Question

In a given system, the sink Y(s) is related to the source X(s) as follows: Y60 - [(42869 =Y(6) *v) (1) (ii) Draw and clearly label the SFG for this system (3 points) Use Mason's Rule to determine the transmittance, T(s) from your SFG. (Note: Show all the steps (variables, etc) involving Mason's Rule) (2 points)

Answer 1

An) Civen ys) are (K. (engles) (x6) - yes) Fless you] you: R.K. (lyde (XLs)- yas) - Pen لا ری 4s - X55) í ca B5) ( Sink) Csoura) Scanned with CamScanner

BCS) - K,. C(s) + K2 BCS) But But «)= Xcs) - BCS) - Bes) = kx (xS)- Bc)] + ky BCS) Byu BCS)= y(s). .: yasli ki [xcs) - Ycs)) + K2:40) By comparing with o **** () es scanned with & K Scanned with CamScanner

Now mason's Grain formula it. B, A1+ B 924 no. Whene P, Pi... Forward path gains from ilp to olp. DE 1- (& single loop ganu) : : .t 7 E (loops E (2 loops that dont touch gain poducet ) +3:-) + Di-- Aše 8 Calculateol by removing the respective bolunod path, From SFG clearly there is only bosward path from input to output Now one Gain of that path = 1x K, x1 Scanned with CamScanner ki:

the noder present remove Now it we aul path no loops no loops au formed bonward in the .: Die C1-0707 - 1. - Piz ki.. Since no other & P2, P₃ --- =o: Forward path, . . Now bol Di . that These are hoo loops are being former they are = 121 two loops - 99 1 Gaine are = K (-) & - Kz i ki Now these two loops are intesteching Es Scanne ateith point CamScanner

So non-touching loop gane so B. a 1- ¿ Cloop gaihu) +0-0- 1- (-kytkez) g. - It K- Kz bul. Ko e o k. ( 1 ) Header :D 18 * ( 4 ) ( ) AS A lten (4) AS Scanned with CamScanner :

maioni gain Foimit - TC) en K. I en tidak be rbau an be *R. Iz As Xu) i es va î yos) s Scanned with CamScanner