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Non-Foster Reactances for Electrically- Small Antennas, High-Impedance Surfaces, and Engineered Materials

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Non-Foster Reactances for Electrically- Small Antennas, High-Impedance Surfaces, and Engineered Materials Non-Foster Reactances for Electrically- Small Antennas, High-Impedance Surfaces, and Engineered Materials James T. Aberle Associate Professor of Electrical Engineering School of Electrical, Computer and Energy Engineering Arizona State University Outline of Presentation • What Does “Non-Foster” Mean? • Possible Applications of Non-Foster Reactances – Electrically Small Antennas – High-Impedance Surfaces – Artificial High-Permeability Materials • Realization of Non-Foster Reactances IEEE Waves and Devices 19 Feb 2010 2 Copyright © 2010James T. Aberle Outline of Presentation • What Does “Non-Foster” Mean? • Possible Applications of Non-Foster Reactances – Electrically Small Antennas – High-Impedance Surfaces – Artificial High-Permeability Materials • Realization of Non-Foster Reactances IEEE Waves and Devices 19 Feb 2010 3 Copyright © 2010James T. Aberle Foster’s Reactance Theorem • The theorem is a consequence of conservation of energy. • The slope of the input reactance (susceptance) of a lossless passive one- port is always positive. • All zeros and poles of the impedance (admittance) function are simple, and a zero must lie between any two poles, and a pole between any two zeros. IEEE Waves and Devices 19 Feb 2010 4 Copyright © 2010James T. Aberle Consequences of Foster’s Reactance Theorem • Impedances (admittances) of passive one- port networks rotate clockwise on the Smith Chart as frequency increases. • There is no such thing as a negative capacitor or a negative inductor (for passive circuits). IEEE Waves and Devices 19 Feb 2010 5 Copyright © 2010James T. Aberle Foster Network L L Term L2 C L1 Term1 C1 R L=40 nH L=40 nH R1 Num=1 R= C=30 pF R= Z=50 Ohm R=50 Ohm 60 40 20 real(Zin1) imag(Zin1) 0 S(1,1) -20 0 50 100 150 200 250 300 freq, MHz freq (10.00MHz to 300.0MHz) IEEE Waves and Devices 19 Feb 2010 6 Copyright © 2010James T. Aberle Non-Foster Network L L Term L2 L L1 Term1 L3 R L=40 nH L=40 nH R1 Num=1 R= L=-40 nH R= Z=50 Ohm R= R=50 Ohm 120 100 80 60 40 S(1,1) real(Zin1) imag(Zin1) 20 0 -20 0 50 100 150 200 250 300 f req, MHz f req (10.00MHz to 300.0MHz) IEEE Waves and Devices 19 Feb 2010 7 Copyright © 2010James T. Aberle Outline of Presentation • What Does “Non-Foster” Mean? • Possible Applications of Non-Foster Reactances –Electrically Small Antennas – High-Impedance Surfaces – Artificial High-Permeability Materials • Realization of Non-Foster Reactances IEEE Waves and Devices 19 Feb 2010 8 Copyright © 2010James T. Aberle VHF Whip: A Canonical ESA •Geometry of monopole antenna as modeled in Antenna Model software. The monopole is a copper cylinder 0.6 meters in length and 0.010 meters in diameter, mounted on an infinite perfect ground plane. •Frequency range is 30 to 90 MHz. IEEE Waves and Devices 19 Feb 2010 9 Copyright © 2010James T. Aberle Input Impedance of VHF Whip From Simulation IEEE Waves and Devices 19 Feb 2010 10 Copyright © 2010James T. Aberle Two Tools to Help With Analysis • Exact two-port representation of antenna in frequency domain in terms of s- parameters. • Approximate lumped equivalent circuit model of antenna over frequency range of interest. IEEE Waves and Devices 19 Feb 2010 11 Copyright © 2010James T. Aberle Two-Port Representation of Antenna jX a Rl Z0 N 1: Z0 The quantities in this box are re-evaluated at every frequency for which we have data. IEEE Waves and Devices 19 Feb 2010 12 Copyright © 2010James T. Aberle Two-Port Representation of Antenna = + =++ Zaa R jX arl R R jX a = = Rr e cd R a radiation resistance = − = R/ (1 ecd ) R a dissipative loss resistance = X a antenna reactance R N = r Z 0 IEEE Waves and Devices 19 Feb 2010 13 Copyright © 2010James T. Aberle Two-Port Representation of Antenna • Antenna impedance and radiation efficiency are used to produce a Touchstone *.s2p file for use in circuit simulation – the exact two-port representation of the antenna at each frequency for which we have data. • Allows concepts like transducer power gain and stability measures to be applied to antennas. The latter being particularly important for considering the use of non-Foster reactances in antenna matching networks. IEEE Waves and Devices 19 Feb 2010 14 Copyright © 2010James T. Aberle Approximate Equivalent Circuit of the Antenna • To model the antenna, we assume that the real part of the antenna impedance varies as the square of frequency, and the imaginary part behaves as a series LC. 2 ω 1 Z = R + jωL − a 0 ω a ω 0 Ca Impedance produced by equivalent circuit IEEE Waves and Devices 19 Feb 2010 15 Copyright © 2010James T. Aberle Approximate Equivalent Circuit of the Antenna • Evaluation of the model parameters ( R0, La and Ca): = ℜ{ (ω )} R0 Za 0 −1 L ω a ℑ{}Z ()ω 1 ω a 1 1 = −1 1 ω ℑ{}Z ()ω 2 ω a 2 2 Ca IEEE Waves and Devices 19 Feb 2010 16 Copyright © 2010James T. Aberle Approximate Equivalent Circuit of the Antenna = Ω R0 30.4 L Term Z1P_Eqn La C = L=194 nH La 194 nH Term1 Z1P1 Ca Num=1 Z[1,1]=4.30*(freq/52e6)**2 R= C=8.69 pF = Z=50 Ohm Ca 69.8 pF 20 0 -100 15 -200 10 -300 real(Zin1) -400 5 imag(Zin1) -500 real(VHF_Whip_S2P..Zin1) 0 imag(VHF_Whip_S2P..Zin1) -600 30 40 50 60 70 80 90 30 40 50 60 70 80 90 freq, MHz freq, MHz IEEE Waves and Devices 19 Feb 2010 17 Copyright © 2010James T. Aberle Matching Network Concept Γ Z0 Matching Network Z L IEEE Waves and Devices 19 Feb 2010 18 Copyright © 2010James T. Aberle Points to Consider • A real passive matching network can only approach and never exceed the performance predicted by the Bode-Fano criterion. • The matchable bandwidth is limited by the Q of the load. • The matchable bandwidth can only be increased by de-Qing the load – that is by intentional introduction of dissipative losses into the matching network – and concomitant reduction in radiation efficiency. IEEE Waves and Devices 19 Feb 2010 19 Copyright © 2010James T. Aberle Bode-Fano Criterion ∆f π ≤ Maximum f 1 allowable 0 Q ⋅ln reflection Γ coefficient m Q of the load Maximum value of fractional bandwidth that can be achieved with any passive, lossless matching network. ∆ = Γ = 1 ⇒ f ≤ Q 81 ,9. m .0 035 3 f0 IEEE Waves and Devices 19 Feb 2010 20 Copyright © 2010James T. Aberle Single-Tuned Mid-band Match L L Term Le Z1P_Eqn La C Term1 L=884 nH Z1P1 L=194 nH Ca Num=1 R= Z[1,1]=4.30*(freq/52e6)**2 R= C=8.69 pF Z=4.30 Ohm m1 m2 freq= 51.80MHz freq= 52.20MHz S(1,1)=-10.409 / -73.141 S(1,1)=-10.477 / 71.883 impedance = Z0 * (0.992 - j0.630) impedance = Z0 * (1.008 + j0.630) m2 ∆ − f ≈ 52 2. 51 8. = S(1,1) .0 008 m1 f0 52 ∆ freq (30.00MHz to 90.00MHz) f 1 Analytical: = = .0 009 f0 2Q IEEE Waves and Devices 19 Feb 2010 21 Copyright © 2010James T. Aberle Wheeler-Lopez Double-Tuned Matching A.R. Lopez, “Wheeler and Fano Impedance Matching”, IEEE Antennas and Propagation Magazine, Vol. 49, No. 4, August 2007 IEEE Waves and Devices 19 Feb 2010 22 Copyright © 2010James T. Aberle Wheeler-Lopez Double-Tuned Matching A.R. Lopez, “Wheeler and Fano Impedance Matching”, IEEE Antennas and Propagation Magazine, Vol. 49, No. 4, August 2007 IEEE Waves and Devices 19 Feb 2010 23 Copyright © 2010James T. Aberle Wheeler-Lopez Double-Tuned Matching with Antenna De-Qing S-PARAMETERS N Zin S_Param SP1 Zin Start=30 MHz Zin1 Stop=90 MHz Zin1=zin(S11,PortZ1) Step=1 MHz 1 2 C R L Ref Term C2 RD Le Term L Term2 Term1 L2 C=53.0 pF R=200 Ohm L=884 nH S2P R= Num=2 Num=1 L=177 nH SNP1 Z=50 Ohm Z=50 Ohm R= File="VHF_whip.s2p" TF TF1 T=0.354 -6 -12 -14 -8 -16 -10 -18 dB(S(1,1)) dB(S(2,1)) -20 -12 S(1,1) -22 -14 -24 30 40 50 60 70 80 90 30 40 50 60 70 80 90 freq, MHz freq, MHz Decent match, poor efficiency freq (30.00MHz to 90.00MHz) IEEE Waves and Devices 19 Feb 2010 24 Copyright © 2010James T. Aberle Matching Network with Non-Foster Reactances L L C L L L1 L2 La1 La Term Ca1 Z1P_Eqn C L Term1 L=-44.9 nH L=-44.9 nH L=-194 nH Z1P1 L=194 nH Ca L3 C=-8.69 pF Num=1 R= R= R= Z[1,1]=4.30*(freq/52e6)**2 R= C=8.69 pF L=44.9 nH Z=50 Ohm R= Dualizer Antenna m1 Cancels frequency squared m1 freq= 90.00MHz S(1,1)=4.843E-4 / -3.517E-5 dependence of radiation resistance. S(1,1) impedance = Z0 * (1.001 - j5.952E-10) Van Der Pol, Proc, IRE, Feb. 1930 freq (30.00MHz to 90.00MHz) IEEE Waves and Devices 19 Feb 2010 25 Copyright © 2010James T. Aberle Antenna with More Practical Matching Network using Non-Foster Reactances. Z0 − ( + ) La Lm − Ca Lm Z0 Active matching network Two-port model of antenna IEEE Waves and Devices 19 Feb 2010 26 Copyright © 2010James T. Aberle Optimized Non-Foster Matching Network 1 2 L Ref C Term Term L2 L Ca1 Term2 Term1 L=-Lneg nH C=-Cneg pF S2P L3 R= Num=2 Num=1 SNP1 Z=50 Ohm Z=50 Ohm L=Lm nH File="VHF_whip.s2p" R= Var Eqn VAR VAR1 Lm=49.5959 {o} Lneg=226.588 {o} Cneg=8.72637 {o} -16 0.0 -18 -0.1 -20 -0.2 -22 S(1,1) -0.3 dB(S(1,1)) -24 dB(S(2,1)) -26 -0.4 -28 -0.5 30 40 50 60 70 80 90 30 40 50 60 70 80 90 freq, MHz freq, MHz freq (30.00MHz to 90.00MHz) IEEE Waves and Devices 19 Feb 2010 27 Copyright © 2010James T.
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