Magnitude of $G_{ho}(jw)$ :

Phase of $G_{ho}(jw)$ :

$\displaystyle \angle G_{h0}(jw)= \angle \sin(\pi w/w_{s})-\frac{\pi w}{w_{s}}$ rad

The sign of $\angle \sin (\pi w/w_{s})$ changes at every integral value of $\dfrac{\pi w}{w_{s}}$ . The change of sign from to can be regarded as a phase change of -180° . Thus the phase characteristics of ZOH is linear with jump discontinuities of -180° at integral multiple of $\omega_{s}$ .

The magnitude and phase characteristics of ZOH are shown in Figure 3.

$\includegraphics[width=8.5cm]{FrZoh.eps}$
Figure 3: Frequency response of ZOH