Читать книгу Introduction To Modern Planar Transmission Lines - Anand K. Verma - Страница 92

To define the [Y] parameters, the voltage is taken as an independent variable and current as of the dependent one for a two‐port network shown in Fig (3.1). In this case, the voltage is a source of excitation, and current at the port is the response. Thus, for a linear network, the total port current is a superposition of currents due to the voltages applied at both the ports:

(3.1.9)

where [V] and [I] are the voltage and current column matrices. The admittance matrix of the two‐port network is

(3.1.10)

The Y‐parameters are defined as the short‐circuited parameters. For the short‐circuited port‐2, V₂= 0, and Y₁₁ and Y₂₁ are defined from equation (3.1.9):

(3.1.11)

Likewise, for the short‐circuited port‐1, the Y‐parameters are

(3.1.12)

The [Y] parameters are extended to a multiport network by defining its matrix elements as follows:

(3.1.13)

Equation (3.1.13) shows that to get Y_ii, i.e. the diagonal elements of the [Y] matrix, all the ports are short‐circuited, except the i^th port. The current is evaluated at the i^th port for the voltage applied at the i^th port itself. To get Y_ij, i.e. the off‐diagonal elements of the [Y] matrix, the voltage is applied at the j^th port. Y_ij is the mutual admittance describing the coupling between the j^th port and the i^th port. The current at the i^th port is evaluated or measured, while all other ports are short‐circuited. The admittance element Y_ij is evaluated as

(3.1.14)