Why does op-amp output impedance / parasitic input capacitance pole cause a noise peak? I was simulating the above circuit in LTspice...  I realize the main problem here is the 2MHz peak (which should be fixable with proper compensation), but I'm curious about the smaller 398kHz peak that's seen in the output noise density plot.  This matches up perfectly with the pole that is created by the LT1028 parasitic input capacitance and output impedance (5pF, 80 ohms).  What is the mechanism of this creating an output noise peak though? I understand that input capacitance increases the noise gain of an amplifier.  However, I'd like to understand why this creates a peak in the noise rather than just an increase in the noise level.
Why does input capacity of an opamp increase noise gain? On the image below you can see an inverting amplifier with input capacity C1 and capacity C_F for general stability.     Now my book shows me following frequency plot:  A_n ... Noise-Gain  A_D ... open-loop gain  A_U ... V_out / V_in --> inverting amplifier gain     You can clearly see that C1 is increasing the noise gain at some point. And C_f is stabilizing A_n and A_U.   But why exactly does C1 increase the noise gain exactly?
How can I press "Insert" on a keyboard without that key? I am trying to prove that all vector spaces can be written as the direct sum of two subspaces.  My attempt: If each vector in vector space V can be uniquely written as the sum of two other vectors in V, the two vectors can be categorized into subspaces and thus V can be written as the direct sum of these subspaces. I am not sure how to show that this is true for all cases though. Edit Sorry for the confusion,to clarify I meantGiven a vector space V with a subspace W, prove that there exists a subspace W' such that the direct sum of W and W' is V.I am not sure about my proof method at all. Thank you. Find the sum of the series $\sum \frac{1}{n(n+1)(n+2)}$ Someone who just thinks they know what they're talking about What is a word or phrase that means a speaker (or writer) is talking about something they know very little about, but they think they know more than they do?  An example: If you read diet message boards, you get dozens of people saying ‘Eat 6 small meals a day,’ or ‘Eat 3 big meals, but don’t snack,’  or ‘Eat more/less protein/carbs/fat.’ Each person is sure they are knowlegable enough to give good advice, but real experts(dieticians or researchers, for example) are rare.  I want a word to describe this attitude.  Bullshit is close, but someone bullshitting usually knows they aren’t an expert, they just want to convince the listener they are.  Also, I’d prefer something politer than bullshit. Do "Best by: XX-XX-XX" foods have an expiration date? How long will foods that have "Best by: XX-XX-XX" on the product last past that date?  I have tried looking online, and all I can find is anecdotal evidence, which isn't very assuring for me since there seems to be no specific "x food will expire y weeks after its best by date".  Is there a rule of thumb or some guide out there that can tell me how long a "best by" food will last? Or is it safe to assume that they never expire, since it's not actually labelled on the product? I have a table like this:   Column  | Type | Modifiers  ---------+------+-----------  country | text |   food_id | int  |   eaten   | date |    And for each country, I want to get the food that is eaten most often.  The best I can think of (I'm using postgres) is:  CREATE TEMP TABLE counts AS     SELECT country, food_id, count(*) as count FROM munch GROUP BY country, food_id;  CREATE TEMP TABLE max_counts AS     SELECT country, max(count) as max_count FROM counts GROUP BY country;  SELECT country, max(food_id) FROM counts     WHERE (country, count) IN (SELECT * from max_counts) GROUP BY country;   In that last statement, the GROUP BY and max() are needed to break ties, where two different foods have the same count.  This seems like a lot of work for something conceptually simple.  Is there a more straight forward way to do it? Unused Business visa I got a 6 months business visa for the UK. But I can't use it.   My relative lives in the USA. In the future, I want to go there to meet with her.  Is there any problem getting a US visa after getting, but not using, a UK business visa? Has anyone used PostgreSQL with PostGIS successfully?   I am a semi-experienced ArcGIS user and want to build out a database and connect it to ArcCatalog.   I've scoured the internet for resources but nobody has really given a good walkthrough. Getting inverse of a transposition key Automatically hide old comments Comments are useful. Many, many posts need some small amount of meta discussion, and comments fulfill this need.   Comments are also noisy and distracting. Occasionally, someone will post an insightful and informative comment that complements the post its attached to... But more often, they're tangential, quickly irrelevant and in the way: stale comments show up first, making newer comments less visible.  The guidance here for a long time has been that comments are transient, . And yet, some do hang around for months or years because .   So let's fix that.   I propose that all comments older than 7 days be hidden by default unless the comment has been up-voted in the past 30 days. Hidden comments should be indicated by a note below the post ("add / show 3 more comments") and made visible to anyone who cares to click it.   This doesn't destroy anything, but it would get it out of the way of most readers - and hopefully encourage folks to edit it into the actual answers as a result.  Note: I previously suggested this . Other  have been . However, I'm not suggesting that comments be automatically deleted, and they should be hidden based purely on the age / activity of the comment itself, not of the post to which they're attached. when to used had been and have been My friend just answered to one of my important questions. Now how should I reply to him?        That question had been in my head for a long time, finally, I got my answer      or        That question has been in my head for a long time, finally, I got an answer.      Basically, I am confused with had and have. Since that question is not anymore in my head after having got an answer, what should be used? (I am also confused whether it is possible to use having instead.) How can I hide my code in visualforce page? I developed my app,   The controller is complete, and also the visualforce, but I need to hide my code at installing the app in another salesforce account.  How can I make this possible?  Is there any way to hide both codes? The apex and the code behind?   Thanks in advance. I've got a circuit in the basement carrying a handful of outlets.  This circuit has no ground wire.  I want to add a couple of outlets and want them to be grounded.  I may even want gfci outlets on them in the future.  I have no reasonable way of getting a ground wire to the panel but I do have easy access to another circuit that does have a ground wire.  Is it acceptable to borrow or share a ground wire between circuits?  If not, why not?  Both circuits are 20A with 12 AWG wire. How to highlight (color/draw attention to) a particular snippet in Minted I'm currently doing some work on error messages in programming languages. As such, I'm showing faulty pieces of code, alongside the compiler-errors accompanying them.  I'm using minted for the code snippets, but ideally, in addition to normal syntax highlighting, I'd like to highlight the sections of the code at which the error is located, by underlining them, putting a red box around them, shading their background, etc.  Is this possible using Minted? pc ram memory 2x1GB or 1x2GB I don't know if it's the right place to ask but can somebody advise me for buying a ram memory for my computer.  I have a Dell Vostro 200 with 1GB of RAM and 667MHz. 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I could see the full folder paths in Glary before the restore, so I know the information is there; it's just not using that information and copying everything to root of my designated destination, rather than relative to the original location. I know that for a Banach space $X$ and a linear functional $T:X\rightarrow\mathbb{R}$ in its dual $X'$ the following holds: \begin{align}T \text{ is continuous } \iff \text{Ker }T \text{ is closed}\end{align} which probably holds for general operators $T:X\rightarrow Y$ with finite-dimensional Banach space $Y$. I think the argument doesn't work for infinite-dimensional Banach spaces $Y$. Is the statement still correct? I.e. continuity of course still implies the closedness of the kernel for general Banach spaces $X,Y$ but is the converse still true? When does Thread.CurrentThread.Join() make sense? Origin of electric charge Natural Sort Order in C#