Engineering     Difference Equations     Kirchoffs Law     Sinusoidal Analysis     Communications     Differential Equations     Dynamic Systems     Probability and Stats     Control Systems Simulations      MATLAB      Examples in MATLAB Links to other websites Johns Hopkins   -   Signals & systems example Cal State San Bernardino   -   Probablity and Statistics Engineering>> Kirchoff's Law Prev |  Next |  Home  | Contact us  | Objective     EXTENSION TO N NODE CIRCUIT OF THE KIRCHOFF’S LAW: Consider N section network to find the voltages at each of the N nodes Applying Kirchoff's current law to the kth node or changing index k to k+1, we get ......................................................................(1) This is called a homogenous difference equation. Solution of (1) gives Vk () , the node voltage at the kth node. Let So, where E is called a shift operator. Rewriting equation (1) or Forming the auxiliary equation m2  -  3 m  +  1=0 ............................(2) Solution of (2) gives two roots    If we let we can verify Hence, solution to (1) is given by ..........................................................................(3) where A,B are two arbitrary constants.   Prev |  Next |  Home  | Contact us  | Objective