# Re: Current through coils

• From: Roy Lewallen <w7el@xxxxxxxxx>
• Date: Sat, 18 Mar 2006 20:14:56 -0800

Gene Fuller wrote:
Cecil Moore wrote:
. . .
The two traveling waves have to be analyzed separately and then superposed to obtain valid results. If you analyze net current without superposition, you are doing the same thing as superposing powers, which is a known no-no.

Both those sentences are false.

In a linear system like an antenna or transmission line, superposition applies. This means, among other things, that we can separately analyze the system's response to various components, and the sum of the results we get are the response to the sum of the excitation components. For example, we can split a current into two -- or more -- components, such as a forward traveling current wave and a reverse traveling current wave, with the actual current (or what Cecil calls "net" or "standing wave" current) at any point being the sum of the two. We can find the voltage across an inductor, for example, which results from the forward traveling current. Then we find the voltage across the inductor resulting from the reverse traveling current. Superposition tells us that the sum of those two voltages is what results from a current which is equal to the sum of the forward and reverse traveling current waves.

We must get exactly the same result, in this example the voltage across the inductor, if we find it by adding the separate voltages due individually to the two current components, or if we find it directly as a result of the total current. We don't have to separate the current into two components then superpose the results as Cecil claims -- we get exactly the same result either way because superposition holds. This has nothing to do with attempted superposition of powers or other properties which don't fit into the boundaries of linear quantities.

We're not restricted to splitting the current into a single forward and reverse wave, either. We can split it into many separate traveling waves, as well as any number of other combinations. As long as all the components add up to the actual total current, we'll get exactly the same result when we separately sum the responses to each individual component that we do when we simply look at the response to the total current.

If Cecil's analysis shows, or his theory requires, that the result be different when adding the responses to traveling current waves than it is by calculating the response directly from the total current, then the analysis or theory is wrong. Superposition requires that the two results be identical.

Roy Lewallen, W7EL
.

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