Matlab Work: Electric field pattern of two isotropic sources (same amplitude with phase difference from 0 to 360 degree)

Electric field pattern is the graphical representation of radiation properties of isotropic sources with their governing mathematical equations. Graphical representation is very important aspect for engineering students in order to visualize facts and real time scenarios. The purpose of this simulation in Matlab GUI is to plot the electric field pattern of two isotropic sources placed in x-axis on either side of origin having same amplitude and variable phase difference. The GUI allows us to understand the field pattern at different phase difference ranging from 0^o to 360^o. The isotropic sources are as follows:

Assumption made is that the two isotropic sources are source 1 and source 2. Let their constant electric field E_o=0.5 V/m and distance of separation d=λ/2. So the relative distance between sources expressed in radian becomes d_r=2πd/ λ=2π(λ/2)/ λ= π. So the general electric field expression: E=2E_o cos(d_rcosφ/2) + (δ /2) reduces to

E=cos(π cosφ/2)+ (δ /2)………………………………….(i)

which can be easily plotted in Matlab. Here φ is the phase angle that also varies from 0 to 360 degree (0 to 2π). 

The plot of E field vs φ for phase difference δ=0⁰ is shown as below. I have used a slider in GUI that has range from 0 to 360 degree and it facilitates us to have virtual analysis as like in real time environment.  

The pattern equation for δ=0⁰ from equation (i) is E=cos(π cosφ/2). The patterns are a bidirectional figure of eight with maxima along the y direction, i.e. normal to the arrays.

Similarly the E patterns for different phase values (δ) are as below:

δ=90^o(π/2)

Field equation is E=cos(π cosφ/2)+ (π /4).

 

δ=180^o(π)

Field equation is E=cos(π cosφ/2)+ (π /2). Field pattern is a relatively broad figure of eight with the maximum field in the same direction as the line joining the source (x-axis).

δ=270^o(3π/2)

Field pattern is E=cos(π cosφ/2)+ (3π /4)

The field pattern tool was very helpful during my Antennas and Propagation course of 7^th semester. You can try similar for the field pattern of more than two isotropic sources or simply for two isotropic sources placed in y-axis, provide the knowledge of field equations.

To view source code, click here.