Signals and Control Systems Flashcards

The transfer function of an ideal differentiator in the Laplace domain is:

Answer: s

Differentiation in the time domain corresponds to multiplication by s in the Laplace domain, so the transfer function of a differentiator is H(s) = s.

A minimum-phase system is one in which:

Answer: Both poles and zeros are in the left-half s-plane

A minimum-phase system has all its poles AND zeros in the open left-half s-plane, ensuring the system and its inverse are both stable and causal.

For a discrete-time LTI system to be BIBO stable, the impulse response h[n] must satisfy:

Answer: Σ|h[n]| < ∞ (absolutely summable)

BIBO stability requires that the impulse response be absolutely summable: Σ|h[n]| < ∞, which guarantees bounded output for any bounded input.

The phase margin of a control system is measured at:

Answer: The gain crossover frequency

Phase margin is measured at the gain crossover frequency (where |G(jω)H(jω)| = 1, or 0 dB) and equals 180° plus the actual phase angle at that frequency.

Which of the following correctly represents the relationship between the DTFT X(e^jω) and the z-transform X(z)?

Answer: X(e^jω) = X(z)|_{z=e^jω}

The DTFT is the z-transform evaluated on the unit circle |z| = 1, i.e., X(e^jω) = X(z)|_{z=e^jω}.

In Mason's Gain Formula, a 'non-touching loop' pair refers to:

Answer: Two loops that share no common nodes

Non-touching loops in Mason's formula are loop pairs that share no nodes or branches, and their product appears in higher-order cofactor terms of the formula.

If the open-loop gain of a feedback amplifier is 1000 and the feedback fraction is 0.099, the closed-loop gain is approximately:

Answer: 10

Closed-loop gain = A/(1 + Aβ) = 1000/(1 + 1000×0.099) = 1000/100 = 10.