**15. Simulated and experimental results**

To test the validity of the model, simulations were run with full wave commercial software CST Microwave Studio © at a frequency of 2.45 GHz with appropriate model as shows in Fig 49.

Fig. 49. Top and bottom model of meander antenna monopole designed with CST Microwave Studio ©.

The transmission line model (TLM) and the full wave simulation were in a good agreement and the difference between the resonant length obtained by TLM and the full wave

Fig. 48. Transmission line model for meander antenna printed on substrate with

Fig. 49. Top and bottom model of meander antenna monopole designed with CST

The transmission line model (TLM) and the full wave simulation were in a good agreement and the difference between the resonant length obtained by TLM and the full wave

To test the validity of the model, simulations were run with full wave commercial software CST Microwave Studio © at a frequency of 2.45 GHz with appropriate model as shows in

s = 0.81 mm for different *x=w/λ*.

Fig 49.

Microwave Studio ©.

**15. Simulated and experimental results** 

*r* =3.38 and


simulations was within 250 MHz as it has been summarised in Table 2. Figs 47 and Fig. 48 show, respectively, the normalized length Lax versus antenna thickness a for different values of w/b and the normalized length *Lax* versus w/b for different values of *x=w/λ*.


Table 2. Resonant frequencies calculated with FIT method.

The antenna sizes derived from the model allow us to obtain a design very close to the final project which can be quickly optimized by avoiding long simulations with commercial software.

Table 2 shows that the antenna sizes derived from the model allow us to get antenna sizes close to the final structure as the antenna resonates almost at 2.45 GHz. Moreover, in order to get exactly 2.45GHz, a quick optimization has to be carried out by running few simulations with a commercial software.

To validate the proposed TLM method, simulations and measurements have been performed. The antenna has been printed on a Rogers R04003C with r =3.38 and thickness 0.81 mm. A prototype is presented in Fig 50. The geometrical sizes chosen were a=0.5 mm, b=8 mm and w=b that has led to a length *Lax* =56mm by considering 6 half meanders (Fig 50). The board total size is *L1*=72mm and *W1*=32mm, by considering also the chassis. The antenna is fed by a microstrip printed on the back of the chassis by terminating with a stub for achieving good matching. The microstrip is 20mm length and the stub is L2=8mm and W2= 4mm. The dimensions of the microstrip line has been optimized using full wave software to provide better impedance matching for the frequency antenna-resonance.

The simulated and measured return loss is shown in Fig 51. Simulation has been performed by using CST Microwave Studio © 2009 and it has shown a value of -44dB at 2.45 GHz.

Fig. 50. Meander antenna monopole printed on the Rogers R04003C substrate.

The measurements were carried out in an anechoic chamber by connecting the antenna at a network analyser through coaxial cables.

The measured return loss in Fig 51 shows a slight shift of the antenna resonant frequency towards lower frequencies from 2.45 GHz to 2.42 GHz. Nevertheless, a good matching is still observed because the reflection coefficient assumes the value -26 dB instead of -44 dB.

Fig. 51. Comparison of S11 simulation results with measured results.

Fig. 52 shows the E field radiation patterns of the antenna at 2.45 GHz on two principal planes, xz plane (Ф=0°) and yz plane (Ф=90°). The comparison of the radiation patterns shows that simulations and measurements are in a good agreement.

Fig. 50. Meander antenna monopole printed on the Rogers R04003C substrate.

network analyser through coaxial cables.


Fig. 51. Comparison of S11 simulation results with measured results.

shows that simulations and measurements are in a good agreement.

 **S11 [dB]**


The measurements were carried out in an anechoic chamber by connecting the antenna at a

The measured return loss in Fig 51 shows a slight shift of the antenna resonant frequency towards lower frequencies from 2.45 GHz to 2.42 GHz. Nevertheless, a good matching is still observed because the reflection coefficient assumes the value -26 dB instead of

> 1.5 1.66 1.82 1.98 2.14 2.3 2.46 2.62 2.78 2.94 3.1 3.26 3.42 **Frequency [GHz]**

> > Simulated Measured

Fig. 52 shows the E field radiation patterns of the antenna at 2.45 GHz on two principal planes, xz plane (Ф=0°) and yz plane (Ф=90°). The comparison of the radiation patterns

b)

Fig. 52. Comparison of measured and simulated E-field at 2.45 GHz for a) = 0° and b) = 90°.

Fig 53 shows the current distribution on the antenna. It can be observed that the current is particularly intense at the end of each half meander. Full wave simulations confirm that each half meander can be studied as a transmission line terminating in a short circuit.

Fig. 53. Current distribution on the meander antenna.

#### **16. Reference**


[1] T. Tamir, \Leaky-wave antennas", ch. 20 in Antenna Theory, Part 2, R. E. Colin and F. J.

[2] A. A. Oliner, \Leaky-wave antennas", ch. 10 in Antenna Engineering Handbook, 3rd ed.,

[4] T. Tamir, A. A. Oliner, \Guided complex waves, part I: \_elds at an interface", Proc. Inst.

[5] T. Tamir, A. A. Oliner, \Guided complex waves, part II: relation to radiation patterns",

[6] L. O. Goldstone and A. a. Oliner, \Leaky-wave antennas I: rectangular waveguide", IRE Trans. Antennas and Propagation, vol. AP-7, pp. 307-319, Oct. 1959. [7] A. Hessel, \General characteristics of traveling -wave antennas", ch. 19 in Antenna Theory, Part 2, R. E. Colin and F. J. Zucher, Eds., McGraw-Hill, New York, 1969. [8] G. Gerosa and P. Lampariello, \Lezioni di Campi Elettromagnetici I", Edizioni

[10] Pozar, David M. and David H. Schaubert, \Microstrip Antennas: The Analysis and Design of Microstrip Antennas and Arrays", John Wiley, New York, NY, 1995. [11] Pozar, David M., \Microwave Engineering", John Wiley, New York, NY, second

[12] Kumar, Girish and K. P. Ray, \Broadband Microstrip Antennas", Artech House, Boston,

[13] Menzel Wolfgang, \A New Travelling-Wave Antenna in Microstrip", Archiv fur

[14] Yau, D., N. V. Shuley, and L. O. McMillan, \Characteristics of Microstrip Leaky-Wave

Elektronik und Ubertragungstechnik (AEU), Band 33, Heft 4, pp. 137-140, April 1979.

Antenna Using the Method of Moments", IEE Proc. Microwave Antennas and

Fig. 53. Current distribution on the meander antenna.

Zucher, Eds., McGraw-Hill, New York, 1969.

Elec. Eng., vol. 110, pp. 310-324, Feb. 1963.

[9] F. Frezza, Lezioni di Campi Elettromagnetici II, March 2004.

Propag, Vol. 146, No. 5, pp. 324-328, October 1999.

Ingegneria 2000, 1995.

edition, 1998.

MA, 2003.

R. C. Hansen, Ed., McGraw-Hill, New York, 1993.

Proc. Inst. Elec. Eng., vol. 110, pp. 325-334, Feb. 1963.

[3] C. H. Walter, \Traveling Wave Antennas", McGraw-Hill, New York, 1965.

**16. Reference** 

