02 elements 05 - rfid-systems · 02 elements 2nd unit in course 3, rf basics and components...

02 Elements02 Elements2nd unit in course 3, 2nd 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

ContentContent

Electrical Elements overview- Inductance

- Capacitance

- Resistance

The complex frequency domain- RF system properties of a parallel resonance circuit

Laplace Transformation- H-field in time-domain, as emitted by the ISO/IEC10373-6 PCD antenna

Electrical Components

How to characterize impedance at HF

Example: Dependencies of a “bad inductor” for NFC

sCZ

1=

sLZ =

Cj

CjZ

ωω

11−==

RZ =

LjZ ω=

RZ =

jBGYjXRZ +=+=

R

jX

R

R

jX

jωL

R

jX

-jωC

1

U

I

θθθθ

U

I

θθθθ

U

I

θθθθ

( ) ( )00 cos ϕω += tIti

( ) ( )00 cos ϕω += tUtu

( ) ( )00 cos ϕω += tIti

( ) ( )°++= 90cos 00 ϕω tUtu

( ) ( )00 cos ϕω += tIti

( ) ( )°−+= 90cos 00 ϕω tUtu

u(t)

i(t)t

t

t

u(t)

i(t)

i(t)

u(t)

Electrical Elements in overviewElectrical Elements in overviewsymbol impedance phasor signal tracessignals

What is the Element Inductance?What is the Element Inductance?

Let us consider two current-carrying conductor loops, and time-variant current:

- The current i1 in the first loop generates a magnetic flux Φ of the flux density B1.

- A part of the primary flux penetrates the second conductor loop.

- This generates a 2nd current, which compensates the part of the primary flux.

C1..…circumference of 1st area

A1..…area enclosed by the 1st conductor

i1...…current in the 1st conductor

....…normal vector to the area A1

...…magnetic flux density vector

( ) ArotBforsdPAdAnBA C

rrro

rro

r===Φ ∫ ∫ ∫

2 2

22222

Br1nr

..…magnetic vector potentialAr


- All contributions to the flux across an area are directly proportional to the

currents in the individual conductor loops, e.g.

2221212 LILI +=Φ

∫ ∫==

1 212

1202112

4C C

R

sdsdLL

ro

r

π

µ

- L with same indices means

self-inductance.

- L with different indices means

mutual inductance.

Resolving the proportionality value, we find

- For the mutual inductance…

- For the self-inductance…( )

22

22

22

2

022

2 24

sddVR

PS

IL

C V

ro

r

∫ ∫∫∫′

′=

π

µ

Examples:Examples:

As ferrite material has an increased relative permeability µR compared to free

space (where µR = 1), the flux density B is increased.

Consequently, Inductance L is increased for a conductor loop near ferrite.

sA

mVwhereHB R

7

00 104 −=⋅⋅= πµµµ

As metal allows ring currents (eddy currents) equal to a closed conductor

loop, Inductance L is decreased for a conductor loop near metal.

…where j expresses the 90 °phase-shift

page 7


- We can understand inductance as “inertia of current”, it is the time-variant

“resistance” which the conductor offers to a time-variant current.

- Inductance results from the relation of time-variant magnetic flux and current to

dI

dL

Φ=

- All the magnetic flux Φ generated by the current i is directly proportional to the

actual value of i.The proportional value is inductance L

( ) ( )di

dN

di

dL

dt

diL

dt

di

di

dN

dt

tdtui

Φ−=−=→−=⋅

Φ−=−=

ψψ

LXforjXIU LL ω=⋅=

- For harmonic sine-wave signals (considering no offset or transient condition) we

can express the derivation by amplitudes, for complex network calculations:

Φ= Nψ…or for the coil flux (N turns)

E.g. mutual inductance of circular coilsE.g. mutual inductance of circular coils

( )

( )α

α

αµ π

drrrrx

rrM C ∫

−++

⋅⋅=

2

0 21

2

2

2

1

2

210

cos2

sin

2

For the simple geometry of circular coils, an exact calculation is possible:

MC..…mutual inductance in Henry (H)

µ0..…permeability constant

r1...…radius of the 1st coil in meters

r2 .…radius of the 2nd coil in meters

x……distance of the coil centers in meters

α ...…tilt angle of the coil axes

( )322

1

2

22

2

110

2 xr

rNrNM CA

+

=π

µ

- Moreover, for coaxial coil orientation (same axis), this simplifies to

AmVs7

0 104 −⋅= πµ

Coupling factorCoupling factor

- In network calculation, the coupling factor k represents the connection of a coil

arrangement.

- It is a pure geometry factor, as the other parameters cancel out.

- It results from the relation of mutual inductance M between two coils, and the

inductance L of the two coils:

MMMforLL

Mk ==

⋅= 2112

21

- E.g. resolving the equation for circular coils in coaxial orientation, we find…

( )322

121

2

2

2

1

xrrr

rrk

+⋅

⋅=

What is the element Inductance?What is the element Inductance?

Inductance (L) is a property of conductors and coils, relating

time-variant voltages to currents.

I

NL

Φ=

π

µµ

8

0lL R=…for the straight conductor…in Henry (H)

…where µ0 is the permeability constantAm

Vs7

0 104 −⋅= πµ

Inductance also is an energy (W) storage and thus can be defined

22

2

ˆRMS

IM LI

iLW ==

Complex network calculation (without pre-charge)

sLIU ⋅=

( ) ( )∫∞−

=t

dttuL

ti1

( ) ( )dt

tdiLtu =

sL

UI =

)(ˆ: amplitudevaluepeakthemeansiNote

…for the long coill

ANL R 02 µµ

=

What is the element Capacitance?What is the element Capacitance?

Capacitance (C) is the ability of a body to store an electrical charge (q).

Typically two conductive plates of area A in distance d store the charge +q

and –q. Capacitance is then given by

U

qC =

d

AC R 0εε=…for the plate capacitor…in Farad (F)

…where ε0 is the electric field constantm

F12

0 10854.8 −⋅=ε

Capacitance also is an energy (W) storage and thus can be defined

22

2

ˆRMS

CE CU

uCW ==

Complex network calculation (without pre-charge)

sCIU

1⋅=( ) ( )∫

∞−

=t

dttiC

tu1

( ) ( )dt

tduCti = sCUI ⋅=

)(ˆ: amplitudevaluepeakthemeansuNote

What is the element Resistance?What is the element Resistance?

Resistance (R) of an electric conductor represents the loss

of effective power, when the conductor carries current.

Conductor materials have a specific conductance σ in S/m.

Resistance is given by

A

lR

⋅=

σ…in Ohm (Ω)

Complex network calculation (there cannot be any pre-charge)

( ) ( )tiRtu ⋅=

( ) ( )R

tuti =

RIU ⋅=

R

UI =

Resistance also means loss power (P)

( ) ( ) tituWRIR

UIUP ⋅==⋅==⋅= ReRe2

2

The complex frequency domainThe complex frequency domain

Properties of a network can be presented in the complex frequency (s) plane

ωσ js +=

Amplification orAmplification or

AttenuationAttenuationOscillation Oscillation

frequencyfrequency

This requires polynomial analysis of the network

function G(s)

jω

σ

stable half-plane

(σ < 1)

( ) ( )( )×

=polesresonancesparallel

zerosresonancesserialsG

,

, o

Considering a parallel resonance circuitConsidering a parallel resonance circuit

As an application for complex network calculation, let us consider a parallel

resonance circuit:

sCZ

1=sLZ =

GR

Y ==1

LRC

Antenne

PPPui

RZ =

sLY

1= sCY =

- This could be a simplified loop antenna fed by induced AC voltage in

alternating H-field.

- Impedance Z and Admittance Y is given in the Laplace Domain.

( )

Cs

LCRCss

sCsLR

sY1

11

112 ++

=++=

- We find the poles as solution to

the characteristic equation…

page 15

Impedance in the complex frequency domainImpedance in the complex frequency domain

LCRCRCs

1

2

1

2

12

2,1 −

±−=

σ

jω

C

L

R2

1cos

1

LC

10 =ω

2

2

11

−=

RCLCjj dω

2

2

11

−−

RCLCj

RC2

1−

- Impedance Z as the inverse of admittance

is given by…

( )( )

LCRCss

Cs

sYsZ

11

1

1

2 ++

==

- Natural angular frequency

(un-damped self-resonance)

- Attenuation coefficient

- Quality factorσ

jωS-Ebene

page 16

RF System propertiesRF System properties

2

2

02

111

−=−=

RCLCjjj d ζωω

0ωj

LC

10 =ω

0ζω−

( )

=

C

L

R2

1cos

1

cos

1

ζ

- A comparison to the general (damped) wave equation results the following

RF system properties for this LCR-network:

022

00

2 =++ ωζω ss

LC

12

0 =ω

C

L

RRC 2

1

2

1

0

==ω

ζ

0

04

1

2

1

ωζ RCQ ==

( )

LCRCss

Cs

sZ11

1

2 ++

=

- Wave equation

LaplaceLaplace--TransformationTransformation

u(t) U(s)

Laplace Transformation

time-domain frequency-domain

G(s) g(t)

network function impulse response

inverse

Laplace Transformation

∫∞

−⋅==0

)()()( dtetftfLsFst

∫+∞

∞−

− ⋅⋅== ωπ

desFsFLtfst)(

2

1)()( 1

The Laplace Transformation corresponds between time-domain and complex

frequency domain. Can be applied on signals and networks.

LaplaceLaplace--TransformationTransformation

The Laplace Transformation corresponds between time-domain and complex

frequency domain. Can be applied on signals and networks.

Historical Note:

Pierre Simon de Laplace (1749 – 1827) did not invent the Laplace

transformation, but a specific “Laplace Integral”.

The Laplace Transformation is a further development of Oliver Heavisides

calculation concept. It is more general than the Fourier-Transformation.

Option 1:

1. Transformation of the input time-function into

the complex frequency-domain.

2. The output function is the product of input

function and network function.

3. Inverse Transformation to get the output

time-function.

)()( tuLsU ee =

)()()()()( tuLsGsUsGsU eea ⋅=⋅=

)()()( 1tuLsGLtu ea ⋅= −

Option 2:

1. Transformation of the network function into

time-domain (= impulse response).

2. The output function is the convolution of input

time-function and impulse response.

It is possible to calculate signals at the output of a network, by applying Laplace

Transformation on input signal u(t) and network function G(s).

How to calculate network output signalsHow to calculate network output signals……

Example: Example: HH--field signal of the ISO/IEC10373field signal of the ISO/IEC10373--6 PCD6 PCD

Component valuesLA....480 nH

RDC....0.14 Ohm

C1.....47 pF

C2.....180 pF

C3.....33 pF

C4.....3 - 30 pF (selected 17 pF)

RE.....0.94 Ohm

RD.....Driver Impedance (50 Ohm)

D

DCEA

DCEA

DCEA

DCEA

DCEA

DCE

RCCCRRsL

RRsL

sC

CCCRRsL

RRsL

RRsL

RRsG

++++++

+++

+++++

++

⋅++

+=

1))((

1

1))(()(

4321

432

Example: Example: HH--field signal of the ISO/IEC10373field signal of the ISO/IEC10373--6 PCD6 PCD

Digital Sampling Osc.Calibration Coil signal

H-field, Mod. Envelope shape

Arbitrary Waveform Gen.

PCD

RF signal in

)()( tuRti aEA ⋅=

)()()( 1 tuLsGLtu ea ⋅= −

Input signal (command modulated on RF carrier)

Output signal, distorted by resonant antenna

Note: current corresponds to H-field

Electrical ComponentsElectrical Components

Components are the practical implementation of lumped elements.

Main properties (elements) are associated with parasitic elements:

Surface mounted devices (SMD) have the least (minimum) parasitics.

Electrical dependencies

- Frequency dependency (e.g. dispersion)

- Power dependency (e.g. saturation), …

Ambient (physical) dependencies

- Temperature, humidity (e.g. aging), pressure, …

Try to characterize under operating conditions!

Resistor Capacitor Inductor

ResistorResistor

SMD resistors offer an excellent representation of the element resistance.

Values are available in logarithmic distance for a decade.

normreihen specified in ISO 60063:

- E3, E6, E12, E24, E48, E96 and E192.

Individual values k are calculated by

where n specifies the number of elements per decade m.

- e.g. E12:

Package sizes specified in inches

- e.g. 1206, 0804, 0603, 0402, 0201

n mk 10≅

2.810...,,5.110,2.110,110 12 1012 212 112 0 ≅≅≅=

means 2.0 mm long and 1.25 mm wide

Package Length Width

mm mm

1206 3,2 1,6

804 2 1,25

603 1,6 0,8

402 1 0,7

201 0,5 0,3

CapacitorCapacitor

Capacitors can be a similar good representation of the element capacitance, if

the dielectric material is choosen right. COG or NP0 for SMD are good HF Caps.

The Electonics Industries Alliance (EIA) standardised 3 capacitor classes:

- Class 1: HF capacitors (typically ceramic) with high parameter stability

- Class 2: High volume efficiency capacitors (for buffers,…)

- Class 3: Volume efficiency ceramic caps (typ. – 22…+ 56 % cap over 10...55 °C)

- Class 4: Semiconductor caps

Class 1 ceramic capacitors are classified for temperature dependency in a

frequency range

- IEC/EN 60384-8/24 means 2-digit code, EIA RS-198 means 3 digit code

- NPO means zero gradient and +/-15 x 106 / K tolerance. EIA code is C0G,

IEC/EN code is C0

The EIA ceased operations in 2011, the Electronic Components Industry

Association (ECIA) will continue EIA standards maintenance.

CapacitorCapacitor

InductorInductor

Inductors are critical / problematic components.

Coil inductors preferred to chip inductors (more stable properties)

Attention to current under operating conditions (e.g. 100 mW ... 1 W RF power)

Losses due to parasitic DC resistance (e.g. 0.5 … 5 Ω for 1 µH in 0805 package)

– Q-factor!

Attention to frequency and power dependency of inductance

Attention to thermal stress

Take care of coupling in layout

HowHow to to characterize impedancecharacterize impedance at HF at HF

RF out

R A B

Analyzer Amplifier Directive Coupler DUT FixtureAttenuator

Notebook Remote

Control

CPRP

CC

CC

YZZ

1

1

10 =

Γ−

Γ+=

PPPC

CPGjBGY

ZR11

Re1

ReRe =

+=

==

ωπ

B

ZfYC

CMEASC

P =

−=

=2

1Im

1Im( ) ( ) 22

PSPSP

PSDUT

CRRRR

RUU

ω++=

The voltage on the DUT is calculated

with a voltage divider (50 Ohm sourceand measured load impedance), from

a previously measured output voltage

to 50 Ohms.

An extended setup for network analysis is used to characterize

impedance over frequency and voltage - also in the operating

point and up to destruction levels.

Example – Chip Inductor (560 nH)

In order to possibly extract an equivalent circuit of the inductor, a frequency

sweep of the inductance was made at 4 different power levels.

Huge frequency and power dependency, extraction to typical equ. circuit is notnot possible!

At 13,56 MHz the inductor shows a significant differencesignificant difference to specified inductance

InductanceInductance and and resistance are voltage dependentresistance are voltage dependent!!

Matching impedance measurement @ 1mW and operation @ 500 mW will be different

630 nH630 nH

1,7 Ω1,7 Ω

780 nH780 nH

7 Ω7 Ω

~ 7,5 V(rms)~ 7,5 V(rms)

Example – Chip Inductor (560 nH)

Measurement of the matching impedance Smith Chart frequency sweep for power steps

VoltageVoltage @ 13,56 MHz @ 13,56 MHz in in MatchingMatching NW NW isis < 0,01V< 0,01V(RMS)(RMS)

Frequency Sweep @ - 45 dBm

13,56 MHz


Voltage @ 13,56 MHz in Matching NW is 0,03 V(RMS))



13,56 MHz


Voltage @ 13,56 MHz in Matching NW is 0,133 V(RMS) = 0,934 V(pp)




13,56 MHz





Frequency Sweep @ 0 dBm

13,56 MHz

Voltage @ 13,56 MHz in Matching NW is 2,5 V(RMS) = 7,08 V(pp)





Frequency Sweep @ 0 dBm

13,56 MHz

Power Sweep @ 13,56 MHz

Measurement of the matching impedance Smith Chart power sweep @ 13.56 MHz

ImpedanceImpedance in in operationoperation

ImpedanceImpedance in in measurementmeasurement

ImpedanceImpedance in in operationoperation …… 28,3 + j 23,9 28,3 + j 23,9 ΩΩ @ 3,52 V@ 3,52 V(RMS) (RMS) = 9,95 V= 9,95 V((pppp))

ImpedanceImpedance in in measurementmeasurement…… 16,36 16,36 –– j 5,43 W @ 0,13 Vj 5,43 W @ 0,13 V(RMS) (RMS) = 0,37 V= 0,37 V((pppp))

Power Power level forlevel for permanent permanent damage reacheddamage reached

Emitted equ. hom. H-field at CalCoil in 10 mmPower sweep into network with (left) and without EMC inductor (right)

No power dependency in the remaining network, only caused by the EMC inductor

Same H-field emitted at 131 mW than at 640 mW

Impedance withImpedance with EMCEMC

RpRp ~ 17 ~ 17 …… 88 88 ΩΩ

CpCp ~ 230 ~ 230 …… -- 220 220 pFpF

Impedance withoutImpedance without EMCEMC

RpRp ~ 860 ~ 860 ΩΩ

CpCp ~ 113 ~ 113 pFpF

Almost linear increase of H with sqrt (RF Power)

P = U² Rp ~ 640 mWP = UP = U²² RpRp ~ 131 mW~ 131 mW Impedance, RF power & H-Field

Thank you for your Thank you for your

Audience!Audience!

Please feel free to ask questions...

02 elements 05 - rfid-systems · 02 elements 2nd unit in course 3, rf basics and components...

Documents