They are necessary for calculations of alternating current, among many of their uses.
This is a nice well written piece. The point being it helps visualize better.
The Case of the Imaginary Numbers [Draft!]
I am not publishing or distributing this. Just for curiosity. Very well written and that's all.
The Case of the Imaginary Numbers [Draft!]
I am not publishing or distributing this. Just for curiosity. Very well written and that's all.
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another simple explanation of use in rotations A Visual, Intuitive Guide to Imaginary Numbers | BetterExplained
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Why this so is because the measurements, what's being monitored, correlates very poorly with what human hearing registers as being important, for listening satisfaction. So long as the 'wrong' things are being tested for, the "struggle" will continue.
Maths is totally self-contained, perfectly consistent within its own universe; audio is bipolar, on one side you have audio engineers with expensive test gear, and on the other people who just want to listen to music with their ears - there's a big chasm inbetween ...
I've heard there's some math in music, from Pythagoras to...
ChordGeometries Demo: Chopin through four-dimensional space on Vimeo
A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice (Oxford Studies in Music Theory): Dmitri Tymoczko: 9780195336672: Amazon.com: Books
ChordGeometries Demo: Chopin through four-dimensional space on Vimeo
A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice (Oxford Studies in Music Theory): Dmitri Tymoczko: 9780195336672: Amazon.com: Books
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OPA627 and LME49990 would not be possible without very expensive test equipment and they correlate extremely well with human listening satisfaction.
I'm looking for the "sufficient" condition being satisfied, as in Necessity and sufficiency - Wikipedia, the free encyclopedia. That those opamps most likely will help the sound to be more satisfactory doesn't guarantee the result: a poorly measuring system can sound brilliant; a brilliantly measuring system can sound poor - that's the dilemma ...
I think you are on the right track, Kastor. It really takes the 'best' op amp and a quality buffer to compete with discrete. Not cheap, not as compact, but better than a typical op amp alone, for sure. I have been recently measuring what happens to typical op amps when loaded with a relatively low resistance, due to engineering tradeoffs, typically. It happens more often than you would think in quality audio equipment.
Appreciate it Mister Curl!
I may have to slightly revise my view about megahertz performance in op-amp's as well after seeing this paper today by Fiori and Crovetti
http://www.uemc.polito.it/papers/opampsusc_01.pdf
"operational amplifiers (opamps) are extremely susceptible to
I may have to slightly revise my view about megahertz performance in op-amp's as well after seeing this paper today by Fiori and Crovetti
http://www.uemc.polito.it/papers/opampsusc_01.pdf
"operational amplifiers (opamps) are extremely susceptible to
RF disturbances. They demodulate RFI added on nominal input signals
and so the nominal output signal is corrupted by in-band interference.
In particular, the presence of continuous-wave (CW) interference generates
an output offset voltage.
This opamp behavior was originally observed in aeronautic electronic
systems and subsequently studied performing immunity tests on
commercial opamps. In particular, measurements of the output offset
voltage induced by RFI conveyed on the input terminals of several feedback
opamps were performed varying interference frequency and amplitude
[4]. These experimental characterization is useful in the design
of EMI filters. More recently, this behavior has been studied by time
domain [5]–[7] and frequency domain (harmonic balance) [8] computer
simulations: several efforts have been expended on research in
order to derive both RFI-oriented numerical models of active devices
and opamp macromodels intended to reduce computer simulation time".
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Kastor extend that thought to any power amplifier also.
H C Lin who I suggest is the originator of practical op amps said they were declassified quickly as the military rejected them for the reason of RFi. If listening to valve amplifier that might have 40 dB distortion than many transistor designs the distortion if anything can be more with the op amps. That distortion I can best guess to be RFi induced. This is why I get a bit upset over fancy regulators when it is the output capacitor doing 90% of the work. Be it shunt or series this will be the major engineering input. Low output impedance also. Dejan if you read any of this try an inductor to your driver stages. Air-cored would be best as I have measured oscillations when ferrite. Not always so try both. After an LM317 ferrite was fine, a small 10 mH ferrite that was also 100 R due to thin wire used, that formed a nice less than $1 solution ( L R C ).
When a valve design sounds distorted it usually is low grade components and bad impedance matching. Some never learnt this as op amps will drive anything within reason. A Leak preamplifier comes with a short dreadful looking piece of TV coax cable. So the enthusiast replaces it with a nice bit of high grade cable. The result is disaster which is thought to be valve sound. The coax that was 30 cm long is about 20 pF. The new more useful 1.5 metre one 500 pF. If the output impedance is 50 k ohms into 1 M ohms the 500 pF will kill any HF and dynamics. You might say a good engineer would fit a cathode follower. Truth is the Leak sounds far better because they didn't. The Quad product of the same era has a cathode follower and is not as expressive ( slow, coloured and boring). the Leak only has 4 x EF 86 pentodes yet does far more than most modern preamps. It is a great alternative to FM Acoustics. This includes many EQ setting for ancient 78's. It is stereo. I has the delightful all in one RIAA using shunt input feedback ( Quad also) . Shunt input looks impossible and works very well. The PU is asked to do a lot of work which might be a good thing. Sounds great if Mullard 86's used rather than Soviet of the past. The difference is interesting. Mullard slightly pink in noise spectrum , Soviet very blue like a transistor. Pentodes I am told are mostly transistors in how they show themselves. Far more versatile. They also have the advantage of being a simple electron steam if such things exist. Crooks proved it to me as he moved a paddle in a vacuum with them . They were seen to be particles as they have mass.
I always say there is no such thing as fiction. There is good or bad fiction. Fiction is a reality check. Imaginary numbers are less of a fiction. The fact they work makes them real. I suspect in time we will see this? As I say i is a good proof of 4 th dimension. It's negative more so even than Alice in Wonderland view of a mirror image. It produces a positive outcome at the 4 th level with might explain the Universe. I find all maths conducted to the third level is solid, forth is useful but not easy. In my analysis posted yesterday in someones PDF sine-waves were looked at without specific reference to time. That seems impossible. He shows by a leap of thinking it is not. It is a remarkable think to see time as a musical component although that is the most obvious quality. Galileo used it as a clock in gravity experiments, a painting exists to show this. That is a ball falling vertically reaches the floor at the same time as one accelerated down a slope. Differences is the other ball travels a greater distance . S = ut + 1/2atxt. ut is the addition. Music was the more accurate clock of the day. We learn the hard way in digital that the nano seconds matters ( please keep RFi out ) . This questions many assumptions.
Someone said if a 2D animal lived in our world it might by advanced maths discover the 3D world. It would have no idea of what it would look like. All it knew is that bad things happen that were related to it. That would be us walking on it. Ironically there is reason to think 3D including time would be easy for it to imagine. And there's that word again, imaginary.
I often debunk conspiracy theories for a friend to post. The one that intrigued me most was the Philadelphia experiment. I debunked most of it except one thing. The experiment was to clock a ship . A useless exercise as radar would show it. There are many unsubstantiated claims, it seems likely people were hurt. One of the more interesting is that the A bomb ended speculation as to which of Einsteins insights were useful. Up to that point all were looked at . Why ? Because if the USA didn't Germany would. The weirdest speculation is the crew saw aliens. From this others speculated that aliens who might exist live co-axially in the same space as Earth. Quantum physics might allow that. The wildest speculation is that Einstein was more gifted than the alien scientists. They have better measuring equipment and we awoke them to our existence due to our A bomb tests. Now that's a plot for a bit of fiction. The most fascinating speculation I read is the aliens are only 800 years advanced on us. An easy mathematical proof I won't bother to share as it needs accepting too many fanciful ideas. This was a very long story but held some water ( like the sound of capacitors ). Star Trek was the best outlet for this.
The French have no present continuous tense. It makes some concepts of time impossible to think of. " Did you put the dustbin out " ? Answer. " I am doing it, is not possible in French". This is mindset. The nearest you can say is " I am in the process of doing it". You never hear it as it not in their way of thinking.
Autism has an interesting consequence when using a foreign language. It often forces the Autistic person to wake up the part of the brain they do not use. This changes many Autistic traits. What is left is put down to being a foreigner. It can be a liberation. I am a softer and more considerate person in French. I have to be frank and say most UK Autistic people seem less Autistic than many of my German friends. I suspect the reason is most of my German friends are engineers. However most German people I meet are more easily led into conversations about philosophy and how life is than the Brits. The language is constructed to do this or is a result of differentiating of peoples ( tribes) . The French I adore. At a tangent and often correct. It is said. There is the right way, the wrong way and then the French way. Maybe the French live with imaginary numbers more?
Music is is baby food. It needs no translation. Language is music with purpose. Mostly mind control of others . It might be the primitive idea of original sin. That suggests early humans sang more than spoke. Not unlike birds.
H C Lin who I suggest is the originator of practical op amps said they were declassified quickly as the military rejected them for the reason of RFi. If listening to valve amplifier that might have 40 dB distortion than many transistor designs the distortion if anything can be more with the op amps. That distortion I can best guess to be RFi induced. This is why I get a bit upset over fancy regulators when it is the output capacitor doing 90% of the work. Be it shunt or series this will be the major engineering input. Low output impedance also. Dejan if you read any of this try an inductor to your driver stages. Air-cored would be best as I have measured oscillations when ferrite. Not always so try both. After an LM317 ferrite was fine, a small 10 mH ferrite that was also 100 R due to thin wire used, that formed a nice less than $1 solution ( L R C ).
When a valve design sounds distorted it usually is low grade components and bad impedance matching. Some never learnt this as op amps will drive anything within reason. A Leak preamplifier comes with a short dreadful looking piece of TV coax cable. So the enthusiast replaces it with a nice bit of high grade cable. The result is disaster which is thought to be valve sound. The coax that was 30 cm long is about 20 pF. The new more useful 1.5 metre one 500 pF. If the output impedance is 50 k ohms into 1 M ohms the 500 pF will kill any HF and dynamics. You might say a good engineer would fit a cathode follower. Truth is the Leak sounds far better because they didn't. The Quad product of the same era has a cathode follower and is not as expressive ( slow, coloured and boring). the Leak only has 4 x EF 86 pentodes yet does far more than most modern preamps. It is a great alternative to FM Acoustics. This includes many EQ setting for ancient 78's. It is stereo. I has the delightful all in one RIAA using shunt input feedback ( Quad also) . Shunt input looks impossible and works very well. The PU is asked to do a lot of work which might be a good thing. Sounds great if Mullard 86's used rather than Soviet of the past. The difference is interesting. Mullard slightly pink in noise spectrum , Soviet very blue like a transistor. Pentodes I am told are mostly transistors in how they show themselves. Far more versatile. They also have the advantage of being a simple electron steam if such things exist. Crooks proved it to me as he moved a paddle in a vacuum with them . They were seen to be particles as they have mass.
I always say there is no such thing as fiction. There is good or bad fiction. Fiction is a reality check. Imaginary numbers are less of a fiction. The fact they work makes them real. I suspect in time we will see this? As I say i is a good proof of 4 th dimension. It's negative more so even than Alice in Wonderland view of a mirror image. It produces a positive outcome at the 4 th level with might explain the Universe. I find all maths conducted to the third level is solid, forth is useful but not easy. In my analysis posted yesterday in someones PDF sine-waves were looked at without specific reference to time. That seems impossible. He shows by a leap of thinking it is not. It is a remarkable think to see time as a musical component although that is the most obvious quality. Galileo used it as a clock in gravity experiments, a painting exists to show this. That is a ball falling vertically reaches the floor at the same time as one accelerated down a slope. Differences is the other ball travels a greater distance . S = ut + 1/2atxt. ut is the addition. Music was the more accurate clock of the day. We learn the hard way in digital that the nano seconds matters ( please keep RFi out ) . This questions many assumptions.
Someone said if a 2D animal lived in our world it might by advanced maths discover the 3D world. It would have no idea of what it would look like. All it knew is that bad things happen that were related to it. That would be us walking on it. Ironically there is reason to think 3D including time would be easy for it to imagine. And there's that word again, imaginary.
I often debunk conspiracy theories for a friend to post. The one that intrigued me most was the Philadelphia experiment. I debunked most of it except one thing. The experiment was to clock a ship . A useless exercise as radar would show it. There are many unsubstantiated claims, it seems likely people were hurt. One of the more interesting is that the A bomb ended speculation as to which of Einsteins insights were useful. Up to that point all were looked at . Why ? Because if the USA didn't Germany would. The weirdest speculation is the crew saw aliens. From this others speculated that aliens who might exist live co-axially in the same space as Earth. Quantum physics might allow that. The wildest speculation is that Einstein was more gifted than the alien scientists. They have better measuring equipment and we awoke them to our existence due to our A bomb tests. Now that's a plot for a bit of fiction. The most fascinating speculation I read is the aliens are only 800 years advanced on us. An easy mathematical proof I won't bother to share as it needs accepting too many fanciful ideas. This was a very long story but held some water ( like the sound of capacitors ). Star Trek was the best outlet for this.
The French have no present continuous tense. It makes some concepts of time impossible to think of. " Did you put the dustbin out " ? Answer. " I am doing it, is not possible in French". This is mindset. The nearest you can say is " I am in the process of doing it". You never hear it as it not in their way of thinking.
Autism has an interesting consequence when using a foreign language. It often forces the Autistic person to wake up the part of the brain they do not use. This changes many Autistic traits. What is left is put down to being a foreigner. It can be a liberation. I am a softer and more considerate person in French. I have to be frank and say most UK Autistic people seem less Autistic than many of my German friends. I suspect the reason is most of my German friends are engineers. However most German people I meet are more easily led into conversations about philosophy and how life is than the Brits. The language is constructed to do this or is a result of differentiating of peoples ( tribes) . The French I adore. At a tangent and often correct. It is said. There is the right way, the wrong way and then the French way. Maybe the French live with imaginary numbers more?
Music is is baby food. It needs no translation. Language is music with purpose. Mostly mind control of others . It might be the primitive idea of original sin. That suggests early humans sang more than spoke. Not unlike birds.
Really interesting how silly construction techniques correlate positively with appreciation (and price). But, they do have a shop, so that may explain something.
The Fiat 124 from personal experience was a wonder car, The Lada was not. The irony being that the Lada had genuine engineering advances over the Fiat although it made it slower. Even allowing for the chaos that was Italy the Soviet Union proves how well capitalism works ( Putin wants it back, Yikes that 4 riders and the lady of Babylon isn't it ? ) . All one needs is an excellent BS filter. Alas no human on Earth has that. The manipulators who pay for our TV use humour . That's cruel as i can't resist that. When I went to Texas I watched the Beverly Hill Billy's all day long, it is addictive ( " There's that funny music again, always happens when someone is at the door," Says Grandma ) . Reason being the adverts were only every 15 minutes as in the UK. Other US TV made me ADD as it seemed every 2 minutes.
I find Family Guy very fascinating . Recent saw the one where they accuse Robbin Williams of being talentless. I wonder if he saw it and ...? That's the other side of freedom and high intellect.
Bible paradox. If we have free will how come prophecy? Thus ignore prophecy. That a lot of happy people out there I hope? Prophecy is guidance or educated guess. Family Guy creators are great at pointing out things like that in a crude way. Brian the dog is priceless. Ren and Stimpy anyone?
I find Family Guy very fascinating . Recent saw the one where they accuse Robbin Williams of being talentless. I wonder if he saw it and ...? That's the other side of freedom and high intellect.
Bible paradox. If we have free will how come prophecy? Thus ignore prophecy. That a lot of happy people out there I hope? Prophecy is guidance or educated guess. Family Guy creators are great at pointing out things like that in a crude way. Brian the dog is priceless. Ren and Stimpy anyone?
Yes and no. Mostly no. Last one made 2012 I think ? The round headlight original Lada looked very similar. The square headlights were a misguided attempt at styling so as to be modern.
The Lada Niva was considered very good, almost cult status. The Lancia Beta rusted away. People put the Beta engine in the Niva. Lancia Integrale. My most favourite car. Well made and practical, they seldom rust away. Such a good car and impossible to repair as parts are difficult and engine out for most things. Turbo pipe comes off and is a five minute job to re-fix. I looked such a hero when I did that. I doubt any Ferrari is better than an Integrale? Build quality equal to my VW any day. People just won't believe it.
What people do not know is Lancias problems came from using Soviet steel. The money was never paid for helping Lada. Fiat were paid in steel. All the pressing tools at the Russian factory are Innocenti Italy. 3 years later Fiat realized how bad the steel was, it rusts from the inside. Fiat were not the best before that. I drove a Lancia Delta which was much like Saab 9000. Great car and they don't rust. I think the companies shared facilities. Saab was excellent on basic build quality, been in one but never driven one. Saab 900 a great car. Said by some to be the safest of it's time by a long way( roll over tests ). Alas Saab is gone. The reason Fiat did it was to placate the red brigade or whatever it was called, a Marxist mafia. They had Auto-reductionone (spelling) . That is wearing a badge they would pay a food store what they thought rather than ticket price, buses and trains also. The Italian government gambled with Lada being seen to be having the right friends.
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