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MATLAB Assignment relating to applications of electromagnetism

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MATLAB Assignment relating to applications of electromagnetism.
 

1. Generate a Matlab code to implement the above Eq. 25, numerically carry out the associated integral, and therefore compute the input impedance Z; of linear

Question dipoles. Your code should generate a plot of both the real and the imaginary

parts of Z; in Q, displayed in the same figure (the real part on the left scale and the imaginary part on the right scale), as a function of frequency. Matlab has available several different intrinsic functions for performing numer-

Suggestion ical integration, and a good simple and robust one to use in this laboratory is the function “trapz,” which implements the trapezoidal rule (the function being integrated is approximated by straight line segments, causing the area under a real integration function to be approximated by trapezoids). The trapezoidal rule has the advantage of being capable of handling integration points non-uniformly spaced, but I personally prefer to use Simpson’s rule for my integrations. Although

Simpson’s rule can’t handle non-uniform point spacing, the function being inte- grated is instead better approximated by parabola segments. Since unfortunately

Matlab does not seem to have an intrinsic function that implements Simpson’s

 rule, the trapezoidal-rule alternative will have to suffice.

 

When using numerical integration algorithms keep in mind that you usually have the choice of the number of integration points to be used. In the intrinsic Matlab function “trapz” this choice is implicitly made through the number of provided
integrand values. Although more points yields higher accuracy, it requires longer

execution times. On this light, please make sure to experiment a bit and operate

with the minimum number of points that accurately handles the task at hand.

2. Calculate the input impedance of a dipole of length 2h = 250 mm with the fre-

Question quency running from 0 to 2.0 GHz, for three values of the antenna diameter 2a,

namely 2a = 0.001, 4, and 20 mm and provide the corresponding three plots in

your laboratory report. Figure 4 gives you some idea of two useful plot formats.

Both formats complement each other, with the logarithm format providing visu-

alization of the full range of input impedances while facilitating the location of

the all-important resonant frequencies.

Dipoles’ Input Impedance, Zz =R+jX Dipoles’ Input Impedance, Z =R+jX

400 1000 8 8

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getting these 900 900 Sy =

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ar x

a x 2 2

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0 500 1000 1500 2000 0 500 1000 1500 2000

Freq (MHz) Freq (MHz)

Figure 4: Dipole antenna impedance (2h = 250 mm and 2a = 4 mm).

Dashed lines represent negative reacta