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-----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&rsquo;t work basically because is the >> wrong frequency region&hellip;

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