Jianying Zhao : Tianjin University Yogesh Ramadass: Texas Instruments

1. MICROELECTRONIC TECHNIQUES FOR FREQUENCY TUNING OF PIEZO-ELECTRIC (PZ) ENERGY HARVESTING DEVICES (EHDs)Interim Report Jianying Zhao: Tianjin University Yogesh Ramadass: Texas Instruments Dennis Buss: Texas Instruments and MIT Prof Jianguo Ma: Tianjin University

2. Summary • Piezo-electric (PZ) Energy Harvesting Devices (EHDs): Background • Four key elements of frequency tuning • High load resistance => high E-field in the PZ material => enables PZ coupling • Inductor in output => Coupled oscillators => Pole Splitting • Variable inductor => Frequency tuning • Bias Flip to approximate large variable inductor • Simulation results • Conclusions

3. External Circuits for Extracting Power from EHDs Rectification Circuit for DC Energy Storage Energy Management Circuit D1 CRECT EHD cond. circuit D2 D3 D4 Linear Circuit for Extracting AC Power is + EHD RL L V -

4. External Circuits for Extracting Power from EHDs Rectification Circuit for DC Energy Storage Energy Management Circuit D1 CRECT EHD cond. circuit D2 D3 D4 Liner Circuit for Extracting AC Power is The focus of this talk will be this conditioning circuit + EHD RL L V -

5. PZ EHDs: Background F X + Mass Voltage V E, D δ, σ t - Current Source Model IP CP RP NOTE: In the open circuit case, D=0, and the effective Young’s modulus is

6. Definition of Key Parameters Mechanical spring constant Mechanical resonance frequency Open circuit (Q=0) spring constant Open circuit resonance frequency Electrical capacitance Mechanically constrained capacitance Normalized parameters

7. Electrical Frequency TuningOutput Voltage in the Case of No Inductor Voltage is normalized to the open circuit voltage at mechanical resonance =0 =0.1 =1 Log10 (Normalized Voltage Magnitude) =10 =50

8. Electrical Frequency TuningOutput Power in the Case of No Inductor Power is normalized to the max power with matched load at mechanical resonance Wpeak=1.095 =1 Log10 (Normalized Average Power) =0.1 =10 =50

9. Pole Splitting Output voltage in the case of an impedance matching inductor of value Wpeak=1.247 Wpeak=0.805 =0 =0.1 =1 Log10 (Normalized Voltage Magnitude) =10 =50

10. Pole Splitting Output voltage in the case of an impedance matching inductor of value Wpeak=1.247 Wpeak=0.805 =0 =0.1 =1 Log10 (Normalized Voltage Magnitude) 1.8 ρ = 0.2 1.4 =10 1.0 Pole Frequencies =50 0.6 0.2 0.2 0.6 1.0 1.4

11. Normalized Power in the Case of an Impedance Matching Inductor of Value =0.1 =1 Log10 (Normalized Average Power) =10 =50 w=ω/ωm

12. Output Power in the Case ofOptimized, Tunable Inductor Inductor value is optimized at each frequency to maximize power delivered to the load =0.1 =1 Log10 (Normalized Average Power) =10 =50

13. Output Power for the case YLN = 0.1Optimized tunable inductor compared to no inductor Log10 (Normalized Average Power)

14. Output Power for the Case YLN = 0.1 Log10 (Normalized Average Power)

15. Operation of the Bias Flip Technique + Cmc Rin IP V(t) L RL - Close Switch iP(t) v(t) Open Switch v(t) ½ Period

16. DC Rectification and Storage VRECT Energy Manage Circuit Voltage VRECT D1 IP Cmc Rin Bias Flip Circuit D2 t CRECT ton toff D3 Cmc = 0 D4 Voltage Voltage VRECT VRECT t t ton toff ton toff Bias flip Large Cmc With BF Large Cmc No BF Neg Bias

17. Rectified DC Power as a Function of Cmc 8% gap Using Bias Flip Log10 (Normalized Power) No Bias Flip Log10(Capacitance )

18. Conclusions • Frequency tuning of a PZ EHD can be achieved when the Electric field in the PZ material is high, and PZ coupling is strong. • When an inductor is added to the output circuit, we have two coupled resonant circuits. When the coupling between them is high, pole-splitting determines the frequencies of max output power. • By varying the inductor value, the device can be “tuned” for max output power at frequencies different from the mechanical resonant frequency. • The Bias Flip technique has been proposed to approximate the effect of a large, tunable inductor. Using a physical model for the PZ EHD, a generalization of the impedance matching concept has been shown to obtain high output power over an extended frequency range.

19. THANK-YOU