**Indefinite Admittance Matrix:**

Consider Indefinite Admittance Matrix of a linear network with n terminals as shown in the Fig. 5.26.

Let us consider a zero potential reference node or datum node arbitrarily outside the n-terminal network. Let the voltage sources connected between the n-terminals of the network and datum node be V_{1},V_{2},V_{3}, … V_{n}. Let the currents entering the terminals be I_{1},I_{2},I_{3}, … I_{n} respectively.

As a network is linear and there are n voltage sources, we can apply superposition theorem for the calculation of current entering each terminal. The current entering each terminals is the partial combination of n sources. The currents are given by,

Above equations resemble short circuit admittance parameters, there is a basic difference between these parameters and the short circuit admittance parameters of a general two port network. The difference is that the parameters are calculated by considering datum node or reference node outside n-terminal network. Above equations can be written in matrix form as,

In general,

The matrix Y_{i }is known as **indefinite admittance matrix**.

Let y_{jk}_{ }be the element of Y_{i} and it is given by

The parameter y_{jk }is the ratio of current entering j^{th} terminal when all the node are shorted to reference node except k^{th} node to the voltage at k^{th} node. To determine y_{jk},

**Short all the terminals to datum node except the terminal k.****Connect known voltage source V**_{k}between k^{th}terminal and datum node.**Measure current entering j**^{th}terminal as I_{j}and find ratio

**Properties:**

The properties of indefinite admittance matrix are as follows,

**The sum of the elements of every column of an indefinite admittance matrix is zero.****The sum of the elements of every row of an indefinite matrix is zero.****If an isolated node is added to n-terminal network then the order of indefinite admittance matrix becomes (n + 1) x (n + 1) and it is obtained by adding a row and column of zeros to n x n matrix of original network.****The value of determinant of indefinite admittance matrix is zero.****For a reciprocal n-terminal network, indefinite admittance matrix is symmetric.****If any one the nodes of n-terminal network is made reference node, then the row and the column corresponding to that terminal may be removed from the indefinite admittance matrix.**