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Originally Posted by Skywave
What are the equations that determine the configuration of the components and their values inside that 'black box' in terms of the 'knowns'?
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Precisely the same equations as were used for pure resistances, except that you have to do complex arithmetic instead of real number arithmetic. You could even use an existing attenuator 'calculator' meant for resistance only and transform the solution to include the reactances, provided that the source and load had exactly the same frequency response. Just scale things.