they set off radar detectors in cars nearby because of the
high frequencies now associated with DC?

They only set off the radar detectors when I turn them on and off. I
have high power lights!! A lightning strike is a much better example of
DC containing high frequencies.


My goal is to better understand electromagnetic phenomena. You have
given some very astute insight many times in the past and thanks for
that. Negative comment is equally valuable, but sometimes a little
harder to swallow.

The pollution of terms such as DC to serve a metaphor that replaces
conventional line mechanics is too shallow glass to attempt to quench
any thirst.

The puzzle here is the insistence on hugging DC, when every element of
all of your links could as easily substitute Stepped Wave and remove
objections. The snake in the wood pile is once having fudged what DC
means, it is only a sideways argument away from rendering the term DC
useless. Is the term Stepped Wave (the convention) anathema for a
leveraging the novel origination (the invention) of DC Wave?

73's
Richard Clark, KB7QHC

We would complicate the concept and thereby begin to confuse people if
we insisted on using the "Stepped Wave" term. It is a simple step to
recognize that if we can make a wave front with one battery, we can use
a lot of batteries and carefully place and switch them to form a sine
wave. The more batteries and switches, the better the representation.

Is there some harm in considering Zo = 1/cC? It should only add to the
tools we have to explain electromagnetic waves.

73, Roger, W7WKB

Is there some harm in considering Zo = 1/cC? It should only add to the
tools we have to explain electromagnetic waves.

73, Roger, W7WKB

yes. because its WRONG. you have made an assumption that is not realistic
for any transmission line. There is no way a transmission line can have a
velocity factor of 1.0, just can't happen... all the equations fall apart
and become meaningless at that point. there is a reason for the velocity
factor, or beta, depending on which you prefer. learn it, and use it
properly, and it will serve you well.

On Fri, 14 Dec 2007 11:35:25 -0800, Roger wrote:

The derivation did several things for me. It clearly explains why we do
not have a runaway current when we first connect a voltage to a
transmission line,

Hi Roger,

It doesn't describe why the current flows in the first place, does it?

what transmission line impedance is, that moving
particles can not be the entire explanation for the electromagnetic wave
(because the energy field moves much faster than the electrons), and
puts into place a richer understanding of inductance.

And here we begin on the wonderful world of spiraling explanations,
not found in the original source: "Moving particles cannot be the
entire explanation?" How about that in the first place, particles
don't inhabit the explanation at all?

What is your point here? Are implying that the formula is incorrect
because a sine wave was not mentioned in the derivation. I am sure that
all of the sophisticated readers of this news group understand that the
sharp corner of the square wave is composed of ever higher frequency
waves.

I'm even convinced most of them would not call this DC too.

We would complicate the concept and thereby begin to confuse people if
we insisted on using the "Stepped Wave" term.

They would've been confused anyway.

It is a simple step to
recognize that if we can make a wave front with one battery, we can use
a lot of batteries and carefully place and switch them to form a sine
wave. The more batteries and switches, the better the representation.

And this is still DC?

Is there some harm in considering Zo = 1/cC?

This is best left in the privacy of the home.

However, none of your comments respond to the question: What is with
this death grip on DC? What makes it so important that it be so
tightly wedded to Waves? What mystery of the cosmos is answered with
this union that has so long escaped the notice of centuries of trained
thought?

73's
Richard Clark, KB7QHC

This general discussion sounds a lot like a description of a traditional
TDR system using a step function. You should be able to find quite a bit
of information about this process on the web.

A number of relationships among delay, Z0, velocity factor, and L and C
per unit length are quite useful, and I've used them for many years. For
example, a transmission line which is short in terms of wavelength at
the highest frequency of interest (related to the rise time when dealing
with step functions) can often be modeled with reasonable accuracy as a
lumped L or pi network. The values of the lumped components can easily
be calculated from the equations relating delay, Z0, L per unit length,
and C per unit length.

Strictly speaking, DC describes only the condition when a steady value
has existed for an infinite length of time. But a frequency spectrum of
finite width also requires a signal which has been unchanging (except
for periodic variation) for an infinite time. In both cases, we can
approximate the condition with adequate accuracy without having to wait
an infinite length of time. In the case of a step response, we wait
until all the aberrations have settled, after which the response is for
practical purposes the DC response. People used to frequency domain
analysis having trouble with the concept of DC characteristics and
responses can often get around the difficulty by looking at DC as a
limiting case of low frequency.

I don't know if it's relevant to the discussion, but the velocity factor
of many transmission lines is a function of frequency. A classic example
is microstrip line, which exhibits this dispersive property because the
fractions of field in the air and dielectric changes with frequency.
Coaxial line, however, isn't dispersive (assuming that the dielectric
constant of the insulator doesn't change with frequency) because the
field is entirely in the dielectric. It will, therefore, exhibit a
constant velocity factor down to an arbitrarily low frequency -- to DC,
you might say. Waveguides, however, are generally dispersive for other
reasons despite the air dielectric. The shape of the step response of a
dispersive line is very distinctive, and is easily recognized by someone
accustomed to doing time domain analysis.

There seems to be a constant search on this newsgroup for amazing new
principles, and "discoveries" are constantly being made by
misinterpretation and partial understanding of very well established
principles. I sense that happening here. Anyone who's really interested
in gaining a deeper understanding of transmission line principles and
operation can benefit from a bit of study of time domain reflectometry
and other time domain applications. All the fundamental rules are
exactly the same, but the practical manifestations are different enough
that it can give you a whole new level of understanding.

Roy Lewallen, W7EL