I need analytic solution..
my idea is we can reduce the circuit by calculating the hybrid parameters of a single RC ckt and multiplying them 25 times..
is there any other method u know ?
You can calculate the general expression instead of computing the 25 products.
But as you can imagine, there will not be a simple formula...
Numbering the steps in decreasing order, we have:
i
= (V
-V(n-1))/r and i
- i(n-1) = V(n-1)·sc
Replacing i and simplifying
V
= (2+src)·V(n-1) - V(n-2)
V1 = (1 + src)·V0 , then can be assigned V0=1 and evaluate (by soft of course
) the sequence up to n
Then H = V0/Vin = 1/V
Also, for large n , is better the general solution of this sequence:
V
= a x1^n + b x2^n
x1,2 zeroes of x^2-(2+src)·x+1 = 0
x1 = (2+src + √(src·(src + 4)))/2
x2 = (2+src - √(src·(src + 4)))/2
V
may be written:
V
= ((V1-x2·V0)·x1^n - (V1-x1·V0)·x2^n)/(x1-x2)
Then H
= Vo/V
= (x1-x2)/((1+src-x2)·x1^n - (1+src-x1)·x2^n)