Below drawing illustrates a transmission line where the source voltage is:
$$v_s(t)=V_0 x\sin\omega t$$
After reading some texts about the subject, I concluded how to decide whether one must consider transmission line effects or not. If I'm not wrong, to consider transmission effects, basically there must be a considerable phase delay between the source and the load voltages.
Let's say just nearby the source the voltage is approximately equal to \$v_s(t)\$. And let's say the length of the line is \$L\$.
At the end of the line near the load we can say the voltage is delayed so it will be around \$v_s(t-\Delta t)\$.
So here \$\Delta t\$ can be written in terms of the velocity of propagation \$v_p\$ and the line length \$L\$ as:
$$\Delta t = \frac{L}{v_p}$$
So the delayed voltage can be written as:
$$v_s(t-\Delta t) = V_0 x \sin\omega(t-\Delta t)$$
or simply
$$v_s(t-\Delta t) = V_0 x \sin\omega(t-\frac{L}{v_p})$$
from above equation we can easily see the phase delay \$\phi\$ becomes:
$$\phi = \omega\frac{L}{v_p}$$
My question is:
We've just written the phase delay \$\phi\$ as:
$$\phi = \omega\frac{L}{v_p} = 2\pi f \frac{L}{v_p} = (2\pi)\cdot\left(f\frac{L}{v_p}\right)$$
(groupped). Now I see that many text conclude when the \$\phi\$ is large the transmission line effects must be taken into account. Obviously they conclude that increasing the frequency will dramatically increase \$\phi\$ and one must consider transmission line effects.
But knowing that if a phasor in complex plane is shifted by \$2\pi\textrm{[integer]}\$, the phasor actually comes to the same point. There is no phase delay.
Imagine we found the phase delay as \$2\pi\textrm{[integer]}\$. Does that mean we should still consider the transmission line effects even though we calculate zero phase delay?
If the phase delay is \$2\pi\textrm{[integer]}\$, and the integer is \$1000\$ does that mean the voltage is moving like a wave and we should consider transmission line effects? (I think we should since we are dealing with moving waves)
But what if the phase delay \$\phi\$ in radian is \$0.1\$ or \$1\$ or etc. What is the criteria to consider the transmission line effects due to \$\phi\$? For \$\phi>\$ what we should consider transmission line effects?
