Virtual Labs

Mapping of S-Plane to Z-Plane Analytically and Verification using Simulation

Q1. The mapping of points from the S-plane to the Z-plane is given by the relation:

Explanation

Q2. If the damping ratio value is zero, then the pole location is:

a: Outside of the unit circle in the z-plane Explanation

Explanation

b: Left half of the z-plane Explanation

Explanation

c: On the unit circle Explanation

Explanation

d: Imaginary axis in the z-plane Explanation

Explanation

Q3. What is the behavior of the pole if the natural frequency increases from zero with a constant damping ratio?

a: Radially moving away from the origin of the S-plane in the left half Explanation

Explanation

b: Moving away from the imaginary axis in right half of the S-plane Explanation

Explanation

c: Moving closer toward the imaginary axis of the S-plane Explanation

Explanation

d: Moving closer toward the real axis of the S-plane Explanation

Explanation

Q4. What is the behavior of the poles in the Z-plane if the damping ratio increases from 0, while the natural frequency remains constant in the S-domain?

a: Poles move towards the unit circle from inside in the Z-plane Explanation

Explanation

b: Poles move away from the unit circle towards the origin in the Z-plane Explanation

Explanation

c: Poles move towards the unit circle from outside in the Z-plane Explanation

Explanation

d: Poles remain on the unit circle in the Z-plane and rotate along a circular path Explanation

Explanation

Q5. What is the behavior of the poles in the Z-plane if the damping ratio is zero and the natural frequency varies in the S-plane?

a: Poles remain on the unit circle in the Z-plane and rotate along a circular path Explanation

Explanation

b: Poles remain on the imaginary axis in the Z-plane Explanation

Explanation

c: Poles move towards the unit circle from outside in the Z-plane Explanation

Explanation

d: Poles move towards the unit circle from inside in the Z-plane Explanation

Explanation