?
?nanoVNAers:
I fear this most interesting discussion is heading off the nanoVNA rails.
Maynard’s offerings are extensions of Oliver Heaviside’s evolution of the Telegrapher’s Equation, as are responses of many on the net.
The equations come from Oliver Heaviside who developed the transmission line model starting with an August 1876 paper, On the Extra Current. The model demonstrates that the electromagnetic waves can be reflected on the wire, and that wave patterns can form along the line.
He managed to turn Maxwell’s work into practicum.
Maynard’s ham station certainly came together sometime after 1876, but his antenna radiated power that was certainly following the theory.
For those who may have heard about the
Telegrapher’s Equation, but just want a cursory view, and maybe enough totals it up during the breaks at Field Day, try this:
Telegrapher's Equation - Derivation, Solved Examples, Applications - GeeksforGeeks ( )
geeksforgeeks.org ( )
( )
If you really want to do a dive into the whole story, read this:
On Heaviside's contributions to transmission line theory: waves, diffusion and energy flux | Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences ( )
royalsocietypublishing.org ( )
( )
Get past the intense stare in the picture, and read up. You’ll be smarter than you were before you read it. You might even give a presentation at your local ham club, and win first prize! (Unless it’s FARS, where the starters are at the Nobel level, and the bench is deep and world class.)
I’d keep a copy of Chipman (1968 - available on eBay etc for $40 or so) in your kit bag.
I’d also discount most well-intended but generally flawed YouTube and social media,
Amazing what these old Coots knew!
Armed with your new knowledge and your nanoVNA and a balun under each arm, you’ll be incredibly knowledgeable, well equipped, and likely insufferable.
If you really want to be the BSD on the topic, read Schelkunoff, Bell Systems Technical Journal, volume 35, number 4,September 1955, Conversion of Maxwell’s Equations into Generalized Telegraphist’s Equations.
I’d refer you to a couple of Owen Dufffy’s posts in the topic, but you may have to hit Wayback for those.
73,
Ed McCann
AG6CX
Sausalito CA
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On Apr 9, 2025, at 6:01?PM, Maynard Wright, P. E., W6PAP via groups.io
<ma.wright@...> wrote:
? One reason for a varying inductance in a line is that the total
inductance per unit length is due to the combination of the internal and
external inductance of the involved conductors. ?At low frequencies where
skin effect is negligible, the combination of the two is relatively
independent of frequency. ?As the frequency rises, the current is
concentrated more and more toward the surface of the conductors and the
magnetic flux that links current internal to the line is reduced.
At high enough frequencies so that the current flows almost entirely in a
very thin surface layer of the conductor, there is little linkage internal
to the conductor and essentially no internal inductance. ?As the frequency
increases under this circumstance, essentially no further meaningful
reduction in internal inductance occurs and the inductance of the
conductor, or conductors, is almost entirely due to external linkage and
the inductance of the line becomes constant with increasing frequency.
73,
Maynard
W6PAP
On 4/9/25 16:30, Maynard Wright, P. E., W6PAP via groups.io wrote:
Yes: I've worked mostly with paired, balanced lines (telephone cable
pairs) but the principle is the same.? AIEE Transaction 59-778,
"Transmission Characteristics of PIC Cable," General Cable Corp., 1959,
presents measurements of plastic insulated telephone cable pairs of
various gauges.? As an example, one measurement of 19 gauge pairs shows:
1 kHz??? 1.0 mH per mile
2 kHz??? 1.0
6 kHz??? 0.98
50 kHz??? 0.93
100 kHz??? 0.90
1 MHz??? 0.76
where I am interpolating from a graph.? From the text concerning the
measurements of inductance: "Inductance changes very little with frequency
as compared to changes observed in the resistance; and even less with
temperature.? The change with frequency in minor up to 40 kc; in the range
from 40 kc up to 1000 kc the change is more important although at the
higher frequencies the inductance is changing less rapidly because, at
some frequency beyond 1000 kc, the inductance will approach a constant
value and not change with either frequency or temperature."
As most of the interest in 1959 was in voice transmission and analog
carrier telephone systems, this study didn't look at transmission above 1
MHz.
73,
Maynard
W6PAP
On 4/9/25 15:10, Jim Lux via groups.io wrote:
I venture L is constant.? L is about the magnetic fields, which in turn is
about current distribution, and the interaction of the magnetic fields in
one part of a circuit (wire, component) with another.?? Aside from the
small effect of skin effect (which would be at higher frequencies, and in
particular “proximity effect” in close wound coils) the current is being
carried in exactly the same geometry.? Can you cite an example from theory
or literature (e.g. Grover’s NBS doc) that shows L varying with frequency?
It is true that if you *measure* L, you might find it appearing to vary:
e.g. parasitic C in the “along the TL” sense:? Segment N-1’s magnetic
field interacts with segment N, which interacts with segment N+1.? And
there’s potentially some small C between N-1 and N, and N+1, too. (that is
it might look like a chain of parallel LCs).? Which is different than C to
“the other side of the line or ground or free space”.
On Apr 9, 2025, at 14:19, Maynard Wright, P. E., W6PAP via groups.io
<ma.wright@...> wrote:
?Hi, Jim,
L is approximately constant at sufficiently high frequencies, but over the
range of frequencies represented by the figure of interest here, L varies
considerably for most lines.? At frequencies below several kHz, L is
essentially constant.? Above that, both R and L vary with frequency
according to a very complex law over and interval of three or four
decades.? Above that interval, L is independent of frequency and R
increases directly as the square root of frequency. ?(From Chipman,
Section 5.5).
73,
Maynard
W6PAP
On 4/9/25 09:49, Jim Lux via groups.io wrote:
I would say that L remains constant (it's mostly determined by the
physical construction, and the length), as long as it's not one of those
funky delay line coaxes where the center is a spiral wrapped on a ferrite
core. Same with C - it's all about the two diameters, and epsilon, which
for most popular dielectrics is pretty constant with frequency.? Unless
there's water or a liquid involved.
The things that change with frequency are R (skin depth) and G (dielectric
loss)
-----Original Message-----
From: <[email protected]>
Sent: Apr 9, 2025 7:42 AM
To: <[email protected]>
Subject: Re: [nanovna-users] Measurement correction for Zc Coax
caracteristic Impedance
If you need to calculate the characteristic impedance over a range of
frequencies that overlaps the curved segment of the figure and, if you can
assume that G=0 for all frequencies of interest, a further simplification
is possible: use the low frequency approximation at all frequencies.
If you are looping through tabular values of C, R, and L, or using
approximating expressions, then as wL / R becomes very large, the low
frequency approximation approaches the high frequency approximation as a
limit.
Although R and L are generally variable with frequency, it is often
possible to assume that C is constant over a wide range of frequencies.
73,
Maynard
W6PAP
On 4/8/25 07:45, Maynard Wright, P. E., W6PAP via groups.io wrote:
True!? The three expressions in the figure represent the exact formula, >
a low frequency approximation, and a high frequency approximation.? On >
the logarithmic scale of the figure, the low frequency approximation is >
asymptotic to a straight line, approaching that line very closely at low >
enough frequencies.
In the figure, the straight line representing the low frequency >
approximation is extended below the horizontal straight line >
representing the high frequency approximation.? But the conditions that >
make the low frequency approximation reasonable, R >> wL, are not true >
above around 300 kHz for virtually all transmission lines and the actual >
impedance begins to move toward the high frequency approximation through >
a curved region for which you must use the exact expression if you want >
accurate calculations.
So the extension of the low frequency approximation represents a segment >
of the curve which will not be useful for representing most, if not all, >
actual lines.
It is important to note that below about 300 kHz, the imaginary >
component of the characteristic impedance is not insignificant and, in >
the limit as the frequency goes lower, will be equal in magnitude to the >
real component so the impedance will have an angle of -45 degrees.? This >
is true of telephone cable pairs at voice frequencies, almost all of >
which exhibit a phase angle of between -44 and -45 degrees.
Since the high frequency approximations are not applicable where the >
phase of the characteristic impedance departs significantly from zero >
degrees, telephone engineers working on voice frequency facilities >
rarely use SWR and reflection coefficient, and use instead return loss >
and reflection loss.
That's not very important to most of us in radio work unless we are >
reading material that was originally intended for folks working at lower >
frequencies.
73,
Maynard
W6PAP
On 4/6/25 10:42, Patricio Greco via groups.io wrote:
This is the part of LF model that don’t work basically because is
the >> wrong frequency region…
On 6 Apr 2025, at 1:49?PM, Team-SIM SIM-Mode via groups.io >>> wrote:
Hi Patricio
Thanks? for clarification ,? I do not understand this graphic zone >>>
circled on red color below
73's? Nizar
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