# Mason's Gain Formula with a not connected loops

We have the following path.

I tried to create the gain with Mason's formula, which lead me to the following:

Forward Path 1: 1
Loop 1: (1/s)*(2/s)*2
Loop 2: (-1)*(2/s)*2


When I put them together I get:

(1/1 - ((1/s)*(2/s)*2) - ((2/s)*2)) * (-1)*(2/s)*2


If I multiply it with s^2 I get

(-4s)/(s^2+4s+4)


But according to the solution it should be

(s^2 + 4s)/(s^2+4s+4)


So my upper part does not match. Do I use Mason's Gain Formula wrong?

• Can you offer a better picture that more easily distinguishes between the characters 2,Z and S. – Andy aka Apr 18 '17 at 8:25
• I added a better one. – Pascal Apr 18 '17 at 8:30
• Isn't loop 1 (1/s)*(2/s)*2? You seem to be using 1/2 instead of 1/s. – Andy aka Apr 18 '17 at 8:38
• ah sorry, I typed it wrong – Pascal Apr 18 '17 at 8:39
• So was that your error? – Andy aka Apr 18 '17 at 8:40