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How would I determine the upper frequency limit of a transmission line from these plots? I plotted these in matlab after being given some RLCG values. About all I can seem to understand from these plots is when I can start using the high frequency approximation formulas for calculating characteristic impedance and etc, which is around 30MHz.

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The definition used (Zo=sqrt(L/C) is when frequency is high enough. It is not the upper limit but the lowest frequency usable as a "perfect line" with Zo = Constant resistive only and "easy" matching impedance is possible. VSWR = 1, no reflected wave.

However, one can use this line at low frequencies as done in the old time of telephony. More complicated. One important problem is "attenuation" and phase "shifting" coefficients and so, there is a "maximum length" of use without amplifiers or "corrections networks". Unless I'm mistaken, the attenuation (Voltage, freq > 30 MHz) is -0.2 db / m.

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