Question

Given

G[s] = 300(s + 100)
s(s + 10)(s + 40)

Sketch the Bode plot (magnitude plot and phase plot), by hand.

Answer 1

To sketch the Bode plot for G(s), break it down into simple components of poles, zeros, and gain, then create separate magnitude and phase plots on a logarithmic scale and combine them for the overall Bode plot.

Step-by-step explanation:

To sketch the Bode plot for the given transfer function G(s) = 300(s + 100) / s(s + 10)(s + 40), we need to follow certain steps.

• Break down the transfer function into simple components that we can easily sketch, such as simple poles, zeros, and gain.
• Plot the magnitude and phase of each component separately on a logarithmic scale as a function of frequency.
• Combine the magnitude and phase plots for all components to get the overall Bode plot.

For G(s), we have a zero at s = -100, poles at s = 0, s = -10, and s = -40, and a gain factor of 300. We'd sketch the magnitude plot by marking the breakpoints of these poles and zeros and then draw a straight line approximation that increases or decreases at a rate of 20 dB/decade or 6 dB/octave for every pole or zero encountered, following the Bode plot rules for slopes. The phase plot would approximate the phase contribution of each pole and zero, which is typically +45° or -45° near the break frequencies, resulting in a piecewise linear plot.