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Normalized travelling waves in S parameter definition

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Hi,

Why S parameters are defined in some books in terms of normalized travelling wave voltages a1, b1 where a1=(V+)/sqrt(Z0) and b1=(V-)/sqrt(Z0).
They can also be expressed in terms of V1+ and V1-. Why normalize?

Is it because it is easy to get power as 1/2.square(a1) ?
 

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