# 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. Mar 25, 2019 at 11:47
• I don't think much interesting can be demonstrated with an eternal, pure sinusoid. All of the interesting transmission line effect are seen with transients or studying the change of gain and phase versus frequency. Jan 28 at 2:01