- #1
niko2000
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Hi,
I am trying to calculate the power of a reflected electromagnetic field and can't find a physical explanation for a given solution.
I've noticed the following example:
The Plane has a radar for altitude measurement which emmits the power Ptx at the frequency ftx. Calculate the power of the received waves when the plane altitude is h=60m and gamma (reflection) factor of the ground is 0.1.
The solution is Prx = Gtx*Grx((c/ftx)/(4*Pi*2*h))^2*gamma^2
What I don't understand here is why is it appropriate to take 2*h as a radius.
c/fth is the wave length
Gtx and Grx are the gains of the receiver and transmitter
and the factor (4*Pi*r)^2 in the denominator comes from spherical geometry (the sphere with radius r has a surface 4*Pi*r^2 - another 4*Pi comes from gain formula derivation)
The factor gamma is squared because the Poynting vector is a product of Electric and magnetic force and the ground reflects both thus gamma^2.
What I don't understand here is why the radius is set as 2*h.
I tried to solve the problem the following way:
The wave power at the point of collision is proportional to 1/(4*Pi*h)^2. At that point we consider the ground reflets 1/gamma^2 of the power and the reflected power at the receiving point is proportional to 1/(4*Pi*h^2).
I would appreciate if anyone could correct my point of view and explain what's the correct way to model a reflected electromagnetic wave.
Thank you!
Niko
I am trying to calculate the power of a reflected electromagnetic field and can't find a physical explanation for a given solution.
I've noticed the following example:
The Plane has a radar for altitude measurement which emmits the power Ptx at the frequency ftx. Calculate the power of the received waves when the plane altitude is h=60m and gamma (reflection) factor of the ground is 0.1.
The solution is Prx = Gtx*Grx((c/ftx)/(4*Pi*2*h))^2*gamma^2
What I don't understand here is why is it appropriate to take 2*h as a radius.
c/fth is the wave length
Gtx and Grx are the gains of the receiver and transmitter
and the factor (4*Pi*r)^2 in the denominator comes from spherical geometry (the sphere with radius r has a surface 4*Pi*r^2 - another 4*Pi comes from gain formula derivation)
The factor gamma is squared because the Poynting vector is a product of Electric and magnetic force and the ground reflects both thus gamma^2.
What I don't understand here is why the radius is set as 2*h.
I tried to solve the problem the following way:
The wave power at the point of collision is proportional to 1/(4*Pi*h)^2. At that point we consider the ground reflets 1/gamma^2 of the power and the reflected power at the receiving point is proportional to 1/(4*Pi*h^2).
I would appreciate if anyone could correct my point of view and explain what's the correct way to model a reflected electromagnetic wave.
Thank you!
Niko