For G(s)H(s) = K, the phase angle is:

• A. −180°
• B. +90°
• C. Frequency-dependent
• D. 0°

Answer: (D)

When G(s)H(s) equals a constant K, it signifies that the product of the transfer function G(s) and H(s) yields a specific gain without a frequency-dependent variation. The phase angle of a constant value, such as K, is straightforward—it is zero degrees. This is because a constant does not change with frequency and maintains the same value across the spectrum of input signals, resulting in no phase shift.

In a control system context, if the system output and the input have the same phase with no delay or lead introduced by the system, the phase angle is indeed 0°. This characteristic is fundamental when designing feedback loops where maintaining stability often requires consideration of phase relationships, and having a constant product like K simplifies analysis significantly.

The other choices involve phase angles that imply frequency dependence or specific phase shifts in a control system context, which do not hold true when G(s)H(s) equals a constant K. Thus, the understanding that a constant gain does not vary with frequency or introduce phase changes reinforces why the phase angle in this scenario is zero degrees.