Coupler Design of Resonant Frequency Detection Based on Passive Electronic Tags

RFID systems are primarily composed of two main components: a reader and a transponder. The reader, as shown in Figure 1, is a data acquisition device that includes a coupling element designed to interact with the transponder. The transponder, illustrated in Figure 2, acts as a data storage unit containing a coupling element made up of a microchip and an antenna coil [1].

Figure 1: Reader | Figure 2: Transponder

Figure 3 illustrates the working principle of the LC oscillator circuit used in passive RFID readers and transponders [2]. The reader contains an LC tank circuit consisting of an inductor L1, which generates an alternating magnetic field at frequency f₀. When the transponder’s coil is placed within this field, its internal distributed capacitance C’ and an external tuning capacitor C form a parallel LC circuit (C₂ and L₂), which resonates at frequency f. If f matches f₀, both circuits resonate, causing a large current to flow through the reader’s coil. This induces a maximum voltage on the transponder’s coil, which is then rectified by a diode to power the microchip and enable communication between the reader and the transponder [3-4].

Figure 3: Working principle of the LC tank circuit in passive RFID

The resonant frequency of the LC circuit can be calculated using the Thomson formula (1):

(1)

This formula allows us to determine the resonant frequency f of the transponder based on the values of C₂ (capacitance) and L₂ (inductance) of the LC tank circuit. The inductance of the transponder’s coil is fixed once it is manufactured, and it can be measured using an inductance meter. Based on the reader’s operating frequency f₀, we calculate the required capacitance C to match the resonant frequency. However, the presence of the coil’s distributed capacitance C’ makes the calculation more complex, as this parasitic capacitance cannot be directly measured. Therefore, selecting the correct tuning capacitor C is critical for achieving resonance. ### 2. Calculation of the Tuning Capacitor C As shown in Figure 4, the author printed a transponder coil using conductive ink, and the target resonant frequency was set to 8.2 MHz according to the reader’s specifications. The measured inductance of the coil was approximately 4.5 μH. Using the Thomson formula, we rearrange it to solve for the required capacitance:

(2)

(3)

Based on this calculation, a standard capacitor of 82 pF was selected to be connected across the coil. As shown in Figure 5, this configuration was applied to the transponder.

Figure 4: Conductive ink-printed transponder coil | Figure 5: Transponder with 82 pF capacitor

However, since the distributed capacitance C’ was not considered in the calculation, the actual total capacitance becomes the sum of C’ and the tuning capacitor C. This means that using 82 pF may cause the resonant frequency to drop below 8.2 MHz, preventing proper resonance with the reader. To correct this, the tuning capacitor value must be adjusted. This process involves repeated measurements of the transponder’s resonant frequency, which requires specialized equipment. Since no standard instrument exists for detecting the resonant frequency of passive tags, the author designed a coupler to perform these tests effectively. ### 3. Working Principle of the Coupler The core of the coupler consists of two sets of coils, labeled 2 and 3, wound around a hollow cylinder with radius r and number of turns N. These coils are positioned parallel and coaxially aligned, with a center-to-center distance L equal to the coil radius r, forming a Helmholtz coil [5-6], as shown in Figure 6.

Figure 6: Schematic of the Helmholtz coil structure

Taking point O, the midpoint of the center line L, as the origin of a 3D coordinate system, the magnetic field distribution is depicted in Figure 7.

Figure 7: Magnetic field uniformity curve of the Helmholtz coil

The relative errors of the magnetic induction H at points I, II, and III compared to the central point O are less than 1.0%, 0.1%, and 0.01%, respectively. This indicates that the magnetic field near the center is highly uniform. The closer the transponder is to the center, the more consistent the magnetic field will be across its surface. Therefore, when measuring the resonant frequency of a passive RFID tag, it is essential to place the tag at the center of the Helmholtz coil’s magnetic field to ensure accurate and reliable results.

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