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Consider the following system -2 D Assuming the condition that a 2y2, what are all the values of a that make this system stable ? Hint: when b > 0, then a +Vb

Consider the following system -2 D Assuming the condition that a 2y2, what are all the values of a that make this system stable ? Hint: when b > 0, then a +Vb

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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**Question 3** Consider the following system: *A diagram is shown with variables and paths indicating a feedback loop system, with an input \( x[n] \) leading to an output \( y[n] \). The system includes a feedback loop with a delay unit denoted by \( D \) and a gain of \( -\frac{1}{2} \).* Assuming the condition that \( \alpha \geq \sqrt{2} \), what are all the values of \( \alpha \) that make this system stable? *Hint: when \( b \geq 0 \), then \( \alpha + \sqrt{b} < c \) if and only if \( \alpha < c \) and \( b < (c - \alpha)^2 \).* Options: - ☐ None - ☐ \( \alpha < \frac{3}{\sqrt{2}} \) - ☐ \( \alpha < \frac{3}{2} \) - ☐ \( \alpha < 2 \) - ☐ \( \alpha < 2\sqrt{2} \) - ☐ All values of \( \alpha \) - ☐ None of the above answers is correct.
Transcribed Image Text:**Question 3** Consider the following system: *A diagram is shown with variables and paths indicating a feedback loop system, with an input \( x[n] \) leading to an output \( y[n] \). The system includes a feedback loop with a delay unit denoted by \( D \) and a gain of \( -\frac{1}{2} \).* Assuming the condition that \( \alpha \geq \sqrt{2} \), what are all the values of \( \alpha \) that make this system stable? *Hint: when \( b \geq 0 \), then \( \alpha + \sqrt{b} < c \) if and only if \( \alpha < c \) and \( b < (c - \alpha)^2 \).* Options: - ☐ None - ☐ \( \alpha < \frac{3}{\sqrt{2}} \) - ☐ \( \alpha < \frac{3}{2} \) - ☐ \( \alpha < 2 \) - ☐ \( \alpha < 2\sqrt{2} \) - ☐ All values of \( \alpha \) - ☐ None of the above answers is correct.
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