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Dave Shrader wrote:
If dV/dt = 0 then I must have maximum voltage. This has meaning. You must be into this new math. What is the slope of a point when dt=0 = the width of a point? :-) Is that point flat, pointing up, or pointing down? :-) -- 73, Cecil http://www.qsl.net/w5dxp -----= Posted via Newsfeeds.Com, Uncensored Usenet News =----- http://www.newsfeeds.com - The #1 Newsgroup Service in the World! -----== Over 100,000 Newsgroups - 19 Different Servers! =----- |
Tdonaly wrote: Cecil seemed to indicate that he thought delta t going to zero meant that t was perpetually zero. If delta-t ever gets to zero, time stands still. All you can allow delta-t to do is to approach zero. Once it reaches zero the ballgame is over. Limit delta-t to a minimum of a yoctosecond and everything will be perfectly OK. -- 73, Cecil http://www.qsl.net/w5dxp Are you trying to start an argument? I wrote "going to zero," not "at zero." Besides, what the hell is a yoctosecond? All this was argued over and discussed in the 18th century. You and Richard Harrison are beginning to sound like Bishop Berkeley. 73, Tom Donaly, KA6RUH |
Richard Harrison wrote:
Keith wrote: "Are you sure you want to discard all thoughts of the instantaneous? Certainly not, but it has little application to power in transmission line problems. Power is the rate of transferring energy or the rate of doing work. Electrical power is measured in joules per seconds or more succinctly in watts. What is the value in watts or joules per second when seconds equal zero? I venture an answer: It is the V x I x cos. theta at that instant, but since work is power x time, it won`t do anything for you in zero seconds. But then instantaneous velocity and instantaneous acceleration won't do anything for you in zero seconds, either. And yet, for example, inertial navigation systems successfully operate by integrating these instantaneous values. Back to your assertion "but it has little application to power in transmission line problems". It is certainly true that for RF, average power is of most interest. It is what gets you communicating. But if you want to understand how things work, exploring the land of the instantaneous is quite valuable. It is instantaneous voltages which make standing waves. It is instantaneous signals which cause distortion in diode demodulators. It is instantaneous voltages and currents which are added and subtracted in Bird wattmeters. It is instantaneous voltages and currents which interact at impedance discontinuities to do all the neat stuff. And it is instantaneous voltages and currents which produce instantaneous power. But I notice an instantaneous willingness to reject the value of instantaneous power. I suspect this is because the conclusions reached when thinking in terms of instantaneous power are inconsistent with some of your long held beliefs and rather than re-examine these beliefs it is simpler to just reject instantaneous power. But to reject instantaneous power in a consistent manner, you need to explain why you do not also reject instantaneous velocity, acceleration, current, flow or any of the many other interesting things which are a derivative with respect to time. For if we accept the argument "in zero time, no energy can flow" then we should also accept: - "in zero time, no charge can flow" -- say bye to instantaneous current - "in zero time, we can move no distance" -- say bye to instantaneous velocity - etc., etc. When you can't find any fundamental reason that the instantaneousness of power is different from the instantaneousness of other common measures like velocity, current, etc., you may wish to return to the original assertion which caused all this fuss: Assertion A: "In a shorted ideal transmission line which has reached steady state, no energy can cross a voltage or current minimum because p(t) = v(t) * i(t) and at a voltage or current minimum, the voltage or current is always zero, so the power is always zero, so there is no energy flow across a voltage or current minimum." This conclusion contradicts a commonly held belief: Belief B: "that in steady-state, energy is flowing along the transmission line to the end where it is reflected and travels back to the beginning." Unless you can find an error in the logic of Assertion A, it would seem reasonable that you re-assess your acceptance of Belief B. Assertion A caused me to reject Belief B and the world did not collapse: - Bird wattmeters still give useful indications - ghosts still occur on TVs - echoes still occur on phone lines - bidirectional communications still occur on two wire lines but the simplistic explanations for these phenomena offered by Belief B need to be re-examined. A better understanding is all that you stand to gain by discarding Belief B. ....Keith ....Keith |
Tom Donaly wrote:
"You and Richard Harrison are beginning to sound lke Bishop Berkeley." We are in good company. Terman says on page 84 of his 1955 opus: "In these equations Zo = sq rt Z/Y is termed the "characteristic impedance" of the line. In the case of radio-frequency lines, Zo can nearly always be assumed to be a pure resistance, as discussed on page 88." When Terman says SWR = Emax / Emin, it makes no difference whether you use instantaneous values or rms values, so long as you are consistent, the ratio is the same. Some complained that nobody provided a trustworthy VSWR related to power. Bird Electronic Corporation does: VSWR = 1+sq rt (reflected pwr/forward pwr) over 1-sq rt (reflected pwr/forward pwr). Millions of conversions have proved this VSWR from measured powers relation. Best regards, Richard Harrison, KB5WZI |
Richard Harrison wrote:
For the power sine wave, though the fact that a minus times a minus is a plus results in 2x the voltage frequency, dP/dt=0 at maxima. Alternatively, from amplitude modulation, the product of two sine waves produces a sum and difference frequency. When the two sine waves have the same frequency (as they due for the voltage and current contributing to the power), the result is a double frequency sine wave and a 0 frequency difference which is the DC or average power. A question raised in this thread is, how can energy, which is joules per second times seconds, be zero when the number of seconds is zero? The answer seems obvious. Zero times anything is zero. Exactly. And when the voltage or current is always zero, so must be the power. ....Keith |
Keith wrote:
"---you need to explain why you do not reject instantaneous velocity, acceleration, ---." I don`t reject instantaneous anything including power. Instantaneous power is not particularly useful in working with radio transmission lines. Like infinity, the infinitesimal is unmeasurable. Like infinity, the infinitesimal is useless in calculations. The idea of the infinitesimal is useful in perceiving targeted values approached as a variable approaches a limit. A differential "d" is an infinitesimal smaller than a difference. "dy" is the differential of y. "dx" is the differential of x. "dt" is the differential of t. The ratio "dy/dx" is a slope defined at a point and is equal to the limit as x goes to zero of the ratio delta y over delta x. The basis of differentation is superfluous to this discussion, but Keith asks, why not reject things which are a derivative with respect to time including acceleration. Acceleration may be a good example. Calculus can give the rate at which a variable varies. On the other hand, it can give a function if the rate of change is given. Velocity is the variable in acceleration. Assume velocity is increasing and you have a definition of the function. For a given velocity the acceleration can be determined, and for a given acceleration, the velocity can be determined. My point, repeated again, is that when delta time is zero, no distance is traversed, not that acceleration and velocity are zero. Power x time = energy. Thast`s how the electric power company calculates your bill. If no time elapses during which power is available, no energy is consumed. Best regards, Richard Harrison, KB5WZI |
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Richard Harrison wrote:
Standing waves are perceived only by using a sensor which does not discriminate by direction and accepts power traveling in both directions at the same time. There actually is no abatement of power in either direction. Sadly for ham radio, this fact of physics has been known to man for 300 years. How can a "technical" hobby be 300 years out of date? -- 73, Cecil http://www.qsl.net/w5dxp -----= Posted via Newsfeeds.Com, Uncensored Usenet News =----- http://www.newsfeeds.com - The #1 Newsgroup Service in the World! -----== Over 100,000 Newsgroups - 19 Different Servers! =----- |
wrote:
But if you want to understand how things work, exploring the land of the instantaneous is quite valuable. OTOH, if you want to understand how EM waves work, exploring the discoveries of the past 500 years in the field of optics is quite valuable - discoveries that you have officially discounted when you reject the total knowledge base embodied in the field of optics. Seems my "sin" is pretty small compared to yours. :-) -- 73, Cecil http://www.qsl.net/w5dxp -----= Posted via Newsfeeds.Com, Uncensored Usenet News =----- http://www.newsfeeds.com - The #1 Newsgroup Service in the World! -----== Over 100,000 Newsgroups - 19 Different Servers! =----- |
Richard Harrison wrote: Standing waves are perceived only by using a sensor which does not discriminate by direction and accepts power traveling in both directions at the same time. There actually is no abatement of power in either direction. Sadly for ham radio, this fact of physics has been known to man for 300 years. How can a "technical" hobby be 300 years out of date? -- 73, Cecil http://www.qsl.net/w5dxp Larding it on a little thick are we, Cecil? 73, Tom Donaly, KA6RUH |
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