Phase calculation formula - can't even use the correct formula properly!!
Whilst, this may be a electronics-centric issue ....it heavily depends on maths, hence asking a forum where folks a clued up wrt maths! (I'm not) - I've asked on electronics forums, but have had a mixed response!
I've an electronic circuit where I desperately need to establish the phase shift for a particular frequency put through the circuit.
There are two components in my particular circuit which will decide the phase shift for a given frequency through the circuit (see the diagram below - C1 & R1)
Capacitor (C) for my circuit, I'm using a value of 0.0000000022
Resistor (R) for my circuit I'm using a value of 47000
Ok, for those two values there's a very simple formula which tells me the frequency where the phase shift will be exactly 90 degrees for the circuit I'm using (an allpass filter), this is the so called 'centre frequency' & is referred Fo, so for the above
Fo = 1 / (2TT * RC) (the TT is meant to look like Pi!)
Fo = 1 / 6.28319 * 47000 * 0.0000000022)
That works out at 1539.22Hz.....so for a capacitor of 0.0000000022 (farads) & a resistor of 47000 (ohms), a 90 degree phase shift (the centre frequency) will occur at 1539.22Hz through the circuit
Great I now have some values which I know are correct that I can apply to a much more foreboding formula!
I'd really like to know the phase shift is for other frequencies through that I put through the same circuit with those same values for C & R (it's not much good only knowing which frequency is moved exactly 90 degrees).Alas the formula (to my eyes at least) is a beast. Here it is....
the article from where I sourced it (Tech Brief 3: Digitally Control Phase Shift - Maxim) is applying the formula to this circuit, so the C1 & R1 is just the numbering scheme for the components (C & R essentially)...
My first hurdle is that 'w' in the above formula relates to frequency in in rad/s (vs Hertz) which is completely new to me.
Fortunately there's online calculator (Convert hertz to rad/sec - Conversion of Measurement Units) , so if I punch in
1539.22HZ .... it converts to 9671.204477466 rad/s
Therefore I now have all the data necessary to input & try & use that foreboding formula.
With my values of C, R and Rad/s, the formula outcome should be 90 (degrees), but being a bit poor at maths, I can't even get the formula to come out anything that resembles an outcome of 90!
Is anyone speedy enough with such things to see if they use/input the following values to that formula above, that the outcome is close to 90?
C = 0.0000000022
R = 47000
w = 9671.204477466
My goal is to have an Excel spreadsheet where I can see the phase shift for different frequencies when changing the values for either frequency Capacitance (C) or Resistance (R)