The radiation characteristic of the electromagnetic field generated by a conductor and a dipol antena.

Moroianu, Corneliu ; Samoilescu, Gheorghe ; Patrichi, Ilie 等

1. INTRODUCTION

In this presentation are shown the simulation results regarding the directivity characteristics of an conductor passed by a electric current and of an symmetric dipole antenna for different reports l = the conductor's length (antenna)/wave length of the current that passes through the conductor (antenna). The simulation has been made after mathematical models.

2. THE MODELING OF MAGNETIC FIELD PRODUCED BY A CONDUCTOR

The magnetic induction and the magnetic field intensity are calculated using the vector magnetic potential [bar.A]. It is considered a rectilinear and filiform conductor of [l.sub.o], Figure 1 length in the air, passed by the current I and the magnetic induction in a point P(r, [phi], z) is calculated. it is used the cylindrical coordinate system (r, 9, z), with Oz axis along the conductor axis fig.1. (Bessonov,1986).

The vector magnetic potential produced by a filiform closed circuit passed by a current I have the known expression:

[bar.A] = [[mu].sub.0] x I / 4[pi] [??] [bar.dl] / R (1)

In the analyzed case, the contribution of filiform circuit portion of [l.sub.0], length, at the value point P(r, [phi], z), is given by the relation:

[FIGURE 1 OMITTED]

In any point, the vector magnetic potential [bar.A] has the direction of the current passing through the conductor, and its value, in the module, is:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

As the vector magnetic potential [bar.A] is oriented to Oz axis, it result that [A.sub.r] = [A.sub.[phi]] = 0 and [A.sub.z] = A, so that the magnetic induction in the point P(r, [phi], z) is given by the expression:

[bar.B] = rot[bar.A] = [partial derivative][A.sub.z] / [partial derivative]r [[bar.n].sub.[phi]] = [partial derivative]A / [partial derivative]r [[bar.n].sub.[phi]] (4)

Taking into account the relation (3) according to (4) the expression of the magnetic induction becomes:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)

3. THE MODELING OF MAGNETIC FIELD PRODUCED BY A DOUBLE-WIRE (BIFILAR) LINE

According to the Figure 2, we consider the bifilar line formed by two wires of l length, passed by the currents of the same intensity but of opposite directions, the distance between the wires being of 2d. The axes of the conductors, as in the previous cases, are parallel to Oz, axis and the plane xOy passes through the half of the conductors. We note with L = l/2, with [r.sub.i] [s.sub.i] [r.sub.2] the distances from the observation point P (x,y,z) to the two wires and with [zeta] the distance corresponding to a certain point on the conductors (fig. 2).

It has been mentioned that [A.sub.y] = [A.sub.x] = 0, [A.sub.z] [not equal to] 0.

[FIGURE 2 OMITTED]

The vector magnetic potential [A.sub.z], in any point P, is equal to the difference of vector potentials generated by the two section of the circuit:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)

After calculation, it results:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)

From the relation:

[bar.B] = rot[bar.A] = rot[[bar.A].sub.z] (8)

It rezults:

[B.sub.x] = [partial derivative][A.sub.z] / [partial derivative]y, [B.sub.y] = [partial derivative][A.sub.z] / [partial derivative]x, [B.sub.z] = 0 (9)

With the relations:

[r.sup.2.sub.1] = [(y - d).sup.2] + [x.sup.2] (10)

[r..sup.2sub.2] = [(y + d).sup.2] + [x.sup.2] (11)

The expression (7) becomes:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (12)

After calculation, it is obtained, with the notation:

[R.sup.2.sub.1] = [L.sup.2] + [r.sup.2.sub.1], [R.sup.2.sub.2] = [L.sup.2] + [r.sup.2.sub.2] (13)

It rezults:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (14)

4. THE SIMULATION RESULTS REGARDING THE DIRECTIVITY CHARACTERISTIC

Bellow are shown the simulation results regarding the directivity characteristics of an conductor passed by a electric current and of an symmetric dipole antenna for different reports 1 = the conductor's length (antenna)/ wave length of the current that passes through the conductor (antenna) (Samoilescu 2006). The simulation has been made after mathematical models

4.1 Isolated conductor passed by a progressive current wave

[FIGURE 4 OMITTED]

4.2 Conductor isolated in no-load at the end

[FIGURE 5 OMITTED]

[FIGURE 6 OMITTED]

4.3 Dipole symmetric antenna

[FIGURE 7 OMITTED]

5. CONCLUSION

The results obtained after the measurements were made, have been compared with the ones obtained after simulations. Generally the modeling of antennas and conductors is made with a large number of soft and a program dedicated to the electromagnetic's field analysis. The obtaining of resulting characteristics was possible by using the Mathlab programme.

6. REFERENCES

Bessonov, L. (1986). Bazele teoretice ale electrotehnicii. Campul Electromagnetic, Theoretical principles of electrotehnics, Magnetic Field, Editura E.D.Varsovia, Moscova

Constantine, B. (1997). Antenna theory, analysis and design, John Wiley & Sons Inc, New York

Hortopan, G. (1998). Principii si tehnici de compatibilitate electromagnetica, Principles and techniques electromagnetic compatibility, Editura Tehnica, ISBN 9733112879, Bucuresti

Nicolau, E. (1982). Antene si propagare, Antenna and aerial propagation, Editura Didactica si Pedagogica, Bucuresti

Samoilescu,G. (2006), Electric Propulsions, Editura ANMB, ISBN 9738303516, Constanta