# Venerabelia

A Veritable Almanac!

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

## Pascal Triangle 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 Venerabelia