Question

The Bode plot of the transfer function $G(s) = 5$ is:

• A. constant magnitude and constant phase shift angle
• B. $-20$ dB/decade and constant phase shift
• C. $+20$ dB/decade and constant phase shift of $\pi/2$
• D. zero magnitude and phase shift

Hint:

\textbf{Remember:} If the transfer function is a constant gain $K$, then the Bode plot has a constant magnitude of $20\log_{10}(K)$ dB and a constant phase shift of $0^\circ$.

Answer 1

The Correct Option is A

We are given a transfer function: $G(s) = 5$
This is a pure gain system, which means it has no poles or zeros in the $s$-domain.
The Bode plot consists of two components: magnitude plot and phase plot.
For the magnitude plot, since the gain is constant and positive, we calculate:
\[ \text{Magnitude (in dB)} = 20 \log_{10}(5) \approx 13.98 \, \text{dB} \]
This value remains constant for all frequencies, resulting in a flat line in the magnitude plot.
For the phase plot, a positive real number like $5$ introduces a zero-degree phase shift.
So, the phase remains constant at $0^\circ$ across all frequencies.
Therefore, both the magnitude and the phase remain unchanged over frequency, which is the hallmark of a constant gain transfer function.