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This paper presents optimization problem formulations to design meander-line antennas for passive UHF radio frequency identification tags based on given specifications of input impedance, frequency range, and geometric constraints. In this application, there is a need for directive transponders to select properly the target tag, which in turn must be ideally isotropic. The design of an effective meander-line antenna for RFID purposes requires balancing geometrical characteristics with the microchip impedance. Therefore, there is an issue of optimization in determining the antenna parameters for best performance. The antenna is analyzed by a method of moments. Some results using a deterministic optimization algorithm are shown.

The low cost of electronic microcircuits and their low power consumption have turned practicable the development of identification systems through radio frequency, especially from the 1990s. Radio frequency identification (RFID) allows not only storing a relatively large amount of information, but also changing and processing information.

Radio frequency identification is a growing and promising technology that has been used in a variety of applications. It has been applied for tracking of products, luggage, books, and animals, where the tags can be attached to the objects, injected under the skin, or mounted in holes made in parts of the itens [

RFID total market value in 2009 grew to $5.56 billion, of which $2.18 billion was spent only on passive tags [

A RFID system consists basically of a receiver (tag), an emitter (reader), and a computational system (direct link). The tags have two main structures: the microchip, which provides the necessary power to transmit and receive information, and the antenna. The tags can be active, passive or semiactive, depending on the mechanism of powering the microchip and transmitting information. Active tags have a local power source and electronics for performing specialized tasks [

The entire RFID system depends on the performance of the tag, which relies on its elements. In the direct link, the reader sends modulated RF power that reaches the tag; this power is captured by the tag antenna and is transmitted to the microchip. In order to ensure a great power transmission coefficient and decrease the losses, the tag antenna impedance must match the complex input impedance of the tag microchip, which is commonly capacitive. Usually, the antenna is the element to be matched to a specific chip available in the market.

Due to the diversity of materials and packages that need to be identified, tag antennas development for passive UHF RFID systems has become challenging. The performance of the tag antennas is very dependent on the properties of the objects which the tags are attached to. The material of the objects can influence the capacitive characteristics of the tag antenna, as well as modify its radiation pattern. Many studies have been carried out in order to investigate these effects on tags attached to metallic surfaces and water [

The design in this paper was motivated by application in coffee business. In this business, the product is stored in sacks in the producers’ farms and needs to be transported to the local cooperatives. Each cooperative receives coffee sacks from different producers, normally using treadmills, and the receiving process demands time and labor force and is usually inefficient. Besides, the origin of the coffee must be traced until it reaches the final consumer and the material flow must be controlled in real time. In this context, RFID systems can be used to improve the productivity and competitiveness and reduce costs.

Tracking coffee containers in real time using RFID technology, from the shipment to the moment the container arrives in the USA, is already being used by a coffee importer named Sara Lee, in Santos harbour (São Paulo, Brazil). Moreover, the ST Café, a Brazilian company, is using RFID tags to identify the coffee sacks individually in rural properties.

Meander-line antennas are one of the most commonly used in UHF RFID tags, mainly because of their tunability and size. Several papers have been published on RFID meander-line antenna design. Some articles have sought achieving improved antenna gains and small size by using different configurations of meander-line antennas for passive RFID, which were explored applying genetic algorithm (GA) optimization and the method of moments (MoM) [

One of the most convenient forms of RFID tags is a labellike, so that they can be stuck on objects. This work analyzes a meander-line antenna that is very suitable for this application.

The application of coffee business required the use of a passive UHF RFID tag antenna (902-928 MHz). In order to perform the simulations, some design specifications were established. The microchip, which has been used as a reference in this work, is ALIEN Higgs TM-3, EPC Class 1 Gen 2, whose equivalent input impedance is (27.41-200.90

Geometry of the meander-line antenna for

The antenna is discretized into regular quasiregular triangles and analyzed using a method of moments with a voltage gap feed which considers

The parameters other than

A meander-line antenna cannot provide high directivity. This is a desired behavior considering that isotropic radiation would not be ideal for the application. The remaining features of interest are input impedance and size, which are used in the multiobjective optimization problem formulation

The optimization problem (

To optimize the worst case SWR inside the frequency range, the monoobjective optimization problem formulation

The optimal variables results of (

Optimization problem variables for multiobjective formulation.

Parameter (mm) | ||||||||||

Max | 0.50 | 12.60 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |

Min | 0.80 | 21.00 | 7.00 | 7.00 | 7.00 | 7.00 | 7.00 | 7.00 | 7.00 | 7.00 |

Opt | 0.78 | 15.11 | 4.70 | 3.98 | 6.42 | 5.66 | 3.80 | 1.42 | 6.00 | 3.77 |

Specifications and optimal antenna profile.

Parameter | Value |
---|---|

_{
min} (mm) | 10 |

_{
max} (mm) | 100 |

_{
min} (MHz) | 902 |

_{
max} (MHz) | 928 |

27.4–200.9 |

Optimal standing wave ratio behavior inside frequency range for multiobjective formulation.

In order to compare the two formulations (multiobjective and worst case), the CEDA algorithm was limited to 395 oracle queries to optimize problem (

Optimization problem variables for formulation worst case.

Parameter (mm) | ||||||||||

Max | 0.50 | 12.60 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |

Min | 0.80 | 21.00 | 7.00 | 7.00 | 7.00 | 7.00 | 7.00 | 7.00 | 7.00 | 7.00 |

Opt | 0.60 | 15.81 | 5.95 | 2.26 | 3.82 | 1.94 | 4.39 | 3.13 | 4.25 | 6.09 |

Optimal standing wave ratio behavior inside frequency range for worst case formulation.

As mentioned before, the optimization algorithm used in the meander-line antenna design, named henceforth the cone of efficient directions algorithm (CEDA) [

If a point is not a local optimum, then there must be a better feasible neighbor point, by definition. If a function

Consider a differentiable multiobjective optimization problem in the form

The multiobjective line search algorithm solves the problem

The maximum step length is given by

The natural stop criteria for the multiobjective optimization algorithm are when any column of

When

The first notable features of CEDA are its monotonic convergence and feasibility preserving theoretical guarantees. They are also very desired in practice, considering that they lead to robustness against bad-behavior functions and provide better intermediate results during the optimization process.

Another notable feature of CEDA is that the stop criteria are met earlier when the number of objective functions increases. This can be observed in the optimization of the meander-line antenna, where minimizing SWR at sample frequencies is faster than minimizing its worst case. This occurs because CEDA treats multiobjective problems as so and the dimension of the Pareto optimal set of a problem is, in nondegenerate cases, the number of objective function minus one. CEDA can be considered an extension of the classical gradient algorithm to multiobjective problems. Indeed, it also presents a slow convergence rate when the functions Hessian matrices are ill conditioned. Second-order directions (e.g., Newton directions) solve this problem for monoobjective and also multiobjective problems [

The best SWR of about 1 was verified inside a frequency range of ±1.4% around 915 MHz for optimal 4-meander antennas, even though with a worst case SWR of about 4. More degrees of freedom could be considered in order to improve worst cases (e.g., increasing the number of meanders or parameterizing each meander height individually). Nevertheless, the main purpose of this paper was achieved: optimal meander-line antennas for a real-life demand using different formulations.

The multiobjective formulation is faster to converge than the single-objective one. Furthermore, the theoretical guarantee of always improving all objective functions after each iteration may be very suitable in real-world applications. However, considering that SWRs of 1 and 40 at sample frequencies could be considered Pareto optimal for the former formulation, the solution of the worst case formulation may be regarded more meaningful, that is, a good decision rule, even though it is either dominated or included in the optimal Pareto set.

This work was supported by CNPq and FAPESB, Brazil.