In an experiment the cutoff frequency of a lumped transmission line is determined by measursing the ratio of the output/input voltages. The lumped transmission line is a ladder network of 40 capacitors and 40 inductors,

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image source: Thermal and Electrical Wave experiments, ICL,2020

This is connected to an oscilloscope which generates sinusoidal waves. Reflection occurs at the BNC input point because the $Z_{transmission-line}>Z_{coaxial-cable}$, $$\frac{V_{reflected}}{V_{in}}=\frac{Z_b(\omega)-Z_a}{Z_b(\omega)+Z_a}$$ where $Z_a=Z_{coaxial}, Z_b=Z_{transmission-line}$ $$Z_b(\omega)=\sqrt{(L/C)(1/(1-\omega^2 LC/4)))}$$ which is the characteristic impedance of the ladder network. Using $$V_{transmitted}/V_{in}=\frac{2Z_a}{Z_b(\omega)+Z_a}$$, here I assume $V_{transmitted }$ is proportional to the voltage measured by the probe of the oscilloscope, so the voltage ratio vs $\omega$ cannot be linear due to $Z_b=Z_b(\omega)$.

However, my experimental data suggests a linear relation

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whereas I expected something (red curve) like due to the last equation. Why is my interpreation incorrect? enter image description here



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