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One word answers...
Lets escape from mixed analysis of VSWR in transient scenarios. Visualise a series circuit of a battery of 100V and negligible internal resistance, a 100 ohm ideal resistor, and an open switch. This circuit is connected to a lossless (ie ideal) transmission line with surge impedance (or characteristic impedance, Zo) of 100 ohms which is open circuit at the far end. It takes T seconds for a wave to travel from one end of the line to the other. The scenario is a source impedance matched to the transmission line, with unmatched load. When the switch is closed, current flows into the line. Until t=2T seconds, the current If that flows into the line equals 100V/(100+100 ohms) = 0.5A, during which time the resistor dissipates heat at the rate of I^2*R = 100W. The voltage of the wave Vf travelling from the source is I*Zo = 50V. This situation is constant until t=2T seconds. At precisely t=T seconds, the wave travelling from the source end reaches the open end of the line, and a reflected wave is established to satisfy the conditions that I at the end of the line must be zero. The reflected wave must have current equal and opposite to the forward wave, so Ir=-If, the negative sign indicates that the wave travels in the opposite direction. Considering the reflected wave, Vr=Zo*Ir = 50V, so the total voltage at the o/c end is Vf+Vr = 50+50 = 100V. At precisely t=2T seconds, the reflected wave reaches the source end of the line, and the voltage at the line terminals instantly becomes Vf+Vr or 100V. At that instant, the current from the source falls to zero, and the dissipation in the source resistor also falls to zero. This situation continues indefinitely. My questions a How much of the energy that was contained in the reflected wave was dissipated in the source resistor? Does existence of a reflected wave necessarily increase dissipation in the equivalent source resistance? Is the reflected wave necessarily absorbed (or partly absorbed) by the equivalent source resistance? Are the principles that apply to this example inconsistent with the general case (eg dc, ac, transient, steady state etc)? One word answers should be sufficient. Owen |
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