8. Bode Plot of Pure Capacitive Process

Pure capacitive process (also known as integrating system) has the following transfer function: \[G(s) = \frac{K_p}{s}\] By substituting \(s=j\omega\), we get \[G(j\omega) = \frac{K_p}{j\omega} = \frac{K_p}{j\omega}\frac{j\omega}{j\omega} = -j\frac{K_p}{\omega}\] \[\text{AR} = \sqrt{0^2+(-Kp/\omega)^2} = \frac{K_p}{\omega} \qquad \text{and} \qquad \phi = \tan^{-1}{-\infty} = -90^\circ\]