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Everything posted by Enthalpy

  1. Now with a diagram : The LT1028 produces beyond 1kHz typically 0.85nV/sqrt(Hz), and as seen previously, its 1pA/sqrt(Hz) convert to 1nV/sqrt(Hz) in the synthesized 990ohm, and the 100kohm add 0.4nV/sqrt(Hz) only. 9.9ohm in the feedback add 0.4nV/sqrt(Hz). This sums to 1.43nV/sqrt(Hz), as much as a 990ohm resistor at 39K. Obtaining all the gain from the first stage preserves the loop's phase margin and makes the second stage's noise negligible. Marc Schaefer, aka Enthalpy
  2. I checked on eBay the price of the HP-48G, and ¡caramba! All newer calculators must be bad since users still want this oldie. So I checked the price of my even older defunct HP-15C and it's even worse, ouch. One company swissmicros.com grasped that and makes an Helvète-Packard copy called DM-15L which sells new and improved for cheaper than old used HP-15C, but it costs something. Free HP-15C emulators run on a PC. Good alternative, especially if you're used to the physical one. HP did offer the emulators for free, a cache is there calculatrices-hp.com over web.archive.org The HP-50G computes complex trigonometric and hyperbolic functions. All hide in submenus even deeper than the HP-48G, so I can't recommend it. The HP-15C does the job. But it has no usable keyboard shortcuts, and you have to click first on the f and g prefixes, so I wouldn't recommend it. But the installer brings the handbooks! Do not take this other HP-15C emulator, it ignores complex numbers: hp15c.com Torsten Manz made the best I've seen, downloaded from there heise.de Its blue and yellow tags around the keys are clickable, it reacts to the PC keyboard, and it's multilanguage. Tried briefly, it does complex acos and acosh as needed for Chebyshev type I and II filters. Nice! Ah, to exit the complex mode, just click g > CF > 8 to clear the flag 8. You guessed.
  3. Here's a type II (or inverse) Chebyshev that fulfils the same 0.1dB in the passband and 40dB in the stopband starting at a frequency 1.5* higher. FilterCad 3.0 doesn't design type II Chebyshev automatically (and its Min Q Elliptic falls short of the wanted frequency response). NuHertz does but isn't free any more beyond 3 poles. The design takes longer. The pocket calculator HP48G solves the complex ch() and ach() easily, as it does with cos() and acos() for type I Chebychev, but mine just died. Mathcad 2000 is rumoured to factor real polynoms as first and second order terms, to be reinterpreted here as (w2+ww0/Q+w02) but I didn't find how. But Mathcad did give the complex roots of T8(alpha)=+-j99.995. Injecting the notches and poles in FilterCad gives the adequate frequency response. The step response is disappointing. Last time I compared, the type II Chebyshev was clearly quieter than the elliptic. Possibly I had a stronger attenuation and more room between the pass- and stopbands. Here some poles of the type II Chebyshev are in the stopband, so obviously it works outside its comfort zone. Marc Schaefer, aka Enthalpy
  4. And? The chromosphere is thick enough to be opaque, so we see only the chromosphere, which radiates like a black body at its temperature. Nothing to change in my previous post. The line absorption spectrum needs atoms cooler than the blackbody radiation and between the emission depth and us. Hence "temperature varying with the depth".
  5. Hybridisation is wrong in QM. I suggest you to check present-day theory, which is molecular orbitals. For instance in methane, there is no sp3 orbital between the carbon and one hydrogen. One molecular orbital, resulting from 2s, extends with the same sign to all four hydrogen atoms, while each of the three 2p orbitals reaches two hydrogens in one lobe and the other two in the other lobe. Spectroscopic measurements confirm two different energies in the molecular orbitals, numerically consistent one from 2s and the other from the three 2p. Hybridisation, with four sp3 hybrids, fails.
  6. The narrower wavefunction as exiting the slit allows the electron to be detected in directions that were inaccessible to it when the wavefunction was wider hence more directional before the slit.
  7. There are several inaccuracies in the first post. Among others: eikx is for a propagating wave, not a standing one. The amplitude psi does not decay with distance r as 1/r after exiting a slit. This would be for a point or spherical source. In the zone useful for interference, the frontwave area increases like a cylindrical area does, and so does psi2 decrease, because it varies like a power density, since a photons is thought like an energy quantum. Beware with the idea of local detection ! This is badly difficult to understand in QM, most book convey a wrong interpretation. The simultaneous histories of a photon don't vanish upon detection. The double slit experiment is misleading in this aspect. You could check different experiments, for instance interferences of atoms that both have or have not absorbed a first photon and then can absorb a second one: the observed atom interferences tell that after the first light ray, the atom is in both states, having absorbed a photon and not. Consequently, said photon too is on both states, having been absorbed and not. More generally, starting QM with the double slit is a very bad idea. Starting with the wave function of pentacene observed by atomic force microscopy would be better. It would show that the wave function is observed, and that the same pair of electrons is observed over the whole molecule size without any destruction. Causality and propagation delay: no huge difficulty. At least two answers cope with it: - External objects, including humans, have no influence. Then the simultaneity does not transport information, because no information can be encoded. Faster than light is then possible. - There has been no collapse at all of the wavefunction. This is the preferred explanation now, especially in light of newer experiments like the eraser. All possible events did happen, so no information transfer is necessary. What looks like a collapse is only that the observer, if he is in the state having made the observation A, does not feel its states having made the observations B because there are so many and uncorrelated that they sum up to zero. Negative probabilities aren't needed. As Swansont said, |psi|2 is computed after summing all necessary psi. This is what lets waves interfere and tells us that photons or electrons are waves. Beware with the destruction of interferences by knowing "which slit". Meanwhile, "weak measurements" have been experimented, and "knowing" isn't binary. That two apertures half as wide work as one of full width is Huygen's principle. And, yes, diffraction exists with single apertures too, for instance optical lenses. The computation method, summing over all possible positions, is the standard one. sinc just results from summing a uniform illumination over a window width. You can just forget the dimension along the slit for that and compute 1D. Write the phase shift along the width of the slit due to the considered propagation direction, you get the sinc. "Zero momentum information" from a point source is wrong. If the particle has a spin, for instance the photon has, then the directions perpendicular to the (emitted or selectively detected) straight spin are more strongly illuminated (stronger psi2 blah blah blah) while the direction aligned with the spin aren't at all, and in between the pattern is a cosine. I'll stop here for lack of time, apologies, even before having gotten a general sense of the thesis. Strong encouragements to go on thinking by yourself, because most explanations about QM are badly wrong. Most books just reproduce the misunderstandings of the very early times of QM, before decisive experiments were done. Only personal thinking can debug that, and is consumes horribly much time, alas. My suggestion is to consider soon other experiments than the double slit, among them, images of the pentacene by atomic force microscope (search words).
  8. To bring heavy equipment to an asteroid, including in the main belt: https://www.scienceforums.net/topic/76627-solar-thermal-rocket/?do=findComment&comment=1014780 To explore the main belt and check if anything is worthy there: https://www.scienceforums.net/topic/76627-solar-thermal-rocket/?do=findComment&comment=1016237 Braking in Earth's atmosphere is for free. From low-Earth-orbit, deorbiting costs less than 100m/s. From the asteroid belt it's much more. What we might find there, I have no idea. The general hope is that precious metals have not sunken there as they did on Earth and would be more accessible. This would need to separate them from worthless Ni and Fe on the asteroid, and I have no idea how to do that. It needs very heavy equipment to extract very little precious metal. Human activity could absorb much more gold than we produce, but not at the present price. Best material for electric contacts, for corrosion protection, for cleanliness, and so on and so forth. It could replace copper if abundant enough.
  9. It's a matter of opacity too (and of reflectance). Stars are opaque because they're big. If they can absorb any incoming wavelength, they can radiate it perfectly too, hence like a blackbody does. The temperature varying with the depth makes this more complicated. More reasons to emit or absorb other wavelengths than the atom's discrete spectrum: In a solid, electrons are shared among many atoms. They get many new energy levels. In a metal, the levels are extremely close to an other. A transition line is fine only if the emission is slow enough. Transitions have their own duration, which is usually shortened by collisions, in a gas, plasma, liquid.
  10. Force from a pole, and a potential, would be the case from an electric field, not a magnetic one. Magnetic fields do act on charges, if there is movement.
  11. Hi Souffler, a photon can and does take electrons from the depth of the valence band too, and send them deep in the conduction band. That's why materials absorb many different wavelength, not just light with energy equalling the bandgap. In silicon (indirect gap) this process is much more efficient: you can check that photons with just the bandgap energy are little absorbed. Other bands can contribute the photon absorption too, or secondary extrema in the bands. Recombination occurs most often among the band edges because this is where there are candidates, at least near thermal equilibrium. But under strong injection, hotter electrons and holes (=empty energy levels) can be available for recombination. This happens at laser diodes, whose wavelength is imperfectly defined. The spin and momentum conservation impose other restriction that may need the help of a phonon, making the process less probable. Impurities are isolated in the crystal if the doping isn't too heavy, and then the doping level is nearly a single energy. Excited states can exist, but they differ by few meV, often neglected. These impurity levels do lose and get electrons to and from both bands, and not only at the edges. Choosing the dopant hence its energy level defines the colour of GaP leds. In both bands, the electrons are largely delocalized. If they are states of perfectly defined energy or momentum, they are delocalized to the whole crystal or doping zone. So overlapping is trivial. In dopant levels, the electrons are localized to the atom, so it can jump to a band, but jumping to an other dopant is difficult.
  12. This can be fluorescence or diffusion for instance. It can work as well when the pumping photon has the energy of the emitted one. Whether one wants to call it the "same" photon, I don't care. If the incoming photon has a decently known direction and the diffused one a direction different enough, we know diffusion has take place. If only one atom is present, for instance one dopant in a crystal (this is done for quantum cryptography) then we know the diffused photon comes from that atom. At the beginning, the photon is very well localized, to the size of an atom, which is much smaller than a photon wavelength. How fast the wavefunction spread results from its equations. An atom is very little directional for being small, so it emits light very broadly. As for time, at least a few quarterwaves away from the small source, the speed of light in the medium applies. In local field, I don't know - looks like EM waves are faster in local field.
  13. If the electron has passed the slit, its wavefunction at the exit is as narrow as the slit.
  14. The very idea of movement is more diverse in QM. When the electron is an orbital, it's by definition a "stationary" function, whose amplitude doesn't depend on time. You can say that the electron is "immobile" if you wish. That's why it doesn't radiate - QM answered this problem that classical physics had. The "immobile" electron still keeps a kinetic energy, though, because the wave has a limited size, and it can have an orbital momentum and orbital magnetic moment if the phase of the wavefunction evolves with the position around the nucleus. In that sense, QM gives the electron only some attributes of the movement. We could deduce some sort of mean electron speed for a stationary electron, for instance from the orbital momentum, some mean radius, and a mass. Or from the kinetic energy and the rest mass. Usually it's not done, and it would depend on the definition. As opposed, the energy and the orbital momentum are well-defined in an orbital. Linear combination are solutions of the electron's equation too. If you combine several orbitals of same energy, like 2px and 2py, you get a stationary solution which is an orbital too. If you take orbitals of different energy like 2p and 1s, the linear combination is no more stationary. It's still a wavefunction but not an orbital. The combination has a (or several) bulge that moves over time, at a frequency equal (to a factor) to the difference of energies. Now you have a movement, in the classical sense too, and the electron emits or absorbs a photon. This movement is as fast as the frequency of light, for instance 5*1014Hz.
  15. In case the electron had a rather well defined direction before the slit, it implies that its lateral position wasn't so precise. A slit narrower than the width of the previous electron's wavefunction (the lateral position) makes the wave narrower if the electron passes through, and then the electron's direction is less defined, so the electron can be detected in a position that was not attainable to it before it passed the slit. This is described in more details for light and is called "diffraction", so you can read for instance the Wiki articles. Electrons do the same for being waves too.
  16. Please remember that a patent is nothing more than a proof that you might use before judges. It doesn't prevent anyone to infringe your invention. In that case, a patent only serves if you're willing to go to court. This can be lengthy, expensive, and random. If an infringing company is in China, Brazil or the US you must go to a court there, and need a patent in said country. Applying for a patent is already expensive, then you must pay very year to keep the patent. This holds for every country, and you must provide the text in all the languages (the EU simplifies that a bit). So do it only if you're wealthy enough. Most patents bring money only to the governments and patent attorneys.
  17. The way I understand it, the bent wire is immobile versus B while the skewed one, of identical nature, moves and is in contact with the bent one. d(flux)/dt gives an induced voltage (with a sign) while the summed wire length gives a resistance. Neglecting the self-inductance (="the field produced by the wires themselves") you get a current. Note that 8T is unusually strong. It take a superconductor or a small duration. 32ohm/m is much even for a resistor wire.
  18. And I was wrong. Equalizing the group delay time works, at least in a first approximation. My mistale was that I had never observed frequencies low enough. Equalizing only 2-3 octaves below the cutoff doesn't suffice and made the time response unbalanced. This is again the 5th order elliptic low-pass, with a 5-pole phase corrector, tuned if not perfectly, and its impulse and step responses: Tuned phase correction cuts in half the ringing amplitude but adds as much before the main transition, in one pulse per corrector pole. This improves much the visual impression on a real filtered signal. A quieter filter keeps its advantage after phase correction. The phase corrector adds group delay below the peak around the cutoff frequency. Above is useless. If keeping the peak in the group delay at cutoff, the filter still delays the signal by as much, but the time response isn't quite pleasant. A nicer time response results from more corrector poles, which increase the group delay up to the cutoff included, and increases the signal delay. On a recorded signal, the delay can be compensated, but then the filtered signal begins to wobble before the raw one. As can be seen above, best symmetric ringing needs a somewhat uneven group delay, more so with fewer corrector poles, and needs hand tuning, which isn't finished here. A continuous time filter or IIR can't be really symmetric, since its response is finite on the left. Marc Schaefer, aka Enthalpy
  19. To improve the step response, a phase corrector is the answer. It appends a few second-order and possibly first-order "all-pass" cells, active or passive, which let the phase rotate around some frequency but leave the amplitude uniformly untouched. But how to tune these all-pass cells ? The universal answer, in all books and courses, is "make the propagation group constant in the passband", or equivalently, "make the phase linear". This is inspired by the pure time lag, whose propagation time is constant and phase linear. At digital FIR filters it works. Either I've understood zilch, or all these authors just repeat something that sounds good but they have never done, because each and every time I tried that way, it failed miserably. As a hint, I have never-ever seen an example of step response by those who recommend a constant propagation group from the phase corrector. Not a single time. So here's a example of failure. I first repeat the frequency response of the 5th order elliptic lowpass, this time with the group delay displayed, where you see the typical big bump around the corner frequency. Then I append three second-order allpass cells and optimize for uniform group delay in the passband. And then the step response is megayuk, much worse than the bare filter. More cells above the corner frequency don't improve. I plan to show a successful phase corrector on that elliptic filter. Marc Schaefer, aka Enthalpy
  20. And this is an elliptic (or Cauer) filter that fulfils the same requirements. With five poles and two notches, it isn't simpler to build than the Chebyshev, but it reacts sooner and steeper than both the Butterworth and Chebyshev, and it rings for shorter. Maybe I put an inverse (or type II) Chebyshev here some time. It rings clearly less and for shorter than the elliptic, very similar to an hourglass filter. But as none is native to FilterCad, it takes me longer. Marc Schaefer, aka Enthalpy
  21. Here comes a Chebyshev with the same passband and stopband requirements. It rings for as long, but it reacts sooner and steeper than the Butterworth, and is half as complex. Marc Schaefer, aka Enthalpy
  22. I use the excellent FilterCad 3.0 software that Linear Technologies made nicely general filtercad.software.informer.com The application is said to run on recent Windows after helping the installer a bit. The first case is a Butterworth. It has 16 poles because the competitors need less. While -3dB is meaningful for audio applications, metrology and present datacomms demand more. Here 0.1dB attenuation or ripple in the passband, which equals 2% power or 1% voltage, is more realistic. This is not the usual "corner frequency" of a Butterworth given at -3dB. The big Butterworth gives unimpressive 40dB attenuation at 1.5* the passband edge, which shall be the definition of the stopband and its attenuation for the other transfer functions. For its built-in transfer functions, FilterCad determines automatically the poles and zeros and draws the frequency and step responses. Marc Schaefer, aka Enthalpy
  23. If the generator shall provide one positive and one negative smooth pulses per turn, it's called a two-poles alternator. Then the good design lets a magnet be the rotor, and the coil surrounds it at the stator. Called Gramme design. Check the drawing there https://en.wikipedia.org/wiki/Alternator https://en.wikipedia.org/wiki/File:Alternator_1.svg Iron at the stator is useful, among others to shield the world from the dangerous magnetic field, but with rare-earth magnets the iron is not mandatory for a decent induction.
  24. Same query as Studiot. Looks quite feasible, but needs more information. Desired stability, what voltage, possibly temperature range, and so on.
  25. Hello everybody! Frequency filters lets signals within the passband through and attenuate everything in the stopband, for instance noise or an adjacent communication channel. Much theory exists for them, works nicely. The stopband attenuation can be big, and the "selectivity", the ratio of the nearest frequencies of the stopband to the passband surprisingly small. But as the frequency response gets sharper, the time response gets slower and bumpier. No wonder, since a Fourier transform links them, like the diffraction rings of a lens, or the noise created by jpeg compression, or Delta(t) and Delta(E) for a particle. I'll consider only lowpass filters here. They are the most common, and only their time response makes much sense for the eye. Simple theorems only restrict the quickness (vague) of the filter for a given selectivity, not how much it rings. But as a typical filter rings at the extreme frequency of its passband, both seem related. The time response of a filter matters in some uses, for instance if you observe shocks with an accelerometer. Then the frequency response can't be too sharp. But some kinds of filters, or "transfer functions" out(F)/in(F), offer a better compromise than others. All the books and courses I know compare the step response of varied transfer functions at identical number of poles - identical complexity more or less. Then, the Butterworth is quietest, the Chebychev is in between, and the elliptic is bumpiest. The Bessel shows no overshot but filters too badly for most uses. (There are a dozen well-known named transfer functions). But the aim of a filter is not to build a cetain number of poles! It must fit some passband with a maximum attenuation there and some stopband with a minimum attenuation. Then an elliptic filter needs fewer poles than a Chebychev that needs fewer than a Butterworth. When comparing at identical constraint on the frequency response, hence with different numbers of poles, I claim that the step response of a Butterworth is bumpier than a Chebychev and an elliptic is quieter. Examples shall follow. Marc Schaefer, aka Enthalpy
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