04 matching networks 06 - rfid-systems · 2016-04-28 · 04 matching networks 4th unit in course 3,...
TRANSCRIPT
04 Matching Networks04 Matching Networks4th unit in course 3, 4th unit in course 3, RF Basics and ComponentsRF Basics and Components
Dipl.-Ing. Dr. Michael Gebhart, MSc
RFID Qualification Network, University of Applied Sciences, Campus 2WS 2013/14, September 30th
page 2
ContentContent
Introduction: How to match the chip output to the antenna impedance?- Loop antenna
- Quality factor
- Low impedance or load matching: Power and Q
- Modulation envelope and Q-requirement (single resonance)
- Network transformation: differential to single-ended
The general matching solution: π and T-topology networks
Impedance adjustment with L-topology- Antenna impedance
- Q-factor adjustment for operating frequency
- Determination of serial and parallel capacitance for impedance adjustment
The resonant coupling system- How near-field coupling affects the air interface
How to match the chip to the antenna?How to match the chip to the antenna?
Narrow-band “matching” for the 13.56 MHz carrier frequency in reader mode
NFC Chip NFC AntennaMatching Network
??antenna impedance @ 13.56 MHz
e.g. 0.6 + j 110 Ω
chip output impedance
e.g. 5 Ω conjugate reactanceconjugate reactance
page 3
NFC device in Reader Mode (TX), a network adjusts (transforms) the antenna
impedance to a desired value for the chip driver output. This allows optimum
power transfer and to meet other contactless property requirements.
Loop antenna for Contactless CommunicationLoop antenna for Contactless Communication
The loop antenna is a distributed component with
inductance (L) as main element and capacitance (C) and
resistance (R) as parasitic network elements.
For simulation it must be
represented by an equivalent equivalent
circuitcircuit network of lumped lumped
elementselements. Over a wide frequency
range this can be a loose coupled
reactive ladder network of
resonance circuits - it has several
resonances in frequency domain.
At 13.56 MHz carrier frequency we use the fundamental fundamental
((lowestlowest) ) resonanceresonance. So we can simplify the equivalent circuit
e.g. to a parallel resonance circuit (since losses are mainly
determined by chip current consumption in Proximity Systems).
Note: This is a narrownarrow--band band approximationapproximation only!
Start of coil turns
End of coil turns
LA RACA
L1
C1
R1
L0 R0C0
Ln
Cn
Rn
page 4
page 5
The Quality factor The Quality factor Originally, the quality factor reports the quality at which the component (coil,
capacitor) represents the pure network element (inductance, capacitance).
For a 2nd order resonant LCR circuit, Q can be determined in
frequency domainfrequency domain. Q is related to the bandwidth and can be
measured from the Resistance trace.
For a 2nd order resonant LCR circuit, Q can also be
determined in time time domaindomain. Q is related to the
envelope according to
( )tQtt
RES
RES
AeAeAeteζω
ω
τ −⋅−−
=== 2)(
( )S
S
R
LQ
ωω =
( )2
@τω
ω RESRESQ =
( ) PP RCQ ωω =CP RPRLS S
RP
f RES
RP
2RP
2
MAX
∆ f
Frequency
Res
ista
nce
( )f
Q RES
∆=
2
ωω
Note: This is only valid, if the broad
band equivalent circuit
representation really is a parallel resonant circuit!
2PR
2PR
Driver Driver conceptsconcepts –– Power and Power and QQ requirementrequirement
QANT ~ QSYS, e.g. ~ 12.5
RSOURCE ~ 0
RANTENNA = 50 ΩPSYS ~ PANT ~ 1/QANT, e.g. ~ 400 mW
QANT ~ 2QSYS, e.g. ~ 25
PSYS ~ PSOURCE + PANT ~ 2PANT ~ 2/2QANT
e.g. ~ 2 * 200 mW
RSOURCE = 50 Ω
RANTENNA = 50 Ω
Low output impedanceLow output impedance
We need a certain operational system Q to achieve time constants for modulation (e.g. ~ 12.5).
In Load Matching, QSYS is half the value of the open antenna – QANT can be doubled. The power consumed in the antenna is related to 1/Q.
For Load Matching, the required total power is the same, as for low output impedance.
But for low output impedance no power is dissipated in the amplifier, all in the antenna network.
Load MatchingLoad Matching
page 6
If we consider the quality factor, it depends how the load / antenna is matched
to the source / driver:
Power and Q requirement
NL
QPIH
ANT
ANTANT ⋅
⋅
⋅≈⇒
ω~
RURIIUP
22 ==⋅=
LXwherejXRZ ω=+=
Q
LR
R
XQ
ω=→=
Q
LIP
ω2
=⇒
Power Consumption over H -field strength
0,1
0,2
0,2
0,3
0,3
0,4
0,4
0,5
0,5
1,4 1,5 1,6 1,7 1,8 1,9 2,0 2,1
H -field strength in A/m (rms)
Driv
er P
ow
er in
Watt
to
50 O
hm
lo
ad Q = 35
Q = 30
Q = 25
Q = 20
Q = 15
page 7
The unloaded H-field strength emitted by an antenna with resonance at carrier
frequency can be approximated by...
page 8
Modulation envelope and Modulation envelope and QQ requirementrequirement
To emit high H-field from low driver power, Q should be high,
To meet modulation timing specifications, Q should be low
Q is only clearly defined for a single-resonance circuit.
For this we get for ISO/EC14443 Type B specifications a maximum system Q…
End of tf
Start of tf
rft thf
hr
End of tr
0t
Start of tr
b1
To note: Modulation index and overshoots may be even more stringent!
page 9
Modulation envelope and Modulation envelope and QQ requirementrequirement
For Type A specifications...
110 %
100 %90 %
60 %
5 %0
t
t
t t
t
4
2
1 3
End of t4
End of t3
1 2
3 4
End of t and t
Start of t and t
Start of t1
Start of t2
Source Network Load
½ VPA
½ RPA 2 C½ R
½ L+
+
Source Network Load
VPA
+
RPA
C L
R
Source Network Load
½ RPA
2 C
½ VPA
½ R½ L
+
+
page 10
Network transformationNetwork transformation: single: single--endedended, differential, differential
In practice, the TX output is usually differential (to be able to have double output
voltage swing from a single supply voltage).
For simplicty reasons, RF System behaviour can be considered for a single-
ended network. Component values for the differential network can then be
calculated by the following considerations:
- Source and load (antenna) impedance is split up for single-ended consideration
Serial components:
Source Network Load
VPA+
RPA
R
LC
SINGLEDIFF RR2
1=
SINGLEDIFF LL2
1=
SINGLEDIFF CC 2=
Parallel components:
SINGLEDIFF RR2
1=
SINGLEDIFF LL2
1=
SINGLEDIFF CC 2=
Source Network Load Source Network Load
½ VPA
½ RPA 2 C½ R
½ L
VPA+
RPA
R
LC
+
+
Source Network Load
VPA
+
RPA
C L
R
Source Network Load
½ RPA
2 C
½ VPA
½ R½ L
+
+&
CANT RANT
½ C0
k, M2 L02 RPA 2 RQ½ C1
½ C2
LANT
ZIN ZANT
+
0
+ VPA
GND
0V
LTP CTP RTP
VC
AR
D_
AC
VCARD_DC
VC
AR
D_
AC
Limiter &Rectifier
page 11
Network transformationNetwork transformation: single: single--endedended, differential, differential
So for the typical matching network, values for a single-ended equivalent circuit
are following quantities of the differential network:
page 12
Impedance Matching: Impedance Matching: ππππππππ or or TT topologytopology
( )( ) ( )
( )
−−=
−−= 1cos
sinsin
cos1 ϕ
ϕϕ
ϕ
A
DADADD
R
RRRj
RRRjZ
( )( ) ( )
( )
−−=
−−= 1cos
sinsin
cos2 ϕ
ϕϕ
ϕ
D
AADADA
R
RRRj
RRRjZ
( )ϕsin3
ADRRjZ −=
ZBZA
ZC
RD RA
Z1 Z2
Z3
RARD
( )( )
( ) ( )1
1cossincos
sin−
−=
−= ϕϕ
ϕ
ϕ
D
AAD
ADA
ADA
R
RRRj
RRR
RRjZ
( )( )
( ) ( )1
1cossincos
sin−
−=
−= ϕϕ
ϕ
ϕ
A
DAD
ADD
ADB
R
RRRj
RRR
RRjZ
( )ϕsinADC RRjZ =ϕ....Phase deviation
output to input
Literature: F. E. Terman, „Network Theory,
Filters, and Equalizers“
Any complex load can be matched to a source impedance using an LC element
network in π - or T topology (general solution). As the antenna impedance varies
over frequency, this matching is for the carrier frequency only.
page 13
Towards a more specific impedance adjustmentTowards a more specific impedance adjustment
Any complex load can be matched to any source impedance using π - or T
topology.
However, there is at least one inductor L, which introduces losses…
We may not need to adjust any load:
- antennas are an inductive load (1st self-resonance > fCAR)
- phase relation output to input for the carrierfrequency is irrelevant
So there is a more specific solution, consisting only of capacitors
- HF capacitors of C0G or NP0 have negligible losses and less tolerance
- Less components also means reduction of costs and PCB area
Impedance Impedance adjustment with adjustment with LL--topologytopology
RA
LA
ANTENNA
CA
R
U
C
D
D
SM
CPM
MATCHINGDRIVER
RE
ZAZM
C0
L0
EMC-FIL
ZE
AAAA
AA
ACLCRj
LjRZ
21 ωω
ω
−+
+=
page 14
An equivalent circuit of the loop antenna may
have the above structure.
It can be extracted from measurement.
Complex antenna impedance ZA can be
calculated (over angular frequency ω).
CARRES ff >>
( )SYSA QQ >>>
( )( ) ( )[ ]FHHzFHzj
HHzjZ A
12626126
66
1035.210314.11056.1321035.258.01056.1321
10314.11056.13258.0
−−−
−
⋅⋅⋅⋅⋅⋅−⋅⋅Ω⋅⋅⋅⋅+
⋅⋅⋅⋅⋅+Ω=
ππ
π
( ) 52.114607.056.13@ jMHzZ A +=
page 15
Antenna coupling Antenna coupling –– NFC NFC antenna onlyantenna only
distance variation to “loading” antenna coupling factor k varies
Coupling affects antenna impedance
significantly
- mutual inductance LA changes
- „Loading“ Q changes
Impedance trace is shown in Smith Chart
QQ--factor adjustment for operating frequencyfactor adjustment for operating frequency
page 16
The quality factor of the antenna conductor shall be high… above the intended
Q-factor for operation at the carrier frequency 13.56 MHz.
We can neglect losses in the capacitor (if good components are chosen)
- For one frequency, the serial equivalent circuit can be calculated to an
equivalent parallel circuit for the inductor, using the Q equation:
A
PARALLEL
SERIAL
AA
L
R
R
LQ
ω
ω≡=
A
INTENDED
AE R
Q
LR −=
ω
- This way, an external resistor in series to the antenna allows to adjust the
intended QA:RE
RA
LA
CA
RA
LA
CA LRCAAA
- To note: This can again be re-
calculated to a “new” antenna
impedance ZA (which might also
be a parallel equivalent circuit).
RA
LA
ANTENNA
CA
R
U
C
D
D
SM
CPM
MATCHINGDRIVER
RE
ZAZM
C0
L0
EMC-FIL
ZE
AAAA
AA
ACLCRj
LjRZ
21 ωω
ω
−+
+=
( )( )APMSMSM
PMSMAEM
ZCCjC
CCZjZZ
ωω
ω
−
++==
1
( )( ) ( )[ ]PMAADA
AAPMSM
CCLRL
LRCC
+−=
221 ωω
qpp
CPM −±−=42
2
A
AA
L
CLp
2
2 22
ω
ω −=
( )( )
2
2446
21A
A
A
AD
A
A
AA CL
C
LR
R
L
RRq +−−
+=
ωωω
CARRES ff ≡
0Im ≡Z
DESIREDRZ ≡Re
page 17
No EMC
Impedance Impedance adjustment with adjustment with LL--topologytopology
page 18
Annex: Exact derivation of reactance matching Annex: Exact derivation of reactance matching
with 2 capacitors (I):with 2 capacitors (I):
( )PA
AA
PA
AA
A
CCssLR
sCsCsLR
Y
+++=
=+++=
11
11
R
U
C
D
D
S
CP
ANTENNAMATCHINGDRIVER
LRC AAA
( ) SAAPAAA
AA
SA
LASTsCRsLCCLRs
LsR
sCYZ
1112
++++
=+=
( )[ ]( )
NennerCsRCLsCCCLRs
RsLCCLRCLRsR
SASAPASAA
AAPAAASAAD ⋅
+++
++++≡
23
2
( ) ( )[ ] AAPAAASAASADSADPASAAD RsLCCLRCLRsCRsRCLRsCCCLRRs ++++=+++ 223
- The admittance of the parallel equivalent
antenna circuit and CP is given by
- Impedance for the parallel equivalent circuit of antenna and reactance matching network is...
- This impedance is set equal to the desired real ( reactance matching)
source impedance (e.g. 50 Ω).
page 19
( ) ( )[ ] AAPAAASAASADSADPASAAD RLjCCLRCLRCRRjCLRCCCLRRj ++++−=+−+− ωωωωω 223
( ) ASADPASAAD LjCRRjCCCLRRj ωωω =++− 3
( )PAAADAD
AaS
CCLRRRR
LC
+−=
2,ω
( )[ ] APAAASAD RCCLRCLR ++−=− 22 ωω
( )( )GAA
APAAAbS
RRL
RCCLRC
−
++−=
2
2
,ω
ω
- Transition s j ω and coefficient comparison of real and imaginary parts:
- Imaginary parts:
- Real parts:
- Both solutions for CS are set equal, to solve for CP
Annex: Exact derivation of reactance matching Annex: Exact derivation of reactance matching
with 2 capacitors (II):with 2 capacitors (II):
page 20
( ) ( ) ( )2224222222222
PAAADPAAADPAAADADDAAA CCLRRCCLRRCCLRRRRRLRL +++−+−=− ωωωωω
[ ][ ]
( )[ ]222422222
22224
2242
2
22
AAADAAADDAAAD
AADAAADP
AADP
CLRRCLRRRRLRR
LRRCLRRC
LRRC
ωωω
ωω
ω
+−−−+
+−+
+
A
AA
L
CLp
2
2 22
ω
ω −=
( ) ( )224
22224 12
AAG
DAAAAAAAAD
LRR
RRCLRCLRRRq
ω
ωωω −−+−=
qpp
C baP −±−=42
2
,
- For CS, a = CS, b follows...
- Sort according the power of CP:
- Resolve the characteristic equation, cancel:
- Knowing CP allows to calculate CS using one or the other equation.
Note: only positive, real values have a physical meaning!
Annex: Exact derivation of reactance matching Annex: Exact derivation of reactance matching
with 2 capacitors (II):with 2 capacitors (II):
page 21
Antenna coupling Antenna coupling –– no EMC no EMC filterfilter
2 RPA
+
0
+ VPA
GND
0V
TX1
CANT
RANT
2 RQ½ C1
½ C2LANT
k, M
distance 80 … 3 mm
page 22
Reasoning for extending the networkReasoning for extending the network
Due to Standard (e.g. ISO/IEC14443) requirements for modulation timing, the
allowable Q-factor for the operated system is rather low (~limited bandwidth).
For efficient H-field emission, a higher reactive current is desirable a 2nd
resonance frequency can increase the bandwith.
Furthermore, this 2nd resonance (LC low-pass) can suppress unwanted
harmonics emission ( name EMC filter)
This comes on the expense of
more signal distortions…
RA
LA
ANTENNA
CA
R
U
C
D
D
SM
CPM
MATCHINGDRIVER
RE
ZAZM
C0
L0
EMC-FIL
ZE
AAAA
AA
ACLCRj
LjRZ
21 ωω
ω
−+
+=
( )( )APMSMSM
PMSMAM
ZCCjC
CCZjZ
ωω
ω
−
++=
1
00
2
0
0
CLZCj
LjZZ
M
ME
ωω
ω
−
+=
CARRES ff ≡
0Im ≡Z
DESIREDRZ ≡Re
page 23
Impedance Impedance adjustment with adjustment with LL--topologytopology
page 24
For the calculation of CP and CS we follow a more systematic approach and re-
calculate a real and imaginary impedance for every step:
1st step: starting from right side, we
calculate an antenna impedance ZA
( )( )
RaXXR
XRZ
LACAA
CAAA =
++=
22
2
Re
( )( )
XaXXR
XXLXRXZ
LACAA
LACAACAACAA =
++
++=
22
222
Im
Impedance Impedance adjustment with adjustment with LL--topologytopology
page 25
2nd step: starting from the left side, we calculate the EMC filter impedance and the
adjustment network impedance ZM
0
0
1
CXC
ω−=
00 LX L ω=
( )( )
RmXXR
XRZ
LC
CM =
++=
2
00
2
0
2
00Re
( )( )
XmXXR
RXXXjXZ
LC
LCLCM =
++
++−=
2
00
2
0
2
000
2
00Im
Impedance Impedance adjustment with adjustment with LL--topologytopology
page 26
This way, we bring the matching condition in the middle of the network.
3rd step: Solving condition for the parallel and serial capacitance (target impedance):
−+⋅±⋅
−= 1
2
2,1
am
a
m
aaa
ma
mP
RR
X
R
RRX
RR
RX
( )22
22
Paa
PaaaPmS
XXR
XXXRXXX
++
++⋅−=
P
PX
Cω
1−=
S
SX
Cω
1−=
Finally, we need to sort out solutions which have no physical meaning…
- only positive capacitance values have a representation
- …not all antennas can be matched (if we violate a pre-condition, it is not
possible…
Note: In practice, the impedance must be checked by measurement, as
parasitics may cause deviations from the ideal conditions
Impedance Impedance adjustment with adjustment with LL--topologytopology
page 27
Antenna coupling Antenna coupling –– withwith EMC EMC filterfilter
CANT
RANT
½ C0
2 L02 RPA 2 RQ½ C1
½ C2LANT
+
0
+ VPA
GND
0V
TX1
k, M
distance 80 … 3 mm
Which loads can be matchedWhich loads can be matched??
CS
CP
For the 2 capacitor network, the area in the Smith Chart is following…
FORBIDDEN
AREA
page 28
Reference: Electronic Applications of the Smith
Chart by Phillip H. Smith, 1969, p. 124
page 29
Which loads can be matchedWhich loads can be matched??
For the network with EMC-filter, it is slightly more difficult
+C2
CANT
LANT
RANT
C0
LTP
k, M
Differential EMC-Filter
+ lumped component impedance adjustment network
PCD antenna
equivalent circuit
PICC antenna
equivalent circuit
I PC
D_A
NT
C1L0RPA
C0 C2
-
+
+
+VPA
RQ
ZIN ZANT
CTP RTP
VCARD_DC
VC
AR
D_
AC
PICC equivalent
circuit
C1L0RPA RQ
GND
0V
TX1
TX2
2VPA
2VPA
LA
LB
LA
LB
Ztarget (ZT)
)(1 00
0
INLC
LINT
ZjXjX
jXZZ
−+
−=
We need to calculate a target impedance (ZT) first,
which depends on our desired input impedance
ZIN, and the (loaded) antenna impedance (ZA).
page 30
+ CP
- CP
+ CS
- CS
Which loads can be matchedWhich loads can be matched??
Region, which can be
matched to desired
network input impedance
Antenna impedance ZA
(including coupling)
Target impedance ZT
Network input impedance
ZIN (@ carrier frequency)
Adjustable range for
parallel cap CP
Adjustable range for
serial cap CS
Frequency trace of ZIN
The region of network input impedances ZIN at carrier frequency, which can be
adjusted to an intended resistance (“matched”), is limited by two circles.
For the parallel capacitor, from short to ZT
For the serial capacitor, from ZT to open.
page 31
Which loads can be matchedWhich loads can be matched??
The CP limit circle is given by
- xT, yT…. coordinates of ZT
- c…center, r… radius
( )( )12
122
−
++−=
T
TT
x
yxc cr −=1
The CS limit circle is given by
( )( )12
122
+
++−=
T
TT
x
yxc cr +=1
Impedance adjustment possible, iff
( ) ( )TA ZZ ReRe ≤
( ) ( )loadinductiveZ A 0Im ≥
The resonant coupling systemThe resonant coupling system
L00C
RX
TX
GND
TX
RX
A
A
B
B
NF
C C
hip
anal
ogue
fro
nt
end
CSPC
RQ
Antenna
Mat
chin
g n
etw
ork
EMC-Fil.
Receive path
VMID
VMID
L R C R C
Antenna Chip
C
Assemb.
A A A
R
R
CC
AS
AS
AS
Pro
xim
ity C
hip
coupling k
Transponder equivalent circuit properties
L, R, C
Resonant system properties
k, f , QRES
Reader equivalent circuit properties
L, R, C
Standard defines properties
at the Air Interface
page 32
page 33
How near-field coupling affects the air interface
110 %
100 %90 %
60 %
5 %0
t
t
t t
t
4
2
1 3
End of t4
End of t3
1 2
3 4
End of t and t
Start of t and t
Start of t1
Start of t2
ANTENNAMATCHINGEMC-FIL
Matc
hin
g-I
mpedance
Cs
CpC0
L0
RALACA
Coupling: 0 %Distance: -- mm
page 34
ANTENNAMATCHINGEMC-FIL
Matc
hin
g-I
mpedance
Cs
CpC0
L0
RALACA
Coupling: 6 %Distance: 25 mm
t1 in ττττC t2 in ττττC t3 in ττττC t4 in ττττC a HOVS
37.80 31.12 2.45 1.52 0.007 1.076
How near-field coupling affects the air interface
page 35
ANTENNAMATCHINGEMC-FIL
Matc
hin
g-I
mpedance
Cs
CpC0
L0
RALACA
Coupling: 13 %Distance: 15 mm
t1 in ττττC t2 in ττττC t3 in ττττC t4 in ττττC a HOVS
37.77 31.47 2.12 1.34 0.007 1.12
How near-field coupling affects the air interface
page 36
Coupling: 21 %Distance: 10 mm
ANTENNAMATCHINGEMC-FIL
Matc
hin
g-I
mpedance
Cs
CpC0
L0
RALACA
t1 in ττττC t2 in ττττC t3 in ττττC t4 in ττττC a HOVS
37.80 29.41 1.99 1.34 0.010 1.16
How near-field coupling affects the air interface
page 37
ANTENNAMATCHINGEMC-FIL
Matc
hin
g-I
mpedance
Cs
CpC0
L0
RALACA
Coupling: 38 %Distance: 5 mm
t1 in ττττC t2 in ττττC t3 in ττττC t4 in ττττC a HOVS
37.78 24.97 1.61 1.04 0.020 1.15
How near-field coupling affects the air interface
page 38
Thank you for your Thank you for your
Audience!Audience!
Please feel free to ask questions...