Signal Flow Graph Part-1 By ECE Tech Notes

1. Find the Transfer Function(TF) of a signal flow graph(SFG) given below.

From the SFG we have,

1. Total forward paths = 1.

P1 = G1G2G3

2. No. of F/b loops = 3.

L1 = -G1G2H1, L2 = -G2H2, L3 = -G2G3H3

3. There are no two non touching loops.

4. Since all the loops are touching to the forward path  P1. So, Δ1 = 1.

Now, Δ = 1 - [ L1 + L2 + L3 ] = 1 - [ -G1G2H1 -G2H2 -G2G3H3 ] 

Δ = 1+ G1G2H1 + G2H2 + G2G3H3

The TF of a SFG is given by mason gain formula,

TF = C(s) / R(s) = P1Δ1/Δ

Substituting the values of P1, Δ1 & Δ we get,

2. Find the Transfer Function(TF) of a signal flow graph(SFG) given below.

From the SFG we have,

1. Total forward paths = 1

P1 = G1G2G3G4 

2. No. of F/b loops = 3

L1= -G3G4H1, L2 = -G2G3H2, L3 = -G1G2G3G4H3, 

3. There are no two non touching loops.

4. Since all the loops are touching to the forward path  P1. So, Δ1 = 1.

Now, Δ = 1 - [ L1 + L2 + L3 ] = 1 - [ -G3G4H1 -G2G3H2 -G1G2G3G4H3 ]

Δ =  1+ G3G4H1+ G2G3H2 + G1G2G3G4H3 

The TF of a SFG is given by mason gain formula,

TF = C(s) / R(s) = P1Δ1/Δ

Substituting the values of P1, Δ1 & Δ we get,

3. Find the Transfer Function(TF) of a signal flow graph(SFG) given below.

From the SFG we have,

1. Total forward paths = 2

P1 = G1G2G3, P2 = G4G3

2. No. of F/b loops = 3

L1 = -G2H2, L2 = -G1G2G3H1 L3 = -G4G3H1

3. Product of all two non touching loops are L1L3 = G2G3G4H1H2

4. Since all the loops are touching to the forward path P1. So, Δ1 = 1.

For the P2, L1 is the non touching loop. So,

Δ2 = 1 - [ L1 ] = 1 - [ -G2H2 ] = 1 + G2H2.

Now, Δ = 1 - [ L1 + L2 +  L3 ] +[ L1L3 ] 

Δ = 1 + G2H2 + G1G2G3H1 + G4G3H1 + G2G3G4H1H2

The TF of a SFG is given by mason gain formula,

TF = C(s) / R(s) = (P1Δ1 + P2Δ2)/Δ

Substituting the values of P1, Δ1, P2, Δ2 & Δ we get,

4. Find the Transfer Function(TF) of a signal flow graph(SFG) given below.

From the SFG we have,

1. Total forward paths = 2.

P1 = G1G2G3, P2 = G1G4

2. No. of F/b loops = 5.

L1 = G1G2H1, L2 = -G1G2G3, L3 = -G1G4, L4 =G4H2, L5 =G2G3H2

3. There are no two non touching loops.

4. Since all the forward paths are touching to all the loops. So,  Δ1 = Δ2 =1.

Now, Δ = 1 - [ L1 + L2 + L3 + L4 + L5 ] = 1 -  [G1G2H1 - G1G2G3 - G1G4 + G4H2 + G2G3H2]

Δ = 1 - G1G2H1 + G1G2G3 + G1G4 - G4H2 - G2G3H2

The TF of a SFG is given by mason gain formula,

TF = C(s) / R(s) = (P1Δ1 + P2Δ2)/Δ

Substituting the values of P1, Δ1, P2, Δ2 & Δ we get,