how to solve series of 25 RC circuits

[revooridinesh]

how to solve this problem ?

 

[v_c]

Do you need an analytical solution? If not, you can just simulate the circuit and plot the frequency response.

 

[revooridinesh]

@V_c thank u for the reply
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 ?

 

[_Eduardo_]

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)

 

[v_c]

I think it might be a better idea to determine the transmission parameters (a type of 2 port parameter) -- this would be a 2x2 matrix and multiply the matrix 25 times.

 

[revooridinesh]

@v_c

transmission parameters mean ABCD paramaters r8 ? then one of the element of matrix would be either S or w( frequency ) so how to multiply that matrix 25 times ?