Wireless Power Meets Super-Directivity Thomas L

WIRELESS POWER MEETS SUPER-DIRECTIVITY THOMAS L. MARZETTA DIRECTOR, NYU WIRELESS DECEMBER 18, 2019

RESEARCH SUPPORTED BY NYU WIRELESS, AND BY GIFT DONATIONS FROM NOKIA AND FUTUREWEI

[A. Karalis, J.D. Joannopoulos, M Soljačić, “Efficient wireless non-radiative mid-range energy transfer”, Annals of Physics, Jan 2008] I R C p p p Cs Rs Is + + + +

Vi Vp Vs Ro Vo

− − − −

• 60 Watts received, at 10 MHz, with 40% efficiency: coupling coefficient   .002 • Can be analyzed two equivalent ways • induction • plane-wave expansion of field, dominated by evanescent waves Super-Directivity

For example, consider a transmitting horn antenna, with an aperture about 10 wavelengths on a side, located in outer space roughly aimed at the earth, With a one wavelength diameter supergain antenna on the earth it is possible to receive virtually all of the power radiated by the horn antenna. Foschini & Gans, Bell Labs Technical Memo, 1995

• Old-fashioned Ernst Guillemin network theory + electromagnetic theory [Sergei Alexander Schelkunoff, “A mathematical theory of linear arrays”, Bell Labs Technical Journal, 1943] Any System of Transmit/Receive Antennas Constitutes an n-Port Network

v11()()()= z  i 

• n-port linear time-invariant network completely described by nn  complex impedance matrix v()()()= Z  i 

• reciprocity ZZ T = (unconjugated transpose)

• real power dissipation is non-negative iH Re Z i 0, i

[M. T. Ivrlac and J. A. Nossek, “Toward a circuit theory of communication”, IEEE Trans. Circuits and Systems, July 2010] M-Element Antenna Array and Single-Antenna Terminal

iA1 vA1 iA2 vA2 iT vT iAM vAM

T MMM 1 1  1 viTT zT g    =   ,,,ZgATz viAA gZA   * • Power transmitted by terminal PTTT= Re i v  M * • Power transmitted by array PAAA= Re imm v m=1 H = ReivAA A New Trick: How to Draw Maximum Power From a Voltage Source

i z L + s • Classical solution: optimize the load impedance vs zL vL −

2 vzRe  P=Re i** v =sL → z = z L L L 2 L s zzsL+

• Alternative solution: optimize the load current

** vs PL=Re i L v L = Re i L( v s − i L z s) → i L =     2Rezs How Efficiently Can Power Be Transferred?

H T P = Re iv * viTT zT g   AAA  PTTT= Re i v   =    viAA gZA   • Equivalent problems • maximize ratio of receive power to transmit power • maximize receive power, subject to a specified transmit power • minimize transmit power, subject to a specified receive power

2 *T Pd −−RezTTTA i Re i gi  • Downlink maxrec = max   Pd i ,i iHHRe Z i+ Re i gi trans TAAAAAT  HH Pu −−iAAAATRe Z i Re i gi  • Uplink maxrec = max   Pu2i ,i Rez i+ Re i*Tgi trans TATTTA  Results

• Optimized up-link efficiency equal to optimized down-link efficiency 2 Rez − RegT Re Z−1 Re g 2 ( TA) effdu= eff = −  − 1,  = 1 + gH Re Z−1 g A • Sufficient conditions for 100% efficiency • tightly coupled system (real part of impedance matrix is singular) T −1 RezTA−= Reg Re Z Re g 0

• or real part of impedance matrix vanishes RezTA= 0, Reg = 0 , Re Z = 0

v1   i L 1 i L 12   i 1  ideal transformer:  =     v2   i L 12 i L 2   i 2  Super-Directivity: Deliberately Create and Exploit Mutual Coupling

• Communication theorists like to discourage or ignore mutual coupling! • Instead, do the opposite!

• End-fire linear array

T (0,0,z ) viTT zT g    =    viAA gZA  

• Acoustic propagation: spherically-symmetric “antennas” of radius R0

coskR self impedance: z (0)= 1 − i0 , k = 2 sin kR0  mutual impedance: z ( R )=sinkR − i cos kR , R  2 R kR kR 0 Power Transfer Efficiency vs. Antenna Spacing

MR==10 antennas; range (from center of array): T 5

• Super-directivity increases power transfer efficiency from .0034 to .025 (factor of 7.4) Conclusions

• Wireless power is a challenging, but exciting, possibility for 6G

• If a practical form of super-directivity can be discovered, it would have huge impact on both wireless communications and wireless power transfer

• Support for risky, fundamental research is urgently needed!