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Powering up the RFID chip - Remotely. Basic Reader-Tag System. Rectifier. Logic & Memory. Reader. Tag. Z1’ and Z2’ can be used to represent resistors, capacitors etc. as required. I 1. I 2. Z 1 ’. Define self-impedance of each loop: Z 1 = Z 1’ +R1+ j w L1 Z 2 = Z 2’ +R2+ jwL2. - PowerPoint PPT Presentation
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Powering up the RFID chip - Remotely
1
Basic Reader-Tag System
Rectifier
Logic & Memory
Tag
Reader
2
Simple Magnetically Coupled Circuit
Vi = Z1.I1 - jM.I2 0 = Z2.I2 - jM.I1
Applying KVL in each loop
Z1’ and Z2’ can be used to representresistors, capacitors etc. as required
Define self-impedance of each loop:Z1 = Z1’ +R1+ jL1 Z2 = Z2’ +R2+ jwL2
Z1’
Z2’
I1
. .+
I2
~ViL1, R1 L2, R2
2
M1
1
i 2
ZZ
I
V Input impedance
Transfer admittance 2
2.1
M1
2.1
M
.2.1
j
i
2
ZZ
ZZ
ZZV
I
General Expressions
Reflected impedance
3
2
M1
1
i 2
ZZ
I
V Input impedance
Transfer admittance 2
2.1
M1
2.1
M
.2.1
j
i
2
ZZ
ZZ
ZZV
I
General Expressions
2
M.j
1
2
ZI
I Current Transfer ratio
4
Vi = (R1 + jL1).I1 - jM.I2 0 = (R2 + jL2).I2 - jM.I1
I2
I1
(R2 + jL2).I2= jM.I1
(R1 + jL1).I1
jM.I2
Vi
Example: Inductively Coupled Resistive Circuit (Transformer)
I1
. .+
I2
~ViL1 L2
R1
R2
VoltageCurrentSource voltage
5
I2
I1
(R2 + jL2).I2= jM.I1
jL1.I1
jM.I2
ViVi = jL1.I1 - jM.I2
0 = (R2 + jL2).I2 - jM.I1
I1
. .+
I2
~ViL1 L2
R1 ~ 0
R2
Ideal Transformer
VoltageCurrentSource voltage
N.k
1
1L
2L.
k
1
2L.1Lk
2L
Mj
2Lj2R
2I
1I
R1 << .L1R2 << .L2k ~ 1
6
Self Quiz
1. Inductively coupled circuit with R1= 1, R2= 2, L1=L2, .L1=200, k= 0.8
If I1= 1A, what is the approximate value of I2? (KVL)
2. If R2 = 1, what is the approximate value of I2?
3. What is approximate input impedance in each case?
4. What is the approximate input impedance if k ~ 1?
7
1. 0.8 A
2. 0.8 A (Same!)
3. (1+ j.72) (Unchanged!)
4. 1
8
Transfer admittance 2
2.1
M1
2.1
M
.2.1
j
i
2
ZZ
ZZ
ZZV
I
Effectiveness to drive current through secondary – would like to maximize for effective power transfer
Introduce resonance
Let resonance occur at
~ C2
I1
. .+
I2
Vi
R2
L2L1
R1C1
Self impedances:Z1 = 1/ jC1 +R1+ jL1 Z2 = 1/ jC2 +R2+ jL2
2C.2L
1
1C.1L
10 which is our excitation frequency
CAVEAT: Series resonance for illustration only!9
At we have Z1 =R1, Z2 =R2 and Transfer admittance is
222Q.1Qk1
2Q.1Qk.
2R.1R
j
2R.1R
M1
2R.1R
M
.2R.1R
j
i
2
V
I
Coupling Coefficient %
22Q.1Qk1
2Q.1Qk
Q1=30Q2=40
Peak occurs at 12Q.1Qk Beyond this value of k, Transfer admittance falls!
0.1 1 10 1000
0.1
0.2
0.3
0.4
0.5
10
Self Quiz
Reader and Tag both has Q =25, and each has ESR (effective series resistance ) = 5. The reader is excited by 1V. What is the current in the Tag for k = 1%, 4%, 10% if both primary and secondary tuned to same frequency?
11
Q= 25 R ohm= 5
k k.Q kQ/(1+kQ^2) I amps I^2. R mW
0.01 0.25 0.235294 0.047 11.07
0.04 1 0.5 0.1 50.00
0.1 2.5 0.344828 0.069 23.78
0.16 4 0.235294 0.047 11.07
12
0.1 1 10 1000
0.1
0.2
0.3
0.4
0.5
Coupling Coefficient %
22Q.1Qk1
2Q.1Qk
Diminishing return – does not help reducing the spacing beyond a certain point
Tight couplingSmall Separation
Weak couplingLarge Separation
Transfer admittance
spacing
~Spacing ↑ => Coupling coefficient ↓
13
Weak Coupling Case
12Q.1Qk If then coupling is weak
2R.1R
M.
2R.1R
2Q.1Qk.j
i
2
V
IThen
0.1 1 10 1000
0.1
0.2
0.3
0.4
0.5
12R.1R
M
In other words
14
Resonant vs. Non-resonant
2.1
Mj
i
2
ZZV
I 1
2.1
M
ZZ
Transfer admittance- general expression
2
2.1
M1
2.1
M
.2.1
j
i
2
ZZ
ZZ
ZZV
I
For weak coupling: =>
2Q.1Q)2jQ1).(1jQ1(2R.1R
)2Lj2R)(1Lj1R(
resonantnon_2
resonant_2
I
I
)2Lj2R)(1Lj1R(
M.j
2.1
Mj
i
2
ZZV
I
For non-resonant situation
2R.1R
Mj
i
2
V
I
For resonant situation
Current increases by Q1.Q2 (Product of loaded Q’s) 15
Effects of Resonance
• Resonance helps to increase current in coupled loop ~1000X
• But it causes strange behavior (reduction of secondary current at close range). Why ?
16
Self Quiz
• The primary coil is tuned to a certain frequency and excited by a voltage source of the same frequency. A secondary coil, also tuned to the same frequency is gradually brought in from far distance. How does the current in the secondary coil behave with changing distance? (qualitative description)
• Two coils each of Q=50 is taken. Current is measured in second coil with and without tuning capacitor (tuned to frequency of excitation). What is the ratio of currents in the two scenarios?
17
Self Quiz
• The primary coil is tuned to a certain frequency and excited by a voltage source of the same frequency. A secondary coil, also tuned to the same frequency is gradually brought in from far distance. How does the current in the secondary coil behave with changing distance?
Increases till k.sqrt(Q1.Q2) = 1, then decreases
• Two coils each of Q=50 is taken. Current is measured in second coil with and without tuning capacitor (tuned to frequency of excitation). What is the ratio of currents in the two scenarios?
50*50 = 2500
18
Self Quiz
• A Reader-tag system has a certain maximum read range determined by current needed to turn on the Tag chip. Q of the tag is halved. How much is the max read range compared to original? [Assume weak coupling]
R2 is doubled (M/R1.R2) halved range halved
19
Vi = [R1 + j(L1-1/C1)].I1 - jM.I2 0 = [R2 + j(L2-1/C2)].I2 - jM.I1
I2
(R2+j.X2).I2= jM.I1
-jM.I2
Inductively Coupled Series Resonant Circuits
VoltageCurrentSource voltage
~ C2
I1
. .+
I2
Vi
R2
L2L1
R1C1
Excitation at higher than resonant frequency
I1
(R1+j.X1).I1
Phase angle between Vi and I1 may be > or < 0 depending on coupling
~
+
++
20
Vi = [R1 + j(L1-1/C1)].I1 - jM.I2 0 = [R2 + j(L2-1/C2)].I2 - jM.I1
I2
I1
R2.I2= jM.I1
-jM.I2
Inductively Coupled Series Resonant Circuits
VoltageCurrentSource voltage
~ C2
I1
. .+
I2
Vi
R2
L2L1
R1C1
R1.I1
Vi
Excitation at resonant frequency
21
Vi = [R1 + j(L1-1/C1)].I1 - jM.I2 0 = [R2 + j(L2-1/C2)].I2 - jM.I1
I2
(R2-j.X2).I2= jM.I1
-jM.I2
Inductively Coupled Series Resonant Circuits
VoltageCurrentSource voltage
~ C2
I1
. .+
I2
Vi
R2
L2L1
R1C1
Excitation at lower than resonant frequency
I1
(R1-j.X1).I1
• Phase angle between Vi and I1 may be > or < 0 depending on coupling
• I1 and I2 flowing in same direction for lossless case 22
Below resonance (capacitive)
Above resonance (inductive)
I1I2I1
I2I1
Resonance (resistive)
1
2
1
2
1
2
I2
+ + +
23
Power Transmission Efficiency
sourcelable fromPower avai
loadipated at Power diss
Rectifier
Logic & Memory
Tag
Reader Equivalent Resistive Load
24
Parallel to Series Transformation
≡RLC
RLs
CsAt a certain frequency
C.RLXC
RLQ
If Q>>1 then:
RL
XCRLs
CCs
2
Example:
f = 13.56 MHzC= 50.0 pF (XC = 235RL = 2000
Cs pF (Exact): 50.7 pFCs pF (Approx): 50.0 pF
RLs (Exact): 27.2 RLs (Approx): 27.6
25
Assuming both Reader and Tag are resonant at excitation frequency
~
C2I1
. .+
I2
Vi
R2
L2L1
R1C1
RLs
Power dissipated at load = |I2|2.RLs
Power available from source = |I1|2.Re(Zin)
2Z
M1ZRe
RLs.
2Z
Mj
)ZinRe(.1I
RLs.2I22
2
2
2
RLs2R
M1R
RLs.
RLs2R
M222
22
Zin
26
1 10 1000
20
40
60
Load resistance Kohm
Pow
er tr
ansf
er e
ffic
ienc
yM = 5
M = 15
For weak coupling, efficiency is maximum when R2 = RLs
22 2C.RL
1
2R
RL↑ => C2 ↓ for given R2Low dissipation chips usually use less tank capacitance 27
Special Case
• Both Reader and Tag are resonant at excitation frequency
L1.C1=L2.C2 = 02
• Weak coupling
R1>> Reflected impedance• Tag is independently matched to load
R2=RLs => Total resistance in Tag = 2R2 = 2RLs• Q of load (XC2/RLs) >> 1
1R2
R
1R.RLs.4
M0 reflect22
reflect2
reflect2
222
2
2
R1I.2
1R.
1R.2
V
RLs
M0
1R.4
VPchip
28
Self Quiz
XC = 200 ohm (C~ 50 pF)
RL = 10Kohm
What is the value of Tag resistance for optimum power transfer at weak coupling?
If XC is changed to 300 ohm, what is the value of Tag resistance for optimum power transfer at weak coupling?
29
Self Quiz
XC = 200 ohm (C~ 50 pF)
RL = 10Kohm
What is the value of Tag resistance for optimum power transfer at weak coupling?
200^2/10e3= 4 ohm [Traces could be too wide for a compact tag!]
If XC is changed to 300 ohm (C~ 33 pF), what is the value of Tag resistance for optimum power transfer at weak coupling?
300^2/10e3= 9 ohm [Compact tag is realistic]
30
Measurement of Resonance Parameters• Resonant frequency• Loaded Q
• Caution:– Maintain weak coupling with
probe loop
Vector Network Analyzer
Sensing Loop
31
Measurement on a Tag attached to curved surface
32
33
Principle of Measurement
0Z1
0Z1M_11
Z
Zs
0Z2
0Z2D_11
Z
Zs
Sensing Loop alone – stored in Memory
Sensing Loop + DUT – ‘Data’
Data – Memory = s11_D - s11_M DUT2 Y.M.
0Z
2
0Z
)12(2
).20Z).(10Z(
)12.(0Z.2
ZZ
ZZ
ZZ
Z1 = R1 + j.L1 Sensing Loop alone
Z2 = R1 + j.L1 + (M)2. YDUT Sensing Loop + DUT
YDUTZ2 - Z2 = (M)2. YDUT
If s-parameter is used
Approximation valid if Z0>> Z1, Z2. error for low values of YDUT
Transmission method is more accurate34
Spectral Splitting
35
0.1 1 10 1000
0.1
0.2
0.3
0.4
0.5
Coupling Coefficient %
22Q.1Qk1
2Q.1Qk
Tight couplingSmall Separation
Weak couplingLarge Separation
spacing
~ secondarycurrent
Are these phenomena related?
36
I1
. .
I2
L1 L2
R1
V1 V2
+ +R2
M
M
L2-ML1-MR1 R2
V1 V2
+ +
I1 I2
≡
V1= (R1+jL1).I1 + jM.I2V2= (R2+jL2).I2 + jM.I1
~ C2
I1
. .+
Vi
R2
L2L1
R1C1
M
L2-ML1-MR1 R2I1
C2Vi ~C1≡
37
If coupling is NOT weak:
At f=f0:R2+j.[0.(L2-M)-1/(0.C2)] = R2- j0.M
I1 Let:(L1, C1) => f0(L2, C2) => f0i.e.0.L1=1/(0.C1)0.L2=1/(0.C2)
If M~0 (weak coupling), I1 exhibits series resonance behavior determined by L1, C1
Parallel resonance chokes current at f0 [+j.M and –j.M in shunt]
Input is capacitive
If R2 ↑ (Q2↓) => choking ↓
M
L2-ML1-MR1 R2
C2Vi ~C1
L1-MR1I1
Vi ~C1
M
~1/02.M
~02.M2/R2
(0.M)/R2>>1
+j.M -j.M
38
Self Quiz
• Lossless Resonators tuned at f1 and f2. When coupling is increased, at what frequency parallel resonance occurs?
39
Self Quiz
• Lossless Resonators tuned at f1 and f2. When coupling is increased, at what frequency parallel resonance occurs?
• f2 when looking from resonator 1 and vice versa
40
Series resonances
L1-MR1I1
Vi ~C1
Mf<f0‘Odd Mode’
L1-MR1I1
Vi ~C1
Mf>f0‘Even Mode’Occurs when shunt arm is shorted
Series and parallel resonances alternate
Frequency↓=> Shunt arm more and more capacitive
Frequency↑=> Shunt arm less and less capacitive and then more and more inductive
L2-M R2
C2
41
R1=R2=6 ohm L1=L2=2700 nH C1=C2=50 pF
Q1=Q2=38.7 f01=f02=13.7 MHz
Critical coupling = 0.026
Excitation voltage = 1V
2Q.1Q
1kc
10 12 14 16 180
20
40
60
80
100
k=kck=0.1k=0.25k=kc/2
Magnetically Coupled Series Resonators
Frequency MHz
Sec
onda
ry c
urre
nt m
A
13.7
42
Resonances for Lossless Identical resonators
C).ML(
10
C.L
10
ParallelSeries Series
L1=L2=L C1=C2=C R1=R2=0
C).ML(
11
CC C
L-M L-M L-M2M
43
Two NFC Tags ~ equally coupled with Sensing Loop
44
Realistic Situation
R1=R2=6 ohm L1=L2=2700 nH C1=50pF C2= 47pF
Q1=38.7 (at f01) Q2=39.9 (at f02) f01=13.7 MHz f02= 14.1 MHz
Critical coupling = 0.025
Excitation voltage = 1V
10 12 14 16 180
20
40
60
80
100
k=kck=0.1k=0.25k=kc/2
Magnetically Coupled Series Resonators
Frequency MHz
Sec
onda
ry c
urre
nt m
A
13.714.1
45
Excitation Frequency as Parameter
1 10 1000
20
40
60
80
100
13.714.113.914.313.5
Coupling coeff %
Sec
onda
ry c
urre
nt m
A
Significant degradation in weakly coupled region when frequency of excitation is outside the band between resonant frequencies with a little bit improvement in close range
%6.22Q.1Q
1
46
• For two magnetically coupled resonators tuned at same frequency, we observed that parallel resonance occurs above a certain M. To arrive at this we used an equivalent T network for magnetically coupled inductors. How this phenomenon is explained by reflected impedance?
Review Quiz
47
Review Quiz
• For two magnetically coupled resonators tuned at same frequency, we observed that parallel resonance occurs above a certain M. To arrive at this we used an equivalent T network for magnetically coupled inductors. How this phenomenon is explained by reflected impedance?
2ωM
R1
12
Z
Primary current ~ is maximized when Z2 is minimum
Series resonance in secondary => parallel resonance in primary
48