Recent content by Vyse007

If I recall correctly (it's been a while, so I might be off), the delay for the entire adder circuit is usually in hundreds of nanoseconds, and individual operations (AND and XOR) take about 40 to 50 nanoseconds each (with 45nm technology). But as you might know already, gate delays depend on...

That is correct. Every function can be described as a sum of minterms, or a product of maxterms.

If you know Coulomb's Law, then all of the questions should seem pretty straightforward. Simple change the variables in the equation for Coulomb's Law and you should get the answers. Try it out, and if you get stuck, post your attempts here.

Am at work right now so will try this problem later on. But on first glance...when the circuit is made, then given that the initial voltage on the 1uf cap is 40V, it should act as a voltage source of V=40V at t=0, and then exponentially discharge, no?

OK the BJT we are talking about here is basically a current controlled current amplifier. What this means is that the collector current depends on the base current(when dealing with the CE configuration). The actual 'amplification' of the current will be easier to understand if you are familiar...

@Omkar13 OK I understood the criterion by referring to Nise. But I am unable to understand how the actual plot is made. I know how to start the plot: Plot the magnitude as the frequency increases. But can you please tell me how does the peculiar shape arise. For eg, in the link that you gave...

In my course for Control Systems Engineering, I came across the Nyquist criterion for stability of a closed loop system, which confused me to no end. I thought the Internet would provide me some relief, but alas, I ended up getting even more confused. Different sources use different terms and...

Hmm...tried that out and did get some pretty ugly fractions. Got stuck at a point, but that's nothing I can't figure out when I get free. Thanks for all your help guys!

I see where you are getting at. But unfortunately, I have no idea how to use residue theorem here, especially when you say that the answer won't have complex terms. Thanks for helping me out though. Much appreciated! :smile:

That doesn't answer my question of how to select the region when none is given. If it were arbitrary, wouldn't the answer be dependent on the region?

Hmmm...did try that. Putting tan(x)=u, I get integral (1-u^{2})^{3/2}/(1+u^{2})(1+u^{3}). I have no idea how to use residue theorem here, considering that the region has not been specified. Should I simply take up a unit circle to be the region? Also, if that were the case then I would end up...

Well if I put the denominator as u, then du=[3sin^2(x)cos(x)-3cos^2(x)sin(x)]dx, right? Now what? Do I take the whole term out and perform integration w.r.t u? That gives some unexpected answers... Sorry I haven't brushed up my integration in a while, so please bear with me. Btw just for fun...

OK I substituted sinx=u, and then got the whole integral in terms of u. Splitting it into partial fractions, I get two terms: 1/\sqrt{1-u^{2}} and another term 1/u^{3}+(1-u^{2})^{3/2}. Am stumped about the second term. Actually I don't even know what I did is right!

Homework Statement I am asked to integrate 1/[(sin^{3}x)+(cos^{3}x)] dx. Indefinite integration.Homework Equations The Attempt at a Solution I tried pretty much everything I could think of. Wrote the integral in terms of sin3x and cos3x, and tried to simplify. Even tried a few more identities...

C'mon guys...someone help me out here. :redface: