**14. TL model for meander antennas**

Commercial and military mobile wireless systems demand for high compactness devices. An important component of any wireless system is its antenna. Whereas significant efforts have been devoted towards achieving low power and miniaturized electronic and RF components, issues related to design and fabrication of efficient, miniaturized, and easily integrable antennas have been overlooked. In this paper a novel approach for antenna miniaturization is presented. The meander topology is proposed as a good approach to achieve miniaturization and a transmission line model for the analysis and synthesis of meander antennas is developed.

Indeed, the miniaturization of an antenna can be accomplished through loads placed on the radiating structure. [32-33]. For example, monopoles were made shorter through center loaded (inductive) or top loaded (capacitive). Hence appropriate loading of a radiating element can drastically reduce the size, however, antenna efficiency may be reduced as well. To overcome this drawback, lumped elements of large dimensions can be created using distributed reactive elements. For this reason, we propose a meander topology that allows us to distribute loading through short-circuited transmission lines.

In the past, meander structures were suitably introduced to reduce the resonant length of an antenna without great deterioration of its performances [34-36].

To exploit the meander topology to miniaturize printed antennas and develop a transmission line model for the analysis and the synthesis of this kind of antennas is proposed an antenna shown in Fig 46. It is a meander printed on the same side of the chassis of a circuit board on a FR4 substrate with r =3.38 and thickness 0.787 mm. The feeding is between the meander structure and the ground plane. Even if the antenna is a printed monopole, it can be studied as an asymmetric dipole and its input reactance has been studied through a transmission line model. It is well known that the resonance condition is obtained when the input impedance is purely resistive [37-39]. The antenna has been modelled as a transmission line periodically loaded from inductive reactances Xm represented by the half meanders shown in Fig 46. We have named half-meander the shorted transmission line of length w/2.

Fig. 46. Meander antenna monopole printed on the same side of the ground plane of the substrate.

The height b of each half meander and their total number *2n* are related to the total length of the monopole *Lax* with the following formula:

$$L\_{\rm ax} = (\mathfrak{L}n + \mathfrak{1})b \tag{25}$$

Each half meander was studied as a short transmission line *w/2* long with a characteristic impedance *Zcm* obtained as:

$$Z\_{\rm cm} = 120 \ln(b \,/\, a) \tag{26}$$

and terminating with a metallic strip having an inductance *Lsc*:

$$L\_{sc} = 2 \ast 10^{\uparrow} b [\ln(8b/a) - 1] \,\text{.}\tag{27}$$

distributed reactive elements. For this reason, we propose a meander topology that allows

In the past, meander structures were suitably introduced to reduce the resonant length of an

To exploit the meander topology to miniaturize printed antennas and develop a transmission line model for the analysis and the synthesis of this kind of antennas is proposed an antenna shown in Fig 46. It is a meander printed on the same side of the chassis of a circuit board on a FR4 substrate with r =3.38 and thickness 0.787 mm. The feeding is between the meander structure and the ground plane. Even if the antenna is a printed monopole, it can be studied as an asymmetric dipole and its input reactance has been studied through a transmission line model. It is well known that the resonance condition is obtained when the input impedance is purely resistive [37-39]. The antenna has been modelled as a transmission line periodically loaded from inductive reactances Xm represented by the half meanders shown in Fig 46. We have named half-meander the

Fig. 46. Meander antenna monopole printed on the same side of the ground plane of the

The height b of each half meander and their total number *2n* are related to the total length of

Each half meander was studied as a short transmission line *w/2* long with a characteristic

(2 1) *L nb ax* (25)

120ln( / ) *Z ba cm* (26)

<sup>7</sup> *L b ba sc* 2 10 [ln(8 / ) 1] . (27)

us to distribute loading through short-circuited transmission lines.

antenna without great deterioration of its performances [34-36].

shorted transmission line of length w/2.

the monopole *Lax* with the following formula:

and terminating with a metallic strip having an inductance *Lsc*:

impedance *Zcm* obtained as:

substrate.

The inductance *Lsc* of the strip with the length *b* and width a was substituted by a line *Lall* long terminating with a short circuit. The length *Lall* was properly chosen because this line had the same inductance of the strip (*Lsc* ).

At the end, the inductance of each meander *Xm* was obtained by the formula (28):

$$X\_{\rm mf} = Z\_{\rm cm} t \text{g} \{ 2\pi \sqrt{\varepsilon\_{c\_{\rm ff}}} \left( w \;/\ 2 + L\_{\rm all} - a \;/\ 2 \right) \}\tag{28}$$

The total characteristic impedance of the transmission line with a length *Lax* and loaded by *2n* half meanders was:

$$Z\_c = 120[\ln(8L\_{ax} \; / \; a) - 1] \tag{29}$$

In Fig. 47 the normalized length *Lax* of the printed monopole versus the normalized thickness a according to the transmission line model for *w / b* = 1 is shown. It is pointed out from the figure that, when *b=w*, the meander length is smaller than the conventional monopole at its resonant frequency.

In Fig 48, for several values of the parameter *x=w/*, the resonant length *Lax/* versus the ratio *w/b* is plotted.

It can be seen that, for each value of *w/b*, a remarkable reduction of the antenna length is obtained by increasing the values of w at the resonant frequency. Therefore, by choosing a value of *w/b*, the model allows to detect the correspondent resonant length of the antenna.

Fig. 47. The normalized length Lax of the printed monopole versus the normalized thickness a according to the transmission line model for *w / b* = 1.

Fig. 48. Transmission line model for meander antenna printed on substrate with *r* =3.38 and s = 0.81 mm for different *x=w/λ*.
