RFID tags with double rectangular spiral antennas, system stability optimization under delayed electromagnetic interference and parasitic effects

In this article, we discuss the crucial subject of RFID tags with double rectangular spiral antennas, system stability optimization under delayed electromagnetic interference and parasitic effects. Two antennas are connected in series by microstrip line with parasitic effects. We define V₁(t) as the voltage on the first antenna inductance and V₂(t) as the voltage on the second antenna inductance. Due to electromagnetic interference there are differences in time delays, with respect to the first and second rectangular spiral antennas voltages and voltage derivatives. The delayed voltages are V₁(t - τ₁) and V₂(t - τ₂) respectively (τ₁ ≠ τ₂) and the delayed voltage derivatives are dV₁(t - Δ₁)/dt, dV₂(t - Δ₂)/dt respectively Δ_μ. Additionally, there is a delay in time for the microstrip parasitic effects Δ_μ. The double rectangular spiral antenna system equivalent circuit can be described in terms of delayed differential equations, depending on variable parameters and delays. The stability of a given steady state is determined by the graphs of some function of τ₁, τ₂, Δ₁, Δ₂ and Δ_μ.