Criteria for considering transmission line effects due to phase delay

Question

Below drawing illustrates a transmission line where the source voltage is:

V_s(t) = V₀ x sin(ωt)

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-Δt).

So here Δt can be written in terms of the velocity of propagation v_p and the line length L as:

Δt = L/v_p

So the delayed voltage can be written as:

V_s(t-Δt) = V₀ x sin(ω(t-Δt)) or simply

V_s(t-Δt) = V₀ x sin(ω(t-L/v_p))

from above equation we can easily see the phase delay φ becomes:

φ = ω x L/v_p

My question is:

We've just written the phase delay φ as:

φ = ω x L/v_p which is

φ = 2 x pi x f x L/v_p or grouping

φ = (2 x pi) x (f x L/v_p)

Now I see that many text conclude when the φ is large the transmission line effects must be taken into account. Obviously they conclude that increasing the frequency will dramatically increase φ and one must consider transmission line effects.

But knowing that if a phasor in complex plane is shifted by

(2 x pi) x integer

the phasor actually comes to the same point. There is no phase delay.

Imagine we found the phase delay as (2 x pi) x 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 x pi) x 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 φ in radian is 0.1 or 1 or ect. What is the criteria to consider the transmission line effects due to φ? For φ > what we should consider transmission line effects?

Answer 1

People often consider the RISETIME as crucial in determining when to terminate a transmission line. lines with NO resistance at the source, nor at the load, will in theory have reflections forever.