NXP Semiconductors
AN11740
PN5180 Antenna design
AN11740
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Application note
COMPANY PUBLIC
Rev. 1.1 — 19 June 2018
345311
14 of 62
A
2
= Card antenna coil area, fixed
L
02
= Card antenna coil single turn inductance, fixed
L
01
= Reader coil single turn inductance
r
= Reader Antenna coil radius
x
= Operating distance in the center of the Reader antenna
µ
0
= relative permeability
The single turn inductance can be described like this:
d
= coil wire diameter with
d << r
Note:
The formula to calculate the inductance of the antenna coil can only be taken as
reference. In real life many details influence the result, which are not taken into
account in this simple formula. So a measurement of the coil parameters as
described below is required anyway.
3.1.1 Number of turns
Changing the number of turns does not change the coupling, since the inductance itself
has no influence on the coupling. So, in principle antenna coils with a single turn can be
used as well as antenna coils with many turns.
The only remaining parameter to optimize the coupling is the antenna radius r (i.e. the
antenna size), and will be discussed in section 3.1.2.
However, the number of turns changes the inductance which on one hand changes the
matching circuit.
Out of experience it turns out to be optimum to have an inductance around L
≈
1µH for a
proper matching, but a wide range of L
≈
300nH up to L
≈
4µH still can be matched
properly, so typically 1 up to 4 turns in the normal range of antenna sizes are used.
The Fig 10 shows the typical inductance values versus the antenna coil radius for 1, 2, 3
and 4 turns. These values are just examples, since the environment, the track width or
wire thickness and some other parameters may influence the inductance.
Furthermore, the typical PCD antenna coil does not use the circular shape, but rather a
rectangular form factor. The given calculated values show the wide range that can be
used, and shall be used as reference only. The antenna coil inductance must be
measured anyway later on to do the antenna matching.
02
01
2
2
3
2
2
2
0
)
(
2
L
L
A
x
r
r
k
⋅
⋅
+
⋅
=
µ
(1)
[ ]
)
2
ln(
2
10
2
7
01
d
r
r
m
L
⋅
⋅
⋅
⋅
⋅
≈
−
π
π
(2)
