Which one of the following rules determine the mapping of s-plane to z...
Explanation: S- plane can be mapped into the z plane with certain rules than right side maps into the outside, left side maps into the inside and imaginary axis maps on the unit circle of the z plane.
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Which one of the following rules determine the mapping of s-plane to z...
Mapping of s-plane to z-plane
The mapping of the s-plane to the z-plane is an important concept in the field of control systems and signal processing. It allows us to analyze continuous-time systems in the discrete-time domain. There are certain rules that determine this mapping, and the correct answer is option 'D', which states that all of the mentioned rules are true.
Explanation:
Let's discuss each of the mentioned rules in detail:
a) Right side of the s-plane maps into outside of the unit circle in the z-plane:
- The right side of the s-plane represents the region of stability for continuous-time systems.
- When mapping the s-plane to the z-plane, the right side of the s-plane maps into the outside of the unit circle in the z-plane.
- This means that stable continuous-time systems will map to stable discrete-time systems, as long as the sampling rate is sufficiently high.
b) Left half of s-plane maps into inside of the unit circle in the z-plane:
- The left half of the s-plane represents the region of instability for continuous-time systems.
- When mapping the s-plane to the z-plane, the left half of the s-plane maps into the inside of the unit circle in the z-plane.
- This means that unstable continuous-time systems will map to stable discrete-time systems.
c) Imaginary axis in s-plane maps into the circumference of the unit circle:
- The imaginary axis in the s-plane represents the oscillatory behavior of continuous-time systems.
- When mapping the s-plane to the z-plane, the imaginary axis in the s-plane maps into the circumference of the unit circle in the z-plane.
- This means that the oscillatory behavior of continuous-time systems will be preserved in the discrete-time domain.
Conclusion:
In summary, the correct answer is option 'D' because all of the mentioned rules determine the mapping of the s-plane to the z-plane. These rules allow us to analyze continuous-time systems in the discrete-time domain and understand the behavior of the system after sampling.