you are a truly gifted teacher- I have watched countless videos on the same topic by now and none of them explained the nuances of this complex topic as clearly as you did. This video covered all bits related to PSD seamlessly whilst maintaining clarity.
PSD is so universal in physics that I have to learn it even though I am not specialized in the electrical engineering. Your mathematical interpretation on this is clear. This video makes me subscribe your channel immediately.
42:17 I think that = + because on top of being uncorrelated we are assuming that the average of x1 or x2, or both, is zero, i.e. =0 and/or =0. In general the correlation Rx1x2 = , also written has E[x1∙x2]. If x1 and x2 are uncorrelated (i.e. they are independent) then Rx1x2 = , also written as E[x1]∙E[x2] If =0 and/or =0 then Rx1x2 = 0. NOTE: do not confuse correlation with covariance Cov(x1,x2) = E[x1∙x2] - E[x1]∙E[x2] which is =0 for independent signals (uncorrelated signals) even if E[x1] ≠ 0 and E[x2] ≠ 0 given the above.
One thing I have been confused about PSD is the transformation between variables. Suppose S_I(f) is the PSD of current and S_V(f) of voltage, I have seen S_I(f) = S_V(f)*(dI/dV)^2. Is it true in general, or do we have to assume constant resistance (i.e. I and V being linear to one another)? Thanks to anyone who answers it in advance.
Sir I know this is not related to this lecture but can you tell me what is the difference between op-amp slew rate and op-amp bandwidth(not formula wise). Are these two factors related to each other?
slew rate is talking about large signal behavior, but the bandwidth is only applied to small signal one. If you care about slew rate, you should see how each transistor behaves (e.g. saturation or linear region) during a large swing VIN, say, 0-Vdd. It is usually non-linear. However, when you talk about small-signal bandwidth, the opamp behavior should be linear. You can model it with poles and zeros.
I think Lei points out the key difference btw slew rate and BW of an amplifier. I can add some of my own understanding. Slew rate (V/us) tells how fast an amplifier can charge/discharge its output voltage, and the differential input voltage is assumed to so large that the negative input FET is off. BW is often measured as the frequency where the amplifier gain rolls off by 3 dB from DC gain, where the input pair FETs are all in saturation if designed well. Basically, the slew rate shows how fast you can change the output voltage in the time domain; BW shows up to what frequency of the input signal the amplifier can still hold a high gain. These 2 specs are indirectly related, things like the design of the output stage and the sizes of C_compensation and C_out may affect both specs.
3:52 "imagine you have a bunch of resistors with exactly the same value" ... just as statistical properties may change over time you can't have resistors with exactly the same value, because resistors have tolerance....🙂 19:52 "true white noise can not exist because then we would have infinite power" ... you asked for it so here it comes the Zero Point Module or ZPM... ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-pRiUwCx_2O4.html ... so maybe this means... that true white noise can exist, but we can not harvest its power yet... 😃
@@AnkhArcRod Hi AnkhArcRod, my first comment was serious, but it is just a comment about the impossibility of two resistors having exactly the same value.... Concerning my second comment about the ZPM.. I was just being funny. If that's alright? However it never hurts to keep an open mind about future discoveries in science so I was just having some fun if that's alright? 😃 Thanks for your concern!
