Yes I know letraset is still available but the price per sheet has skyrocketed.
I saw some for as high as $28.00/10 sheets. I paid 00.50c in the eighties. Not many suppliers left and limited selection. I looked at this recently.
If it gets any more complicated then I may as well just order from FrontPanel.
Not always exactly the case though. The physicist Lenoard Suskind was asked how he learned to visualize higher dimensional spaces. He said that human brains can't do that, but, he said, you do develop some intuitions about the math, and sometimes those intuitions would come first and then he would investigate where the intuition might lead by manipulating some equations. So, yes intuition first, but it can about something pretty abstract like the math itself.
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"Simplicity is the Ultimate sophistication." - L. DaVinci
"The paradox of simplicity is that making things simple is hard work!" -B.Jensen
[from Conceptual Wavelets in DSP]
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You could parallel them but I guess you would have to select for Idss or use some source degeneration. Ovidiu Popa (Syn08) did some interesting work in this area a few years ago (but not using tubes).
I don't think you can really say one comes "before" the other. It's not linear like that. Insight can occur at any point.
A child will have insights about stacking blocks. A carpenter will have insights about wooden frame construction. The child may make some useful observations for the carpenter, but you cannot expect the child to work at the same level. Many insights to be had in carpentry cannot be made without the level of experience of a carpenter. So it is in any profession.
There are several notable physicists at this time that think the math is all that matters. I forgot his name but one was featured on Nova IIRC. Very interesting stuff certainly worth a listen if one has an open mind. And as I recall Feynman has voiced the same sentiment as you mention above concerning the limits of intuition.
Yes the beta is not that different on the two, and as mentioned before you always need to check for RF oscillation on BF862 circuits and it can be at 100's of MHz.
Einstein wasnt a mathematician and had poor understanding of then nascent tensor theory, at first it was his wife, a confirmed math professor, that did all theorical calculations, later he was helped by a mathematician namely Marcel Grossman, so it s no surprise that he somewhat dissmissed the maths as it wasnt his domain per se, in a way he downplayed the contributions he couldnt have done himself, so the saying you quoted is all but a neutral opinion from him...
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Wahab,
I would say it is very important that anyone who is attempting to do any development in whatever subject we are interested in to broaden our base of knowledge, If you are capable in physics learn the math, if math the other way around. If you are a carpenter then learn some engineering to understand the limits etc. It is those people who have an open mind and who are willing to always learn something new or to ask for help from others who know something that you don't know yourself who create the breakthroughs.
I would say it is very important that anyone who is attempting to do any development in whatever subject we are interested in to broaden our base of knowledge, If you are capable in physics learn the math, if math the other way around. If you are a carpenter then learn some engineering to understand the limits etc. It is those people who have an open mind and who are willing to always learn something new or to ask for help from others who know something that you don't know yourself who create the breakthroughs.
Math could be considered a form of very concise language that can be used for reasoning, somewhat analogous to verbal reasoning.
Regarding abstraction, to most people electrical schematics seem very abstract, or perhaps something like sheet music to non-musicians. Same for idealized equivalent circuits. And those things are abstractions, it's just that once you get fluent with them, they can aid certain kinds of thinking.
Regarding abstraction, to most people electrical schematics seem very abstract, or perhaps something like sheet music to non-musicians. Same for idealized equivalent circuits. And those things are abstractions, it's just that once you get fluent with them, they can aid certain kinds of thinking.
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I think you hit the nail on the head there. Some folks are truly blessed and have a wide array of mathematical tools/techniques they can call upon to describe physical or conceptual ideas and then develop from that a set of solutions.
I read about some of the stuff going on in particle physics, or astrophysics and my mind boggles at how these people tease this stuff out of a few measurements and a lot of calculations.
We can't speak for A.E., but I am sure he was quite good at math. However, he was in a league on his own when it came to having a (counter)intuitive appreciation of how stuff works.
Not sure about any previous results, but selecting or degenerating jfets is never really required, other than for marketing reasons ("hand matched jfets provide a superior sound").
- They don't hog current. Increasing the temperature of a jfet decreases the mobility of the charge carriers in the channel, effectively reducing the current through the channel. However, increasing the temperature also narrows the depletion regions of the pn junctions, thereby increasing the drain current. As a net result, the tempco around Idss is zero, or very close to.
- Noise has a weak dependency on the drain current, so any current imbalance will have virtually zero impact on the overall noise performance. In fact, I suspect any source degeneration will be more critical in this respect.
Not quite, that is only true for FET's with Vp near .6V. High Vp FET's have a nominally 0 TC at a lower current, you could check some data sheets for old 2N series JFET's. Since mobility does not have a linear TC there ends up being some curvature in the end. Another point is that biasing an LTP at 0 TC does not do any good for drift, it turns out the variance in Vp and Idss makes the drift of a diff-pair depend on current ratio. A perfect pair will have 0 drift at any current.
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