2. Introduction to Feedback Systems / © 1999 Önder YÜKSEL 25.02.1999EE 302 - Block Diagrams - O. Yuksel 1

3. Introduction to Feedback Systems / © 1999 Önder YÜKSEL 25.02.1999EE 302 - Block Diagrams - O. Yuksel 2 A block diagram Is a graphical representation of an(a set of) algebraic equation(s) Indicates relationships between different signals Thus gives more insight in to the pysical problem

4. Introduction to Feedback Systems / © 1999 Önder YÜKSEL 25.02.1999EE 302 - Block Diagrams - O. Yuksel 3 Signals are multiplied by constants or transfer functions: G xy y=G.x A “Gain Element” or “Coefficient Multiplier” Note: signal flow direction must be indicated!

5. Introduction to Feedback Systems / © 1999 Önder YÜKSEL 25.02.1999EE 302 - Block Diagrams - O. Yuksel 4 Also represents a LTI dynamical system G xy Signals in frequency domain Gain is a transfer function x(s)y(s) G(s)

6. Introduction to Feedback Systems / © 1999 Önder YÜKSEL 25.02.1999EE 302 - Block Diagrams - O. Yuksel 5 Signals are added or subtracted: z=x+y x y z A summing point

7. Introduction to Feedback Systems / © 1999 Önder YÜKSEL 25.02.1999EE 302 - Block Diagrams - O. Yuksel 6 A signal is fed to more than one point x y z y=z=x A distribution point

8. Introduction to Feedback Systems / © 1999 Önder YÜKSEL 25.02.1999EE 302 - Block Diagrams - O. Yuksel 7 Gain elements Summing points Distribution points

9. Introduction to Feedback Systems / © 1999 Önder YÜKSEL 25.02.1999EE 302 - Block Diagrams - O. Yuksel 8 Block diagram reduction Two blocks can be reduced into one, if they are in one of the three basic interconnection patterns: parallelcascadefeedback

10. Introduction to Feedback Systems / © 1999 Önder YÜKSEL 25.02.1999EE 302 - Block Diagrams - O. Yuksel 9 Parallel interconnection A B x x x Bx y=Ax+Bx Ax A+B Inputs common Outputs added Gains added!

11. Introduction to Feedback Systems / © 1999 Önder YÜKSEL 25.02.1999EE 302 - Block Diagrams - O. Yuksel 10 Attention! Equivalence valid only between input & output Intermediate variables are lost!! A+B ? A B

12. Introduction to Feedback Systems / © 1999 Önder YÜKSEL 25.02.1999EE 302 - Block Diagrams - O. Yuksel 11 Cascade interconnection HG x1x1 y 1 =Gx 1 =x 2 y 2 =Hx 2 =GHx 1 G.H

13. Introduction to Feedback Systems / © 1999 Önder YÜKSEL 25.02.1999EE 302 - Block Diagrams - O. Yuksel 12 Attention! ? ?

14. Introduction to Feedback Systems / © 1999 Önder YÜKSEL 25.02.1999EE 302 - Block Diagrams - O. Yuksel 13 Feedback interconnection G 1+GH G H + _ x

15. Introduction to Feedback Systems / © 1999 Önder YÜKSEL 25.02.1999EE 302 - Block Diagrams - O. Yuksel 14 Attention! G H + _ Fails in these cases:

16. Introduction to Feedback Systems / © 1999 Önder YÜKSEL 25.02.1999EE 302 - Block Diagrams - O. Yuksel 15 Tricky cases None of the 3 basic reduction tools applicable! Must find some tricks!

17. Introduction to Feedback Systems / © 1999 Önder YÜKSEL 25.02.1999EE 302 - Block Diagrams - O. Yuksel 16 G G G

18. Introduction to Feedback Systems / © 1999 Önder YÜKSEL 25.02.1999EE 302 - Block Diagrams - O. Yuksel 17 G G G

19. Introduction to Feedback Systems / © 1999 Önder YÜKSEL 25.02.1999EE 302 - Block Diagrams - O. Yuksel 18 GG For G  0 1/G

20. Introduction to Feedback Systems / © 1999 Önder YÜKSEL 25.02.1999EE 302 - Block Diagrams - O. Yuksel 19 G 1/G For G  0 G

21. Introduction to Feedback Systems / © 1999 Önder YÜKSEL 25.02.1999EE 302 - Block Diagrams - O. Yuksel 20 End of Section General index Restart sectionNext section Next chapterRestart chapter End show The End i