polloss

Begin with a 45° polarized transmitted field and a receiver that is horizontally polarized. By default, the transmitter and receiver local axes coincide with the global coordinate system. Compute the polarization loss in dB.

fv_tr = [1;1];
fv_rcv = [1;0];
rho = polloss(fv_tr,fv_rcv)

rho = 
3.0103

The loss is 3 dB as expected because only half the power of the field matches to the receive antenna polarization.

Begin with identical transmitter and receiver polarizations. Place the receiver at a position 100 meters along the y-axis. The transmitter is at the origin (its default position) and both local coordinate axes coincide with the global coordinate system (by default). First, compute the polarization loss. Then, move the receiver 100 meters along the x-axis, and compute the polarization loss again.

fv_tr = [1;0];
fv_rcv = [1;0];
pos_rcv = [0;100;0];
rho(1) = polloss(fv_tr,fv_rcv,pos_rcv);
pos_rcv = [100;100;0];
rho(2) = polloss(fv_tr,fv_rcv,pos_rcv)

rho = 1×2

     0     0

No polarization loss occurs at either position. The spherical basis vectors of each antenna are parallel to other antenna and the polarization vectors are the same.

Start with identical transmitter and receiver polarizations. Put the receiver at a position 100 meters along the y-axis. The transmitter is at the origin (default) and both local coordinate axes coincide with the global coordinate system (default). Compute the loss, and then rotate the receiver 30° around the y-axis. This rotation changes the azimuth and elevation of the transmitter with respect to the receiver and, therefore, the direction of polarization.

fv_tr = [1;0];
fv_rcv = [1;0];
pos_rcv = [0;100;0];
ax_rcv = azelaxes(0,0);
rho(1) = polloss(fv_tr,fv_rcv,pos_rcv,ax_rcv);
ax_rcv = roty(30)*ax_rcv;
rho(2) = polloss(fv_tr,fv_rcv,pos_rcv,ax_rcv)

rho = 1×2

         0    1.2494

The receiver polarization vector remains unchanged. However, rotating the local coordinate system changes the direction of the field of the receiving antenna polarization with respect to global coordinates. This change results in a 1.2 dB loss.

Start with identical transmitter and receiver polarizations. Put the receiver at a position 100 meters along the y-axis. The transmitter is at the origin (default) and both local coordinate axes coincide with the global coordinate system (default). First, compute the polarization loss. Then, move the transmitter 100 meters along the x-axis and 100 meters along the y-axis, and compute the polarization loss again.

fv_tr = [1;0];
fv_rcv = [1;0];
pos_rcv = [0;100;0];
ax_rcv = azelaxes(0,0);
pos_tr = [0;0;0];
rho(1) = polloss(fv_tr,fv_rcv,pos_rcv,ax_rcv,pos_tr);
pos_tr = [100;100;0];
rho(2) = polloss(fv_tr,fv_rcv,pos_rcv,ax_rcv,pos_tr)

rho = 1×2

     0     0

There is no polarization loss at either position because the spherical basis vectors of each antenna are parallel to their counterparts and the polarization vectors are the same.

Specifying identical transmitter and receiver polarizations, plot the loss as the local receiving antenna axes rotate around the $$x$$-axis.

fv_tr = [1;0];
fv_rcv = [1;0];

The position of the transmitting antenna is at the origin and its local axes align with the global coordinate system. The position of the receiving antenna is 100 meters along the global $$x$$-axis. However, its local $$x$$-axis points towards the transmitting antenna.

pos_tr = [0;0;0];
axes_tr = azelaxes(0,0);
pos_rcv = [100;0;0];
axes_rcv0 = rotz(180)*azelaxes(0,0);

Rotate the receiving antenna around its local $$x$$-axis in one-degree increments. Compute the loss for each angle.

angles = [0:1:359];
n = size(angles,2);
rho = zeros(1,n); % Initialize space
for k = 1:n
    axes_rcv = rotx(angles(k))*axes_rcv0;
    rho(k) = polloss(fv_tr,fv_rcv,pos_tr,axes_tr,...
        pos_rcv,axes_rcv);
end

Plot the polarization loss.

hp = plot(angles,rho);
hax = hp.Parent;
hax.XLim = [0,360];
xticks = (0:(n-1))*45;
hax.XTick = xticks;
grid;
title('Polarization loss versus receiving antenna rotation')
xlabel('Rotation angle (degrees)');
ylabel('Loss (dB)');

The angle-loss plot shows nulls (Inf dB) at 90 degrees and 270 degrees where the polarizations are orthogonal.