# Criteria for considering transmission line effects due to phase delay

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?

• 2 pi is still a phase delay if any information transfer is involved, and thus in any situation that matters. A pure sinusoid does not transmit any information. – Edgar Brown Mar 25 '19 at 11:47