# Thread: Finding the transfer function (simultaneous equations)

1. ## Finding the transfer function (simultaneous equations)

Hi, I have been staring at this all day and cannot solve it! It is a question for a DSP module. I have 5 equations and need to re-arrange them eliminating V1 - V4 so that I am left with Y(z)/X(z). I have attached an image with the equations. Could anybody help me out? It's driving me mad.

2. ## Re: Finding the transfer function (simultaneous equations)

Step 1. First substitute $\displaystyle V_3$ in equations (2) and (4) with the expression given in the equation (3).

Step 2. Next, in the equation (5) express $\displaystyle V_2$. Use that expression as a substitution for $\displaystyle V_2$ in equation (4). Now equation (4) should represent $\displaystyle V_4$ in terms of z's, k's and Y(z).

Step 3. Next use the expression for $\displaystyle V_4$ in equation (4) as a substitution for $\displaystyle V_4$ in equation (1). Now equation (1) should give you the expression for $\displaystyle V_1$ in terms of z's,k's and X(z) and Y(z).

Now you have to deal with the equation (2). Substitute $\displaystyle V_1$ with the expression in the equation (1) from the step 3. On the left side of the equation term $\displaystyle V_2(z)$ substitute with the expression obtained from the equation (5) (see step 2.)
After that that equation should contain no V's and I presume thats the equation you've been chasing all along?