Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN: 9780133923605
Author: Robert L. Boylestad
Publisher: PEARSON
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**Understanding Closed-Loop System Stability:**

- **Stable Systems:** 
  - If a closed-loop (CL) system is stable, it is possible to increase the gain (by up to a certain amount) while maintaining CL stability.

- **Unstable Systems:**
  - Conversely, if the CL system is unstable, decreasing the gain (by up to a certain amount) can still result in CL instability.

**Given Scenario:**
- The gain margin of a nominal loop transfer function (with no right-half plane open-loop pole) is found to be -40 dB.

**Questions:**
1. **The closed-loop system is** unstable.
2. **Gain Adjustment:**
   - You may increase (or decrease) the gain up to **100**, calculated using \( 20\log_{10}(100) = 40 \).

**Note:**
- The instruction for adjusting gain is based on the system's stability:
  - If the system is **stable**, the gain can be increased up to a specified amount to maintain stability.
  - If the system is **unstable**, reducing the gain to a specified level will still maintain instability.
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Transcribed Image Text:**Understanding Closed-Loop System Stability:** - **Stable Systems:** - If a closed-loop (CL) system is stable, it is possible to increase the gain (by up to a certain amount) while maintaining CL stability. - **Unstable Systems:** - Conversely, if the CL system is unstable, decreasing the gain (by up to a certain amount) can still result in CL instability. **Given Scenario:** - The gain margin of a nominal loop transfer function (with no right-half plane open-loop pole) is found to be -40 dB. **Questions:** 1. **The closed-loop system is** unstable. 2. **Gain Adjustment:** - You may increase (or decrease) the gain up to **100**, calculated using \( 20\log_{10}(100) = 40 \). **Note:** - The instruction for adjusting gain is based on the system's stability: - If the system is **stable**, the gain can be increased up to a specified amount to maintain stability. - If the system is **unstable**, reducing the gain to a specified level will still maintain instability.
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