Recent content by Debdut

Hi, I found the solution using the method of determinants. It was not difficult. Thanks.

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}##.

Yes, these are the equations. Thank you very much.

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.

OK, thank you again.

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)...

Found an article where they're saying Y(s) should be Y(s) = e-as . Laplace{x(t + a)}

Thanks for the quick reply. Do you mean e-asX(s). But that is the laplace of x(t - a). Am I wrong?

y(t) = u(t - a) . x(t) u(t) is a unit step function. I have to find Y(s)/X(s). Do I have to do convolution in frequency domain?

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!

x(t) and y(t) are related by y(t)=1/(x(t) -k), how should I derive Y(s)/X(s)?

So how am I going to approach the parts (b) and (c). Many thanks for the above posts.

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...