Current Optimization for Electrically Small Antennas Miloslav - PowerPoint PPT Presentation

Current Optimization for Electrically Small Antennas Miloslav ˇ Capek Department of Electromagnetic Field CTU in Prague, Czech Republic miloslav.capek@fel.cvut.cz Seminar at KTH Stockholm, Sweden January 18, 2017 ˇ Capek, M., CTU in Prague Current Optimization for Electrically Small Antennas 1 / 34

Outline 1 Current Optimization 2 Minimum Quality Factor Q 3 Modal Approach 4 Optimal Composition of Modes 5 On the Natural Bases 6 Summary and Concluding Remarks In this talk: ◮ electric currents in vacuum, ◮ only surface regions are treated, ◮ time-harmonic quantities, i.e. , A ( r , t ) = Re { A ( r ) exp (j ωt ) } are considered, ◮ be extremely careful when comparing different sources (papers): different notation! ˇ Capek, M., CTU in Prague Current Optimization for Electrically Small Antennas 2 / 34

“Is it beneficial to be here today?” Do you know the following publications well? ◮ Gustafsson, M., Tayli, D., Ehrenborg, C., Cismasu, M. and Norbedo, S.: “Antenna Current Optimization using MATLAB and CVX”, FERMAT , vol. 15, pp. 1-29, 2016. ◮ Capek, M. and Jelinek, L.: “Optimal Composition of Modal Currents For Minimal Quality Factor Q ”, IEEE Trans. Antennas Propagation , vol. 64, no. 12, pp. 5230–5242, Dec. 2016. ◮ Jelinek, L. and Capek, M.: “Optimal Currents on Arbitrarily Shaped Surfaces”, IEEE Trans. Antennas Propagation , vol. 65, no. 1, pp. 329–341, Jan. 2017. ◮ Capek, M., Gustafsson, M., and Schab, K.: “Minimization of Antenna Quality Factor”, submitted to IEEE Trans. Antennas Propagation , arxiv: 1612.07676. ˇ Capek, M., CTU in Prague Current Optimization for Electrically Small Antennas 3 / 34

Current Optimization Antenna Analysis × Synthesis and Antenna Design analysis Feeding Point Antenna characteristics  0 -5 s 11 [ dB] -10 -15 Q max = 7 -20 electric current f 0 Perfect Electric Conductor synthesis Antenna analysis × antenna synthesis. ˇ Capek, M., CTU in Prague Current Optimization for Electrically Small Antennas 4 / 34

Current Optimization Antenna Analysis × Synthesis and Antenna Design Antenna analysis studies. . . ◮ antenna parameters for a given antenna. analysis Feeding Point Antenna characteristics  0 -5 s 11 [ dB] -10 -15 Q max = 7 -20 electric current f 0 Perfect Electric Conductor synthesis Antenna analysis × antenna synthesis. ˇ Capek, M., CTU in Prague Current Optimization for Electrically Small Antennas 4 / 34

Current Optimization Antenna Analysis × Synthesis and Antenna Design Antenna analysis studies. . . ◮ antenna parameters for a given antenna. analysis Feeding Point Antenna synthesis seeks for. . . ◮ optimal currents, Antenna characteristics  ◮ optimal feeding (placement), 0 -5 s 11 [ dB] -10 ◮ optimal material. -15 Q max = 7 -20 electric current f 0 Perfect Electric Conductor synthesis Antenna analysis × antenna synthesis. ˇ Capek, M., CTU in Prague Current Optimization for Electrically Small Antennas 4 / 34

Current Optimization Antenna Analysis × Synthesis and Antenna Design Antenna analysis studies. . . ◮ antenna parameters for a given antenna. analysis Feeding Point Antenna synthesis seeks for. . . ◮ optimal currents, Antenna characteristics  ◮ optimal feeding (placement), 0 -5 s 11 [ dB] -10 ◮ optimal material. -15 Q max = 7 -20 electric current f 0 Perfect Electric Conductor Antenna design tries to find. . . synthesis ◮ the optimal combination of Antenna analysis × antenna synthesis. shape, material and feeding from infinitely many candidates. ˇ Capek, M., CTU in Prague Current Optimization for Electrically Small Antennas 4 / 34

Current Optimization Historical Overview Former approaches to antenna design predominantly made use of ◮ circuit quantities 1 ( V in , Z in , Γ, . . . ) → equivalent circuits, 1 H. L. Thal, “Exact circuit analysis of spherical waves”, IEEE Trans. Antennas Propag. , vol. 26, no. 2, pp. 282–287, 1978. doi : 10.1109/TAP.1978.1141822 ˇ Capek, M., CTU in Prague Current Optimization for Electrically Small Antennas 5 / 34

Current Optimization Historical Overview Former approaches to antenna design predominantly made use of ◮ circuit quantities 1 ( V in , Z in , Γ, . . . ) → equivalent circuits, ◮ field quantities 2 ( E , H ). 1 H. L. Thal, “Exact circuit analysis of spherical waves”, IEEE Trans. Antennas Propag. , vol. 26, no. 2, pp. 282–287, 1978. doi : 10.1109/TAP.1978.1141822 2 L. J. Chu, “Physical limitations of omni-directional antennas”, J. Appl. Phys. , vol. 19, pp. 1163–1175, 1948. doi : 10.1063/1.1715038 R. E. Collin and S. Rothschild, “Evaluation of antenna Q”, , IEEE Trans. Antennas Propag. , vol. 12, no. 1, pp. 23–27, 1964. doi : 10.1109/TAP.1964.1138151 ˇ Capek, M., CTU in Prague Current Optimization for Electrically Small Antennas 5 / 34

Current Optimization Historical Overview Former approaches to antenna design predominantly made use of ◮ circuit quantities 1 ( V in , Z in , Γ, . . . ) → equivalent circuits, ◮ field quantities 2 ( E , H ). However, ◮ all antenna parameters can be inferred from source current 3 ( J , M ) p = � J , L ( J ) � . � f ∗ ( r ) · L ( g ( r )) d V � f , L ( g ) � = Ω 1 H. L. Thal, “Exact circuit analysis of spherical waves”, IEEE Trans. Antennas Propag. , vol. 26, no. 2, pp. 282–287, 1978. doi : 10.1109/TAP.1978.1141822 2 L. J. Chu, “Physical limitations of omni-directional antennas”, J. Appl. Phys. , vol. 19, pp. 1163–1175, 1948. doi : R. E. Collin and S. Rothschild, “Evaluation of antenna Q”, , IEEE Trans. Antennas Propag. , vol. 12, no. 10.1063/1.1715038 1, pp. 23–27, 1964. doi : 10.1109/TAP.1964.1138151 3 J. Schwinger, “Sources and electrodynamics”, Phys. Rev. , vol. 158, no. 5, pp. 1391–1407, 1967. doi : 10.1103/PhysRev.158.1391 R. F. Harrington, Field computation by moment methods . Wiley – IEEE Press, 1993 ˇ Capek, M., CTU in Prague Current Optimization for Electrically Small Antennas 5 / 34

Current Optimization Operators to Rule Them All.. . All antenna parameters can be inferred directly from source current p = � J , L ( J ) � . (1) ˇ Capek, M., CTU in Prague Current Optimization for Electrically Small Antennas 6 / 34

Current Optimization Operators to Rule Them All.. . All antenna parameters can be inferred directly from source current p = � J , L ( J ) � . (1) ˇ Capek, M., CTU in Prague Current Optimization for Electrically Small Antennas 6 / 34

Current Optimization Operators to Rule Them All.. . All antenna parameters can be inferred directly from source current p = � J , L ( J ) � . (1) Observations: ◮ only properties of the operators are important, ◮ physics is imprinted in their structure, ◮ can be represented in many different ways, e.g. , [ � ψ m , L ψ n � ], [ � J p , L J q � ], ◮ as compared to fields, the current support is limited. � f ∗ ( r ) · g ( r ) d V � f , g � = Ω ˇ Capek, M., CTU in Prague Current Optimization for Electrically Small Antennas 6 / 34

Current Optimization Example: Radiated and Reactive Power Consider Electric Field Integral Equation 4 written as n × E i ( J ) Z ( J ) = − ˆ n × ˆ (2) 4 W. C. Chew, M. S. Tong, and B. Hu, Integral equation methods for electromagnetic and elastic waves . Morgan & Claypool, 2009. ˇ Capek, M., CTU in Prague Current Optimization for Electrically Small Antennas 7 / 34

Current Optimization Example: Radiated and Reactive Power Consider Electric Field Integral Equation 4 written as n × E i ( J ) Z ( J ) = − ˆ n × ˆ (2) and let us represent it in a basis { ψ n } , n ∈ { 1 , . . . , N } as Z = [ Z mn ], in which � � e − j k | r − r ′ | � � Z mn = � ψ m , Z ( ψ n ) � = − j Z 0 m · ψ n − 1 m ∇ ′ · ψ n | r − r ′ | d Ω ′ d Ω k ψ ∗ k ∇ · ψ ∗ 4 π Ω Ω ′ (3) 4 W. C. Chew, M. S. Tong, and B. Hu, Integral equation methods for electromagnetic and elastic waves . Morgan & Claypool, 2009. ˇ Capek, M., CTU in Prague Current Optimization for Electrically Small Antennas 7 / 34

Current Optimization Example: Radiated and Reactive Power Consider Electric Field Integral Equation 4 written as n × E i ( J ) Z ( J ) = − ˆ n × ˆ (2) and let us represent it in a basis { ψ n } , n ∈ { 1 , . . . , N } as Z = [ Z mn ], in which � � e − j k | r − r ′ | � � Z mn = � ψ m , Z ( ψ n ) � = − j Z 0 m · ψ n − 1 m ∇ ′ · ψ n | r − r ′ | d Ω ′ d Ω k ψ ∗ k ∇ · ψ ∗ 4 π Ω Ω ′ (3) or even more as (1 + j λ m ) δ mn = 1 2 � I m , ZI n � = 1 2 I H m ZI n . (4) 4 W. C. Chew, M. S. Tong, and B. Hu, Integral equation methods for electromagnetic and elastic waves . Morgan & Claypool, 2009. ˇ Capek, M., CTU in Prague Current Optimization for Electrically Small Antennas 7 / 34