where [Z.sub.o,s] is the impedance matrix
corresponding to observation group o and source group s; [I.sub.s] is the coefficient vector of RWG basis functions in group s; [B.sub.o] denotes near neighbors of group o; [T.sub.o,s] is the translator; [D.sub.o] and [A.sub.s] are the disaggregation and aggregation matrices.
The unknown expansion coefficients [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] can be related utilizing impedance matrix
The number of columns and raws of the self-impedance matrix [Z.sub.s] and the mutual impedance matrix
[Z.sub.m] is N by N.
The second one sets the load impedances as the conjugates impedances of the corresponding receiving antennas, the third one sets the impedance matrix
of the matching network as the conjugate of antennas' impedance matrix
and consider the mutual couplings of the matching network, while the last one optimize the impedances of transmission lines between receivers and loads, but it does not take into account the mutual couplings of the matching network existing practically.
To directly generate the impedance matrix
, the position vectors of the source points and field points will be repeatedly computed for diferent orders and consumed time.
After modeling a target with a set of N expansion functions and performing the traditional Galerkin testing for the integral equations, a N x N dense impedance matrix
where j = 1,2,..., n, n is the sum of the connection substructures, [mathematical expression not reproducible] refers to the connection impedance matrix
of the jth connection substructure, o denotes the DOF sum of the jth connection substructure, and [z.sub.ab] denotes the connection impedance between ath and bth DOFs that denotes the force needed to act on the bth DOF when the ath DOF happens to be a unit displacement.
The total impedance matrix
contains two parts: self-coupling blocks and mutual coupling blocks.
After obtaining the reduced admittance matrix, the impedance matrix
seen from terminals 1 and 2 is calculated by its inverse.
where [Z] is the system equivalent impedance matrix
and [m] is a fully coupling matrix.
where [Z.sup.GP] is the gear pair impedance matrix
, [V.sup.GP] is the gear pair velocity vector, [F.sup.GP] is the applied external force vector, and [F.sup.mesh] is the static transmission error excitation force vector.
and by substitution of (11) into (10), the scattering parameters are now found in terms of impedance matrix