I am sorry for not elaborating. The equations are obtained by KCL of the above image.
Here ##V_1##, ##V_x##, ##V_{in}## and ##V_{out}## are variables and all else are constants. I need to find the relation between ##V_{in}## and ##V_{out}##.
Here is the equation I obtain after simplification, I don't know if it is correct:
gmc * V1 + s * C2 * Vout = [{s * (C1 + C2) * ro2 + 1} * Vout - s * C1 * ro2 * V1] * (s * rb * C2 + 1) / {ro2 * rb * (s * C2 - gm2)}
I need to eliminate V1 to find the relation between Vin and Vout.
Thank you very much sir.
I must say that I don't fully understand the above expression. The only formulae that I have got are from this site:
http://tutorial.math.lamar.edu/pdf/Laplace_Table.pdf
Could you please offer some explanation or redirect me to any reference where I can learn it more?
I have two functions ##\phi(t)=\cos(\omega t)## and ##f(t)=u(t)−u(t−k)## with ##f(t)=f(t+T)##, ##u(t)## is the unit step function.
The problem is to find Laplace transform of ##\phi(t) \cdot f(t)##.
I have tried convolution in frequency domain, but unable to solve it because of gamma functions...
I have the following laplace function
F(s) = (A/(s + C)) * (1/s - exp(-sα)/s)/(1 - exp(-sT))
I think that the inverse laplace will be-
f(t) = ((A/C)*u(t) - (A/C)*exp(-Ct)*u(t)) - ((A/C)*u(t-α) - (A/C)*exp(-C(t-α))*u(t-α))
and
f(t+T)=f(t)
Now I want to find the Fourier series expansion of f(t)...
I'm thinking of expanding the inverse term in its Taylor series form. But it would involve terms like (x(t))^2, (x(t))^3, etc if I am right. That would lead to convolution in Laplace domain which according to me is becoming more complicated!
I think the distribution function will look like this,
f(x)=1/20 , 10<x<30
=0 , otherwise.
The problem is Uniform Distribution is a continuous random variable. The probability at a certain value of x (e.g. 10:15 or 10:25) is meaningless. It will however give probability over a range...