Why is there a phase difference of 180 degrees in the Transmission Matrix between Thh and Tvv in a pure LOS transmission?

Franziska Rasp

Hi Everyone,

 

I have a question regarding the transmission matrix (Thh, Thv; Tvh, Tvv) in the full polarimetric simulation in WinProp:

Why is there a phase difference of 180 degrees between Thh and Tvv in a pure LOS transmission?

The transmission matrix itself is clear to me (as described here: What does the transmission matrix values (Tvv, Tvh, Thv, Thh) represent? - WinProp - Altair Products - Altair Community)

• T=[Thh, Thv

Tvh, Tvv]

In my case I investigate a very simple setup: Pure LOS transmission (see in attachment)

• 1 omni directional Tx, 1 omni directional Rx, distance d between them
• propagation method: SRT, only transmission (no reflection, to transmission, no reflection..)
• fresnel Coefficients

 

In my understanding both, Thh and Tvv should be identical:

• attenuation: lambda/(4*pi*d) 
• phase: beta*d=d* c/lambda

• T=attenuation*exp(-j*phase)*1/sqrt(2)*[1,0;0, 1]

Yet the result is different: I observe that Thh has a phase shift of 180 degrees to Tvv:

• T= attenuation*exp(-j*phase)*1/sqrt(2)*

  [-1, 0

  0, 1]

 

Can anyone explain that to me? I searched lots of literature and papers, yet I could not find an explanation for that.

Thank you!

 

 

 

 

 

Zeina

Hi Franzisks,

When dealing with polarization, you should first consider the direction of propagation of the wave. This is to be done from the perspective of each antenna. When a transmitting antenna is radiating a signal in a given direction w.r.t. its local coordinate system, the receiving antenna is receiving it in the opposite direction (180 degrees) w.r.t the same coordinate system.

In analogy to reflection at normal incidence by a planar interface, vertically polarized field components do not change direction when the direction of propagation of the wave is 180 degrees inverted, whereas the horizontally polarized components have a 180 degrees phase shift. The (-) in the Thh component of the transmission matrix you have observed probably reflects that.

I hope this was helpful!

Franziska Rasp

Thank you very much for your answer @Zeina, that makes sense.