**4. Modelling of radiation and scattering characteristics of frame antennas**

## **4.1. Loop antenna of closed and open arrays**

Various types of loop antennas are used in radio communication, radiolocation, TV. Further in this chapter, two types of loop antennas are studied: on the basis of closed arrays with a lateral length 0,25 *L* (fig.34a) and on the basis of open arrays with a lateral length *L* 0,5 (fig.34b). Double loop antennas and arrays of such antennas are studied. The double loop antennas are used with a reflector (fig.34c) and without a reflector. The distance between the plane of the array and the reflector is Н.

The polarization of the antenna is linear. The E-plane is the XY plane, the H-plane is the plane φ=const. The antenna characteristics depend on geometrical sizes of L, β, d, Le, Lh, Dh, H. The antenna is excited by voltage between points 1 and 2. In version (a), the resistance between points (input resistance of the antenna) can be made equal to 50 Ohm, in version (b) – an active part of the input resistance – 200-300 Ohm. Gain in the version (b) of the antenna is 3 dB bigger, than in the version (a) of the antenna. In versions (a) and (b), directors can be used to increase the gain, fig. 35.

In the literature, the methods of antenna excitation were studied, their key properties were studied briefly [Rothammels K, 1995], but there is no information about the main regularities. Further, these regularities are examined for version 34а only, because this version is generally used.

**Figure 34.** Franklin antenna with linear reflectors and directors

**Figure 35.** Loop antennas

**Figure 33.** Dependence of Gain on number of dipoles

0

2

4

G, dB

6

8

**4.1. Loop antenna of closed and open arrays** 

between the plane of the array and the reflector is Н.

directors can be used to increase the gain, fig. 35.

If to apply a system of reflectors or (and) directors to an antenna, it is possible to make a directional pattern sector-shaped in the H-plane. Fig. 33 shows such an antenna and its

0 2 4 6 8 10 12 14

N

A Franklin antenna and its modifications can be used as transmitting antennas in radio

**4. Modelling of radiation and scattering characteristics of frame antennas** 

Various types of loop antennas are used in radio communication, radiolocation, TV. Further in this chapter, two types of loop antennas are studied: on the basis of closed arrays with a

double loop antennas are used with a reflector (fig.34c) and without a reflector. The distance

The polarization of the antenna is linear. The E-plane is the XY plane, the H-plane is the plane φ=const. The antenna characteristics depend on geometrical sizes of L, β, d, Le, Lh, Dh, H. The antenna is excited by voltage between points 1 and 2. In version (a), the resistance between points (input resistance of the antenna) can be made equal to 50 Ohm, in version (b) – an active part of the input resistance – 200-300 Ohm. Gain in the version (b) of the antenna is 3 dB bigger, than in the version (a) of the antenna. In versions (a) and (b),

In the literature, the methods of antenna excitation were studied, their key properties were studied briefly [Rothammels K, 1995], but there is no information about the main regularities. Further, these regularities are examined for version 34а only, because this

(fig.34b). Double loop antennas and arrays of such antennas are studied. The

(fig.34a) and on the basis of open arrays with a lateral length

K1 – N=2; K2 – N=4; K3 – N=7; K4 – N=13

directional pattern.

lateral length 0,25 *L*

version is generally used.

links.

*L* 0,5

**Figure 36.** Loop antennas with directors

Fig. 36a shows the dependence of an active part of an input resistance (R) on an angle β, if a reactive part of the input resistance is equal to zero ( 0 *X* ). The condition 0 *X* is met by changing a lateral length of an array ( *L* ) for each preset value of *H H* ' / . Fig. 36b shows the dependence of *L L* ' / on an angle β (values of *L*' meet the condition 0 *X* ). The calculations have been made for the antenna with a wire diameter of Do=0,006 λ, d=0,006 λ.

Numerical Simulations of Radiation and Scattering Characteristics of Dipole and LOOP Antennas 185

*ff f f* (10-20)%. The values of Gain and F/B

270 280 290 300 310 320 330 340 <sup>0</sup>

Frequency, MHz

 Gain F/B

It follows from the results of the numerical simulation, that at a level of VSWR<2, the

in the said bandwidth vary little. The matched bandwidth increases, if R increases at a medium frequency. To widen the matched bandwidth, additional elements are used in the

Interaction of loop of antennas as a part of an array results in changing of their characteristics. It shall be taken into consideration, when designing antenna arrays. Fig. 39 shows directional patterns in the Е and Н-planes of a loop antenna with an input resistance of 50 Ohm: isolated one (a); when taking into account its interaction with two neighbouring emitters – one on the left and one on the right (b); and taking into account its interaction with four neighbouring emitters – two on the left and two on the right. The values of input resistance, gain and parametre F/B are also shown in the figures. The calculations have been made for a linear array, in which emitters are located in the E-plane, at a frequency of 300 MHz (as an example). The distance between the neighbouring emitters is equal to 0,65λ. It follows from the results of simulation that the interaction influences an input resistance and F/B parametre insignificantly. The directional pattern and gain influence the interaction greatly, but differences in influence of various number of interacting loop antennas are insignificant (fig.39b and 39c). It means that when simulating multiple-unit arrays of loop antennas, it is possible to take into consideration interaction of each emitter only with its nearest emitters, and further to use the theorem of multiplication of directional patterns.

(a) (b)

dB

Fig. 40 illustrates difference in influence of interaction in a linear array and in an annular array. The figure shows directional patterns of a loop antenna with the same geometrical sizes without taking interaction into consideration (a), when taking interaction into consideration with two neighbouring emitters (b), and with four neighbouring emitters (c). The linear distance between the neighbouring emitters is equal to 0.65λ, the angle between

percentage bandwidth is max min ( ) / 100 *<sup>o</sup>* 

270 280 290 300 310 320 330 340 0.8

Frequency, MHz

 1 2

**Figure 39.** Dependence of VSWR, Gain and F/B parametre on frequency

**4.2. Interaction of loop antennas as part of antenna array** 

axes of antennas is equal to 12°.

loop antenna.

1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6

VSWR

**Figure 37.** Dependence of input resistance (a) and array lateral length (b) on angle β

It follows from fig. 36а that, by selecting the values of L and β at preset Н, it is possible to make input resistance R preset and to meet the condition 0 *X* .

The antenna band properties are illustrated by fig. 37, 38. The calculation has been made for the antennas calculated so that at a frequency of 300 MHz the input resistance was equal to *R* 50 Ohm, 0 *X* , see fig. 37a, and *R* 75 Ohm, 0 *X* , see fig. 37b. Fig. 38a shows the dependence of VSWR on frequency. For antenna 1 with the input resistance of 50 Ohm at a frequency of MHz, VSWR has been calculated in a line with the characteristic resistance of 50 Ohm (graph 1), for antenna 2 with the input resistance of 75 Ohm, VSWR has been calculated in a line with the characteristic resistance of 75 Ohm (graph 2). It is evident that the antenna with a higher input resistance is matched to a bigger bandwidth. Fig. 38b shows the dependences of gain and F/B parametre for the second antenna.

**Figure 38.** Dependence of input resistance on frequency

It follows from the results of the numerical simulation, that at a level of VSWR<2, the percentage bandwidth is max min ( ) / 100 *<sup>o</sup> ff f f* (10-20)%. The values of Gain and F/B in the said bandwidth vary little. The matched bandwidth increases, if R increases at a medium frequency. To widen the matched bandwidth, additional elements are used in the loop antenna.

**Figure 39.** Dependence of VSWR, Gain and F/B parametre on frequency

184 Numerical Simulation – From Theory to Industry

 H'=0,16 H'=0,18 H'=0.20

the dependence of *L L* ' /

Ohm

R, Ohm

Fig. 36a shows the dependence of an active part of an input resistance (R) on an angle β, if a reactive part of the input resistance is equal to zero ( 0 *X* ). The condition 0 *X* is met by

calculations have been made for the antenna with a wire diameter of Do=0,006 λ, d=0,006 λ.

It follows from fig. 36а that, by selecting the values of L and β at preset Н, it is possible to

(a) (b)

L'

The antenna band properties are illustrated by fig. 37, 38. The calculation has been made for the antennas calculated so that at a frequency of 300 MHz the input resistance was equal to *R* 50 Ohm, 0 *X* , see fig. 37a, and *R* 75 Ohm, 0 *X* , see fig. 37b. Fig. 38a shows the dependence of VSWR on frequency. For antenna 1 with the input resistance of 50 Ohm at a frequency of MHz, VSWR has been calculated in a line with the characteristic resistance of 50 Ohm (graph 1), for antenna 2 with the input resistance of 75 Ohm, VSWR has been calculated in a line with the characteristic resistance of 75 Ohm (graph 2). It is evident that the antenna with a higher input resistance is matched to a bigger bandwidth. Fig. 38b shows

(a) (b)

Ohm

140 R

X

40 60 80 100 120

Betta, deg.

270 280 290 300 310 320 330 340 -60

Frequency, MHz

on an angle β (values of *L*' meet the condition 0 *X* ). The

 H'=0,16 H'=0,18 H'=0.20 . Fig. 36b shows

changing a lateral length of an array ( *L* ) for each preset value of *H H* ' /

**Figure 37.** Dependence of input resistance (a) and array lateral length (b) on angle β

make input resistance R preset and to meet the condition 0 *X* .

the dependences of gain and F/B parametre for the second antenna.

**Figure 38.** Dependence of input resistance on frequency

280 290 300 310 320 330 -40

Frequency, MHz

 R X 40 60 80 100 120

Betta, deg.

#### **4.2. Interaction of loop antennas as part of antenna array**

Interaction of loop of antennas as a part of an array results in changing of their characteristics. It shall be taken into consideration, when designing antenna arrays. Fig. 39 shows directional patterns in the Е and Н-planes of a loop antenna with an input resistance of 50 Ohm: isolated one (a); when taking into account its interaction with two neighbouring emitters – one on the left and one on the right (b); and taking into account its interaction with four neighbouring emitters – two on the left and two on the right. The values of input resistance, gain and parametre F/B are also shown in the figures. The calculations have been made for a linear array, in which emitters are located in the E-plane, at a frequency of 300 MHz (as an example). The distance between the neighbouring emitters is equal to 0,65λ. It follows from the results of simulation that the interaction influences an input resistance and F/B parametre insignificantly. The directional pattern and gain influence the interaction greatly, but differences in influence of various number of interacting loop antennas are insignificant (fig.39b and 39c). It means that when simulating multiple-unit arrays of loop antennas, it is possible to take into consideration interaction of each emitter only with its nearest emitters, and further to use the theorem of multiplication of directional patterns.

Fig. 40 illustrates difference in influence of interaction in a linear array and in an annular array. The figure shows directional patterns of a loop antenna with the same geometrical sizes without taking interaction into consideration (a), when taking interaction into consideration with two neighbouring emitters (b), and with four neighbouring emitters (c). The linear distance between the neighbouring emitters is equal to 0.65λ, the angle between axes of antennas is equal to 12°.

. Fig. 42b illustrates the dependence of the input

resistance on the number of arrays. The sizes of elements of the arrays are chosen so that the

**Figure 41.** Directional patterns of a loop antenna, when taking into consideration its interaction as a

(a) (b)

102030405060708090 100

Ohm

(a) (b) (c)

**Figure 43.** Dependence of parametres of a loop antenna on the number of arrays at 0,25 *L*

 Gain F/B

 R X

<sup>23456</sup> -60 -50 -40 -30 -20 -100

Mp

number of Mp arrays at 0,25 *L*

part of an annular array

10.0 10.5 11.0 11.5 12.0 12.5 13.0 13.5 14.0 14.5 15.0 15.5 16.0 16.5 17.0 17.5 18.0 18.5 19.0 19.5 20.0

dB

input resistance was equal to 50 Ohm at Мp=2.

**Figure 42.** Connecting pattern of arrays in linear array

23456

Mp

2

1

**Figure 40.** Loop antenna directional patterns (a) and when taking into consideration its interactions as a part of a linear array (b), (c).

It follows from the comparison of fig. 39 and fig. 40 that interaction between loop antennas in an annular array is less than interaction in a linear array.

#### **4.3. Linear antenna arrays with coherent excitation**

To increase gain, it is possible to use linear arrays of loop antennas with series excitation. Fig. 41 shows the schema of connections of arrays among themselves at a lateral length of the array *L* 0,25 (a) and at a lateral length of the array *L* 0,5 (b) by the example of the antennas with Mp=4. The gain increases, if the number of the arrays increases due to narrowing of the main lobe in the H-plane. Fig. 42 shows the dependence of the gain on the number of Mp arrays at 0,25 *L* . Fig. 42b illustrates the dependence of the input resistance on the number of arrays. The sizes of elements of the arrays are chosen so that the input resistance was equal to 50 Ohm at Мp=2.

**Figure 41.** Directional patterns of a loop antenna, when taking into consideration its interaction as a part of an annular array

**Figure 42.** Connecting pattern of arrays in linear array

186 Numerical Simulation – From Theory to Industry

part of a linear array (b), (c).

the array *L* 0,25

**Figure 40.** Loop antenna directional patterns (a) and when taking into consideration its interactions as a

(a) (b) (c)

It follows from the comparison of fig. 39 and fig. 40 that interaction between loop antennas

To increase gain, it is possible to use linear arrays of loop antennas with series excitation. Fig. 41 shows the schema of connections of arrays among themselves at a lateral length of

antennas with Mp=4. The gain increases, if the number of the arrays increases due to narrowing of the main lobe in the H-plane. Fig. 42 shows the dependence of the gain on the

(b) by the example of the

(a) and at a lateral length of the array *L* 0,5

in an annular array is less than interaction in a linear array.

**4.3. Linear antenna arrays with coherent excitation** 

**Figure 43.** Dependence of parametres of a loop antenna on the number of arrays at 0,25 *L* 

It follows from the results of simulation that it is not reasonable to make Mр>4 in the antenna. For each M value, it is necessary to optimise the sizes of elements of arrays in order to obtain the preset input resistance.

Numerical Simulations of Radiation and Scattering Characteristics of Dipole and LOOP Antennas 189

The simulation results, given in this chapter, complete the information about dipole and loop antennas that is available in the literature, and can be used to choice a type of an antenna according to specified requirements and after estimating its main characteristics. Numerical simulation of an antenna can be done with the use of the formulas given in the description of a mathematical model. When using a program developed on the basis of these formulas, it is necessary to carry out research into the convergence of the results of calculation. The most sensitive parametre of the antenna in relation to the number of segments of division of conductors (M) is the input resistance. When using impulse functions as the basis and weight ones, it is possible to be oriented towards the following recommendations: the ratio of a segment length to a conductor diameter *L Ao* / 2 0,8-1,2;

In some cases, the results given in the graphs can be used directly with the use of

We express aur gratitude to D.Moskalev and V.Kizimenko for the useful discussion of the

*Antenna Theory*. (1997). Analysis and design. Second Edition Balanis, C.A. John Wiley&Sons.

Aisenberg, G.Z, Jampolsky, V.G. and Terjoshin, O.N. (1977). *Antennas UHF.* M.Svjaz.

Brown, G.H., Epstein, J and Liwis, R.F. (1937). Groud System as a Factor in Antenna

*Computer Techniques for Electromagnetics*. Edition by Mittra, R. (1973). Pergamon Press. New

Drabkin, A.L. and Zuzenko, V.L. (1961). *Antenna-feeder devices*. M. Sovetskoe radio.

Bruckmann, H. (1938).*Uber die Theorie der Erdvarluste von Antennen*.//TFT 27, H.2 pp.29-38. Crispin, J.W., Maffett A.L.(1965). *Radar Cross-Section Estimation for Complex* 

*Shapes*.//Proceeding of the IEEE. −Vol. 53. − № 8. − 1965. pp.1115-1125.

Fletcher, C.A.J. (1984). *Computational Galerkin method*. Springer-Verlag, New York.

**5. Conclusion** 

electrodynamic scaling.

**Author details** 

**6. References** 

Inc.

Russia.

York.

Russia.

results described in this chapter.

Oleg A. Yurtsev and Grigory V. Ptashinsky

Efficiency.//Proc. IRE, June 1937, pp.753-787.

Franckin, C.S. (1924). British patent № 242342.

Fradin, A.Z. (1977). *Antenna-feeder devices*. M.Sviaz. Russia.

*Belarusian State University of Informatics and Radioelectronics, Belarus* 

the number of segments at a wavelength: 80-200.

In a linear array consisting of arrays with a lateral length *L* 0,5 , the gain is 3 dB more approximately.

Fig. 43а shows the version of a linear array with a quasi-isotropic directional pattern in the E-plane. Such a pattern can be obtained, if to bend all the arrays along the Z axis at an angle =35-40°. It is possible to ensure the preset input resistance by choosing the sizes of elements. Fig. 43b,c shows the directional patterns and the values of the parameters of G (Gain), NR (nonuniformity of a directional pattern in the E-plane), R, X, values of VSWR in a line with a wave resistance of 50 Ohm.

**Figure 44.** Loop antenna with quasi-isotropic directional pattern in E-plane
