UK Vintage Radio Repair and Restoration Discussion Forum - View Single Post - Transcendental magic: Schade's peak voltage equation and my discovery!!

TonyDuell · 14th Nov 2017, 3:03 pm

Mathematically you will never get e^-(pi/4Q) to be unity. e^0 is unity (as indeed any positive real number raised to the power 0 is unity), but that is the limit as Q->infinity. You will get very close for large values of Q, close enough for practical purposes I think. What you are seeing, though, is a limit of the accuracy of your calculator.

At least one of my calculators has a function to calculate e^x-1 to avoid this problem. It would give a very small number here, which if you added 1 to it would remain 1 (due ot the limited accuracy of the machine). But most calculators don't have that function and e^(small number) is 1 to the machine accuracy, although not mathematically.

14th Nov 2017, 3:03 pm	#3
TonyDuell Dekatron Join Date: Jun 2015 Location: Biggin Hill, London, UK. Posts: 5,208	Re: Transcendental magic: Schade's peak voltage equation and my discovery!! Mathematically you will never get e^-(pi/4Q) to be unity. e^0 is unity (as indeed any positive real number raised to the power 0 is unity), but that is the limit as Q->infinity. You will get very close for large values of Q, close enough for practical purposes I think. What you are seeing, though, is a limit of the accuracy of your calculator. At least one of my calculators has a function to calculate e^x-1 to avoid this problem. It would give a very small number here, which if you added 1 to it would remain 1 (due ot the limited accuracy of the machine). But most calculators don't have that function and e^(small number) is 1 to the machine accuracy, although not mathematically.