Calculating the antenna coil inductance

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Calculating the antenna coil inductance

The coil inductance at the carrier frequency resonance is:

.

The quality factor Q of the simplified circuit is calculated as follows:

.

Example of the calculation of an antenna coil inductance:

Figure 7 describes the steps of the antenna design procedure that gives an easy and

reliable method of designing an antenna coil prototype.

and tools to produce antenna coil prototypes.

By determining dimensions and values, the execution of the first run gives the best out of

three coils meeting the requirements. Usually, the best results appear after the second run.

Table 1.

frequency

Product

Tuning frequency

(MHz)

Antenna coil inductance (µH)

LR (long-range)

21

13.56

6.56

28.5

13.56

4.83

23.5

13.56

5.86

97

13.56

1.42

SR (short range)

64

13.56

2.15

64

14.40

1.90

f

0

1

2

π L

ant

C

tun

⋅

-----------------------------------------

=

L

ant

1

2

πf

0

()

2

C

tun

⋅

--------------------------------------

=

Q

R

eq

2

π f

0

L

ant

⋅⋅

------------------------------------

=

L

ant

1

2

π 13.56 MHz

×

()

2

21 pF

⋅

-------------------------------------------------------------------------

6.56 µH

==