Interrelations And Interconnections of parameters

                  Interrelations and interconnections of parameters

                 -Vinish Soni, Sarvesh Wadi, Kaustubh Wakodkar, Yash Shamnani, Sameeran Zingre

For analysing various electrical circuits there are many methods to analyse it. It is important to design such circuit which gives relationship between input and output. For this we can use Two-port network connection.

Here the pairs present at left sides can be called as 1 port and the pair present at right side can be called as 2 port. Here there are 4 variables V₁,V_2,I₂,I₁ with the help of them so we will get six possible equations. These equation represents dependent variable in terms of independent variable. The coefficient of independent variables are called as parameters.

         Two port network Parameters –

                These  are types of this two port network-

1. Z parameters
2. Y parameters
3. T parameters
4. T' parameters
5. H parameters
6. ABCD parameters
7. G parameters

In this z, y, h, abcd, h parameters are famous and is useful in electrical network we can represent one parameter into another and that is called interrelations of parameters. It is important to analyse this conversions.

Interrelations of parameters -

There are the following steps for the transformation:

Step 1. Write the standard equations for both sets.

Step 2. Solve the equations (or rearrange) of the second set for the dependent (unknown) variables of the first set of equations and express the resulting equations in the form of the equations of the first set.

Step 3. Compare the equations obtained in step 2 with those of the first set to obtain the required parameters.

1.       1.  Z-parameters into y parameters :

T                      

            The standard equation of z and y parameters are:  

            Now rearrange Equations 3 and 4 into the form of Equations 1 and 2,

           Now comparing equation 1 and 2 with equation 3 and 4

   In this way we have converted z parameters in terms of y parameters.

1.             2.   Z-parameters in terms of ABCD parameters:

             The standard equation of ABCD parameters:

              Now arranging them in a proper order, we obtain that

So now after comparing all the equations we find that

So in this way we can represent one parameter into another parameter. The main process is by using 3 steps listed above

Interconnections of algorithm-

     Interconnection of ports can be of many types such as series connection of two ports, parallel connections of two ports, cascade connections,etc.

Series connection of two ports:

Consider two networks N’ and N” are connected in series as shown in Fig. When there are 2 ports which are connected in series then, we can add their Z- parameters to get overall z parameter of the overall series connections. Let the z-parameters of network N’ be z’₁₁, z’₁₂, z’₂₁, z’₂₂. Let the z parameters of network N” be z”₁₁, z”₁₂, z”₂₁, z”₂₂. Let the overall z-parameters of series connection be z₁₁, z₁₂, z₂₁, z₂₂.

   For the series connection we have,

Now we will find the equations both for N’ and N’’. First of all the equation for N’ is:

The equation for N’’ is :

For equation 1,2,3 and 4 we can write that:

The matrix form of this equation is:

Hence all the z parameters are ,

Hence, the z-parameters of the series connection are the sum of z-parameters of the individual network connected in series.

       In the same way we can implement parallel-parallel, cascade interconnections. Interrelation and interconnections are important because we can represent the 2 parameters w.r.t each other. These parameters have different applications such as in long distance relationship, the parameters can used in circuits involving Symbian technology, in wave form shaping technology, etc. Hence, interrelations and interconnections of parameters are important.