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I was trying to analyse a lumped element-delay line by changing the frequency and measuring \$ V_{in}\$ , as shown in the graph the goal of my analysis is to find the time-delay and the attenuation for the circuit thus finding, the capacitance and inductance for the circuit shown below lumped element delay line

The problem that I am currently facing is I can't relate the time delay, nor the attenuation with the frequency, and the measured \$ V_{in}\$. I have an equation that relate the coefficient of the reflection and propagation waves. as follow

$$V_n=A(e^{i(\omega t-n\phi)}+re^{i(\omega t+n\phi)}$$

where \$ \omega=2\pi f\$, \$n\$ is the voltage in the \$n^{th}\$ section \$ \phi\$ is the phase change per section.

I obtained results for different terminal impedance, namely resistance equal to infinity, zero, and other value for resistance. Any help in how what should I do from here to find attenuation will be appreciated.

<span class=\$ V_{in}\$ is a function of frequency" />

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  • \$\begingroup\$ try measuring the phase of Vout with respect to Vin \$\endgroup\$
    – Neil_UK
    Nov 28 '20 at 19:44
  • \$\begingroup\$ I tried to measure that, but the main problem that I am facing is that the x-axis is measured by frequency, not time. \$\endgroup\$
    – Maxwell
    Nov 28 '20 at 20:26

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