AN2972

Basic principles and equations

Doc ID 15629 Rev 6

9/25

The antenna is a wire, so its equivalent electrical circuit is a wire with a resistance

Figure 7.

Equivalent circuit of the M24LRxx and its antenna

1.3

Basic equations

Resonant frequency

The resonant frequency of the LC circuit is defined by the equation:

LC

ω² = 1

where:

●

L is the inductance in Henry

●

C is the capacitance in Farad

●

ω is the angular frequency in radians per second (ω = 2 × π × f, with f = frequency in Hz)

1.4

Optimum antenna tuning

The total impedance of an LC loop is given by the sum of the inductive and capacitive

impedances:

and then substituting in the previous equation, you have:

Z = j

ωL + 1/jωC

Now, extracting a common denominator yields:

Z = (1 – LC

ω²) /jωC

Note:

The total impedance Z is zero at the resonant frequency of the LC circuit (the numerator is

zero when LC

received by the [L,C] loop; in this case, the M24LRxx (capacitor C) and the antenna

(inductor L).

Consequently, the dual interface device’s antenna must be tuned so that its resonating

frequency matches the RFID reader antenna’s tuning frequency as much as possible. At this

ai17178b

A

B

M24LRxx

External antenna