Pascal Triangle

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Pascal Triangle

 

Blaise Pascal 19 June 1623 – 19 August 1662

 

 

 

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1

1 6 15 20 15 6 1

1 7 21 35 35 21 7 1

1 8 28 56 70 56 28 8 1

1 9 36 84 126 126 84 36 9 1

 

Using the Pascal Triangle to evaluate Ladder Networks

The simplest ladder network is shown above and using the load over total formula for potential dividers gives:-

 

Vo/Vi = R2/R2 +R1

 

therefore Vi/Vo = 1 + R1/R2

 

but 1/R2 = Y an admittance

 

let R1 = Z

 

then Vi/Vo = 1 + ZY

 

Example: Let R1 =10k and R2 = 1k

 

Then Vi/Vo = 1 + 10,000/1000

 

= 11

 

therefore Vo = 1/11 of Vi

 

Using the Pascal Triangle On a More Complex Ladder NetwrThe triangle needs to be arranged as below:-

 

1

1 1

1 2 1 1 stage = 1.1

1 3 3 1

1 4 6 4 1 2 stage = 1.3.1

15 10 10 5 1

1 15 20 15 6 1 3 stage = 1.6.5.1

1 7 21 35 35 21 7 1

1 8 28 56 70 56 28 8 1 4 stage = 1.10.15.7.1

19 36 84 126 126 84 36 9 1

 

 

 

 

Find Vo/Vi for the following:Vi/Vo = 34

 

Another example, find Vi/Vo for the following ladder network:-

 

Vi/Vo = 47.69

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