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and hence is stable. Note that the fact that PM>0 implies that $T\left(j\overline{\omega }\right)<1$, where $\overline{\omega }$ is the frequency at which $\text{arg}\left(T\left(j\overline{\omega }\right)\right)=\pi$, that is, the gain margin is also positive.

From Equation 67 it follows that

$\text{arg}\left(T\left(j{\omega }_{c}\right)\right)={\omega }_{c}{T}^{+}+{\mathrm{tan}}^{-1}\frac{{\omega }_{c}}{K}+{\mathrm{tan}}^{-1}\frac{{\omega }_{c}}{2{N}^{-}/C{\left({T}^{+}\right)}^{2}}+{\mathrm{tan}}^{-1}\frac{{\omega }_{c}}{1/{T}^{+}}$ (73)

(73)

Since

${\omega }_{c}=0.1\mathrm{min}\left\{\frac{2{N}^{-}}{{\left({T}^{+}\right)}^{2}C},\frac{1}{{T}^{+}}\right\}$

it follows that

${\omega }_{c}{T}^{+}=0.1\mathrm{min}\left\{\frac{2{N}^{-}}{{T}^{+}C},1\right\}$

so that ...

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