Final answer:
The frequency at which the phase shift is 180° for the given feedback amplifier with open loop gain A(s) = 2000 / (1 + s/10⁵)³ is 10⁵ / (2π) Hz.
Step-by-step explanation:
To determine the frequency at which the phase shift is 180° for the given feedback amplifier, we need to analyze the open-loop gain A(s) of the amplifier. The open-loop gain is given by A(s) = 2000 / (1 + s/10⁵)³. This is a third-order system, which means that each of the three poles will contribute a phase shift of up to 90° at high frequencies. To reach a total phase shift of 180°, the frequency will have to be such that two of the poles contribute this maximum phase shift.
The phase shift contributed by a single pole at frequency ω is given by arg(1 + jω/ω0), where ω0 is the pole frequency. For a third-order system with equal pole frequencies, the phase shift condition is met when the frequency is at the pole frequency. Therefore, the frequency at which the phase shift is 180° occurs at ω = 10⁵ rad/s because this is the pole frequency. To express this in Hertz (Hz), divide by 2π to obtain f = ω / (2π) = 10⁵ / (2π) Hz.