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, 147 tri Column-wise vector with elements in the lower triangle, atr Trace along the anti-diagonals

.. .. Transmitted-power,

.. .. Definitions,

.. .. Losslessness,

.. .. Impedance,

.. .. Impedance,

, State space representation

, 2 Rational form of the transfer function obtained from its state space representation

.. .. Mcmillan-degree,

. .. , Transmission zeros and transmission polynomial

.. .. Darlington, 38 2.10 Rational form of the impedance matrix Z

. .. Belevitch-form, 44 2.13.2 Non-reciprocal multi-band transfer functions, p.45

, Classical matching problem

, General broadband matching problem

, Helton's solution to the matching problem

. .. The-problem,

.. .. The,

. Baratchart-seyfert-olivi,

, An algorithm for point-wise matching

, The result: perfect matching points with a matching network of fixed degree

, Fano-Youla's contribution to the broadband matching problem, p.58

. Fano-youla,

.. .. Fano-youla-characterisation,

. Fano,

, Bode's result for an RC-load

C. ,

. .. The-problem,

. .. The-result,

, Optimisation problem in Fano-Youla framework

.. .. The,

. .. The-matching-network,

. .. , Necessary conditions on the global system, p.76

. .. Statement, 78 4.2 A convex relaxation to the matching problem

.. .. Admissible,

.. .. Statement,

.. .. Properties,

.. .. Statement,

.. .. ,

, Practical characterisation of the admissible set: a perspective of admissibility as a classical Nevanlinna-Pick interpolation problem 99

, 100 5.2 Introduction to Hardy spaces of vector valued functions, p.102

, Reproducing kernel Hilbert space

, Vectorial formulation of the Nevanlinna-Pick interpolation problem: generalised Pick matrix

R. .. ,

P. ). , 109 5.5 Remarks about the positivity of the Pick matrix

.. .. The,

, The matching problem

R. .. ,

. .. Minimum-phase-property,

.. .. Examples,

. .. , 123 6.10.1 Effect of the filter transmission zeros, Single band matching and example of matching filter design

, Further applications: multi-band matching

. .. The-bandwidth-problem,

.. .. ,

, Parametrisation by means of linear matrix inequalities, p.150

.. .. Trace,

, Dealing with several intervals

R. .. , , p.157

. .. , Formulation of the general matching SDP, p.159

P. .. , , p.160

, Derivatives of the spectral factorisation

, Semi-definite program statement: criterium and objective function

.. .. Initial,

, The log barrier

. .. Shifted-logarithm-barrier,

, A barrier function for non-linear constraints

, A non-constrained convex problem

. .. The-newton-solver,

.. .. De-embedding-of-the-load,

, Alternative characterisation of the admissible polynomials by means of scalar inequalities

. .. , Example of reducible matching problem, p.206

, Forced Blaschke simplification. A matching problem with prescribed reflection zeros

, A fixed-point version of the optimisation algorithm, p.211

, application of the point-wise matching algorithm, p.213

. .. , Local optimisation of the matching network, p.214

.. .. Summary,

. .. Small-superdirective-antenna, 1.1.2 Load de-embedding and matching filter optimisation, p.225

. .. High-degree-antenna, 228 10.2.2 Fixed-point algorithm and de-embedding of the load, p.230

.. .. Yagi,

.. .. Dual-band-rhcp-antenna,

.. .. Concluding,

. .. Radiated-efficiency,

. .. , 259 11.4.1 Filter model and optimisation

.. .. Multiplexing,

, 276 12.2.1 Rhodes and Levy's theory. Classical multiplexer synthesis, State of art and techniques for manifold-type multiplexer synthesis, p.278

, Dealing with the problem of manifold peaks

, Manifold model and manifold peaks 283

. .. , 286 13.2.1 Channel filters and passbands

.. .. Manifold,

.. .. Concluding,

. .. , Application to multiplexer synthesis 305 14.1 Framework and notation

. .. , 307 14.2.1 Simultaneous computation of matching filters

, 311 14.3.1 Derivation of analytic formulas providing the derivative of the load 312 14.3.2 Derivative of the Chaining Expression

, Multiplexer design and results 317

.. .. Matching,

.. .. Results,

.. .. Concluding,

.. .. The,

, Application to the synthesis of multiplexers, p.347

. .. , Optimal synthesis of transfer function for matching synthesis

, B Nevanlinna-Pick interpolation and schur recursion with interpolation conditions inside the lower half plane 363 B.1 Schur recursion

, Elementary de-chaining matrix for a transmission zero on the boundary, vol.372

, Interpolation problem with boundary interpolation conditions, p.375

, Dealing with transmission zeros at infinity

, D Global system synthesis with optimal oscillating transfer functions. Proof of unicity

, Unicity of the solution to problem

, E Manufactured prototypes 393 E.1 Six-poles dual-mode filter

.. .. Analyticity-domain,

, Rational feasible functions

.. .. Schur,

, Admissible minimum phase functions

. .. Multiplicity, 92 set: a perspective of admissibility as a classical Nevanlinna-Pick interpolation problem101 Definition 5.1.1 Nevanlinna-Pick interpolation

. .. , Positive semi-definite Hermitian matrices, p.107

R. .. ,

.. .. Trace,

, Chapter 11 Radiation efficiency and dissipation 256

, Chapter 13 Manifold model and manifold peaks 285

, Definition 13.1.1 Transmission zeros of multi-port devices, p.285

, Scalar chaining onto a multi-port

, Length of a branch

, Appendix A Angular derivatives, p.356

, Appendix D Global system synthesis with optimal oscillating transfer functions. Proof of unicity, vol.384

, Optimal multi-band filter synthesis

. .. , Problem 2.13.4 Generalised multi-band filter synthesis, p.45

.. .. P-i,

, Placement of the perfect matching points

. .. , 89 transmission zeros on the boundary

, General matching problem with slack polynomials, p.156

. Non-linear and . .. Sdp,

. .. , Problem 8.2.2 Non-linear SDP without equality constraints, p.178

S. .. Simple,

, Problem SDP(t) with strict feasible barrier, p.187

, Problem SDP(?,s) with non-strict feasible barrier

, 309 Problem 14.2.2 Matching conditions as a function of ?