1) The document discusses signal flow graphs, which provide a graphical representation of linear algebraic equations in a system. Nodes represent variables and branches show relationships.
2) It compares block diagrams and signal flow graphs, noting that signal flow graphs only need to be drawn once, saving time and space over repeatedly redrawing block diagrams.
3) Mason's gain formula allows directly calculating the overall transfer function of a system from its signal flow graph representation, without lengthy reduction steps.
This presnetation gives complete idea about block diagram representation and reduction techniques to find transfer function. Also gives complete idea about Signal flow graph method to find transfer function.
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Signal flow graphs consist of:
๐ Nodes โrepresent signals
๐ Branches โrepresent system blocks
Branches labeled with system transfer functions
This presnetation gives complete idea about block diagram representation and reduction techniques to find transfer function. Also gives complete idea about Signal flow graph method to find transfer function.
It Defines what is Programmable Logic Array(PLA) also explains it in easy wording with syntax and Example...
It also cover what is Combinational & Sequential Logic Circuit and the Difference b/w these both. :)
An amplifier is one of the most important applications of transistor. Generally, transistor in CE configuration was used for faithful amplification of signal due to high gain, high input impedance and high power gain. But it has been observed that feedback in an amplifier introduces significant improvement in gain and gives amplified output in required form.
Control Signal Flow Graphs lecture notesabbas miry
ย
Signal flow graphs consist of:
๐ Nodes โrepresent signals
๐ Branches โrepresent system blocks
Branches labeled with system transfer functions
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3. 1. introduction
๏The graphical representation of the variables of set of linear
algebraic equation representing the system is called signal flow
graph
๏There are two important elements constituting signal flow graph
๏Nodes:- as variable of system are represented first in signal flow
graph by small circle called nodes
๏Branches:- the lines joining the nodes are called branches. The
relationship between various nodes are represented by joining the
nodes as per the equation
NODES
BRANCHES
4. 2. Comparison of BD and SFG
)(sR
)(sG
)(sC
)(sG
)(sR )(sC
Block diagram Signal flow graph
๏ In this case at each step block
diagram is to be redrawn.
๏ Thatโs why it is tedious method.
๏ So wastage of time and space.
๏ Only one time SFG is to be
drawn and then masonโs
gain formula is to be
evaluated.
๏ So time and space is saved.
5. 3. SFG terms representation
Source node
b1x
2x
c
1
3x
3x
Dummy node
Feedback loop OR
Individual loop
branch
node
Sink node
Loop gain= b x c
Chain node
1
6. 4. Masonโs gain formula
๏ We know that in block diagram representation ,reduction method is
time consuming.
๏ In signal flow graph approach, direct use of one formula leads to the
overall system transfer function
๐ถ(๐ )
๐ (๐ )
.
๏ This formula is given by mason and hence it is know as masonโs gain
formula.
T =
๐ถ(๐ )
๐ (๐ )
=
1
โ
๐ ๐พ โ ๐พ
๏ STEP of masonโs gain formula
1. Step 1 : calculating forward path gains
2. Step 1 : individual loop gain
3. Step 3 :gain product of non touching
loops
4. Step 4:Calculate โ, โ ๐พ.
5. STEP 5 : Calculate T
7. 5. EXAMPLE 1
1.FIND
๐ถ(๐ )
๐ (๐ )
BY USING MASONโS GAIN FORMULA.
Solution:- STEP 1 : GAIN OF FORWARD PATH = ๐1= ๐บ1 ๐บ2 ๐บ3 ๐บ4
STEP 2 : GAIN OF INDIVIDUAL LOOP
๐11= -๐บ2 ๐บ3 ๐ป2
-๐ฏ ๐
-1
-๐ฏ ๐
2 3 4 5 6
1 1
1 7
๐ฎ ๐
๐ฎ ๐
๐ฎ ๐
๐ฎ ๐
8. โฆ
๐21= โ๐ป1 ๐บ4 ๐บ3
๐31= -๐บ1 ๐บ2 ๐บ3 ๐บ4
STEP 3: GAIN OF NON โ TOUGHING LOOP
NO NON-TOUGHING LOOP
STEP 4: TO CALCULATE โ, โ ๐พ.
โ = 1- (SUM OF ALL INDIVIDUAL LOOPS GAIN ) + (MULTIPLICATION OF NON
TOUGHING LOOPS GAIN)
= 1- (-๐บ2 ๐บ3 ๐ป2 โ๐ป1 ๐บ4 ๐บ3-๐บ1 ๐บ2 ๐บ3 ๐บ4)+ 0
= 1+ ๐บ2 ๐บ3 ๐ป2 +๐ป1 ๐บ4 ๐บ3 + ๐บ1 ๐บ2 ๐บ3 ๐บ4
9. In our case K =1
โ 1=1-(If L 1 , P 1 is non touching than put L 1)
But in this case there are no non-toughing loop
=1
T =
๐ถ(๐ )
๐ (๐ )
=
1
โ
๐ ๐พ โ ๐พ
=
๐1โ1
โ
=
๐บ1 ๐บ2 ๐บ3 ๐บ4 x 1
1+ ๐บ2 ๐บ3 ๐ป2+๐ป1 ๐บ4 ๐บ3+๐บ1 ๐บ2 ๐บ3 ๐บ4
10. 6. Example 2
2. Find
๐ถ(๐ )
๐ (๐ )
by using masonโs gain formula.
๏ STEP 1 : Gain of forward path = ๐1= ๐บ1 ๐บ2 ๐บ3 ๐บ4, ๐2= ๐บ5 ๐บ4
๏ STEP 2 : Gain of individual loop
๐11= -๐บ2 ๐ป1
๐ฎ ๐
-๐ฏ ๐
-๐ฏ ๐
2 3 4 5 6
1 1
1 7
๐ฎ ๐ ๐ฎ ๐
๐ฎ ๐
๐ฎ ๐
11. ...
๐21= -๐บ1 ๐บ2 ๐บ3 ๐บ4 ๐ป2
๐31= โ๐บ5 ๐บ4 ๐ป2
๏ STEP 3: Gain of non โ toughing loop
๐11= -๐บ2 ๐ป1
๐31= โ๐บ5 ๐บ4 ๐ป2
๏ STEP 4: To calculate โ, โ ๐พ.
โ = 1- (sum of all individual loops gain ) + (multiplication of non toughing
loops gain)
= 1-(-๐บ2 ๐ป1-๐บ1 ๐บ2 ๐บ3 ๐บ4 ๐ป2-๐บ5 ๐บ4 ๐ป2) + (๐บ2 ๐ป1 ๐บ5 ๐บ4 ๐ป2)
=1+๐บ2 ๐ป1 + ๐บ1 ๐บ2 ๐บ3 ๐บ4 ๐ป2 + ๐บ5 ๐บ4 ๐ป2 + ๐บ2 ๐ป1 ๐บ5 ๐บ4 ๐ป2
12. ...
In our case K =2
For ๐1 all loops are touching
โ 1= 1-(If ๐11, ๐21, are non touching to P 1)
= 1-0
= 0
โ 2= 1-(If ๐11, ๐21, are non touching to P 2)
= 1-(L 1)
= 1+๐บ2 ๐ป1
T =
๐ถ(๐ )
๐ (๐ )
=
1
โ
๐ ๐พ โ ๐พ
=
๐1โ1+๐2โ2
โ
=
๐บ1 ๐บ2 ๐บ3 ๐บ4 x 1+๐บ5 ๐บ4(1+ ๐บ2 ๐ป1)
1+ ๐บ2 ๐ป1+๐บ1 ๐บ2 ๐บ3 ๐บ4 ๐ป2+๐บ5 ๐บ4 ๐ป2+ ๐บ2 ๐ป1 ๐บ5 ๐บ4 ๐ป2