1. Electronics Technology Fundamentals Chapter 16 RL and RC Circuit Pulse Response

2. Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 2 16.1 Square Wave Response: RL Time Constants – P1 Rectangular and Square Waves PW – Pulse Width SW – Space Width Period = PW + SW

3. Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 3 16.1 Square Wave Response: RL Time Constants – P2 Voltage and Current Transitions In a purely resistive circuit, the V R and current waveforms have the same shape as V S

4. Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 4 16.1 Square Wave Response: RL Time Constants – P3 Inductor Voltage (V L ) – the inductor slows the change in current

5. Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 5 16.1 Square Wave Response: RL Time Constants – P4 Inductor Voltage (V L ) (Continued)

6. Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 6 16.1 Square Wave Response: RL Time Constants – P5 More on RL Circuit Waveforms Time intervals identified using the Greek letter tau (  ) Rise and decay curves are symmetrical

7. Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 7 16.1 Square Wave Response: RL Time Constants – P6 The Universal Curve – one that can be used to predict the operation of any specified type of circuit

8. Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 8 16.1 Square Wave Response: RL Time Constants – P7 The Universal Curve (Continued) where e = the base of the natural log system (approximately 2.71828) x= the variable exponent

9. Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 9 16.1 Square Wave Response: RL Time Constants – P8 Plotting the Universal Curve

10. Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 10 16.1 Square Wave Response: RL Time Constants – P9 The Decay Curve

11. Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 11 16.1 Square Wave Response: RL Time Constants – P10 The RL Time Constant (  ) where  = the duration of each time interval, in seconds L= the total series inductance R= the total series resistance

12. Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 12 16.1 Square Wave Response: RL Time Constants – P11 The RL Time Constant (  ) (Continued) Example: L = 10 mH, R = 100 

13. Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 13 16.1 Square Wave Response: RL Time Constants – P12 Defining the Time Constant (  ) RL Time Constant – the time required for the current in an RL switching circuit to increase (or decrease) by 63.2% of its maximum possible  I

14. Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 14 16.1 Square Wave Response: RL Time Constants – P13 Time Calculations where ln = the natural log function

15. Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 15 16.1 Square Wave Response: RL Time Constants – P14 Time Calculations (Continued)

16. Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 16 16.1 Square Wave Response: RL Time Constants – P15

17. Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 17 16.2 Square Wave Response: RC Time Constants – P1 RC Circuit Waveforms

18. Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 18 16.2 Square Wave Response: RC Time Constants – P2 The Universal Voltage Curve – almost the same as the universal current curve for RL switching circuits

19. Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 19 16.2 Square Wave Response: RC Time Constants – P3 RC Circuit Waveforms Time intervals identified using the Greek letter tau (  ) Rise and decay curves are symmetrical

20. Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 20 16.2 Square Wave Response: RC Time Constants – P4 The Curve Equations where e = the base of the natural log system (approximately 2.71828) x= the variable exponent

21. Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 21 16.2 Square Wave Response: RC Time Constants – P5 The RC Time Constant (  ) where  = the duration of each time interval, in seconds C= the total series capacitance R= the total series resistance

22. Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 22 16.2 Square Wave Response: RC Time Constants – P6 The RC Time Constant (  ) (Continued) Example: C = 10  F, R = 1k 

23. Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 23 16.2 Square Wave Response: RC Time Constants – P7 Defining the Time Constant (  ) RC Time Constant – the time required for the current in an RC switching circuit to increase (or decrease) by 63.2% of its maximum possible  V

24. Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 24 16.2 Square Wave Response: RC Time Constants – P8 Time Calculations where ln = the natural log function

25. Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 25 16.2 Square Wave Response: RC Time Constants – P9 Time Calculations (Continued)

26. Electronics Technology Fundamentals, 3 rd ed. Paynter and Boydell © 2009 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 26 16.2 Square Wave Response: RC Time Constants – P10