Explanation of Lambda by 2 for waveguides

hello,
from my understanding of wave guides that when we walk λg/2 from one point we get to an identical point (this agrees with smith chart as the perimeter is equivelant to λ/2) ,i am confused here cause lets say if we considered that the wave vector is β , then the phase shift between the two points is βd=β*λ/2=(2π/λ)*(λ/2)=π >> i dont get why the phase shift is π and not as i was expecting to be 2π.
thnx.
a.safwat

Hi

You have to remember that lambda/2 is 180 degress and this correspond to pi.
So what you have done is correct.

Regards

well that is what i dont get , how it is pi and in the same time we say that the two points are the same

That is because the two points are NOT the same. If you measured the difference between a waveguide of length L, and one that is L + λ/2 long, you would see that the TRANSMISSION PHASE varies by 180 degrees at the frequency where the longer guide was λ/2 longer.

However, if you are talking about a load at the end of a waveguide, and you are looking at the impedance at the other end, then you have to send a signal down the guide, reflect it off of the load, and have it travel back to the source. So, for a REFLECTION measurement, if you make a measure of a load at the end of a waveguide of L length, and then substitute another waveguide of length L + λ/2, in the later case the signal travels down the original length PLUS 180 degrees, reflects off of the load, and travels back to the source thru the original length PLUS ANOTHER 180 degrees. The total additional phase shift is then 360 degrees, so the reflection coefficient in either case has the exact same phase angle.

hello safwat

Any sine wave with wavelength λ is periodically with a period = λ .. so how it is λguide/2 in T.L ?

As we know the components of the system are
source,
T.L,
load.

The src send a traveling (moving) sine wave with wavelength λ along the T.L until it reaches the load.

If the load is not matched with the characteristic impedance of T.L some of the power will be reflected back as a traveling sine wave with wavelength λ so it will move in opposite direction to the incident one.

So we have 2 waves one moving from left to right >>>> and the other from right to left <<<<

these 2 waves will be added to each other to form another wave (don't forget that we add to moving signal)

the amplitude of the resulted signal (which is called the SWR pattern) will be inphase by λg/2.