This document outlines 10 rules for reducing block diagrams, including combining blocks in series and parallel, eliminating feedback loops, shifting summing and takeoff points, and applying associative laws. It also provides a procedure for using the rules to systematically simplify block diagrams by reducing series and parallel blocks, eliminating feedback, and shifting points to obtain the simplest form and overall transfer function.

1. Rules for
Block Diagram Reduction
By
Kaustubh Harihar Shedbalkar.
Department of Electrical Engineering,
SITCOE, Yadrav
Rules for Block Dia.
Reduction

2. Rules for Block Dia.
Reduction
Rule 01: - Blocks in series or cascade.
G1(s) G2(s)
G1(s). G2(s)
R(S)
R(S)
C(S)
C(S)

3. Rules for Block Dia.
Reduction
Rule 02: - Block in parallel.
G1(s)
G2(s)
G3(s)
R(S) C(S)
+
+
-
G1(s)+G2(s)-
G3(s)
R(S) C(S)

4. Rules for Block Dia.
Reduction
Rule 03: - Eliminate Feedback Loop.
G(s)
H(s)
R(S) C(S)
G(s)/1+G(s).H(s)
R(S) C(S)
+
-

5. Rules for Block Dia.
Reduction
Rule 04: -Associative law for summing points in
series.
R(S) C(S)
+ +
+ -
B1 B2
R(S) C(S)
+ +
- +
B2 B1

6. Rules for Block Dia.
Reduction
Rule 05: - Shifting of summing point before block.
G(s)
R(S) C(S)
+
+
X
C(S) = R(S).G(S)+X
G(s)
R(S)
+
C(S)
C(S) = (R(S)+X).G(S)
= R(S).G(S)+X.G(S)
X
+

7. Rules for Block Dia.
Reduction
Rule 05: - Shifting of summing point before block.
G(s)
R(S) C(S)
+
+
X
C(S) = R(S).G(S)+X
G(s)
R(S)
+
C(S)
C(S) =R(S).G(S)+X
X
+
1/G(s)

8. Rules for Block Dia.
Reduction
Rule 06: - Shifting of summing point after block.
G(s)
R(S) C(S)
C(S) = R(S).G(S)+X.G(S)
G(s)
R(S) C(S)
C(S) = R(S).G(S)+X
+
+
X
X
+
+

9. Rules for Block Dia.
Reduction
Rule 06: - Shifting of summing point after block.
G(s)
R(S) C(S)
C(S) = R(S).G(S)+X.G(S)
G(s)
R(S) C(S)
C(S) = R(S).G(S)+X.G(S)
+
+
X
X
+
+
G(s)

10. Rules for Block Dia.
Reduction
Rule 07: - Shifting of take off point before block.
G(s)
R(S) C(S)
X
C(S)= R(S).G(S)
X= R(S).G(S)
R(S) C(S)
X
C(S)= R(S).G(S)
X= R(S)
G(s)

11. Rules for Block Dia.
Reduction
Rule 07: - Shifting of take off point before block.
R(S) C(S)
X
C(S)= R(S).G(S)
X= R(S).G(S)
R(S) C(S)
X
C(S)= R(S).G(S)
X= R(S).G(S)
G(s)
G(s)
G(s)

12. Rules for Block Dia.
Reduction
Rule 08: - Shifting of take off point after block.
G(s)
R(S) C(S)
X
C(S)= R(S).G(S)
X= R(S)
R(S) C(S)
X
C(S)= R(S).G(S)
X= R(S).G(S)
G(s)

13. Rules for Block Dia.
Reduction
Rule 08: - Shifting of take off point after block.
G(s)
R(S) C(S)
X
C(S)= R(S).G(S)
X= R(S)
R(S) C(S)
X
C(S)= R(S).G(S)
X= R(S)
G(s)
1/G(s)

14. Rules for Block Dia.
Reduction
R(S)
+
+
Y
Rule 09: - Shifting of take off point after summing
block.
Z
C(S) C(S)=R(S)+Y
Z= R(S)
R(S)
+
+
Y
Z
C(S) C(S)=R(S)+Y
Z= R(S)
-
+

15. Rules for Block Dia.
Reduction
R(S)
+
+
Y
Rule 10: - Shifting of take off point before
summing block.
Z
C(S) C(S)=R(S)+Y
Z= R(S) + Y
R(S)
+
+
Y
Z
C(S) C(S)=R(S)+Y
Z= R(S) + Y
+
+

16. Rules for Block Dia.
Reduction
Procedure to solve block dia. Reduction problems -
 Reduce blocks connected in series.
 reduce blocks connected in parallel.
 Eliminate feedback paths.
 Always try to shift take off points towards right and
summing points towards left.
 Repeat above procedure till you get simplest form.
Find transfer function of complete system.