# How to find Phase crossover frequency?

I make the imaginary part of $$\loop \ gain=0\$$ to find phase crossover frequency.

But in one video, the person told that this method can only be applied when Polar plot crosses the real axis and cannot be used when it touches the real axis.

I don't get why he should be right as Imaginary part equated to zero implies the phase is either 0 or pie or point lies in origin then where does touching and crossing came into the difference.

Also, will I consider such point that is if polar plot touches real axis as $$\{Kmarginal}\$$ for calculation of $$\Gain \ Margin\$$ using formula $$\\frac{Kmarginal}{Kgiven}\$$?

• To obtain the crossover frequency, one can check the frequency root $f_c$ which brings the magnitude of the loop gain equal to 1: what $f_c$ value satisfies $|T(f_c)|=1$? – Verbal Kint Jul 24 '19 at 7:13
• @VerbalKint as much as I know what you are referring to is called gain crossover frequency while I am asking about phase cross over frequency – SUNITA GUPTA Jul 24 '19 at 7:17
• Ok, when you have $f_c$ using what I proposed, simply determine $argT(f_c)$ and you'll have the phase at that frequency. The phase at crossover depends on the compensation strategy and the plant transfer function so you can't directly determine this value without having $f_c$ first. – Verbal Kint Jul 24 '19 at 12:33