Question

For the given transfer function \( G(s) = \frac{5(s+4)}{(1+4s)(1+0.25s)} \), for large values of \( \omega \), the slope of the transfer function on the Bode plot is

• A. −20 dB/decade
• B. −40 dB/decade
• C. 40 dB/decade
• D. +20 dB/decade

Hint:

Each first-order pole contributes −20 dB/decade; zeros contribute +20 dB/decade.

Answer 1

The Correct Option is B

At high frequencies, the numerator contributes +20 dB/decade, and each of the two first-order terms in the denominator contributes −20 dB/decade each. \[ \text{Net slope} = 20 - 20 - 20 = -40~\text{dB/decade} \]