Draw the asymptotic magnitude Bode diagram for H o 10 1 jo jo 1 j0:5o 1 j0:6 o=50 jo=50

Chapter 13, Problem P13.3-31

(choose chapter or problem)

Draw the asymptotic magnitude Bode diagram for

\(\mathbf{H}(\omega)=\frac{10(1+j \omega)}{j \omega(1+j 0.5 \omega)\left(1+j 0.6(\omega / 50)+(j \omega / 50)^2\right)}\)

Hint: At \(\omega=0.1 \mathrm{rad} / \mathrm{s}\), the value of the gain is \(40 \mathrm{~dB}\) and the slope of the asymptotic Bode plot is \(-20 \mathrm{~dB}\) /decade. There is a zero at \(1 \mathrm{rad} / \mathrm{s}\), a pole at \(2 \mathrm{rad} / \mathrm{s}\), and a second-order pole at \(50 \mathrm{rad} / \mathrm{s}\). The slope of the asymptotic magnitude Bode diagram increases by \(20 \mathrm{~dB} /\) decade as the frequency increases past the zero, decreases by \(20 \mathrm{~dB} /\) decade as the frequency increases past the pole, and, finally, decreases by \(40 \mathrm{~dB} /\) decade as the frequency increases past the second-order pole.