Selectively Removing the Polar Axis Labels in Matlab

In Matlab polar plots, the default is to show the whole 360 degrees of the whole graph and also include the polar labels up to 360. If some of the labels are desired not the displayed selectively, one remedy is to replace the corresponding strings with empty string. The procedure is pretty simple and I am showing it below.

First assume that we have such a code that plots the polar plot of a radiation pattern of an antenna array.

set(0,'defaultFigureColor',[1 1 1]) 

clear all; clc;

freq=1e9;
c=3e8;
lambda=c/freq;
T= 1/freq;
omega=2*pi*freq;
k=2*pi/lambda;

Ns=20;
ds=lambda/Ns;

Nt=25;
dt=T/Nt;
t=0:dt:(1*T);

R=(0*lambda):ds:(8*lambda);
Ntheta=240;
dtheta=2*pi/Ntheta;

theta=0:dtheta:(2*pi);


x=R.'*cos(theta);
y=R.'*sin(theta);

delta=(pi/3);

figure (10); clf; 
d = lambda/2;
A = [1 1 1 1 1 1 1]; % Amplitude of each array antenna
Fa=zeros(1,length(theta));
for i=0:(7-1)
    temp =  (A(i+1) * exp(-1i*i*delta + 1i*k*(i*d-3*d)*cos(theta)));
    Fa = Fa + temp;
end
Fa=abs(Fa);
kk=polar(theta,-Fa/max(Fa));   hold on; axis off;

 
The resulting plot is shown below where polar labels up to 330 degrees are shown.

Assume that we do not want to display the labels larger than 180 degrees, the remedy is simply to find the corresponding handle to that string and then replace it with empty string as shown below.

set(findall(gca,'String','210'),'String',' ')
set(findall(gca,'String','240'),'String',' ')
set(findall(gca,'String','270'),'String',' ')
set(findall(gca,'String','300'),'String',' ')
set(findall(gca,'String','330'),'String',' ')



 

Corner Reflector (FDTD Animation)

Two corner reflectors with two different tilt angles have been simulated for demonstrating their reflection properties. The simulations are rendered using the total-field/scattered-field finite-difference time-domain algorithm. An identical incoming plane wave in the negative vertical direction hits the corner reflectors. Although having different tilt angles, they reflect the incoming way in the same positive vertical direction. Corner reflectors are known to be retro-reflectors and consists of 2 or more mutually perpendicular and intersecting flat surfaces. They automatically reflect the waves back towards to the source. In practice, they are used for calibration purposes (e.g. meteorological radars) and range detection. Also in maritime and air navigation, they are used to mark the desired objects on the radar screen (e.g. buoys, ships, runways etc). Corner reflectors are also used to as safety reflectors for cars, bikes, traffic signs and similar devices. Here, the reflectors are in the passive mode, but can also be used in semi-active mode to enhance the directivity of dipole antennas. Basically, by placing the dipole antenna in front of a corner reflector, the combined corner-reflector dipole antenna has a better directivity.

Standing Wave Patterns in Medium with Multiple Interfaces

The generation of standing wave patterns in a medium with three different dielectric permittivities. The reflection and transmission along the two interfaces are shown. Since there are infinitely many reflections, only the overall left and right traveling and the total waves are shown in the animation. When the total traveling field is plotted in space at different time instants (as in the bottom figure), the standing wave patterns can easily be observed.

For similar animations involving a single interface, see below:



Standing Wave Pattern (SWR) and Propagation in Lossy Medium

Standing Wave Pattern (SWR) and Propagation in a Lossless Medium

Phased Array Beam Steering Animation

Beam steering via phased antenna arrays is demonstrated. The arrays are  composed of 7 point sources uniformly spaced in a linear fashion (uniform linear array (ULA). The antenna separation is denoted by the parameter d. When the separation is smaller, the directivity of the array is narrower. Each antenna element in the array is fed with a relative phase shift of "delta" with respect to the adjacent on (the rightmost antenna is the reference antenna where no phase shift is applied, i.e. delta=0).

Doppler Effect Animation

Effect of Perfectly Matched Layers (PML) in FDTD Simulations

Although it is pretty straightforward for researchers in the field of modeling via FDTD or FEM, PML can puzzle those who do not have any modeling background. Therefore, here we try to simply show what happens with and without a PML in a free space propagation modeling.

Basically, we demonstrate the effects of the perfectly matched layers in finite-difference time-domain (FDTD) simulations. Here, a point source transmits a spherical wave and the simulation domain is truncated in two different ways. In the first case (left one) no PML region is utilized whereas in the second one (right) PML region is included. It is clearly observed that PML absorbs the incoming waves mimicking a infinite domain simulation whereas the simulation without PML, spurious reflections occur due to termination of the computational boundary.

Periodic Band Gap (PGB) Waveguide and Propagation - FDTD Simulation

Inspired by the following video:
http://www.youtube.com/watch?v=O-6l0bvAda0

Guiding EM waves via periodic structure. The frequency of operation is 11.085 GHz. The relative dielectric permittivity of the square blocks are 11.56 and the ambient medium is air. Each block is 3.5 mm x 3.5 mm.

The main reference is the below dissertation:
Marcelo Bruno Dias, "Estudo da Propagação de Ondas Eletromagnéticas em Estruturas Periódicas". Graduation Dissertation - Electrical Engineering Course, Universidade Federal do Pará (UFPA), Belém, Pará Brazil, 2003.

More details can be found in their lab web site:
www.lane.ufpa.br/publicacoes.html

Dipole Antenna Radiation

Finite-difference time-domain (FDTD) simulation of a 2 wavelengths long dipole antenna at 400 MHz in free space. The radiation pattern is very different than that of the traditional half-wavelength dipole antenna. Nulls in the broadside and endpoints are clearly visible

Dish Antenna Animation (Parabolic reflector)