|
Hi, Ed,
Maybe off the rails except that many folks here make measurements of transmission lines and maybe some of them will venture into low enough frequencies so that the high frequency approximations are not applicable.
Maxwell and Heaviside, in my opinion, both achieved rather amazing insights without which electromagnetic theory might have lost years of progress.
I should note that, although the internal inductance of a wire will decrease with frequency at a rate that depends on diameter because of skin effect, the low frequency internal inductance is not dependent on the diameter of the wire but is the same for all solid conductors of round cross section: approximately 50 nH per meter.
73,
Maynard
W6PAP
toggle quoted message
Show quoted text
On 4/9/25 19:28, AG6CX via groups.io wrote: ?
?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
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: <nanovna-users@groups.io>
Sent: Apr 9, 2025 7:42 AM
To: <nanovna-users@groups.io>
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
|
?
?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
toggle quoted message
Show quoted text
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: <nanovna-users@groups.io>
Sent: Apr 9, 2025 7:42 AM
To: <nanovna-users@groups.io>
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
|
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
toggle quoted message
Show quoted text
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: <nanovna-users@groups.io>
Sent: Apr 9, 2025 7:42 AM
To: <nanovna-users@groups.io>
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
|
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
toggle quoted message
Show quoted text
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: <nanovna-users@groups.io>
Sent: Apr 9, 2025 7:42 AM
To: <nanovna-users@groups.io>
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
|
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”.
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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: <nanovna-users@groups.io>
Sent: Apr 9, 2025 7:42 AM
To: <nanovna-users@groups.io>
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
|
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
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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: <nanovna-users@groups.io>
Sent: Apr 9, 2025 7:42 AM
To: <nanovna-users@groups.io>
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
|
As someone who does both measuring and modeling.. Modeling is what gives you insight into things like sensitivity and variability. Measuring, to some extent, confirms what you modeled, or, that you’ve got something wrong in the model.
Modeling also can give you a much wider tradespace - building a new model is essentially free.
I build a fair number of antennas for various uses - Here’s an example: I’ve got a spacecraft that has two dipoles about 5 meters long, crossed at right angles. Easy enough to model, or build a mockup and measure (a bit harder, but doable). But I might have a question about “if there’s an angular misalignment of 10cm at the tip, does that make a difference in my measurement”. Easy question to answer with modeling, very, very difficult with measurement (time consuming, if nothing else). Consider someone putting up a LPDA with 10 elements - modeling can tell you what happens to the performance if the elements are skewed by 10 degrees pretty quickly. Testing would be a pain.
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On Apr 9, 2025, at 10:05, Team-SIM SIM-Mode via groups.io <sim31_team@...> wrote:
?Hi Maynard
Electrical modelisation is appreciated as a first approche of computing in the history, after what we procede with computers simulation last twenty years, in present time there is no better then a good measurement at the desired frequency, its become possible with the cheap devices as nanovna , just need some good method and practice , lt should defeat all mathematical modelisations or PC simulations.
73s Nizar
|
Hi Maynard
Electrical modelisation is appreciated as a first approche of computing in the history, after what we procede with computers simulation last twenty years, in present time there is no better then a good measurement at the desired frequency, its become possible with the cheap devices as nanovna , just need some good method and practice , lt should defeat all mathematical modelisations or PC simulations.
73s Nizar
|
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)
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-----Original Message----- From: <nanovna-users@groups.io> Sent: Apr 9, 2025 7:42 AM To: <nanovna-users@groups.io> 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
|
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
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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 <sim31_team@...> wrote:
Hi Patricio
Thanks? for clarification ,? I do not understand this graphic zone circled on red color below
73's? Nizar
<Capture d_????cran 2025-04-06 174532.png>
|
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
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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 <sim31_team@...> wrote:
Hi Patricio
Thanks for clarification , I do not understand this graphic zone circled on red color below
73's Nizar
<Capture d_????cran 2025-04-06 174532.png>
|
This is the part of LF model that don’t work basically because is the wrong frequency region…
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On 6 Apr 2025, at 1:49?PM, Team-SIM SIM-Mode via groups.io <sim31_team@...> wrote:
Hi Patricio
Thanks for clarification , I do not understand this graphic zone circled on red color below
73's Nizar
<Capture d_????cran 2025-04-06 174532.png>
|
Hi Patricio
Thanks for clarification , I do not understand this graphic zone circled on red color below
73's Nizar
|
This chart shows the typical behaviour of a loosy coaxial cable over frequency. Basically there are two models , the low frequency model in this case the dielectric loose are very small then G tends to zero and is removed from the Zo formula. The serial equivalent loose resistor this is basically the resistance of the metallic boundary of the cable. It drops to lower frequency to a minimum this is determined by the conductor resistivity and uses to be very small but never zero , L goes up from the High Frequency model because appears magnetic fields inside de conductors… as frequency goes down the Zo goes up. In the other hand on high frequency region L an C are dominant on Zo formula and results on a more stable value. Skin effect reduces de magnetic field inside de conductor and L becomes defined basically by metallic boundaries.
At all this is not a problem in the practical world because the coaxial cables are used on high frequency regions , at audiofrecuencies becomes a shielded cable and Zo concept are irrelevant. In metrology these variations are taken to correct high precision measurements and standards characterization.
At very low frequencies where transmission lines are required usually higher Zo is adopted too . This is the frequency where LF and HF curves crosses are higher as Zo is lower. This is of course with the same materials on each case.
I?m sorry for my engllsh is not very good. If you have any difficulties to understand that I say please let me know.
Regardd, Patricio.
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On 6 Apr 2025, at 5:31?AM, Team-SIM SIM-Mode via groups.io <sim31_team@...> wrote:
Hi Patricio
I do not understand this chart, can you explaine it more pse.
73's Nizar
|
Hi
With same coax, same method, same NanoVNA H4 (1.2.40 DiSlord) surprisingly i have some different Zc values for 50Mhz & 100Mhz
50Mhz ---> Zc = 49.0 Ohm
100Mhz ---> Zc = 43.5 Ohm
73's Nizar
2Mhz ---> Zc = 52.6 Ohm
3Mhz ---> Zc = 52.5 Ohm
7Mhz ---> Zc = 52.0 Ohm
14Mhz ---> Zc = 53.0 Ohm
18Mhz ---> Zc = 53.0 Ohm
21Mhz ---> Zc = 54.0 Ohm
24Mhz ---> Zc = 54.0 Ohm
29Mhz ---> Zc = 52.0 Ohm
Direct measurement with Dislord Coax function gives Zc = 51.77 Ohm with same cable.
|
Hi Patricio
I do not understand this chart, can you explaine it more pse.
73's Nizar
|
Oops! I should have R >> jwL, not R >> jwC. My error.
73,
Maynard
W6PAP
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On 4/5/25 16:20, Maynard Wright, P. E., W6PAP via groups.io wrote: An interesting chart.? Note that below about 300 kHz, the imaginary component of the characteristic impedance can no longer be ignored and, if you are working on any cables at voice frequencies or where R >> jwC, the angle of the characteristic impedance will be around -45 degrees, which is characteristic of most telephone cable pairs (or any other transmission lines) at voice frequencies.
73,
Maynard
W6PAP
On 4/5/25 12:10, Patricio Greco via groups.io wrote:
?
On 5 Apr 2025, at 12:03?PM, Jim Lux via groups.io <jimlux@...> wrote:
Not unexpected
Zc is sqrt( (R+jomegaL)/(G+jomegaC))
Mostly determined by L/C, but the R is in there too, and it goes up as frequency goes up, because of skin effect. For HF the dielectric loss (G) is really tiny, so the R term dominates.
On Apr 5, 2025, at 05:34, Patricio Greco via groups.io <> <patricio_greco@... <mailto:patricio_greco@...>> wrote:
?Interesting , the Zo uses to rise a little when the frequency goes down.
On 5 Apr 2025, at 6:43?AM, Team-SIM SIM-Mode via groups.io <> <sim31_team@... <mailto:sim31_team@...>> wrote:
Hi
for same RG213? cable (25m length) loaded by a 50.3 Ohm resistor
I used the same?? circle methode centered on smith graph with the renormalized Z0 impedance ( option added by DiSlord)? for different ferquency's band (span always fixed? to 4 Mhz)? :
2Mhz?? --->? Zc = 52.6? Ohm
3Mhz? --->? Zc = 52.5 Ohm
7Mhz?? --->? Zc = 52.0 Ohm
14Mhz? ---> Zc? = 53.0 Ohm
18Mhz? ---> Zc = 53.0 Ohm
21Mhz? ---> Zc = 54.0 Ohm
24Mhz? ---> Zc = 54.0 Ohm
29Mhz? ---> Zc = 52.0 Ohm
Direct measurement with Dislord Coax function gives Zc = 51.77 Ohm with same cable.
73's? Nizar
|
An interesting chart. Note that below about 300 kHz, the imaginary component of the characteristic impedance can no longer be ignored and, if you are working on any cables at voice frequencies or where R >> jwC, the angle of the characteristic impedance will be around -45 degrees, which is characteristic of most telephone cable pairs (or any other transmission lines) at voice frequencies.
73,
Maynard
W6PAP
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On 4/5/25 12:10, Patricio Greco via groups.io wrote: ?
On 5 Apr 2025, at 12:03?PM, Jim Lux via groups.io <jimlux@...> wrote:
Not unexpected
Zc is sqrt( (R+jomegaL)/(G+jomegaC))
Mostly determined by L/C, but the R is in there too, and it goes up as frequency goes up, because of skin effect. For HF the dielectric loss (G) is really tiny, so the R term dominates.
On Apr 5, 2025, at 05:34, Patricio Greco via groups.io <> <patricio_greco@... <mailto:patricio_greco@...>> wrote:
?Interesting , the Zo uses to rise a little when the frequency goes down.
On 5 Apr 2025, at 6:43?AM, Team-SIM SIM-Mode via groups.io <> <sim31_team@... <mailto:sim31_team@...>> wrote:
Hi
for same RG213 cable (25m length) loaded by a 50.3 Ohm resistor
I used the same circle methode centered on smith graph with the renormalized Z0 impedance ( option added by DiSlord) for different ferquency's band (span always fixed to 4 Mhz) :
2Mhz ---> Zc = 52.6 Ohm
3Mhz ---> Zc = 52.5 Ohm
7Mhz ---> Zc = 52.0 Ohm
14Mhz ---> Zc = 53.0 Ohm
18Mhz ---> Zc = 53.0 Ohm
21Mhz ---> Zc = 54.0 Ohm
24Mhz ---> Zc = 54.0 Ohm
29Mhz ---> Zc = 52.0 Ohm
Direct measurement with Dislord Coax function gives Zc = 51.77 Ohm with same cable.
73's Nizar
|
?
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On 5 Apr 2025, at 12:03?PM, Jim Lux via groups.io <jimlux@...> wrote:
Not unexpected
Zc is sqrt( (R+jomegaL)/(G+jomegaC))
Mostly determined by L/C, but the R is in there too, and it goes up as frequency goes up, because of skin effect. For HF the dielectric loss (G) is really tiny, so the R term dominates.
On Apr 5, 2025, at 05:34, Patricio Greco via groups.io <> <patricio_greco@... <mailto:patricio_greco@...>> wrote:
?Interesting , the Zo uses to rise a little when the frequency goes down.
On 5 Apr 2025, at 6:43?AM, Team-SIM SIM-Mode via groups.io <> <sim31_team@... <mailto:sim31_team@...>> wrote:
Hi
for same RG213 cable (25m length) loaded by a 50.3 Ohm resistor
I used the same circle methode centered on smith graph with the renormalized Z0 impedance ( option added by DiSlord) for different ferquency's band (span always fixed to 4 Mhz) :
2Mhz ---> Zc = 52.6 Ohm
3Mhz ---> Zc = 52.5 Ohm
7Mhz ---> Zc = 52.0 Ohm
14Mhz ---> Zc = 53.0 Ohm
18Mhz ---> Zc = 53.0 Ohm
21Mhz ---> Zc = 54.0 Ohm
24Mhz ---> Zc = 54.0 Ohm
29Mhz ---> Zc = 52.0 Ohm
Direct measurement with Dislord Coax function gives Zc = 51.77 Ohm with same cable.
73's Nizar
|
Hi Jim Lux
"L , C & R exhibit some frequency-dependent variation; they do not have a perfectly flat response across frequency. This behavior depends on the dielectric material used, skin effect and the physical design of the coaxial cable. so theroritical formula is 1sft order modelisation , NanoVNA mesure them physically, just we should have the good method and practice at a reasonnable accuracy.
73's Nizar
|
