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: ............................................................(3) where A,B are two arbitrary constants. To find A,B we need two initial conditions or boundary conditions We know ..............................................(4) We need one more condition. To get this, we need to find the current coming out of the voltage source, as shown in the previous case. Replace the circuit looking towards the terminal node from node k by an equivalent thevenin resistance Rk. Hence, Where Rk-1 is the equivalent resistance at node (k-1). or, ..........................................................(5) with boundary condition RN = R Hence, etc. If we let RN-i = C N-i R i.e. Rj = C j R...............................................................................(6) .......................................................................(7) with CN=1 Iteratively solve (7) to get C1 and hence R1 = C 1 R Once R1 is obtained Applying KCL to node 1 or, .........................................(8) Using (8) in (3) gives .............................................(9) Use (4) and (9) to get A,B ; substitute these values of A,B back in (3) to get the node voltage for Vk for any k in (1,2,...........N).   Example       Prev |  Next |  Home  | Contact us  | Objective