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**Powering up the RFID chip - Remotely**

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**Basic Reader-Tag System**

Rectifier Logic & Memory Reader Tag

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**Simple Magnetically Coupled Circuit**

Z1’ and Z2’ can be used to represent resistors, capacitors etc. as required Define self-impedance of each loop: Z1 = Z1’ +R1+ jwL1 Z2 = Z2’ +R2+ jwL2 Z1’ Z2’ I1 . + I2 ~ Vi L1, R1 L2, R2 Vi = Z1.I1 - jwM.I2 0 = Z2.I2 - jwM.I1 Applying KVL in each loop Reflected impedance Input impedance General Expressions Transfer admittance

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Input impedance Current Transfer ratio General Expressions Transfer admittance

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**. 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 Vi I1 . + I2 ~ Vi L1 L2 R1 R2 I2 I1

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**. Ideal Transformer jwM.I2 Voltage Current R1 << w.L1**

Source voltage R1 << w.L1 R2 << w.L2 k ~ 1 jwL1.I1 (R2 + jwL2).I2 = jwM.I1 Vi = jwL1.I1 - jwM.I2 0 = (R2 + jwL2).I2 - jwM.I1 Vi I1 . + I2 ~ Vi L1 L2 R1 ~ 0 R2 I2 I1

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Self Quiz 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) If R2 = 1W, what is the approximate value of I2? What is approximate input impedance in each case? What is the approximate input impedance if k ~ 1?

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0.8 A 0.8 A (Same!) (1+ j.72) W (Unchanged!) 1 W

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**Introduce resonance . Transfer admittance**

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 L2 L1 R1 C1 Self impedances: Z1 = 1/ jwC1 +R1+ jwL1 Z2 = 1/ jwC2 +R2+ jwL2 which is our excitation frequency CAVEAT: Series resonance for illustration only!

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**At w = w0, we have Z1 =R1, Z2 =R2 and Transfer admittance is**

Q1=30 Q2=40 Coupling Coefficient % Peak occurs at Beyond this value of k, Transfer admittance falls!

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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?

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Q= 25 R ohm= 5 k k.Q kQ/(1+kQ^2) I amps I^2. R mW 0.01 0.25 0.047 11.07 0.04 1 0.5 0.1 50.00 2.5 0.069 23.78 0.16 4

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

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

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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)

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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 ?

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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?

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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

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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 (wM/R1.R2) halved range halved

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**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 -jwM.I2 I2 I1 Vi = [R1 + j(wL1-1/wC1)].I1 - jwM.I2 0 = [R2 + j(wL2-1/wC2)].I2 - jwM.I1 ~ C2 I1 . + I2 Vi R2 L2 L1 R1 C1 Phase angle between Vi and I1 may be > or < 0 depending on coupling

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**Inductively Coupled Series Resonant Circuits**

Excitation at resonant frequency Voltage Current Source voltage R2.I2 = jwM.I1 I2 Vi I1 R1.I1 Vi = [R1 + j(wL1-1/wC1)].I1 - jwM.I2 0 = [R2 + j(wL2-1/wC2)].I2 - jwM.I1 -jwM.I2 ~ C2 I1 . + I2 Vi R2 L2 L1 R1 C1

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**Inductively Coupled Series Resonant Circuits**

Excitation at lower than resonant frequency (R1-j.X1).I1 Voltage Current Source voltage -jwM.I2 I2 I1 (R2-j.X2).I2 = jwM.I1 Vi = [R1 + j(wL1-1/wC1)].I1 - jwM.I2 0 = [R2 + j(wL2-1/wC2)].I2 - jwM.I1 ~ C2 I1 . + I2 Vi R2 L2 L1 R1 C1 Phase angle between Vi and I1 may be > or < 0 depending on coupling I1 and I2 flowing in same direction for lossless case

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**Below resonance (capacitive) Resonance (resistive) **

1 2 1 2 1 2 + + + Below resonance (capacitive) Resonance (resistive) Above resonance (inductive) I2 I1 I2 I1 I1 I2

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**Power Transmission Efficiency h**

Rectifier Logic & Memory Reader Equivalent Resistive Load Tag

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**Parallel to Series Transformation**

Cs ≡ At a certain frequency C RL RLs Example: f = 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 If Q>>1 then:

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**. . Zin Power dissipated at load = |I2|2.RLs**

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

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**For weak coupling, efficiency is maximum when R2 = RLs**

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

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**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

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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?

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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]

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**Measurement of Resonance Parameters**

Resonant frequency Loaded Q Caution: Maintain weak coupling with probe loop Vector Network Analyzer Sensing Loop

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**Measurement on a Tag attached to curved surface**

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**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 YDUT If s-parameter is used Sensing Loop alone – stored in Memory Sensing Loop + DUT – ‘Data’ Data – Memory = s11_D - s11_M Approximation valid if Z0>> Z1, Z2. error for low values of YDUT Transmission method is more accurate

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Spectral Splitting

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**Are these phenomena related?**

Weak coupling Large Separation Tight coupling Small Separation ~ secondary current Coupling Coefficient % spacing

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**. . . + + + + ≡ V1= (R1+jwL1).I1 + jwM.I2 V2= (R2+jwL2).I2 + jwM.I1 ≡**

L1-M L2-M R2 R1 R2 + + + + V1 L1 L2 ≡ V2 V1 M V2 V1= (R1+jwL1).I1 + jwM.I2 V2= (R2+jwL2).I2 + jwM.I1 ~ C2 I1 . + Vi R2 L2 L1 R1 C1 M L2-M L1-M ≡

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**Parallel resonance chokes current at f0 [+jw.M and –jw.M in shunt] **

Let: (L1, C1) => f0 (L2, C2) => f0 i.e. w0.L1=1/(w0.C1) w0.L2=1/(w0.C2) R1 L1-M L2-M R2 C1 Vi ~ M 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 L1-M R1 I1 Vi ~ C1 M ~1/w02.M ~w02.M2/R2 (w0.M)/R2>>1 +jw.M -jw.M Parallel resonance chokes current at f0 [+jw.M and –jw.M in shunt] Input is capacitive If R2 ↑ (Q2↓) => choking ↓

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

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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

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**Series resonances Frequency↓=> Shunt arm more and more capacitive**

L1-M Frequency↓=> Shunt arm more and more capacitive C1 f<f0 ‘Odd Mode’ Vi ~ M I1 R1 L1-M L2-M R2 Frequency↑ => Shunt arm less and less capacitive and then more and more inductive f>f0 ‘Even Mode’ Occurs when shunt arm is shorted C1 Vi ~ M C2 Series and parallel resonances alternate

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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

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**Resonances for Lossless Identical resonators**

L1=L2=L C1=C2=C R1=R2=0 Series Parallel Series C L-M C L-M C L-M 2M

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**Two NFC Tags ~ equally coupled with Sensing Loop**

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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

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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

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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?

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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

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