A General n-Port Network’s Equivalent Current Sources Theorem

Abstract

In this paper a general n-port network’s equivalent current theorem has been derived out, for n = 1, 2…. the traditional Norton’s Theorem is only a special case of it for n=1. When an n-port passive linear time-invariant network is connected to another n-port linear time-invariant network which contained sinusoidal sources with same frequency, this theorem provides a new way to calculate the port-current of the n-port passive network. But the short-port currents of the n-port network contained sinusoidal sources must be known at first. In sinusoidal networks, currents are vector quantity or complex quantity, including magnitude and phase angle. Ammeter can only be used to measure the magnitude of the current, not including its phase angle. So it is impossible to get the short-port currents by the short-port experiment. Moreover the short-port experiment may cause some dangerous events. So a special method to get the short-port currents is introduced in this paper, First to find out the open-port voltage vector ( including magnitude and phase angle), by measuring the voltages magnitude between some two points of the open-port with a voltmeter and by drawing a series of voltage vector triangles that one side vector is the sum of other two side vectors , if the phase angle of one side vector in a triangle is known, the phase angles of the other side vectors in the same triangle can be decided. In the first triangle, the first open-port voltage vector is contained, its phase angle can be assigned to be zero, then the phase angles of the other two voltage vectors in the first triangle can be decided. In the second triangle, one of the two above voltage vectors is contained, then the phase angles of the other two voltage vectors in the second triangle can be decided. Thus go on step by step, all the open-port voltage vectors can be obtained. And the open-port voltage complex matrix has been obtained. The equation related the short-port current complex matrix and the open-port voltage complex matrix has been derived out in this paper. So the short-port current complex matrix can be obtained.