Toward Integrated Circuit Size Reduction

In this article, voltage-basis, current-basis, and normalized scattering matrices were introduced and it was shown that three different scattering matrices are the same only with equal termination impedances but only the normalized scattering matrix is correct with arbitrary termination impedances. The scattering matrices can be calculated from impedance, admittance, or ABCD matrices characterizing a network. However, if the network has more than three ports, the calculation process from the admittance or impedance matrices is not simple. For this, conversion formulas of the ABCD parameters into the normalized scattering parameters were presented for the impedance-transforming directional couplers. If one can have any choice of the termination impedances of the directional couplers as shown in this article, the total size of a microwave integrated circuit can be reduced.