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
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