# Time delay in lumped element delay line

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

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.

$V_{in}$ is a function of frequency" />

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