Gain and Phase Margin

For the Feedback Amplifier

Given an Amplifier with gain $A(s)$ and adding feedback $B(s)$ we find feedback gain $A_{f}=\frac{A(s)}{1+A(s)*B(s)}$ .

Consider the loop gain $A(s)*B(s)$ for $B(s)=1$ and $A(s)=\frac{10^4}{(1+\frac{s}{10^6})*(1+\frac{s}{10^8})^2}$ and its Bode plot:

We are really interested in points defined by $\psi=-180^{\circ}$ and $|A(s)*B(s)|=0dB$ and define a measure of their closeness as the phase and gain margins.

Notice that by varying $B(s)$ as a scalar we shift the gain plot up and down and thus adjust the gain and phase plots. For example if we want to decrease the phase margin to 45° we need to shift the gain plot down by 5dB. Therefore we set $B(s)=\frac{1}{10^{0.5}}=0.316$.

The interpretation is...

High Gain Margin	Higher chance of instability
Low Gain Margin	Lower chance of instability
High Phase Margin	Higher chance of instability
Low Phase Margin	Lower chance of instability

What I don't know -> do the signs of gain and phase margins matter? Also, what is this 20log(1/B) thing at the end of 301 slideset 20?