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Published byDerick Rayner Modified about 1 year ago

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Powering up the RFID chip - Remotely 1

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Basic Reader-Tag System Rectifier Logic & Memory Tag Reader 2

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Simple Magnetically Coupled Circuit Vi = Z1.I1 - j M.I2 0 = Z2.I2 - j M.I1 Applying KVL in each loop Z1’ and Z2’ can be used to represent resistors, capacitors etc. as required Define self-impedance of each loop: Z1 = Z1’ +R1+ j L1 Z2 = Z2’ +R2+ jwL2 Z1’Z1’ Z2’Z2’ I1I1.. + I2I2 ~ ViVi L1, R1 L2, R2 Input impedance Transfer admittance General Expressions Reflected impedance 3

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Input impedance Transfer admittance General Expressions Current Transfer ratio 4

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Vi = (R1 + j L1).I1 - j M.I2 0 = (R2 + j L2).I2 - j M.I1 I2 I1 (R2 + j L2).I2 = j M.I1 (R1 + j L1).I1 j M.I2 Vi Example: Inductively Coupled Resistive Circuit (Transformer) I1I1.. + I2I2 ~ ViVi L1 L2 R1 R2 Voltage Current Source voltage 5

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I2 I1 (R2 + j L2).I2 = j M.I1 j L1.I1 j M.I2 Vi Vi = j L1.I1 - j M.I2 0 = (R2 + j L2).I2 - j M.I1 I1I1.. + I2I2 ~ ViVi L1 L2 R1 ~ 0 R2 Ideal Transformer Voltage Current Source voltage R1 << .L1 R2 << .L2 k ~ 1 6

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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

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1.0.8 A 2.0.8 A (Same!) 3.(1+ j.72) (Unchanged!) 4.1 8

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Transfer admittance Effectiveness to drive current through secondary – would like to maximize for effective power transfer Introduce resonance Let resonance occur at ~ C2 I1I1.. + I2I2 ViVi R2 L2 L1 R1 C1 Self impedances: Z1 = 1/ j C1 +R1+ j L1 Z2 = 1/ j C2 +R2+ j L2 which is our excitation frequency CAVEAT: Series resonance for illustration only! 9

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At we have Z1 =R1, Z2 =R2 and Transfer admittance is Coupling Coefficient % Q1=30 Q2=40 Peak occurs at Beyond this value of k, Transfer admittance falls! 10

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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

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Q=25R ohm=5 kk.QkQ/(1+kQ^2)I ampsI^2. R mW 0.010.250.2352940.04711.07 0.0410.50.150.00 0.12.50.3448280.06923.78 0.1640.2352940.04711.07 12

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Coupling Coefficient % Diminishing return – does not help reducing the spacing beyond a certain point Tight coupling Small Separation Weak coupling Large Separation Transfer admittance spacing ~ Spacing ↑ => Coupling coefficient ↓ 13

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Weak Coupling Case If then coupling is weak Then In other words 14

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Resonant vs. Non-resonant Transfer admittance - general expression For weak coupling: => For non-resonant situation For resonant situation Current increases by Q1.Q2 (Product of loaded Q’s) 15

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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

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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

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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

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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

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Vi = [R1 + j( L1-1/ C1)].I1 - j M.I2 0 = [R2 + j( L2-1/ C2)].I2 - j M.I1 I2 (R2+j.X2).I2 = j M.I1 -j M.I2 Inductively Coupled Series Resonant Circuits Voltage Current Source voltage ~ C2 I1I1.. + I2I2 ViVi R2 L2 L1 R1 C1 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

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Vi = [R1 + j( L1-1/ C1)].I1 - j M.I2 0 = [R2 + j( L2-1/ C2)].I2 - j M.I1 I2 I1 R2.I2 = j M.I1 -j M.I2 Inductively Coupled Series Resonant Circuits Voltage Current Source voltage ~ C2 I1I1.. + I2I2 ViVi R2 L2 L1 R1 C1 R1.I1 Vi Excitation at resonant frequency 21

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Vi = [R1 + j( L1-1/ C1)].I1 - j M.I2 0 = [R2 + j( L2- 1/ C2) ].I2 - j M.I1 I2 (R2-j.X2).I2 = j M.I1 -j M.I2 Inductively Coupled Series Resonant Circuits Voltage Current Source voltage ~ C2 I1I1.. + I2I2 ViVi R2 L2 L1 R1 C1 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

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Below resonance (capacitive) Above resonance (inductive) I1I1 I2I2 I1I1 I2I2 I1I1 Resonance (resistive) 1 2 1 2 1 2 I2I2 + + + 23

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Power Transmission Efficiency Rectifier Logic & Memory Tag Reader Equivalent Resistive Load 24

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Parallel to Series Transformation ≡ RL C RLs Cs At a certain frequency If Q>>1 then: Example: f = 13.56 MHz C= 50.0 pF (XC = 235 RL = 2000 Cs pF (Exact): 50.7 pF Cs pF (Approx): 50.0 pF RLs (Exact): 27.2 RLs (Approx): 27.6 25

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Assuming both Reader and Tag are resonant at excitation frequency ~ C2 I1I1.. + I2I2 ViVi R2 L2 L1 R1 C1 RLs Power dissipated at load = |I2| 2.RLs Power available from source = |I1| 2.Re(Zin) Zin 26

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M = 5 M = 15 For weak coupling, efficiency is maximum when R2 = RLs RL↑ => C2 ↓ for given R2 Low dissipation chips usually use less tank capacitance 27

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Special Case Both Reader and Tag are resonant at excitation frequency L1.C1=L2.C2 = 0 2 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 28

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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

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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

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Measurement of Resonance Parameters Resonant frequency Loaded Q Caution: –Maintain weak coupling with probe loop Vector Network Analyzer Sensing Loop 31

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Measurement on a Tag attached to curved surface 32

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Principle of Measurement Sensing Loop alone – stored in Memory Sensing Loop + DUT – ‘Data’ Data – Memory = s11_D - s11_M Z1 = R1 + j. L1 Sensing Loop alone Z2 = R1 + j. L1 + ( M) 2. Y DUT Sensing Loop + DUT Y DU T Z2 - Z2 = ( M) 2. Y DUT If s-parameter is used Approximation valid if Z0>> Z1, Z2. error for low values of Y DUT Transmission method is more accurate 34

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Spectral Splitting 35

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Coupling Coefficient % Tight coupling Small Separation Weak coupling Large Separation spacing ~ secondary current Are these phenomena related? 36

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I1I1.. I2I2 L1 L2 R1 V1 V2 ++ R2 M M L2-ML1-M R1 R2 V1V2 + + I1I1I2I2 ≡ V1= (R1+j L1).I1 + j M.I2 V2= (R2+j L2).I2 + j M.I1 ~ C2 I1I1.. + ViVi R2 L2 L1 R1 C1 M L2-ML1-M R1 R2 I1I1 C2 ViVi ~ C1 ≡ 37

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If coupling is NOT weak: At f=f0 : R2+j.[ 0.(L2-M)-1/( 0.C2)] = R2- j 0.M I1I1 Let: (L1, C1) => f0 (L2, C2) => f0 i.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-M R1 R2 C2 ViVi ~ C1 L1-M R1 I1I1 ViVi ~ C1 M ~1/ 0 2.M ~ 0 2.M 2 /R2 ( 0.M)/R2>>1 +j .M -j .M 38

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Self Quiz Lossless Resonators tuned at f1 and f2. When coupling is increased, at what frequency parallel resonance occurs? 39

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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

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Series resonances L1-M R1 I1I1 ViVi ~ C1 M f

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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 42

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Resonances for Lossless Identical resonators ParallelSeries L1=L2=L C1=C2=C R1=R2=0 C CC L-M 2M 43

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Two NFC Tags ~ equally coupled with Sensing Loop 44

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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 45

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Excitation Frequency as Parameter 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

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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

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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 ~is maximized when Z2 is minimum Series resonance in secondary => parallel resonance in primary 48

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