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Formulas and calculations are not my strongest areas. However, something is telling me peak power is more then 1.414 times average. We agree that peak voltage is 1.414 times RMS but what is happening to the current has been overlooked. Power is volts times amps. If you raise the peak voltage 1.414 times, you have also raised the peak current into the 50 ohm load by the same amount. The end result is a larger figure.