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The phase shift of a second-order system with a transfer function 1 / s2 is:
1. 180°
2. 90°
3. -90°
4. -180°

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Correct Answer - Option 4 : -180°

Concept:

Each zero at origin gives a phase shift of + 90°

For N zeros at origin gives a phase shift of + 90N°

Each pole at origin gives a phase shift of - 90°

For N poles at origin gives a phase shift of - 90N°

Calculation:

The given transfer function = 1/s2

Number of poles at origin = 2

Phase shift = 2 × (- 90°) = - 180°

Minimum phase system: It is a system in which poles and zeros will not lie on the right side of the s-plane.

For a minimum phase system:

\(\mathop {\lim }\limits_{\omega \to \infty } \angle G\left( s \right)H\left( s \right) = \left( {P - Z} \right)\left( { - 90^\circ } \right)\)

Where P & Z are finite no. of poles and zeros of G(s)H(s)

Non-minimum phase system: It is a system in which some of the poles and zeros may lie on the right side of the s-plane.

In particular, zeros lie on the right side of the s-plane.

All pass system:  An all-pass network is the network that is the combination of the minimum and non-minimum phase systems and have the unity magnitude for all

frequencies and imparts only a 180-degree phase shift. The pole and zero of an all-pass filter are at the same distance from the origin. 

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