LAN/WAN Optimization Techniques Chp.1~Chp.4. Harrell J. Van Norman Presented by Shaun Chang. Outline. Networks Local-Area Networks (LANs) Wide-Area Networks (WANs) Network Design Network Engineering Process Network Design Tools. Networks. LANs Short-distance networks (less than 1 mile)
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Harrell J. Van Norman
Presented by Shaun Chang
In this method, the overall gain of SFG from a source node to a sink node may be obtained by eliminating the intermediate nodes.
Mason's rule is a general gain formula can be used to determine the transfer functions directly. (i.e., relates the output to the input for a SFG. )
Thus the general formula for any SFG is given by :
Pi : the total gains of the ith forward path
D = 1 - ( of all individual loop gains) + ( of loop gains of all possible non-touching loops taken two at a time) - ( of loop gains of all possible non-touching loops taken three at a time) + …
Di = the value of D evaluated with all gain loops touching Piare eliminated.
Notice: In case, all loops are touching with forward paths (Pi) , Di = 1
Touching loops: Loops with one or more nodes in common are called touching.
A loop and a path are touching when they have a common node.
Non-touching loops : Loops that do not have any nodes in common
Non-touching loop gain : The product of loop gains from non-touching loops.
Example :Find C/R for the attached SFG.
Forward Path gain: (Only one path, So, i =1) P1 = G1.G2.G3.G4.G5 ……………. (1)
Non-touching loops taken two at a time:
L1&L2 : G2.H1.G4.H2
L1&L3 : G2.H1.G7.H4
L2&L3 : G4.H2.G7.H4
Non-touching loops taken three at a time:
According to Mason’s rule:
sum of gain products of all possible non-touching loops taken two at a time
= 1 - (G2.H1 + G4.H2 + G7.H4 + G2.G3.G4.G5.G6.G7) +
[G2.H1.G4.H2 + G2.H1.G7.H4 + G4.H2.G7.H4] – [G2.H1.G4.H2.G7.H4] ……. ……. ……… (2)
Then, we form ibyeliminating from the loop gains that touch the forward path (Pi).
1= - loop gains touching the forward path (Pi).
sum of gain products of all possible non-touching loops taken three at a time
Now Substituting equations (1) , (2) & (3) into the Mason’s Rule as :
The following procedure is used to solve any SFG using Mason's rule.
1) Identify the no. of forward paths and their gains (Pi).
2) Identify the number of the loops and determine their gains (Lj).
3) Identify the non-touching loops taken two at a time, a three at a time, … etc.
4) Determine D .
5) Determine i .
6) Substitute all of the above information in the Mason's formula.