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learn:courses:real-analog-chapter-7:start [2017/04/28 22:05] – [Example 7.2: Switched Circuit Natural Response] Marthalearn:courses:real-analog-chapter-7:start [2022/10/04 11:38] (current) – external edit 127.0.0.1
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 ====== Real Analog: Chapter 7 ====== ====== Real Analog: Chapter 7 ======
--->Chapter 7 Downloads# +[[{}/learn/courses/real-analog-chapter-6/start|Back to Chapter 6]] 
-  * {{ :learn:courses:real-analog-chapter-7:realanalog-circuits1-chapter7.pdf |Chapter 7 PDF}} +-->Chapter 7 Materials#   
-    * {{ :learn:courses:real-analog-chapter-7:lab7p2p1.pdf |Lab 7.2.1}}: Passive RC Circuit Natural Response +  * Lecture Material: 
-      * {{ :learn:courses:real-analog-chapter-7:lab7p2p1_worksheet.docx |7.2.1 Worksheet}} +    * {{ :learn:courses:real-analog-chapter-7:lecture16_b_.ppt |Lecture 16(b) PowerPoint Slides}}: Inductors, introduction to first-order circuits, RC circuit natural response 
-    * {{ :learn:courses:real-analog-chapter-7:lab7p3p1.pdf |Lab 7.3.1}}: Passive RC Circuit Natural Response +    * {{ :learn:courses:real-analog-chapter-7:lecture17.ppt |Lecture 17 PowerPoint Slides}}: RL circuit natural response, general first-order system natural response, first-order circuit examples 
-      * {{ :learn:courses:real-analog-chapter-7:lab7p3p1_worksheet.docx |7.3.1 Worksheet}} +    * {{ :learn:courses:real-analog-chapter-7:lecture18.ppt |Lecture 18 PowerPoint Slides}}: Forced response of first-order circuits, active first-order system examples, step response of first-order circuits 
-    * {{ :learn:courses:real-analog-chapter-7:lab7p4p1.pdf |Lab 7.4.1}}: Inverting Differentiator +    * {{ :learn:courses:real-analog-chapter-7:lecture19.ppt |Lecture 19 PowerPoint Slides}}: Steady-state response & DC gain, step response examples 
-      * {{ :learn:courses:real-analog-chapter-7:lab7p4p1_worksheet.docx |7.4.1 Worksheet}} +    * {{ :learn:courses:real-analog-chapter-7:lecture20.ppt |Lecture 20 PowerPoint Slides}}: First-order circuit step response, introduction to second-order systems 
-    * {{ :learn:courses:real-analog-chapter-7:lab7p5p1.pdf |Lab 7.5.1}}: Passive RC Circuit Step Response +    * [[http://www.youtube.com/watch?v=exK3dZOSw48&list=PLDEC730F6A8CDE318&index=18&feature=plpp_video| Lecture 16(b) Video]] 
-      * {{ :learn:courses:real-analog-chapter-7:lab7p5p1_worksheet.docx |7.5.1 Worksheet}} +    * [[http://www.youtube.com/watch?v=cOkLo21C0K0&list=PLDEC730F6A8CDE318&index=19&feature=plpp_video| Lecture 17 Video]] 
-    * {{ :learn:courses:real-analog-chapter-7:lab7p5p2.pdf |Lab 7.5.2}}: Passive RC Circuit Step Response +    * [[http://www.youtube.com/watch?v=lid-oZFQtHU&list=PLDEC730F6A8CDE318&index=20&feature=plpp_video| Lecture 18 Video]] 
-      * {{ :learn:courses:real-analog-chapter-7:lab7p5p2_worksheet.docx |7.5.2 Worksheet}} +    * [[http://www.youtube.com/watch?v=I86jABHbKEw&list=PLDEC730F6A8CDE318&index=21&feature=plpp_video| Lecture 19 Video]] 
-    * {{ :learn:courses:real-analog-chapter-7:lab7p5p3.pdf |Lab 7.5.3}}: Active RC Circuit Step Response +    * [[http://www.youtube.com/watch?v=cYceSN9hg4s&list=PLDEC730F6A8CDE318&index=22&feature=plpp_video| Lecture 20(a) Video]] 
-      * {{ :learn:courses:real-analog-chapter-7:lab7p5p3_worksheet.docx |7.5.3 Worksheet}} +  * Chapter 7 Videos: 
- +    * [[http://www.youtube.com/watch?v=6qcHcQSg1oY&list=PL170A01159D42313D&index=16&feature=plpp_video| Lab 7 Video 1]]: RC Circuit Natural Response: We create an RC circuit natural response in two ways: by (1) converting the source to an open circuit and (2) converting the source to a short-circuit. 
 +    * [[http://www.youtube.com/watch?v=ld2e4eT0Yuc&list=PL170A01159D42313D&index=17&feature=plpp_video| Lab 7 Video 2]]: RC Circuit Forced Response: The step responses of both passive and active first-order RC circuits are measured. Loading effects on the two circuits are examined. 
 +  * {{ :learn:courses:real-analog-chapter-7:real-analog-chapter-7.pdf | Chapter 7 Complete PDF}} 
 +    * {{ :learn:courses:real-analog-chapter-7:lab7p2p1.pdf |Lab 7.2.1}} 
 +      * {{ :learn:courses:real-analog-chapter-7:lab7p2p1_worksheet.docx |Worksheet 7.2.1}} 
 +    * {{ :learn:courses:real-analog-chapter-7:lab7p3p1.pdf |Lab 7.3.1}} 
 +      * {{ :learn:courses:real-analog-chapter-7:lab7p3p1_worksheet.docx |Worksheet 7.3.1}} 
 +    * {{ :learn:courses:real-analog-chapter-7:lab7p4p1.pdf |Lab 7.4.1}} 
 +      * {{ :learn:courses:real-analog-chapter-7:lab7p4p1_worksheet.docx |Worksheet 7.4.1}} 
 +    * {{ :learn:courses:real-analog-chapter-7:lab7p5p1.pdf |Lab 7.5.1}} 
 +      * {{ :learn:courses:real-analog-chapter-7:lab7p5p1_worksheet.docx |Worksheet 7.5.1}} 
 +    * {{ :learn:courses:real-analog-chapter-7:lab7p5p2.pdf |Lab 7.5.2}} 
 +      * {{ :learn:courses:real-analog-chapter-7:lab7p5p2_worksheet.docx |Worksheet 7.5.2}} 
 +    * {{ :learn:courses:real-analog-chapter-7:lab7p5p3.pdf |Lab 7.5.3}} 
 +      * {{ :learn:courses:real-analog-chapter-7:lab7p5p3_worksheet.docx |Worksheet 7.5.3}}
   * {{ :learn:courses:real-analog-chapter-7:realanalog-exercisesolutions-chapter7.pdf |Exercise Solutions}}: Chapter 7 exercise solutions   * {{ :learn:courses:real-analog-chapter-7:realanalog-exercisesolutions-chapter7.pdf |Exercise Solutions}}: Chapter 7 exercise solutions
   * {{ :learn:courses:real-analog-chapter-7:homework7.docx |Homework}}: Chapter 7 homework problems   * {{ :learn:courses:real-analog-chapter-7:homework7.docx |Homework}}: Chapter 7 homework problems
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 The overall solution, then, from equations (7.48), (7.50), and (7.52) is: The overall solution, then, from equations (7.48), (7.50), and (7.52) is:
  
-$$y(t)=K_e^\frac{-t}{\tau} + K_2     (Eq. 7.53)$$+$$y(t)=K_1e^\frac{-t}{\tau} + K_2     (Eq. 7.53)$$
  
 The unknown constants $K_1$ and $K_2$ are typically determined from evaluating the circuit’s behavior for $t=0$ and $t \rightarrow \infty$ .  The unknown constants $K_1$ and $K_2$ are typically determined from evaluating the circuit’s behavior for $t=0$ and $t \rightarrow \infty$ . 
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 KCL at node “A” of the circuit shown above results in: KCL at node “A” of the circuit shown above results in:
  
-$$\frac{10-v_C)(100\Omega} = \frac{v_C}{200\Omega}+1x10^{-3} \frac{dv_C}{dt}$$+$$\frac{10-v_C}{100 \Omega} = \frac{v_C}{200\Omega}+1x10^{-3} \frac{dv_C}{dt}$$
  
 Placing this in the form of equation (7.46) results in: Placing this in the form of equation (7.46) results in:
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 {{ :learn:courses:real-analog-chapter-7:chapter7bc.png |Example image 4.}} {{ :learn:courses:real-analog-chapter-7:chapter7bc.png |Example image 4.}}
  
 +
 +[[{}/learn/courses/real-analog-chapter-6/start|Back to Chapter 6]]
 +[[{}/learn/courses/real-analog-chapter-8/start|Go to Chapter 8]]