Core Subject Knowledge & Technical Concepts Flashcards

The Laplace transform of the unit step function u(t) is:

Answer: 1/s

The Laplace transform of u(t) is 1/s for Re(s) > 0.

A system is BIBO stable if and only if its impulse response h(t) satisfies:

Answer: ∫|h(t)|dt < ∞

A system is BIBO stable if and only if its impulse response is absolutely integrable (L1 norm is finite).

In a second-order control system, the damping ratio ζ = 0.5 corresponds to which response?

Answer: Underdamped

When 0 < ζ < 1 (here ζ = 0.5), the system is underdamped and exhibits oscillatory response.

The Nyquist sampling theorem states that the sampling frequency must be:

Answer: At least twice the signal's highest frequency

The sampling frequency must be at least 2fmax (Nyquist rate) to allow perfect reconstruction of the signal.

For a causal LTI system, which condition must the region of convergence (ROC) of its z-transform satisfy?

Answer: ROC extends to infinity (includes |z| = ∞)

For a causal (right-sided) sequence, the ROC is of the form |z| > r and must include |z| = ∞.

The phase margin of a stable control system is defined as:

Answer: 180° + the phase of the open-loop transfer function at the gain crossover frequency

Phase margin = 180° + ∠G(jω) at the gain crossover frequency where |G(jω)| = 1 (0 dB).

In AM modulation with modulation index m, the ratio of sideband power to total power is:

Answer: m²/(2 + m²)

Total AM power = Pc(1 + m²/2); sideband power = Pc·m²/2, so ratio = (m²/2)/(1 + m²/2) = m²/(2 + m²).