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
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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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