Thinking about it, there are 2 Pi radians in a complete cycle, so the ln(-2) being i Pi + ln(2) is showing a 180 degree phase shift. I tried computing the log base e of -2 i, which would be a 90 degree phase shift. That gives i Pi/2?+ ln(2).
I have never played with the logs of negative numbers before, but it does make some sense.
On Wed, 31 Aug 2022 at 00:19, Dr. David Kirkby <drkirkby@...> wrote:
On Wed, 31 Aug 2022 at 00:15, Dr. David Kirkby <drkirkby@...> wrote:
On Tue, 30 Aug 2022 at 22:53, Rodger Bean <rodgerbean@...> wrote:
Further to the application of dB to inverting amplifiers.
?
All of the calculators that I have checked this on, return an error message when the ratio (Vout/Vin) is negative.
I will show you a calculator that does not - see attached.
Oops, I forgot to attach the result of Mathematica computing the log base e, and the log base 10 of -2. I must admit, I can't make sense of that, but I'm not a mathematician!?
But thank you for making the spreadsheet available.