ST AN2866 APPLICATION NOTE

AN2866

Application note

How to design a 13.56 MHz customized tag antenna

Introduction

RFID (radio-frequency identification) tags extract all of their power from the reader’s field. The tags’ and reader’s antennas form a system of coupled inductances as shown in Figure 1. The loop antenna of the tag acts as a transformer’s secondary.

The efficient transfer of energy from the reader to the tag depends on the precision of the parallel resonant RLC loop antennas tuned to the carrier frequency (usually 13.56 MHz).

The purpose of this application note is to give a step-by-step procedure to easily design a customized tag antenna.

Figure 1. RFID tag coupled to a reader’s magnetic field

Tag

Reader

ai15802

Figure 2. An antenna designed for a specific chip and frequency

Antenna

Chip

ai15802

January 2009

Rev 1

1/24

www.st.com

Contents	AN2866

Contents

1	Simplified equivalent inlay circuit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		. 5
2	Equivalent inlay circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		6
3	Calculating the antenna coil inductance . . . . . . . . . . . . . . . . . . . . . . . . .		8
4	Designing the antenna coil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		10
	4.1	Inductance of a circular loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	10
	4.2	Inductance of a spiral coil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	10
	4.3	Inductance of an antenna with square coils . . . . . . . . . . . . . . . . . . . . . . .	10
5	Contactless measurement method . . . . . . . . . . . . . . . . . . . . . . . . . . . .		14
	5.1	Antenna coil prototype verification with an analyzer . . . . . . . . . . . . . . . .	14

5.1.1 Preparing the equipment and connections . . . . . . . . . . . . . . . . . . . . . . 14 5.1.2 Instructions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

5.2Antenna coil prototype verification without an analyzer (first

method) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

5.2.1 Preparing the equipment and connections . . . . . . . . . . . . . . . . . . . . . . 15 5.2.2 Instructions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

6	Non-contactless (contact) measurement method . . . . . . . . . . . . . . . .	18
	6.1 Without an analyzer (second method) . . . . . . . . . . . . . . . . . . . . . . . . . . .	18

6.1.1 Preparing the equipment and connections . . . . . . . . . . . . . . . . . . . . . . 18 6.1.2 Instructions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 6.1.3 Example using an LRI2K device . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

7	Frequency versus application: recommendations . . . . . . . . . . . . . . .	22
8	Revision history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	23

2/24

AN2866	List of tables

List of tables

Table 1. Antenna coil inductances for different Ctun values at a given tuning frequency . . . . . . . . . . 8 Table 2. K1 & K2 values according to layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Table 3. Document revision history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3/24

List of figures	AN2866

List of figures

Figure 1. RFID tag coupled to a reader’s magnetic field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Figure 2. An antenna designed for a specific chip and frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Figure 3. Equivalent circuit of a chip and its antenna . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Figure 4. Equivalent circuit of a chip, its antenna (modeled with a series

resistance) and connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Figure 5. Equivalent circuit of a chip, its antenna (modeled with a parallel

resistance) and connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Figure 6. Simplified equivalent circuit of a chip, its antenna and connections . . . . . . . . . . . . . . . . . . . 7 Figure 7. Antenna design procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Figure 8. Spiral coil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Figure 9. Square coils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Figure 10. User interface screen of the planar rectangular coil inductance calculator. . . . . . . . . . . . . 12 Figure 11. Rectangular planar antennas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Figure 12. Measurement equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Figure 13. Resonance traces of the prototype at different powers . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Figure 14. ISO standard loop antenna. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 Figure 15. Without an analyzer: first measurement method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 Figure 16. Oscilloscope views . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Figure 17. Synthesis of resonance traces for different voltages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Figure 18. Measurement circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Figure 19. Determining the resonance frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Figure 20. Coil samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Figure 21. Coil characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Figure 22. New coil samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Figure 23. Second coil characterization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Figure 24. Best antenna coil prototype . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

4/24

AN2866	Simplified equivalent inlay circuit

1 Simplified equivalent inlay circuit

The chip and its antenna can be symbolized using their equivalent electrical circuit.

Figure 3 shows the equivalent electrical circuit of the chip (parallel association of a resistance which emulates the current consumption of the chip and a capacitance added to the chip to ease tuning).

The antenna is a wire, so its equivalent electrical circuit is a wire with a resistance symbolized by Rant. The antenna also has an inductance denoted by Lant. The capacitance Cant is the representation of parasitic elements (produced by the bridge).

Figure 3. Equivalent circuit of a chip and its antenna

A

Rant

Ctun

Cant

Rchip

Lant

B

Chip

Antenna

ai15804

5/24

Equivalent inlay circuit	AN2866

2 Equivalent inlay circuit

The schematic shown in Figure 3 is but a first approach to the problem because it does not take into account the connection between the chip and the antenna. The assembly phase of the chip onto the antenna may lead to the introduction of parasitic elements. These parasitic elements are symbolized by two resistances and a capacitance as shown in Figure 4 and

Figure 5.

The equivalent circuit of the antenna may include either a series (see Figure 4) or a parallel (see Figure 5) resistance.

Figure 4. Equivalent circuit of a chip, its antenna (modeled with a series resistance) and connections

A

R1con

Rs_ant

Ctun

Cant

Rchip

Ccon

Lant

B

R2con

Chip

Connection

Antenna

ai15805

Figure 5. Equivalent circuit of a chip, its antenna (modeled with a parallel resistance) and connections

A

R1con

Ctun

Cant

Rp_ant

Rchip

Ccon

Lant

B

R2con

Chip

Connection

Antenna

ai15841

The symbols in Figure 4 and Figure 5 correspond to:

Rchip:

current consumption of the chip for a given power value

Ctun:

tuning capacitance of the chip

Rcon:

equivalent parasitic resistance generated by the connection between the chip and

the antenna

Ccon:

equivalent parasitic capacitance generated by the connection between the chip and

the antenna

Cant:

equivalent parasitic capacitance of the antenna coil

Rs_ant: Antenna coil series resistance

Rp_ant: Antenna coil parallel resistance

Lant:

Antenna coil inductance

6/24

AN2866	Equivalent inlay circuit

This equivalent circuit (Figure 4) can also be simplified as illustrated in Figure 6 (use the simplified circuit for calculations).

Figure 6. Simplified equivalent circuit of a chip, its antenna and connections

Ctun	Req	Lant

ai15806

Req is calculated as follows:

Lant

× ω

Req

Rchip

× Rp_ant

with Rp_ant

=

Rs_ant

1 +

2

where ω is the angular frequency.

= -------------------------------------

+ R

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

R

chip

p_ant

R

s_ant

7/24

Calculating the antenna coil inductance	AN2866

3 Calculating the antenna coil inductance

	The resonant frequency f0 of a parallel resonant LC circuit can be calculated by:
	f0 =	1
		Lant	Ctun
	2π
	The coil inductance at the carrier frequency resonance is: Lant =							1	.
								(-------------------------------------2πf0)2
									Ctun
	The quality factor Q of the simplified circuit is calculated as follows: Q =								Req	.
									π f0
								2		Lant
	Example of the calculation of an antenna coil inductance:
	Lant =		1		= 6.56 µH
	( 2π × 13.56 MHz)2 21 pF
	Table 1.	Antenna coil inductances for different Ctun values at a given tuning
		frequency
	Product			Ctun (pF)		Tuning frequency	Antenna coil inductance (µH)
						(MHz)
				21		13.56	6.56
	LR (long-range)			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

Figure 7 describes the steps of the antenna design procedure that gives an easy and reliable method of designing an antenna coil prototype.

This procedure uses the Ctun capacitance of the chip, a software tool called antenne.exe, 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.

8/24