I'm having trouble understanding how to draw phase bode plots. For example in a simple low-pass RC circuit, the Gain = 1/(1+jwCR) and from this I find it easy to draw magnitude plot but how do you get the information to do phase? I keep seeing arctan = real G(s)/imG(s) but I don't understand how actual numbers are extracted from this and how it tells you the behavior. If someone could please go through phase plots in step by step detail it would help a lot and I'd be ever so grateful.
The low pass RC gain function you mentioned is a complex number. For a given RC pair, the value of the complex gain value varies as the angular frequency varies. If R=C=1 for simplicity then G=1/(1+jω) The complex value can be found at any ω in the polar form ... at ω=0.1 is G=1/(1+j0.1)=0.995 @ angle -5.71° at ω=1 is G=1/(1+j)=0.707 @ angle -45° at ω=10 is G=1/(1+j10)=0.0995 @angle -84.3° and so on. So for your first order function on a logarithmic scaled frequency axis, the phase starts changing roughly a decade before the pole [i.e. @ ω=1/(RC)] and ends about a decade after the pole - the total phase change being 90° over the entire frequency range. At the pole, the phase change is exactly one half of the total phase change. Each transfer function phase plot will have a variation on this, depending on factors including the overall order (1st, 2nd 3rd etc.) and the pole & zero locations of the transfer function. But you can calculate the phase at any value of ω by direct substitution into the transfer function complex frequency form. There are several rules of thumb for drawing Bode plots which the reading any suitable text book will reveal.
Take a look at the following page for extensive information including a Matlab GUI for generating asymptotic Bode plots. http://www.swarthmore.edu/NatSci/echeeve1/Ref/LPSA/Bode/Bode.html