本文采用三角不等式求得了有用功率的上确界
推导了正定情况下最优负载阻抗的一般公式
获得了半正定情况下的最优电流
指出其解的个数并不多于正定情况。
In this paper
a method based on the triangular unequality is used to explain themaximum power transfer theorem in n-ports network. This method of proof is not only rigid and terse
it can also determine directly the condition of the maximum power transfer and the supremum of the available power drawn by the terminated load. Moreover
with this method
it is not necessary to decide whether the extreme value is of local or global optimum nor is it necessary to determine whether the objective function is convex or non-convex prior to finding the extreme value. However
these are unavoidable requirements if the usual varia-tional method is employed.The general formula of the optimum load impedance is derived in a detailed manner when internal impedance of network
Hermite matrix Zs+Zs*
is positive definite. It would appear that there are infinite numbers of the optimal load impedance matrices satisfying the maximum power transfer condition
where all solutions except one are nontrivial. The set composed of all these solutions constitutes a n2-n dimensional linear submanifold in complex space Cn2 . It is to be noted that trivial solution may evade influence of source vectors
and as is well known
this is an important characteristic in its implementation
but it requires to achieve match between corresponding components of the mutual impedance respectively. In contrast
those nontrivial solution may avoid such a difficult task of matching between corresponding components of the mutual impedance
but the influence of source vectors cannot be avoided.This paper applies
some mathematical accomplishments based on intuitive conception of projective geometry and the theory of generalized inverses
which are good at dealing with the problem considered impossible to solve in the sense of a solution of a nonsingular problem
i. e. the so-called "ill-posed" linear problem. Obviously
the optimal current will be solved if internal impedance of network Zs+Zs* is positive semidefinite. Hence
the optimal load impedance matrices may be found provided that results obtained in the positive definite condition are utilized directly. Finally
it also shows by the operation of cardinal numbers that the numbers of optimal load impedances make no difference between the positive definite and positive semidefinite conditions.
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