Wikipedia:Reference desk/Archives/Science/2012 October 3
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October 3
editMotherboard oscillators in the GHz..
editHow does the oscillator circuit that generate 2.0 .. 4.2 GHz on ordinary motherboards for the CPU look like?, seems hard to find the "anonymous chip" among all other components. It would be interesting too see how wire paths has been done to deal with RF-issues. Electron9 (talk) 02:25, 3 October 2012 (UTC)
- In any case, you might be interested to know that most high-frequency digital logic chips are driven by fairly low-frequency clock sources. These frequencies are stepped up to high frequency, including the microwave range, on the silicon die, where the processes and parasitic effects can be controlled more carefully. You might want to read about frequency multipliers and phase locked loops.
- For example, Intel's reference design for their 82583 10-Gigabit Ethernet Controller (which internally uses one of the highest frequencies present anywhere on many computer main logic boards) is driven by a 25 MHz (megahertz) crystal.
- Once you've mastered low-frequency design, you can migrate to microwave engineering; and ultimately reach Planar Microwave Engineering, or, the art of putting very high frequency circuits together in a way that can be built into a silicon wafer or printed circuit board. Nimur (talk) 03:17, 3 October 2012 (UTC)
- I believe most processors on "ordinary motherboards" use a simple 14.318 MHz crystal which the processor inernally multiplies to acheive the GHz clock rates, as the above replies describe. You can find the crystal by doing a google image search of clock crystal motherboard. But I don't think you'll find anything fancy about it, all the "RF issues" would be dealt with inside the processor it self. Vespine (talk) 03:40, 3 October 2012 (UTC)
- The 14.318 MHz oscillator is the "dot clock" for the NTSC colour video system. It's an integer multiple of all the frequencies required in the NSTC system and its use began with the original IBM PC. It has no relavence to the CPU clock in modern PC's. Nimur has gien the correct answer. Keit121.221.215.67 (talk) 11:09, 3 October 2012 (UTC)
- I believe most processors on "ordinary motherboards" use a simple 14.318 MHz crystal which the processor inernally multiplies to acheive the GHz clock rates, as the above replies describe. You can find the crystal by doing a google image search of clock crystal motherboard. But I don't think you'll find anything fancy about it, all the "RF issues" would be dealt with inside the processor it self. Vespine (talk) 03:40, 3 October 2012 (UTC)
I should have thought of the multiplier.. ;), what's the highest FSB frequency in use? and how does that circuit look like? Electron9 (talk) 12:11, 3 October 2012 (UTC)
- The FSB doesn't exist with most modern mainstream consumer CPUs having died out with the Hammer architecture on the AMD side (i.e. the first Athlon 64 processors) in favour of HyperTransport and with the Nehalem (microarchitecture) on the Intel side (i.e. the Core iX processors) in favour of the Intel QuickPath Interconnect. Intel Atoms still use a FSB, but it's unclear for how much longer. Nil Einne (talk) 14:42, 3 October 2012 (UTC)
- keit, do you have any source for: It has no relavence to the CPU clock in modern PC's. ? This source (I agree it's far from academic) suggests that the 14.318 MHz crystal has been used for cpu clock reference since the dawn of PCs. I'm not saying it's right, I just haven't seen any evidence that its wrong. Also, just to clarify, I did not dispute anything in Nimur's reply. Vespine (talk) 22:45, 3 October 2012 (UTC)
- Here is a better article in which Figure A pretty clearly shows a 14.318 MHz crystal. Vespine (talk) 22:56, 3 October 2012 (UTC)
- I think the article has several misconceptions. The 14,318 MHz crystal perhaps is used for the CPU in sub 28 MHz systems. Not ones with CPU puming away in 500 .. 5000 MHz. The "RF chokes" in Figure B is used for SMPS intermediate energy storage in energy pumping as can be deducted from the surrounding 3-pin chip and capacitors and proximity to the CPU.
- So far modern sockets use seperate clock connection and data transfers where the clock is increased in frequency by a multiplier inside the CPU. So I'm interested how the oscillator that drives the CPU sockets on modern motherboards looks like on the PCB. Electron9 (talk) 23:27, 3 October 2012 (UTC)
- Not that I don't believe you, but I still don't see any source to support what you are saying. I have a bit of experience building circuits with microcontrollers, I built a project using the Microchip PIC32 which typically uses an 8Mhz crystal to run at a clock speed of 80MHz, (having a quick look at the datasheet, you can run it from a 3 or 4MHz crystal). Ok, 80MHz is not 2500MHz, but 4 to 80 is still a much higher ration then 14 to 28, so I don't really see why a 14.318 couldn't be multiplied up further. Vespine (talk) 00:11, 4 October 2012 (UTC)
- There are hundreds, perhaps thousands, of Intel and competitive main CPU models. Similarly, there are thousands of main logic board designs. I'm certain if we look wide enough, we'll find a modern CPU main logic board with a 14.318 MHz crystal on it, driving the CPU. I know I've seen 25 MHz clock drivers on a lot of Intel designs lately, but this is hardly a universal standard; and Intel is not the only manufacturer of computer processors. If we consider esoteric designs by non-mainstream vendors, or low-volume, special-purpose systems, the variety increases even more. Really, the exact specification of the clock frequency is a minor detail. Crystals, or other digital reference clocks, can be built with almost any specified frequency. The original question was asking what the circuit looks like: and the circuit "often" looks like a phase locked loop on the main silicon die, driven by a low-frequency crystal oscillator external to the chip. If anyone wants to be more specific than that, we've got to stop speaking in the abstract and start naming part-numbers and technology steps. Nimur (talk) 01:41, 4 October 2012 (UTC)
- My reply was specifically addressing keit's rebuke of my 1st answer: It has no relavence to the CPU clock in modern PC's. I showed a couple of sources that showed it wasn't completely irrelevant. Microchip use an 8 MHz clock in nearly all of their reference designs and starter kits. I would not be surprised if a arbitrary value had been chosen to use on PC motherboards way back when, so that one particular crystal became the standard, even if the only benefit was from volume manufacturing. In the past, and in some specific cases, the crystal value wasn't inconsequential, and it's not that hard to imagine that the crystal choice these days is just a remnant of when it did matter, why change it when it does the job it's supposed to? But yes, this is essentially OT. Vespine (talk) 05:24, 4 October 2012 (UTC)
- Just for some additional info on the two main players in the x86 field. In Intel's case [1] [2] (from [3]) suggests the baseclock for the Sandy Bridge (microarchitecture) (and I think Ivy Bridge and likely all following processors for a while) is 100mhz which is the only clock needed by the CPU. This clock is provided by the Platform Controller Hub (i.e. an Intel chipset) [4]. (This of course greatly limits overclocking with locked multipliers.) I don't know what the internal crystal is, it doesn't of course (and probably isn't) 100 mhz.
- With the AMD Hammer and following architectures, it's more complicated and of course it's also been a long time so things have changed somewhat over time (PCI express didn't exist at launch, PCI & AGP were the standards for normal desktop computers). As per [5] [6], a variety of clocks need to be provided including a 14.318 mhz reference clock, although some of these are for the motherboard/north bridge instead of the CPU so will depend on that. Many AMD chipsets, possibly since the SB7xx line of chipsets [7] [8] [9] [10] have an internal clock generator but it wasn't generally used on the SB700 due to a bug and I think remains optional (the motherboard designer can choose to provide their own internal clock generator). I belive this includes the SB950 [11] although I couldn't find an AMD data sheet to confirm this. BTW to give an example of a more modern system compared to the older Hammer example, you can see the RD990/980/970 mentions the need for an external clock generator (as per earlier I believe this can be provided by the SB) to provide a few 100mhz differential pair clocks for the PCI-express and HyperTransport links (and a 100mhz differential pair clock is also used by the CPU AFAIK, including the latest Trinity line) and also a 14.318mhz reference clock [12].
- You can also see an example here of a clock generator for an AMD GPU [13] which provides a 100mhz clock for the memory and 27mhz reference clock for the GPU itself (it uses a 27mhz crystal).
- Nil Einne (talk) 04:07, 5 October 2012 (UTC)
- My reply was specifically addressing keit's rebuke of my 1st answer: It has no relavence to the CPU clock in modern PC's. I showed a couple of sources that showed it wasn't completely irrelevant. Microchip use an 8 MHz clock in nearly all of their reference designs and starter kits. I would not be surprised if a arbitrary value had been chosen to use on PC motherboards way back when, so that one particular crystal became the standard, even if the only benefit was from volume manufacturing. In the past, and in some specific cases, the crystal value wasn't inconsequential, and it's not that hard to imagine that the crystal choice these days is just a remnant of when it did matter, why change it when it does the job it's supposed to? But yes, this is essentially OT. Vespine (talk) 05:24, 4 October 2012 (UTC)
- There are hundreds, perhaps thousands, of Intel and competitive main CPU models. Similarly, there are thousands of main logic board designs. I'm certain if we look wide enough, we'll find a modern CPU main logic board with a 14.318 MHz crystal on it, driving the CPU. I know I've seen 25 MHz clock drivers on a lot of Intel designs lately, but this is hardly a universal standard; and Intel is not the only manufacturer of computer processors. If we consider esoteric designs by non-mainstream vendors, or low-volume, special-purpose systems, the variety increases even more. Really, the exact specification of the clock frequency is a minor detail. Crystals, or other digital reference clocks, can be built with almost any specified frequency. The original question was asking what the circuit looks like: and the circuit "often" looks like a phase locked loop on the main silicon die, driven by a low-frequency crystal oscillator external to the chip. If anyone wants to be more specific than that, we've got to stop speaking in the abstract and start naming part-numbers and technology steps. Nimur (talk) 01:41, 4 October 2012 (UTC)
- Not that I don't believe you, but I still don't see any source to support what you are saying. I have a bit of experience building circuits with microcontrollers, I built a project using the Microchip PIC32 which typically uses an 8Mhz crystal to run at a clock speed of 80MHz, (having a quick look at the datasheet, you can run it from a 3 or 4MHz crystal). Ok, 80MHz is not 2500MHz, but 4 to 80 is still a much higher ration then 14 to 28, so I don't really see why a 14.318 couldn't be multiplied up further. Vespine (talk) 00:11, 4 October 2012 (UTC)
- Here is a better article in which Figure A pretty clearly shows a 14.318 MHz crystal. Vespine (talk) 22:56, 3 October 2012 (UTC)
- keit, do you have any source for: It has no relavence to the CPU clock in modern PC's. ? This source (I agree it's far from academic) suggests that the 14.318 MHz crystal has been used for cpu clock reference since the dawn of PCs. I'm not saying it's right, I just haven't seen any evidence that its wrong. Also, just to clarify, I did not dispute anything in Nimur's reply. Vespine (talk) 22:45, 3 October 2012 (UTC)
Audio waveform graphs
editWhat is the official name for these sort of graphs? Is there a Wikipedia article about them?
What do the numbers on the Y axis correspond to? I gather they refer to amplitude, but what sort of unit are the values in? I've seen graphs where the values go from: 1 to 0 to -1 (like the one above); 30000 to 0 to -30000[14]; and -1 to -infinity to -1 (some audio software). Why the heck are these numbers so random? Do they actually mean something? Kaldari (talk) 02:41, 3 October 2012 (UTC)
- These are line graphs of waveforms. I'm not aware of any "official" name for them; it looks like you took a screen shot of Audacity (software). The numbers can be just about anything; if they range from -1.0 to +1.0, they are normalized; if they range from about -30,000 to about +30,000, the axis is probably directly displaying the value of the signed 16-bit PCM sample data. (Even if the audio-file originally started as an encoded file, like an MP3, its decoded signal may be represented by PCM data internally by the software). Other times, axes will be labeled logarithmically; or in normalized decibel levels. (Logarithmic graphs often represent a "zero" signal-level as "negative infinity", which is a "correct" mathematical representation for the value of log(0); though there are various other conventions used for signal-processing, such as a logarithm of a moving average). As with any graph, if the axis isn't labeled with units, the data format is ambiguous, but we can draw reasonable conclusions based on common practice. Nimur (talk) 02:55, 3 October 2012 (UTC)
- Thanks for the explanation. A follow-up question: If it is a normalized logarithmic graph, what would be the "correct" values for the top and bottom of the chart? Would they both be -1, both be 1, or would one be 1 and one be -1? And if it's not too much trouble: Why? Kaldari (talk) 04:13, 3 October 2012 (UTC)
- Just to clarify, the normalized (-1, +1) range is probably a linear plot of amplitude, not a logarithmic plot. There are lots of different, valid ways to represent a logarithmic plot, and a normalized log plot means that the signal's maximum amplitude has been defined at 0 dB, and the minimum amplitude could be anything, depending on the signal, including -infinity for a signal that goes to zero amplitude. This takes advantage of the convenient properties of logarithms: scaling the entire signal by a constant amplification just changes the markings on the y-axis, without changing the log plot at all. So, I'd expect the axis labels on a normalized log plot to be (-infinity, 0). Nimur (talk) 14:38, 3 October 2012 (UTC)
- Thanks for the explanation. A follow-up question: If it is a normalized logarithmic graph, what would be the "correct" values for the top and bottom of the chart? Would they both be -1, both be 1, or would one be 1 and one be -1? And if it's not too much trouble: Why? Kaldari (talk) 04:13, 3 October 2012 (UTC)
It's called a time history. The y axis may be in volts, (-5 to +5) typically, Pa (-1 to +1 perhaps), % full scale (-100 to +100), or signed integer (-32000 to 32000) or almost anyhthing else. You can't represent negatve numbers on a logarithmic plot, easily. This may disagree with the previous answers, oh well. Greglocock (talk) 04:36, 4 October 2012 (UTC)
- Mp3 sample rates are 32,000hz 44,000 and 48,000 ish. Maybe it is from an mp3 and the 30,000 represents the hertz. Just a guess sorry. Check out spectograms. ~ R.T.G 10:24, 4 October 2012 (UTC)
- No, not on those graphs. Greglocock (talk) 00:59, 5 October 2012 (UTC)
Selective dissolution
editWhat solutions will dissolve calcite (calcium carbonate), but not sphalerite (zinc sulfide), pyrite (iron sulfide) or galena (lead sulfide)? 203.27.72.5 (talk) 04:17, 3 October 2012 (UTC)
- Water? --Jayron32 04:19, 3 October 2012 (UTC)
- According to the CRC handbook, those compounds all have solubilities in water which are comparable to that of CaCO3 (0.013g/L); 0.00086g/L for Pbs, 0.0069 g/L for ZnS and 0.0049-0.0062g/L for the various forms of iron sulfide. 203.27.72.5 (talk) 04:45, 3 October 2012 (UTC)
- Acidified water? Calcium Carbonate should fizz and dissolve in a moderately acidic solution. None of the rest will. --Jayron32 04:47, 3 October 2012 (UTC)
- Better do weak acid (vinegar should be sufficient) - I've found conflicting reports, but it seems that pyrite anyway might dissolve in strongly acidic solutions. Buddy431 (talk) 05:03, 3 October 2012 (UTC)
- All of those sulfide minerals react to form H2S in acidic conditions, including acetic acid (vinegar). 203.27.72.5 (talk) 05:12, 3 October 2012 (UTC)
- I don't think so, at least not quickly [15]. Carbonate minerals will dissolve very quickly in even weakly acidic solutions. Sulfides, if they do at all, will be much slower to dissolve in weak acids. Buddy431 (talk) 05:28, 3 October 2012 (UTC)
- The article you cited calls pyrite a "metal" and conflates high pH with high acidity. I've tried it. Adding vinegar causes an instant odour of hydrogen sulfide. 203.27.72.5 (talk) 05:34, 3 October 2012 (UTC)
- It should be noted that the human nose's ability to detect even the smallest traces of H2S is well documented; a sample of calcium carbonate would long have dissolved to nothingness before a noticeable change (other than the smell) occurred with any of the sulfides. So one could certainly distinguish between them on that regard. Of course, they're all readily distinguishable on appearance only. I've never met someone who couldn't tell calcite from galena from pyrite just by looking at them. --Jayron32 06:23, 3 October 2012 (UTC)
- The idea is actually to remove calcite from several pieces of composite sulfide minerals, not as a test to distinguish them. Anyways, I've found boiling NaEDTA solution works well and doesn't dissolve the Fe, Zn or Pb at all, as confirmed by elemental analysis of the liquor. 203.27.72.5 (talk) 06:33, 3 October 2012 (UTC)
- It should be noted that the human nose's ability to detect even the smallest traces of H2S is well documented; a sample of calcium carbonate would long have dissolved to nothingness before a noticeable change (other than the smell) occurred with any of the sulfides. So one could certainly distinguish between them on that regard. Of course, they're all readily distinguishable on appearance only. I've never met someone who couldn't tell calcite from galena from pyrite just by looking at them. --Jayron32 06:23, 3 October 2012 (UTC)
- The article you cited calls pyrite a "metal" and conflates high pH with high acidity. I've tried it. Adding vinegar causes an instant odour of hydrogen sulfide. 203.27.72.5 (talk) 05:34, 3 October 2012 (UTC)
- I don't think so, at least not quickly [15]. Carbonate minerals will dissolve very quickly in even weakly acidic solutions. Sulfides, if they do at all, will be much slower to dissolve in weak acids. Buddy431 (talk) 05:28, 3 October 2012 (UTC)
- All of those sulfide minerals react to form H2S in acidic conditions, including acetic acid (vinegar). 203.27.72.5 (talk) 05:12, 3 October 2012 (UTC)
- Better do weak acid (vinegar should be sufficient) - I've found conflicting reports, but it seems that pyrite anyway might dissolve in strongly acidic solutions. Buddy431 (talk) 05:03, 3 October 2012 (UTC)
- Acidified water? Calcium Carbonate should fizz and dissolve in a moderately acidic solution. None of the rest will. --Jayron32 04:47, 3 October 2012 (UTC)
- According to the CRC handbook, those compounds all have solubilities in water which are comparable to that of CaCO3 (0.013g/L); 0.00086g/L for Pbs, 0.0069 g/L for ZnS and 0.0049-0.0062g/L for the various forms of iron sulfide. 203.27.72.5 (talk) 04:45, 3 October 2012 (UTC)
Car servicing
editWhy the car manufacturers suggest you to get your car serviced based on the time passed even though the distance travelled during this time is very low? Is it a business policy to sell more and more lubricants and other accessories or there is any engineering logic behind it?
- Some degradation of the vehicle can be a function of time - corrosion of parts, slow leaks from hydraulic systems, and the settling and congealing of lubricants and other fluids. A periodic check also allows the garage to check the vehicle's VIN against outstanding recalls and safety notices and perform any checks, maintenance, and repairs that those suggest. -- Finlay McWalterჷTalk 10:36, 3 October 2012 (UTC)
- Also the mileage isn't always a good indication that the car hasn't been driven; for some users a car may only be driven a few miles each day, which results in very low mileage but a relatively high number of starts and a higher proportion of cold operation. -- Finlay McWalterჷTalk 10:45, 3 October 2012 (UTC)
- Oils and greases degrade by oxidation regardless of how much the vehicle is used. Roger (talk) 11:34, 3 October 2012 (UTC)
- And of course, as is often pointed out, it's the lower temperature part of driving that degrades the oil the most; unburned fuel as well as water, carbonic acid, sulfuric acid, etc. as combustion products leak past the rings and end up in the oil; sustained higher temp operation eventually boils them out, but low mileage over a longer time often means a lot of short-time, low temp operation and little high temp operation.Gzuckier (talk) 16:51, 3 October 2012 (UTC)
Fishing or harvest algae from a submarine?
editIs there any technical or economical hindrance for fishing or harvesting algae from a submarine while submerged (or possible above surface) ..? why.. because on board supplies are limited to 3 months. Electron9 (talk) 14:46, 3 October 2012 (UTC)
- Assuming you're talking a military sub, then sure. Opening holes in a submerged sub is a technical (though not insurmountable, as is the case for most of this) hindrance. Adding a bunch of drag, and potentially noise, to a military sub is a massive operational hindrance. Turning algae into food sailors want to eat is a technical hindrance. Doing any of this stuff surfaced is likewise a massive operational hindrance. Paying to do all this stuff when resupplying every few months is a perfectly reasonable (and for morale purposes, functionally necessary) activity is an economical hindrance. — Lomn 15:25, 3 October 2012 (UTC)
- Now, all that said, I wouldn't be surprised to learn that World War-era submarines fished for some food, but that's because of the confluence of submarines having long range (thus more likely to try to get fresh meat) but conventionally running on the surface (thus in a good position to trail a few lines regularly). Of course, subs of that era weren't looking at food as their primary endurance constraint. — Lomn 15:38, 3 October 2012 (UTC)
- In the U.S. Navy the submarine service makes a point of having the best food in the fleet by way of compensation for the isolation. I don't think algae-derived food would be well-received. In any case, few sailors will want their tours extended beyond 90 days, so food isn't a limiting factor. Dehydrated food could be supplied that would keep people fed for longer than that, so nutrition (as opposed to food) isn't the limiting factor. If one wants greater use out of the submarine, a rotating crew deployment can be implemented: ballistic missile submarines, for example, have alternating crews (the Blue/Gold crew system) that maximizes the sub's deployed time Acroterion (talk) 15:34, 3 October 2012 (UTC)
- on an annoyingly theoretical level, if you can supply a whale with food from fish or plankton while at sea, it should be possible to supply a submarine.Gzuckier (talk) 16:55, 3 October 2012 (UTC)
- This page discusses food on a WWII U-boat; The food onboard the U-boats. I seem to recall that WWI U-boat crews used to hang a fishing line over the side when they had an extended period on the surface, but I can't find a reference for it now. I can't imagine many sailors wanting to eat seaweed though. Alansplodge (talk) 23:47, 3 October 2012 (UTC)
- If you really wanted to support fishing from submarines, I suppose you could design them with "scoops" in front which filter out solid objects (like fish), from the water, like a baleen whale. This would be better than trailing fishing nets or lines which could get snagged. StuRat (talk) 00:01, 4 October 2012 (UTC)
- I've just found How Do Submariners Eat? They Catch their Fish from the Bottom of the Sea. Sadly there's no date for this and Google can't find it anywhere else on the web. The illustration looks 1920s or 1930s to me. Alansplodge (talk) 00:03, 4 October 2012 (UTC)
- What a cool illustration! I wonder if that method was regularly (or ever) employed ~WWII era. Also, that webpage cites popular mechanics, 1920 for its "copy/image."SemanticMantis (talk) 03:38, 4 October 2012 (UTC)
- I don't know why I didn't look before, but the United States H class submarine USS H-5 (SS-148) mentioned in the article, was only in commission between Sep 1918 and Oct 1922. It's interesting that the magazine article refers to a US submarine as "a U-boat"! Alansplodge (talk) 21:18, 4 October 2012 (UTC)
- My late father in law was aboard the USS Flounder (SS-251) for her third, fourth and fifth war patrols in the southwest Pacific; as the article notes, those boats could only stay out about 30 days before they had to re-provision and refuel. He said they started a patrol with food in every conceivable place; unfortunately I never asked him about fishing, but given the areas they were patrolling I doubt they had more than a minimum of people topside at any time when surfaced so they could dive quickly if spotted. Acroterion (talk) 03:27, 4 October 2012 (UTC)
- My living father-in-law was a supply officer on Ohio-class submarines and I'll confirm, from his stories, the above. He said that at the start of any sojourn people felt about a foot shorter than at the end, because the walkways were lined with food. You were literally walking on your dinner. It was crammed into every open space. I don't believe that fishing was considered an option. --Jayron32 05:11, 4 October 2012 (UTC)
- Note one concern is that you wouldn't want to clean the fish inside a sealed sub, as that would really stink the place up badly. StuRat (talk) 04:43, 4 October 2012 (UTC)
- Depending on how long they've been submerged, it might actually be an improvement. ←Baseball Bugs What's up, Doc? carrots→ 11:48, 4 October 2012 (UTC)
- <smart_ass_warning>I'm guessing the fish have been submerged all their lives. </smart_ass_warning> StuRat (talk) 21:37, 6 October 2012 (UTC)
try adjusting the phase
editSee http://en.wiki.x.io/wiki/Time_constant#Relation_of_time_constant_to_bandwidth - an equation is derived which essentially describes the amplitude V as a function the time constant and the forced frequency omega when the forcing term is a sinusoid. Is there a comparable relationship between the phase and (tau,omega) ? Widener (talk) 18:11, 3 October 2012 (UTC)
- A full and easy-to-understand algebraic derivation is provided in the section on forced oscillators in Mechatronics, (Alciatore & Histand), in the chapter on System Response for complex systems. Nimur (talk) 20:46, 3 October 2012 (UTC)
- Can you reproduce it here? I don't have a copy of that book. Widener (talk) 22:32, 3 October 2012 (UTC)
- Have you looked at the links from that page, in particular the freely-available PDFs of MathCAD examples? Not sure, but they might have what you need. -- Scray (talk) 23:10, 3 October 2012 (UTC)
- Thanks, I managed to find the result in "first order system frequency response" ; a derivation would be nice though. Widener (talk) 02:53, 4 October 2012 (UTC)
- Starting from the general solution at Time_constant#Relation_of_time_constant_to_bandwidth: for the solution reduces to . The phase difference is the argument of , which is minus the argument of , which is . -- BenRG (talk) 01:31, 5 October 2012 (UTC)
- Thanks, I managed to find the result in "first order system frequency response" ; a derivation would be nice though. Widener (talk) 02:53, 4 October 2012 (UTC)
- Chapter 4, System Response, equation cheat-sheet? Now that there's an internet, it seems that nobody wants to expend even the slightest effort investigating interesting topics anymore... this is really a tragic development, because it's never before been easier to find all the information you ever wanted. I recall a time, not so very long ago, that if one wanted to know things, one had to read and study extensively; and sometimes even travel great distances to get access to useful educational resources. Nimur (talk) 23:19, 3 October 2012 (UTC)
- Have you looked at the links from that page, in particular the freely-available PDFs of MathCAD examples? Not sure, but they might have what you need. -- Scray (talk) 23:10, 3 October 2012 (UTC)
- Can you reproduce it here? I don't have a copy of that book. Widener (talk) 22:32, 3 October 2012 (UTC)