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August 18th 03, 04:18 PM
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W5DXP wrote:
wrote: W5DXP wrote: I forgot to add. At the "zero-power points", either voltage or current is zero. All that means is that all the energy is contained in the opposite field. Not quite all. It also means that there is NO power since P = V x I. It means there is no NET power transfer. Do not be afraid to admit that you have changed the definition of P = V x I and therefore do not accept the standard definition. When I learned Pinst = Vinst x Iinst there were no caveats about how Pinst meant Pnet. Instantaneous energy is flowing or it is not. When Pinst is 0 for all time, then there is no energy flowing. To satisfy your theory (and minimize double think), you have had to change this to Pnet is zero to allow these cancelling powers to flow. So be it. There are power flow vectors in both directions that are equal in magnitude. Reference: _Fields_ and_Waves_in_Communications_Electronics_ by Ramo, Whinnery, & Van Duzer, section 6.10, page 350, where they describe Pz-, the reflected wave Poynting vector and Pz+, the forward wave Poynting vector. There can be lots of energy present but none of it is flowing past the zero voltage or zero current point; hence no power. There is a forward power flow vector and a reflected power flow vector. There is no net power flowing past any point. True, sort of. At the quarter wave points where voltage or current are always zero, there is no energy flowing. Period. At other points, energy flows in one direction for a quarter cycle and then in the other direction for the next quarter cycle, producing a net of zero. A true instantenouse power meter (one which measures V and I and displays V x I) will easily demonstrate this. As a thought experiment, move such a true power meter along a shorted or open line and think if its indications in the time domain, then do the averages. It will be quite instructive. Repeat for a line terminated in other than its characteristic impedance. By the way, since energy flows forward for a quarter cycle and backwards for the next, the maximum distance travelled by this energy is one quarter wavelength on the line. It is not flowing all the way to the end of the line and then back. There is not enough time for this to happen (on a multi-wavelength line) since it changes direction every quarter cycle. There are, however, equal magnitude component constant power flow vectors flowing in both directions. To believe that energy is flowing across a zero voltage or zero current point requires the rejection of the view that instantaneous power is equal to instantaneous voltage multiplied by instantaneous current. No, it doesn't. It only requires acceptance of Ramo, Whinnery, & Van Duzer. However, to reject energy flow across a zero voltage or zero current point requires a confusion of cause and effect. Energy flow in both directions is the *CAUSE* of the standing waves. You simply cannot turn around and say that standing waves eliminate their own cause but continue to exist anyway. Not quite. Standing voltage and current waves (which are not waves in the normal sense) can be observed on the line. They can be measured with real voltage and current instruments; as can real energy flows with a real (V x I) power meter (but not a 'Bird watt' meter which is doing something quite different). It happens that if you assume the existence of forward and reverse voltage and current waves, mathematical functions can be derived that will produce the same distribution of voltage and current as observed on the line. This is extraordinarily convenient some analysis but does not mean that these assumed waves are real. A mechanical analogue would be to look at a guy wire on a pole. You can analyze the forces as two vectors at 90 degrees (or any other angle of convenience!), but never make the mistake of assuming that there are actually two guy wires present. Just because it is mathematically convenient to assume the existence of two vectors does not mean they exist. Rejection of P = V x I would have wide impacts on our understanding of electrical power and energy flows. Nobody is rejecting it. If the lossless stub is one second long, it takes two seconds of *POWER* to bring it to steady-state. If the stub contains no moving energy, where did all those joules go? This energy is indeed stored in the stub. None of it moves across zero voltage or current boundaries. Between these boundaries, it is indeed moving as it changes from being stored in the capacitance and inductance of the line. This time variation of the location of the stored energy produces the observed voltages and currents on the line. They cannot disappear Absolutely. They do not disappear. or stand still. With AC excitation they do not stand still, but when similar analysis is done for a line excited with a DC source, the energy does indeed stand still. An open line stores the energy in the capacitance and a shorted line stores it in the inductance. If they are moving, power exists. Yes, but it never moves more than a quarter wavelength. ....Keith |
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