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Powering up the RFID chip - Remotely
1
Basic Reader-Tag System
Rectifier
Logic &
Memory
Reader
Tag
2
Simple Magnetically Coupled Circuit
I1
Z1’
. .
+
Vi ~
Z1’ and Z2’ can be used to represent
resistors, capacitors etc. as required
I2
L1, R1
Vi = Z1.I1 - jwM.I2
0 = Z2.I2 - jwM.I1
L2, R2
Z2’
Define self-impedance of each loop:
Z1 = Z1’ +R1+ jwL1
Z2 = Z2’ +R2+ jwL2
Applying KVL in each loop
Reflected impedance
Input impedance

Vi
wM 2
 Z1 
I1
Z2
General
Expressions
wM
Transfer admittance
I2

Vi
j
Z1.Z 2
.
Z1.Z 2
 wM 

1  
Z
1
.
Z
2


2
3
Input impedance
Current Transfer ratio

Vi
wM 2
 Z1 
I1
Z2
I 2 jw.M

I1
Z2
General
Expressions
wM
Transfer admittance
I2

Vi
j
Z1.Z 2
.
Z1.Z 2
 wM 

1  
Z
1
.
Z
2


2
4
Example: Inductively Coupled Resistive Circuit (Transformer)
jwM.I2
Voltage
Current
Source voltage
(R1 + jwL1).I1
(R2 + jwL2).I2
= jwM.I1
Vi = (R1 + jwL1).I1 - jwM.I2
0 = (R2 + jwL2).I2 - jwM.I1
I1
I2
. .
R1
+
Vi ~
Vi
L1
L2
R2
I2
I1
5
Ideal Transformer
jwM.I2
Voltage
Current
Source voltage
jwL1.I1
(R2 + jwL2).I2
= jwM.I1
Vi = jwL1.I1 - jwM.I2
0 = (R2 + jwL2).I2 - jwM.I1
I1
Vi
I2
R1 ~ 0
+
Vi ~
R1 << w.L1
R2 << w.L2
k~1
L1
. .
L2
R2
I2
I1 R 2  jwL2
L2
1 L2
1


 .

I2
jwM
k L1.L2 k L1 k.N
I1
6
Self Quiz
1.
Inductively coupled circuit with R1= 1W, R2= 2W,
L1=L2, w.L1=200W, k= 0.8
If I1= 1A, what is the approximate value of I2? (KVL)
2.
If R2 = 1W, 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.
2.
3.
4.
0.8 A
0.8 A (Same!)
(1+ j.72) W (Unchanged!)
1W
8
wM
I2

Vi
Transfer admittance
j
.
Z1.Z 2
Z1.Z 2
 wM 

1  
Z
1
.
Z
2


2
Effectiveness to drive current through secondary – would like to maximize
for effective power transfer
Introduce resonance
I1
C1
+
Vi
~
I2
R1
L1
. .
Self impedances:
Z1 = 1/ jwC1 +R1+ jwL1
Z2 = 1/ jwC2 +R2+ jwL2
R2
L2
Let resonance occur at w0 
C2
1
L1.C1

1
L2.C2
which is our excitation frequency
CAVEAT: Series resonance for illustration only!
9
At w  w0, we have Z1 =R1, Z2 =R2 and Transfer
admittance is
wM
I2

Vi
j
R1.R 2
.
R1.R 2
 wM 

1  
 R1.R 2 
2

j
.
k Q1.Q2

R1.R 2 1  k Q1.Q2

2
0.5
Q1=30
Q2=40
0.4
k Q1.Q2

1  k Q1.Q2

0.3
2
0.2
0.1
0
0.1
1
10
100
Coupling Coefficient %
Peak occurs at
k Q1.Q2  1
Beyond this value of k, Transfer admittance falls!
10
Self Quiz
Reader and Tag both has Q =25, and
each has ESR (effective series
resistance ) = 5W. 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
k
R ohm= 5
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
Transfer admittance
0.5
0.4
k Q1.Q2

1  k Q1.Q2

0.3
2
0.2
Weak coupling
Large Separation
Tight coupling
Small Separation
0.1
0
0.1
1
10
100
Coupling Coefficient %
spacing
Spacing ↑ => Coupling coefficient ↓
Diminishing return – does not help reducing the spacing beyond a certain point
13
Weak Coupling Case
0.5
0.4
If
k Q1.Q2  1
then coupling is weak
0.3
0.2
In other words
Then
wM
0.1
 1
0
0.1
1
10
100
R1.R 2
k Q1.Q2
I2
w.M
 j.

Vi
R1.R 2
R1.R 2
14
Resonant vs. Non-resonant
wM
Transfer admittance
- general expression
For weak coupling:
I2

Vi
wM
j
Z1.Z 2
 1
Z1.Z2
For non-resonant situation
I2
wM
wM
j
 j.
Vi
Z1.Z2
(R1  jwL1)( R 2  jwL2)
.
Z1.Z 2
 wM 

1  
 Z1.Z 2 
=>
2
I2
wM
j
Vi
Z1.Z 2
For resonant situation
I2
wM
j
Vi
R1.R 2
I 2 _ resonant
(R1  jwL1)( R 2  jwL2)

 (1  jQ1).(1  jQ 2)  Q1.Q2
I 2 _ non  resonant
R1.R 2
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  (wM/R1.R2) halved  range
halved
19
Inductively Coupled Series Resonant Circuits
Excitation at higher than resonant frequency
Voltage
Current
Source voltage
(R2+j.X2).I2
= jwM.I1
+
~
(R1+j.X1).I1
+
I2
Vi = [R1 + j(wL1-1/wC1)].I1 - jwM.I2
0 = [R2 + j(wL2-1/wC2)].I2 - jwM.I1
I1
C1
+
Vi
~
-jwM.I2
I1
I2
R1
L1
. .
R2
L2
C2
Phase angle between Vi and
I1 may be > or < 0 depending
on coupling
20
Inductively Coupled Series Resonant Circuits
Excitation at resonant frequency
Voltage
Current
Source voltage
R2.I2
= jwM.I1
R1.I1
Vi = [R1 + j(wL1-1/wC1)].I1 - jwM.I2
0 = [R2 + j(wL2-1/wC2)].I2 - jwM.I1
I1
C1
+
Vi
~
Vi
I2
R1
L1
. .
I2
-jwM.I2
R2
L2
C2
I1
21
Inductively Coupled Series Resonant Circuits
Excitation at lower than resonant frequency
(R1-j.X1).I1
Voltage
Current
Source voltage
I2
-jwM.I2
I1
Vi = [R1 + j(wL1-1/wC1)].I1 - jwM.I2
0 = [R2 + j(wL2-1/wC2)].I2 - jwM.I1
I1
C1
+
Vi
~
(R2-j.X2).I2
= jwM.I1
I2
R1
L1
. .
R2
L2
C2
• Phase angle between Vi
and I1 may be > or < 0
depending on coupling
• I1 and I2 flowing in same
direction for lossless case
22
2
2
1
1
+
+
Below resonance
(capacitive)
2
1
+
Resonance
(resistive)
Above resonance
(inductive)
I2
I1
I1
I2
I1
I2
23
Power Transmission Efficiency h
Rectifier
Logic &
Memory
Reader
Equivalent Resistive Load
Tag
Power diss ipated at load
h
Power available from source
24
Parallel to Series Transformation
C
≡
Cs
At a certain frequency
RL
RLs
RL
Q
 RL .wC
XC
Cs  C
If Q>>1 then:
XC 2
RLs 
RL
Example:
f = 13.56 MHz
C= 50.0 pF (XC = 235W
RL = 2000 W
Cs pF (Exact): 50.7 pF
Cs pF (Approx): 50.0 pF
RLs (Exact): 27.2 W
RLs (Approx): 27.6 W
25
I1
C1
+
Vi
I2
R1
. .
R2
L1
~
C2
RLs
L2
Zin
Power dissipated at load = |I2|2.RLs
Power available from source = |I1|2.Re(Zin)
2
2
jwM
h 2

.
Z2
I1 . Re( Zin )
I2 .RLs
RLs

w2 M 2 

Re  Z1 
Z2 

Assuming both Reader and Tag are resonant at excitation frequency
h
w2 M 2
R 2  RLs 2
.
RLs
w2 M 2
R1 
R 2  RLs
26
Power transfer efficiency
wM = 15W
60
40
wM = 5W
20
0
1
10
100
Load resistance Kohm
For weak coupling, efficiency is maximum when R2 = RLs
1
R 2  2RL 2
w .C2
RL↑ => C2 ↓ for given R2
Low dissipation chips usually use less tank capacitance
27
Special Case
•
•
•
•
Both Reader and Tag are resonant at excitation frequency
L1.C1=L2.C2 = w02
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
R
w0 2 M 2
h
 reflect
4.RLs .R1
2R1
V 2 w0 2 M 2
V2
1 2
Pchip 

.
R

.I1 R reflect
reflect
2
2
2
4.R1 RLs
2.R1
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
Z1 = R1 + j.wL1
Sensing Loop alone
Z2 = R1 + j.wL1 + (wM)2. YDUT
Sensing Loop + DUT
Z2 - Z2 = (wM)2. YDUT
YDU
T
If s-parameter is used
s11 _ M 
Z1  Z0
Z1  Z0
s11 _ D 
Z 2  Z0
Z 2  Z0
Sensing Loop alone – stored in Memory
Sensing Loop + DUT – ‘Data’
Data – Memory = s11_D - s11_M 
2.Z0.( Z2  Z1)
2(Z2  Z1)
2


.wM 2 .YDUT
( Z0  Z1).( Z0  Z2).
Z0
Z0
Approximation valid if Z0>> Z1, Z2. error for low values of YDUT
Transmission method is more accurate
34
Spectral Splitting
35
Are these phenomena related?
0.5
k Q1.Q2

1  k Q1.Q2
0.4

2
0.3 Weak coupling
Tight coupling
Small Separation
Large Separation
~ secondary
current
0.2
0.1
0
0.1
1
10
100
Coupling Coefficient %
spacing
36
I1
I2
M
. .
R1
+
L1
V1
I1
R1
R2
+
L2
L2-M
R2
I2
+
+
≡
V2
L1-M
M
V1
V2
V1= (R1+jwL1).I1 + jwM.I2
V2= (R2+jwL2).I2 + jwM.I1
I1
C1
+
Vi
~
I1
R1
L1
. .
R2
L2
≡
C2
Vi
~
R1
L1-M
L2-M
R2
C1
M
C2
37
I1
Let:
R1
Vi
~
L1-M
L2-M
R2
C1
M
C2
(L1, C1) => f0
(L2, C2) => f0
i.e.
w0.L1=1/(w0.C1)
w0.L2=1/(w0.C2)
If M~0 (weak coupling), I1 exhibits series resonance behavior determined by L1, C1
If coupling is NOT weak:
At f=f0:
R2+j.[w0.(L2-M)-1/(w0.C2)] = R2- jw0.M
I1
Vi
~
R1
C1
Parallel resonance chokes
current at f0
[+jw.M and –jw.M in shunt]
~1/w02.M
L1-M
M
~w02.M2/R2
Input is capacitive
+jw.M
-jw.M
(w0.M)/R2>>1
If R2 ↑ (Q2↓) => choking ↓
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
I1
f<f0
‘Odd Mode’
Vi
~
R1
C1
I1
f>f0
‘Even Mode’
Occurs when
shunt arm is
shorted
Vi
~
C1
L1-M
Frequency↓=> Shunt
arm more and more
capacitive
M
R1
L1-M
L2-M
M
R2
C2
Frequency↑
=> Shunt arm less
and less capacitive
and then more and
more inductive
Series and parallel resonances alternate
41
R1=R2=6 ohm L1=L2=2700 nH
C1=C2=50 pF
Q1=Q2=38.7 f01=f02=13.7 MHz
kc 
1
Q1.Q2
Critical coupling = 0.026
Excitation voltage = 1V
Magnetically Coupled Series Resonators
Secondary current mA
100
13.7
80
60
40
20
0
10
k=kc
k=0.1
k=0.25
k=kc/2
12
14
16
18
Frequency MHz
42
Resonances for Lossless Identical resonators
L1=L2=L C1=C2=C R1=R2=0
Series
Parallel
L-M
C
2M
w0 
1
(L  M).C
C
L-M
w0 
Series
C
1
L.C
L-M
w1 
1
(L  M).C
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
Magnetically Coupled Series Resonators
Secondary current mA
100
13.714.1
80
60
40
20
0
10
k=kc
k=0.1
k=0.25
k=kc/2
12
14
16
18
Frequency MHz
45
Excitation Frequency as Parameter
Secondary current mA
100
1
80
 2.6%
Q1.Q2
60
13.7
14.1
13.9
14.3
13.5
40
20
0
1
10
100
Coupling coeff %
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
46
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?
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?
Primary current ~
1
ωM 2
R1 
Z2
is maximized when
Z2 is minimum
Series resonance
in secondary =>
parallel resonance
in primary
48