I have some components here to make an SMPS from mains for a CV/CC power supply for my workshop, and I decided to add a linear post-regulator to smooth the output. To avoid big heatsinks I wanted the SMPS voltage to follow the post-regulator voltage when I adjust it, and I've found a possible solution from . However my simulations showed better results while using an OpAmp (image below). As you can see, I set up the comparator of the SMPS in a way that the output voltage of the post-regulator will determine the output voltage of the SMPS (keeping it always 5V more then the post-regulator output for example, precision is not a problem). The circuit works fine on simulation, however I wanted to know if ripple, noises or imperfections of hardware that doesn't exist in my simulation might make this a bad idea, and what filters should I study to put on the output of this OpAmp (if any) to avoid any problems with this &quot;follower&quot; circuit before I buy the components I need. I have another comparator not shown in the image that is doing the current sensing.
I'm trying to find a way of building a new power supply for my workshop, in order to keep it small and not so hot I will be using a spare xformer to step down mains to 24v and then a variable buck converter to adjust it (and CC mode, displays and blinky stuff).   I thought it would be a good idea to use a linear regulator on the output stage to smooth things out, but I can't seem to think of a control scheme that allows me to change the voltage using only one potentiometer. The buck stage is this topology but with a external PNP transistor.(It has already been prototyped, it works alright, I know the mc34063A is old)   The only idea I got that ""works"" is using the buck converter output as a reference for a linear regulator (IC or discrete parts), but using a SMPS output as reference for anything is a bad idea, due to the amount of noise and fluctuations.   This is the sort of output stage I can and have built (or bought) over time. Just a big discrete regulator.  In short: How to control a MC34063A step down (buck) converter so it follows the output stage +1-3 V of headroom.
Show that $\mathbb{E}(T) = \sum\limits^\infty_{k=1}\mathbb{P}(T \geq k)$ for $T$ nonnegative integer valued and $E[T] < \infty$ Let T be a non-negative integer-valued random variable with $\mathbb{E}(T) &lt; \infty $. Prove that $\mathbb{E}(T) = \sum^\infty_{k=1}\mathbb{P}(T \geq k)$.  Had a few attempts, haven't really got anywhere. I'm wondering as I'm typing this if proof by induction is a good way to go.  Edit: One major thing I forgot to add, am I correct in thinking that also, $\mathbb{E}(T) = \sum^\infty_{k=1}k\mathbb{P}(T = k)$? My competitor is using Alexa to see what I am doing. I need to get stop Alexa from including my sites in their rankings. How can I do so?   Is it possible to deny access to any visitor with the Alexa toolbar and deny access to Alexa bot requests? Usage of singular or plural SI base units when written in both symbol as well as name I have multiple doubts related to the usage of singular or plural SI base units when written in both symbol as well as name.  I have framed this question under two parts, namely, Part (a) and Part (b). Each part has three sentences which I have written on the basis of my understanding.  Please answer these 6 sentences/questions.   Part (a):   says that while using prefix for e.g., centi as in centimeter, it is   l = 75 cm long.(correct) l = 75 cms long. (wrong)    Does this rule is used for all SI prefixes (having powers of 10)? In this regard, we should be saying, or writing that, "how many cm are there in one metre?" (while saying we should say centimter or centimetres?) Please strike-through the wrong SI unit in the following sentences.  My weight is 70 kg / kgs,  or My weight is 70 kilogram / kilograms.   Part (b):  and the page next to above web link says, we should write:  2.6 m/s, or 2.6 metres per second.   In this regard, we should say, or write:   Its speed is 0.26 metres per second.  This pipe is 0.75 metres long. How many cm are there in 2 metres? How can I keep Ubuntu updated automatically? I want help to  make Ubuntu 'update &amp;&amp; upgrade' itself automatically, select the settings for this automatic system.  How can I do it? Please advice about  where to find the menu (GUI) or file (command line) to do it, what settings that can be recommended (if different from the default).  As a bonus, please describe how different types of program packages are treated,  program packages from Ubuntu repositories and PPAs snap packages flatpak packages other kinds of programs/packages. Missed the MyOpenID demise; account lost forever? Is there any way to get my old account + metadata back if I have lost an account ties to MyOpenID? Horned Mohawk looking insect. What is it? Any ideas? I didn't know any other way to explain it.  I live in Indiana, USA if that helps.   Someone said it might be a "stink bug" but I'm not sure and not willing to find out! How do popular free RAW editor/converter compare to each other on Windows? I'm looking for a free RAW editor/converter on Windows. Can you tell me some strong/weak points of them comparing with Capture NX and/or Adobe Photoshop Elements?       - conversion &amp; EXIF  - white balance  - registration not possible anymore   EXIF editing would be a nice bonus.  Related: $\infty = -1 $ paradox An example for a homomorphism that is not an automorphism Give read-only access to specific folders? Evaluating the double limit $\lim_{m \to \infty} \lim_{n \to \infty} \cos^{2m}(n! \pi x)$ I have to find out the following limit $$\lim_{m\to\infty}\lim_{n\to\infty}[\cos(n!πx)^{2m}]$$ for $x$ rational and irrational. for $x$ rational $x$ can be written as $\frac{p}{q}$ and as $n!$ will have $q$ as its factor the limit should be equal to 1. the second part of irrational is giving me problems. I first thought that limit should be zero as absolute value of cosine term is less than 1 and power it to infinity you should get $0$. But then I realised that it was wrong. I brought the limit down to this form. $$e^{-\sin^2(n!πx)m}$$ after this I find the question quite ambiguous as they have just said $x$ is irrational. If I take $x$ as $\frac{1}{n!π\sqrt{m}}$ I get the limit as $\frac{1}{e}$ but if I take  $x$ as $\frac{2}{n!π\sqrt{m}}$ I get the limit as $\frac{1}{e^4}$. please help me and tell me where have I gone wrong? I am trying to understand Maximum likelihood estimation but it looks like I am missing something rather elementary.          suppose we have an iid random sample $X_1, X_2,..., X_n$ for which the probability density function of each $X_i$ is $f(x_i; \theta)$ where $\theta$ is an unknown parameter. Then, the joint probability density function of $X_1, X_2,..., X_n$ is given by:          $f(X_1=x_1,X_2=x_2,\cdots,X_n=x_n)=\prod_{i=1}^{n} f(x_i, \theta)$      In Maximum Likelihood estimation, we try to maximize $f$ as a function of $\theta$.  Question: Why do we maximize probability density instead of probability? In what way does it make sense?  Edit: As explained in the answers, the probability of choosing a finite number of sample points from a continuous probability distribution is zero, so maximizing probability doesn't make sense, but how does maximizing probability density make sense? My work has decided to issue their own  (CA) to handle different aspects of our work securely without paying for certificates.   Cryptographically sign emails Encrypt email contents Make access to things like the company  client-certificate based. Revoke the keys of former employees automatically   They sent me a .pem file, and I'm not sure how to add it to my Ubuntu install. The instructions sent were: "Double-clicking on it on a Mac should install it."&nbsp;  How do I proceed? Do I need to do something with  to create a .key, .csr, or .crt file? How can I calculate the R-squared of a regression with arima errors using R? If I have an arima object like a:  set.seed(100) x1 &lt;- cumsum(runif(100)) x2 &lt;- c(rnorm(25, 20), rep(0, 75)) x3 &lt;- x1 + x2  dummy = c(rep(1, 25), rep(0, 75))  a &lt;- arima(x3, order=c(0, 1, 0), xreg=dummy) print(a)   .  Series: x3  ARIMA(0,1,0)                      Call: arima(x = x3, order = c(0, 1, 0), xreg = dummy)   Coefficients:         dummy       17.7665 s.e.   1.1434  sigma^2 estimated as 1.307:  log likelihood = -153.74 AIC = 311.48   AICc = 311.6   BIC = 316.67   How do calculate the R squared of this regression? In computer science we discuss an abstract machine called a "deterministic finite automaton". The standard initialism for this term is "DFA". This makes sense in the singular usage of the initialism.  However, the pluralization of the word "automaton" is "automata". One speaks of "an automaton" or "many automata". Consequently, it seems intuitive to form an initialism of the phrase "deterministic finite automata" as "DFA".   This does not seem correct, as "DFA" could be either plural or singular. On the other hand, "DFAs" also does not seem correct because it would seem to expand to "deterministic finite automatons", a phrase which no self-respecting computer scientist would ever utter.   This appears to be a duplicate of the question here   But that question was never clearly resolved. What to do? I'm on the hunt for a great sounding, non-in-ear set of headphones with working mic, play/pause, and volume buttons.  I have Bang &amp; Olufsen's , which are among the best sounding headphones I've ever used. And all three button work perfectly in my MacBook Air and iPhone.  Obviously they don't work perfectly in my Nexus 4, since Android devices uses a different way of reading volume up/down buttons.  So, my question is rather simple, does anyone know how to make them work with Android, or alternatively any equally good headphones to the EarSet 3i's that work on Android? 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I already made vim the default editor, and use it as a substitute for gedit to open php, .txt, .c and .h files, by placing a vim.desktop file in ~/.local/share/applications/ and by correctly editing either  ~/.local/share/applications/mimeapps.list or /etc/gnome/defaults.list. However apparently this does not apply to nano.    Any clue ? Copy a large data from sql query result In my sql server 2008, after running the query the data return is very huge say in millions. I tried copying but it gives an exception sql memory error. Can you let us know how can i copy the entire data and paste it into excel.  I don't want to export it to txt file as the data is not getting aligned. So i want to manually copy and paste it into excel. Please let me know the solution for thhis