STMicroelectronics CR95HF contactless transceiver Application note

AN3394
Application note
Antenna design and impedance matching guidelines
for CR95HF multiprotocol contactless transceiver IC
Introduction
The goal of this application note is to provide guidelines to design a CR95HF antenna which
impedance matches to the CR95HF impedance. This allows to achieve the best RF
communications between the CR95HF transceiver integrated circuit (IC) and ISO15693 or
ISO14443 RF memory tags.
The DEMO-CR95HF-A is a demonstration board for the CR95HF 13.56 MHz contactless
transceiver. It is designed as a ready-to-use circuit board to interface with the CR95HF PC
host demonstration software through an USB bus. The DEMO-CR95HF-A is powered by the
USB bus and no external power supply is required. It is based on the CR95HF contactless
transceiver with a 47x34 mm 13.56 MHz inductive etched antenna and its associated tuning
components, and on a STM32F103CB 32-bit microcontroller that communicates with the
CR95HF via the USB bus.
This document is structured as follows:
October 2011
■
Description of the DEMO-CR95HF-A board
– Definition of CR95HF output impedance
– Use of inductive antenna
– Impedance matching
■
Description of equivalent circuit
– CR95HF RF circuit modeling and description of antenna impedance matching circuit
– Calculation of the matching circuit optimized for ISO15693 memory tags
■
Read range estimate based on magnetic field calculation method for a rectangular
antenna
■
Main criteria for key antenna design
Doc ID 018754 Rev 5
1/29
www.st.com
Contents
AN3394
Contents
1
2
Description of DEMO-CR95HF-A
and criteria for impedance matching . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.1
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.2
Output impedance of the DEMO-CR95HF-A
demonstration board output circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3
Inductive antenna impedance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.4
Need for impedance matching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.5
Impedance matching circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.5.1
Antenna circuit description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.5.2
Entire equivalent circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Application to DEMO-CR95HF-A demonstration board . . . . . . . . . . . . 13
2.1
2.2
Antenna parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1.1
Antenna serial equivalent model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1.2
Antenna parallel equivalent model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
CR95HF receiving circuit equivalent models . . . . . . . . . . . . . . . . . . . . . . 14
2.2.1
2.3
3
4
5
CR95HF receiving circuit parallel equivalent model . . . . . . . . . . . . . . . 14
Numerical application of C2, C6, C3 and C17
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Read range estimate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.1
Magnetic field calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.2
Read range calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Main criteria for key antenna design . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
4.1
Inductance of a circular antenna . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
4.2
Inductance of a spiral antenna . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
4.3
Inductance of a square antenna . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4.4
ST antenna calculation tool . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Appendix A Demonstration of C11 and C22 calculation. . . . . . . . . . . . . . . . . . . . 23
A.1
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Equivalent circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
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6
Contents
A.2
Serial to parallel equivalence RL impedance, and example of RL load . . 24
A.3
Serial to parallel equivalence RC impedance, and example of RC load . . 26
Revision history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
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List of tables
AN3394
List of tables
Table 1.
Table 2.
Table 3.
4/29
K1 and K2 values depending on layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
DEMO-CR95HF-A component commended values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Document revision history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
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AN3394
List of figures
List of figures
Figure 1.
Figure 2.
Figure 3.
Figure 4.
Figure 5.
Figure 6.
Figure 7.
Figure 8.
Figure 9.
Figure 10.
Figure 11.
Figure 12.
Figure 13.
Figure 14.
Figure 15.
Figure 16.
Figure 17.
Figure 18.
Figure 19.
Figure 20.
Figure 21.
Figure 22.
Figure 23.
Figure 24.
DEMO-CR95HF-A demonstration board equivalent circuit. . . . . . . . . . . . . . . . . . . . . . . . . . 6
CR95HF equivalent output impedance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Chip simplified equivalent impedance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Antenna demonstration board equivalent circuit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Impedance matching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Antenna circuit description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Equivalent circuit of the CR95HF and associated matching circuit. . . . . . . . . . . . . . . . . . . 10
CR95HF matching circuit intermediate simplification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
CR95HF parallel matching circuit intermediate simplification . . . . . . . . . . . . . . . . . . . . . . . 11
CR95HF final equivalent circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Antenna parameters without EMI filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Antenna serial-to-parallel RL equivalent circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
CR95HF serial-to-parallel RC circuit equivalence. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Circuit including Rinput internal resistor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Rectangular antenna . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Read range evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Spiral antenna. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Square antennas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
User interface for planar rectangular coil inductance calculation . . . . . . . . . . . . . . . . . . . . 20
Rectangular planar antennas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
DEMO-CR95HF-A circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Final equivalent circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Serial-to-parallel RL equivalent circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
Serial-to-parallel RC equivalent circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
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Description of DEMO-CR95HF-A and criteria for impedance matching
1
Description of DEMO-CR95HF-A
and criteria for impedance matching
1.1
Overview
AN3394
Figure 1 shows the part of the circuit concerned by the impedance matching.
Figure 1.
DEMO-CR95HF-A demonstration board equivalent circuit
!ND
28
2
48
Ω
#
/PEN
#
#2(&
#
20!
,0!
/PEN
#
Ω
48
28
2
-36
Legend and Abbreviations
:
:
:
:
:
:
TX:
RX:
RPA:
LPA:
C2,C6:
C3,C17:
R1,R5:
6/29
EMC Filter: For information on the EMC filter, contact your local ST sales team.
Matching circuit.
Inductive antenna.
Block.
Pin.
Component.
CR95HF output driver.
CR95HF receiver input stage.
Antenna equivalent parallel resistor. [Ω]
Antenna equivalent parallel inductance. [H]
Serial capacitance of the matching circuit impedance. [F]
Parallel capacitance of the matching circuit impedance. [F]
330 Ω. These resistors are used to limit the signal level on RX1-RX2. They must be
considered in the calculation of the impedance matching circuit.
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1.2
Description of DEMO-CR95HF-A and criteria for impedance matching
Output impedance of the DEMO-CR95HF-A
demonstration board output circuit
To generate the magnetic field, the antenna is excited by the two CR95HF differential
generators (see Figure 2: CR95HF equivalent output impedance).
Each generator has an output impedance of 13.5 Ω.
Zout is the CR95HF differential output impedance between TX1 and TX2. It is a pure
resistor. The resulting output impedance, Rout, can be measured as shown in Figure 3: Chip
simplified equivalent impedance:
Z out = R out = 27Ω
Figure 2.
CR95HF equivalent output
Figure 3.
impedance
Ω
Chip simplified equivalent
impedance
48
;=6
:OUT
Ω
( 3V )
48
;=6
#HIP 2OUTΩ
6OUT
6
48
48
-36
-36
Where
Zout:
Matching impedance. [Ω]
Rout:
Matching resistor. [Ω]
Vout:
Supply voltage of the chip. [V]
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Description of DEMO-CR95HF-A and criteria for impedance matching
1.3
AN3394
Inductive antenna impedance
The CR95HF requires an inductive antenna to communicate at a frequency of 13,56 MHz.
The equivalent impedance (Zload) of the inductive loop antenna is shown in Figure 7:
Equivalent circuit of the CR95HF and associated matching circuit.
DEMO-CR95HF-A antenna dimensions are 47 mm x 34 mm.
Figure 4.
Antenna demonstration board equivalent circuit
2!
:LOAD
,!
-36
Where
Zload: Antenna equivalent parallel impedance. [Ω]
1.4
RA:
Antenna equivalent series resistor. [Ω]
LA:
Antenna equivalent series inductance. [H]
Need for impedance matching
The maximum power transfer between the CR95HF and the load is obtained when the
condition Zout = Zload* is satisfied. Zload* is the complex conjugate of Zload.
The antenna equivalent impedance described in Section 1.3: Inductive antenna impedance
does not meet this condition.
The measure of Zload gives:
Equation (I.4)
Z load = ( 0.6 + j × 36.6 )Ω
To achieve the maximum power transfer between the CR95HF and its inductive antenna,
impedance matching must therefore be performed between Zout and Zload. It allows to:
●
Optimize the read range
●
Transmit the maximum power
●
Optimize the chip consumption
●
Maximize the radiated magnetic field
Figure 5.
Impedance matching
:OUT
6OUT
:LOAD
-36
8/29
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AN3394
Description of DEMO-CR95HF-A and criteria for impedance matching
1.5
Impedance matching circuit
1.5.1
Antenna circuit description
The impedance matching circuit is composed of a serial capacitance circuit (C2and C6) and
a parallel capacitance circuit (C3and C17).
Successive impedance transformation allows to simplify the antenna equivalent circuit and
to calculate C2, C6, C3 and C17 capacitances easily.
Figure 6.
Antenna circuit description
28
2
48
2OUT
#INPUT
˖
#
/PEN
6OUT
#
#
20!
,0!
/PEN
˖
48
#
2
28
#2(&
-ATCHINGCIRCUITASSOCIATEDCOMPONENTSANDANTENNA
-36
Where
R1,R5:
330 Ω. These resistors are used to limit the signal level on RX1-RX2. They must be
considered in the calculation of the impedance matching circuit.
Cinput:
22 pF. Cinput is the integrated capacitor between RX1-RX2. As R1,R5, it must be considered
for the impedance matching circuit.
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Description of DEMO-CR95HF-A and criteria for impedance matching
1.5.2
AN3394
Entire equivalent circuit
Without the EMI filter, the circuit is reduced as shown in Figure 7: Equivalent circuit of the
CR95HF and associated matching circuit:
Figure 7.
Equivalent circuit of the CR95HF and associated matching circuit
28
2
48
2OUT
#INPUT
#
6OUT
#
#
20!
,0!
#
48
2
28
-36
From antenna point of view, the CR95HF receiving circuit impedance (R1, R5 and Cinput) is
in parallel of C3,C17 as described in the equivalent circuit shown in Figure 8: CR95HF
matching circuit intermediate simplification. R1 and R5 are equal and can be replaced by
RRX.
Figure 8.
CR95HF matching circuit intermediate simplification
48
#
2OUT
#INPUT
#
6OUT
#
20!
,0!
228
#
48
-36
Where
:
input impedance of the CR95HF reception circuit
Both serial capacitances (C2and C6) are equivalent to a serial capacitance
C11 = C2/2 = C6/2. Both parallel capacitances (C3 and C17) are equivalent to a parallel
10/29
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AN3394
Description of DEMO-CR95HF-A and criteria for impedance matching
capacitance C22 = (C3+ C17).Cinput,and RRX can be transformed in a parallel equivalent
circuit (see Figure 9: CR95HF parallel matching circuit intermediate simplification).
Figure 9.
CR95HF parallel matching circuit intermediate simplification
48
#
2OUT
#
6OUT
48
#INPUTP
2280
20!
,0!
-36
The resulting equivalent circuit allows to calculate the matching circuit composed of C11 and
C22 that satisfies the condition Zout= Zeq* where Zeq* is the complex conjugate of Zeq.
Figure 10. CR95HF final equivalent circuit
2OUT
#
#
6OUT
2EQ
228020!
,0!
#INPUTP
-36
Where
:
Equivalent circuit.
The calculation described in Equation (A.I.7) and Equation (A.I.9) leads to:
R eq
1
C 11 = -------------------- × ⎛ ----------- – 1⎞
⎝ R out
⎠
R eq × ω
1
C 22 = ---------------------2- – C 11 – C input – p
L eq × ω
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Description of DEMO-CR95HF-A and criteria for impedance matching
Where
12/29
RRXP:
Equivalent parallel resistor of RRX. [Ω]
Req:
Equivalent parallel resistor of RRX and RPA. [Ω]
Cinput-p:
Equivalent parallel capacitance of Cinput. [F]
C11:
Equivalent serial capacitance of C2and C6 capacitances. [F]
C22:
Equivalent serial capacitance of C3 and C17 capacitances. [F]
Zeq:
Equivalent impedance of circuits 2, 3 and 4.
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AN3394
2
Application to DEMO-CR95HF-A demonstration board
Application to DEMO-CR95HF-A demonstration
board
This section describes in detail the numerical application corresponding to the DEMOCR95HF-A demonstration board.
If your application requires a different antenna, use the DEMO-CR95HF-A Gerber files
available for http://ww.st.com to design your own antenna. Guidelines on how to design an
antenna can be found in Section 4: Main criteria for key antenna design.
2.1
Antenna parameters
This section describes part 3 of circuit shown in Figure 9: CR95HF parallel matching circuit
intermediate simplification.
2.1.1
Antenna serial equivalent model
Figure 11. Antenna parameters without EMI filter
2!
,!
-36
Where values from Equation (I.4) give:
RA = O.6 Ω and LA = 36.6* ω.
As a result, LA = 430 nH.
The capacitance is included in the inductance presented above. As a result:
Equation (II.1)
[ IM ( Zload ) ] ω × L A
Q A = --------------------------------- = ----------------- = 61, 1
RE ( Zload )
RA
Where
Q A:
Antenna quality factor, defined with antenna parameter.
IM(x):
Imaginary part of the complex number x.
RE(x): Real part of the complex number x.
ω:
Resonance pulsation [rad/s]. ω = 2π f with f = 13.56 MHz.
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Application to DEMO-CR95HF-A demonstration board
2.1.2
AN3394
Antenna parallel equivalent model
Figure 12. Antenna serial-to-parallel RL equivalent circuit
2!
:LOAD
:LOAD0
20!
,0!
,!
-36
The values given hereafter are the numerical application of Equation (A.II.5) and Equation
(A.II.6):
RPA = 2238 Ω
LPA = 430,1 nH
Where
Zload:
Antenna equivalent series impedance. [Ω]
ZloadP:
Antenna equivalent parallel impedance. [Ω]
2.2
CR95HF receiving circuit equivalent models
2.2.1
CR95HF receiving circuit parallel equivalent model
This section describes part 4 of the circuit shown in Figure 9: CR95HF parallel matching
circuit intermediate simplification.
Figure 13. CR95HF serial-to-parallel RC circuit equivalence
228
:28
:280
2280
#INPUTP
#INPUT
-36
The values hereafter are the numerical application of Equation (A.III.5) and Equation
(A.III.6):
RRXP = 1091 Ω
Cinput-p = 8.69 pF
The circuit includes a 80 kΩ Rinput in parallel with ZRXP, as shown in Figure 14: Circuit
including Rinput internal resistor. For more details, refer to the CR95HF datasheet. Rinput
resistance should be neglected as demonstrated below.
14/29
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Application to DEMO-CR95HF-A demonstration board
Figure 14. Circuit including Rinput internal resistor
2INPUT
2280
#INPUTP
-36
Equation (II.2)
1 R RXP × R input
R RXP = ------------------------------------R RXP + R input
Numerical application of Equation (II.2):
1
R RXP = 1077Ω
The coefficient error is:
ΔR RXP 1091 – 1077
-----------------= --------------------------------- = 0, 67
1
1091 + 1077
R RXP
% of error.
Rinput is equivalent to an open circuit, and can be neglected.
Where
2.3
ZRX:
Antenna equivalent series impedance. [Ω]
ZRXP:
Antenna equivalent parallel impedance. [Ω]
Rinput:
Differential input resistor between RX1/RX2 inputs. [Ω]
Numerical application of C2, C6, C3 and C17
This section gives the numerical application of part 2 of the circuit shown in Figure 9:
CR95HF parallel matching circuit intermediate simplification.
The numerical application for Equation (A.I.7) is:
C11 = 82,2 pF
C2 = C6 = 2.C11 = 164,4 pF
The numerical application for Equation (A.I.9) is:
C22 = C3 + C17 = 229,4 pF
To keep the most possible C11 and C22 values and to optimize the performance, the
following values have been chosen for C2, C6, C3 and C17:
●
C2 = C6 = 150 pF
●
C3 = 220 pF
●
C17 = 15 pF
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Read range estimate
3
AN3394
Read range estimate
This section explains how to obtain the maximum read range between tag and CR95HF.
3.1
Magnetic field calculation
For a rectangular antenna, the radiated magnetic field can be estimated using the following
formula:
Figure 15. Rectangular antenna
B
D(
A
D
D(X
I
-36
Equation (III.1)
2×N×i×a×b
1
1
H x (d,r) = ----------------------------------------------------------- × ⎛⎝ --------------------------- + ---------------------------⎞
2
2
2
2⎠
2
2
2
a
+
4
×
d
b
+
4
×
d
π × (a + b + 4 × d )
Where
16/29
a:
Antenna length. [m]
b:
Antenna width. [m]
d:
Distance from tag to antenna. [m]
N:
Number of turns
i:
Current in the antenna. [A rms]
Hx :
Magnetic field. [A/m rms]
rms:
Root mean square.
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Read range calculation
Figure 16: Read range evolution shows the magnetic field strength radiated by the DEMOCR95HF-A demonstration board. Neglecting the effect of mutual coupling between the
CR95HF antenna and tag, it is possible to estimate the read range for a given tag.
As an example, the minimum operating fields for a M24LR64-R dual mode memory
mounted on the ANT1-M24LR-A reference board is around 50 mA/m.
Reporting this value on Figure 16: Read range evolution gives an estimated read range of
10 cm.
Figure 16. Read range evolution
(;!MRMS=
3.2
Read range estimate
-36
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Main criteria for key antenna design
4
AN3394
Main criteria for key antenna design
The following sections explain how to determine the antenna dimensions for a given value of
antenna inductance (L).
4.1
Inductance of a circular antenna
Equation 1
L ant = μ 0 × N
4.2
1.9
r
× r × ln ⎛ ----⎞ , where:
⎝ r 0⎠
●
r is the radius in millimeters
●
r0 is the wire diameter in millimeters
●
N is the number of turns
●
µ0 = 4π · 10–7 H/m
●
Lant is expressed in Henry
Inductance of a spiral antenna
Equation 2
d ant
2
L ant = 31.33 × μ 0 × N × ------------------------------ , where:
8d ant + 11c
●
dant is the mean antenna diameter in millimeters
●
c is the thickness of the winding in micrometers
●
N is the number of turns
●
µ0 = 4π · 10–7 H/m
●
Lant is expressed in Henry
Figure 17. Spiral antenna
AI
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4.3
Main criteria for key antenna design
Inductance of a square antenna
Equation 3
d ant
2
L ant = K1 × μ 0 × N × ------------------------- , where:
1 + K2 ⋅ p
●
dant= (dout + din)/2 in millimeters, where: dout = outer diameter
din = inner diameter
●
p = (dout – din)/(dout + din) in millimeters
●
K1 and K2 depend on the layout (refer to Table 1 for values)
Figure 18. Square antennas
Table 1.
K1 and K2 values depending on layout
Layout
4.4
K1
K2
Square
2.34
2.75
Hexagonal
2.33
3.82
Octagonal
2.25
3.55
ST antenna calculation tool
ST provides a simplified software tool (antenne.exe) to compute rectangular planar antenna
inductances. This tool gives good approximations of the inductance value. It is
recommended to verify the obtained results.
ST tool is based on the Grover method (see Equation 4.1: Grover method).
Equation 4.1: Grover method
L ant = L 0 + ∑ M , where:
●
M is the mutual inductance between each of the antenna segments
●
L0 is as given by
Equation 4.2
s
L0 =
∑ Lj
, where:
j=1
●
s is the number of segments
●
Lj is the self inductance of each segment
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Main criteria for key antenna design
AN3394
A user interface allows to enter the antenna parameters which will be used to compute the
antenna coil inductance:
●
The number of turns
●
The number of segments
●
w: the conductor width in millimeters
●
s: the conductor spacing in millimeters
●
the conductor thickness in micrometers)
●
Length in millimeters
●
Width in millimeters
The number of turns is incremented each time a segment is added to a complete turn.
Figure 19 shows the user interface corresponding to the DEMO-CR95HF-A antenna and
Figure 20 the characteristics of the rectangular planar antenna etched on the DEMOCR95HF-A PCB.
The resulting impedance, Lant, is 423.07 nH instead of 430 nH, knowing that this value
includes the parasitic capacitance. Without the parasitic capacitance, the measured value of
Lant is 420.2 nH.
Figure 19. User interface for planar rectangular coil inductance calculation
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Doc ID 018754 Rev 5
AN3394
Main criteria for key antenna design
Figure 20. Rectangular planar antennas
1
1
10
3 turns, 10 segments
8
2 turns, 8 segments
w
s
Width
thickness
(cross-section)
Length
ai15815
Once the antenna coil inductance has been calculated, a prototype coil is realized. The
value of the so-obtained prototype must then be validated by measurement. This can be
done using either a contactless or a non-contactless method.
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Conclusion
5
AN3394
Conclusion
Figure 21. DEMO-CR95HF-A circuit
28
2
48
Ω
#
/PEN
#
#2(&
#
20!
,0!
/PEN
#
Ω
48
2
28
-36
The following table summarizes the component values mounted on the DEMO-CR95HF-A
demonstration board:
Table 2.
DEMO-CR95HF-A component commended values
Component
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Recommended value
C2
150 pF
C6
150 pF
C3
220 pF
C17
15 pF
RPA
2238 Ω
LPA
430 nH
R1
330 Ω
R5
330 Ω
Doc ID 018754 Rev 5
AN3394
Demonstration of C11 and C22 calculation
Appendix A
A.1
Demonstration of C11 and C22 calculation
Equivalent circuit
Ztot defines the input impedance of the matching circuit and the equivalent parallel antenna.
Figure 22. Final equivalent circuit
:TOT
##
#
2EQ
228020!
###
6OUT
,0!
#INPUTP
1.
-36
Calculation of Req:
Equation (A.I.1)
R RXP × R PA
R eq = -------------------------------R RXP + R PA
2.
Calculation of Ztot:
Equation (A.I.2)
2
R eq × ( 1 – L PA × ω × ( C 22 + C 11 ) ) + j × ω × L PA
1
Z tot = --------------------------- × ----------------------------------------------------------------------------------------------------------------------------2
j × C 11 × ω
R (1 – L × C × ω ) + j × ω × L
eq
3.
PA
22
PA
Resonance pulsation:
Z tot = R tot + j × X tot
To determine the resonance pulsation, the imaginary part of Ztot must be cancelled. The
conditions are:
R tot = R out
and
X tot = 0
Equation (A.I.3)
2
2
2
2
– R eq × L PA × C 11 × ω × ( 1 – L PA × ω ( C 22 + C 11 ) + ω × L PA × R eq × C 11 × ( 1 – L PA × ω × C 22 ) )
R tot = --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------2
2
2 2
2
( R eq × C 11 × ω ) × ( 1 – L PA × C 22 × ω ) + ( ω × L PA × C 11 )
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Demonstration of C11 and C22 calculation
AN3394
Equation (A.I.4)
2
2
2
2
2
R eq × ( 1 – L PA × ω × C 22 ) ( 1 – L PA × ω × ( C 22 + C 11 ) ) + ω × L PA
X tot = – ω × C 11 × -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------2
2
2 2
2
( R eq × C 11 × ω ) × ( 1 – L PA × C 22 × ω ) + ( ω × L PA × C 11 )
Neglecting ω2 x LPA2, then resolving the numerator leads to two different resonance
pulsation ω0 and ω1:
Equation (A.I.5)
ω0 =
1
-----------------------------------------------L PA × ( C 22 + C 11 )
Equation (A.I.6)
ω1 =
1
-------------------------L PA × C 22
Finally inserting Equation (A.I.5) in Equation (A.I.3) leads to:
Equation (A.I.7)
R eq
1
C 11 = ----------------------- × ⎛⎝ ----------- – 1⎞⎠
R out
R eq × ω 0
Equation (A.I.8)
1
C 22 = -------------------------2- – C 11
L PA × ω 0
Equation (A.I.9)
1
C 22 = -------------------------2- – C 11 – C input – p
L PA × ω 0
In addition, Cinput-p is in parallel with C22, and Cinput-p has to be subtracting to C22.
A.2
Serial to parallel equivalence RL impedance, and example of
RL load
Figure 23. Serial-to-parallel RL equivalent circuit
2!
:LOAD
:LOAD0
20!
,0!
,!
-36
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AN3394
Demonstration of C11 and C22 calculation
Z load = Z loadP
R PA × L PA × j × ω
R A + j × ω × L A = --------------------------------------------R PA + L PA × j × ω
Equation (A.II.1)
2
2
2
R PA × L PA × ω
R PA × L PA × ω
- + j × -----------------------------------------------R A + j × ω × L A = -----------------------------------------------2
2
2
2
R PA + ( L PA × ω )
R PA + ( L PA × ω )
Consider that:
Equation (A.II.2)
ℑ ( Z load )
ℜ ( Z loadP )
ω × LA
R PA
Q A = -------------------------- = ----------------- = ----------------------------- = -------------------ℜ ( Z load )
RA
ℑ ( Z loadP )
L PA × ω
Equation (A.II.2) in equation (A.II.1) leads to:
Q A × R PA
R PA
R A + j × ω × L A = -------------------2- + j × -----------------------2
1 + QA
1 + QA
Identify the real part and the imaginary parts:
Equation (A.II.3)
R PA
R A = -------------------21 + QA
Equation (A.II.4)
Q A × R PA
ω × L A = -----------------------2
1 + QA
From equation (A.II.3):
Equation (A.II.5)
2
R PA = R A × ( 1 + Q A )
By equation (A.II.4):
Equation (A.II.6)
2
L PA
( 1 + QA )
= L A × -----------------------2
QA
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Demonstration of C11 and C22 calculation
A.3
AN3394
Serial to parallel equivalence RC impedance, and example of
RC load
Figure 24. Serial-to-parallel RC equivalent circuit
228
:28
2280
:280
#INPUTP
#INPUT
-36
Z RX = Z RXP
R RXP
1
2 × R RX + ---------------------------------- = -----------------------------------------------------------------------j × ω × C input
j × ω × R RXP × C input – p + 1
So:
Equation (A.III.1)
2
R RXP × C input – p × ω
R RXP
1
2 × R RX – j × -------------------------- = ------------------------------------------------------------------------2- – j × ------------------------------------------------------------------------2ω × C input
1 + ( R RXP × C input – p × ω )
1 + ( R RXP × C input – p × ω )
Consider that:
Equation (A.III.2)
IM ( Z RX )
1
Q RX = ------------------------- = ----------------------------------------------------- = ω × C input – p × R RXP
RE ( Z RX )
2 × ω × C input × R RX
Equation (A.III.2) in equation (A.III.1) leads to:
2
Q RX
R RXP
1
1
2 × R RX – j × -------------------------- = -----------------------2- – j × -----------------------2- × --------------------------------C
ω × C input
input – p × ω
1 + Q RX
1 + Q RX
Identify the real and the imaginary parts:
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AN3394
Demonstration of C11 and C22 calculation
Equation (A.III.3)
R RXP
2 × R RX = -----------------------21 + Q RX
Equation (A.III.4)
2
Q RX
1
1
-------------------------- = -----------------------2- × --------------------------------ω × C input
C input – p × ω
1 + Q RX
By equation (A.III.3):
Equation (A.III.5)
2
R RXP = 2 × R RX × ( 1 + Q RX )
By equation (A.III.4):
Equation (A.III.6)
2
Q RX
C input – p = C input × -----------------------21 + Q RX
Where
QRX = quality coefficient.
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Revision history
6
AN3394
Revision history
Table 3.
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Document revision history
Date
Revision
Changes
10-June-2011
1
Initial release.
12-Jul-2011
2
Updated DEMO-CR95HF-A antenna dimensions Section 1.3:
Inductive antenna impedance.
25-Jul-2011
3
Corrected C22 equivalent serial capacitance name in Section 1.5.2:
Entire equivalent circuit
22-Aug-2011
4
Modified document title.
Updated Introduction.
Updated Section 2: Application to DEMO-CR95HF-A demonstration
board overview to add the case of user-designed antenna.
Added Section 4: Main criteria for key antenna design.
Updated disclaimer on last page.
03-Oct-2011
5
Modified C3 and C17 in Table 2: DEMO-CR95HF-A component
commended values.
Doc ID 018754 Rev 5
AN3394
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