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Derivation of Reflection Coefficient vs SWR
Keith Dysart wrote:
When we analyze this circuit we find that there is no voltage re-reflection when the wave gets back to the generator. This is clear because Vf does not change, which it would have to do if any of Vr was re-reflected. Nope, Vf doesn't have to change for there to be a reflection. Looking at what happens to the power dissipation in the source resistor, Rs, when the reflected wave arrives, we see that the energy being supplied by the source drops by 99.85%. Most of the energy in the forward wave is supplied by the reflected wave, starting at the time the reflected wave arrives and causes destructive interference. And yet it appears that you are claiming that power is reflected at the generator. How can power be reflected if voltage is not? To be technically correct, reflected energy is redistributed back toward the load during the process of destructive interference. The conditions before the reflected wave arrives and after the reflected wave arrives are extremely different. Before the reflected wave arrives, the source resistor, Rs, is dissipating 25 watts. After the reflected wave arrives, the source resistor, Rs, is dissipating 0.03845 watts. Clearly, something drastic has happened and that is: 99.85% of the forward energy originally supplied by the source has been replaced with reflected energy being redistributed back toward the load. Because of destructive interference, reflected energy *never* flows through the source resistor, Rs, and is instead redistributed back toward the load. Nothing else is possible since the source is supplying only 1.9608 watts during steady-state. 92.3% of the forward power is not being supplied by the source during steady-state. The energy incident upon a point must equal the energy exiting the point. The energy incident upon the generator terminals is 1.92234 joules/sec from the source and 23.0777 joules/sec from the reflected wave. The energy exiting that point is 25 joules/sec. The reflected wave energy obviously reverses direction and joins the forward wave and that is what we call a "reflection". -- 73, Cecil http://www.w5dxp.com |
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