04 Matching Networks 06 - RFID-Systems · 2016-04-28 · 04 Matching Networks 4th unit in course 3, RF Basics and Components Dipl.-Ing. Dr. Michael Gebhart, MSc RFID Qualification

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


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


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!


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


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


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


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


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


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


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


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


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


page 35


Matc

hin

g-I

mpedance

Cs

CpC0

L0

RALACA



37.77 31.47 2.12 1.34 0.007 1.12


page 36



Matc

hin

g-I

mpedance

Cs

CpC0

L0

RALACA


37.80 29.41 1.99 1.34 0.010 1.16


page 37


Matc

hin

g-I

mpedance

Cs

CpC0

L0

RALACA



37.78 24.97 1.61 1.04 0.020 1.15


page 38

Thank you for your Thank you for your

Audience!Audience!

Please feel free to ask questions...

04 Matching Networks 06 - RFID-Systems · 2016-04-28 · 04 Matching Networks 4th unit in course 3, RF Basics and Components Dipl.-Ing. Dr. Michael Gebhart, MSc RFID Qualification

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