## A Study of the Network-synthesis Approximation Problem for Arbitrary Loss Functions |

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### Contents

FILTER AND NONFILTER PROBLEMS | 6 |

THE Wj_ FUNCTION | 10 |

THE Wg FUNCTION | 16 |

5 other sections not shown

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### Common terms and phrases

approximation problem arbitrary loss function band pass filter boundary conditions branch cut calculated charge density charge is performed charges at infinity Charges at Zero complete procedure complex frequency plane complex potential function complex potential plane conducting plate constant Doctor of Philosophy encirclement equal-ripple approximation equal-ripple result equations equi-potential line error curve Figure 29 flux lines given loss function Hence imaginary axis infinite loss insertion loss Jacobian elliptic functions line charge mapping minimum ripple multi-valued function natural frequencies negative filament charges nepers network synthesis Newton's method number of positive obtained p-plane physical reasoning based plotted in Figure points of infinite poles and zeros positive charges positive filament charges potential analogy method prescribed band prescribed function quantization of charge real axis real potential function results are plotted Riemann surfaces saddle point shown in Figure solve the potential specified STANFORD symmetry tical total charge transformation uniform continuous charge Wt plane zero frequency