Keywords

1 Introduction

To improve the performance of microwave circuits and particularly the passive RFID tags suggested the use of non uniform transmission lines due to their appropriate frequency behaviour [1].

Their fundamental property allows the reduction of the geometric dimensions and improvement of the tag’s radiation pattern [2, 3] .The analysis of such structures is achieved by a numerical calculation program based on the work of Hill, which consists of determining the general solution of the propagation distribution equation of the electric and magnetic fields and deducing the accurate model of the transmission line. Therefore, several non uniform transmission lines with various profiles (hyperbolic, linear and exponential) have been analyzed. Their contribution to improve the pattern and reduce the dimension of passive antenna RFID TAG has been experimentally validated.

2 Analysis of NUTLs

The modelling of a non uniform structure passes by determining the explicit expression describing accurately its behaviour and deducing its scattering matrix S.

The first step is to derive the propagation equations adequately for the non uniform profile. Secondly, we perform mathematical manipulations to transform these equations in the form of a traditional Hill’s equation without a first derivative term. Next, the obtained equation is solved using the Floquet theorem, to explicit the general and particular solutions, respectively. Finally, we use these solutions to calculate the different elements of the scattering matrix S of the lines. More investigations will be carried out to validate this analytic approach and by further developments and experimental prototypes. Results obtained of a simple, exponential and hyperbolic lines optimized to resonate at a fundamental frequency equal to 1 GHz (Figs. 1, 2 and 3) are showed in Table 1.

Fig. 1
figure 1

a Simple λ/4 short-circuits line W1 = 2.988 mm, W2 = 2.88 mm and L = 3.14 cm substrate: epoxy 1.52 mm. b Non uniform λ/4 short-circuits line with linear and hyperbolic profile W1′′′ = 2.988 mm, W2′′′ = 2.88 mm and L′′′ = 4.73 cm Substrate: Epoxy 1.52 mm. c Non uniform λ/4 short-circuits line with exponential profile, W1′ = 2.988 mm, W2′ = 2.88 mm and L′ = 4.73 cm substrate: epoxy 1.52 mm

Full size image
Fig. 2
figure 2

Impedance of different NUTLs depending on the frequency

Full size image
Fig. 3
figure 3

Passive UHF RFID tag designed with simple lines

Full size image
Table 1 Resonant frequency of simple and non uniform lines
Full size table

Actually, the non uniform transmission lines have a frequency behaviour which strictly depends upon their forms and their profiles of non homogeneity. While the transmission structures resonate in a regular multiple of fundamental frequencies, the non uniform lines resonate on frequencies which are different from integer multiples of fundamental.

3 Experimental Application of LNUT

Our methodology consists of replacing uniform structures present on the RFDI TAG and its passive antenna, by equivalent non uniform parts. Indeed, classical passive RFID TAGs in microwave are based on elements used as antennas [4]. Usually, these elements are designed like uniform transmission lines.

The purpose of this work is to develop the same printed circuit structure for both types of RFID chips that operate on two separate frequencies, one at 2.45 GHz and the other at 5.8 GHz. With a Substrate: FR4 (Epoxy glass) and Tag Size: 30 × 90 mm.

Figures 4, 6 and 8 perfectly illustrates the value of using “NULTs” in this type of device. We expect RFID chips in our industrial partner to validate our concept and contribution of adjustments according to the results of measurement campaigns (Figs. 5 and 7).

Fig. 4
figure 4

Operating frequency and radiated pattern of RFID TAG designed with simple lines

Full size image
Fig. 5
figure 5

Passive UHF RFID tag designed with non uniform line LNUT1

Full size image
Fig. 6
figure 6

Operating frequency and radiated pattern of RFID TAG designed with LNUT1

Full size image
Fig. 7
figure 7

Passive UHF RFID tag designed with non uniform line NUTL2

Full size image
Fig. 8
figure 8

Operating frequency and radiated pattern of RFID TAG designed with NUTL2

Full size image

4 Conclusion

Analysis of NUTLs using Hill’s equation is achieved using an efficient iterative method based on Fouquet’ exponents determination. Once voltages and currents are defined over each point along the transmission structure, S parameters and other pertinent parameters s can be easily derived.

Te NUTLs have a frequency behaviour depending tightly on their geometric profiles. This fundamental property was used for reducing RFID tag dimension and improving its radiation pattern. Non uniform structures have exhibited attractive results and obtained results showed good agreement with experience.