Dualty:-The two n/w are should to be dual n/w of each other. If the mesh eq. of given n/w are node eq. of other n/w. the dual network are based on kirchof's voltage and current law. In one network eq. are writen as sumetion of voltage drop in other n/w. If equation are written by summing of current atom node.
"principle of duality ony implies that ckt eq. are of the same mathematical form and the dual n/w be have similarly but with interchange verribles."
The requirment for the dual n/w are as follows:-
No. of mesh is given n/w must be equal to the no. of node in given n/w.
The total impidence of given n/w must be equal to the total admeetance of a dual n/w.
The impeedence of common branch to two maches must be equal to the admeetance b/w two nodes in the dual n/w.
voltage source common to both the loop must be represented as a current source b/w two nodes.
The switch opening at t=0 in given n/w must be shown as switch closeing at t=0 in dual n/w.
Element and Dual Element:-
"It an inductence is crossed in the original n/w by drowing a line b/w dots then draw with capacitence b/w the node in the dual network."
Qus:-Draw the dual n/w of the?
"principle of duality ony implies that ckt eq. are of the same mathematical form and the dual n/w be have similarly but with interchange verribles."
The requirment for the dual n/w are as follows:-
No. of mesh is given n/w must be equal to the no. of node in given n/w.
The total impidence of given n/w must be equal to the total admeetance of a dual n/w.
The impeedence of common branch to two maches must be equal to the admeetance b/w two nodes in the dual n/w.
voltage source common to both the loop must be represented as a current source b/w two nodes.
The switch opening at t=0 in given n/w must be shown as switch closeing at t=0 in dual n/w.
Element and Dual Element:-
Procissor to find dual of a n/w:-
- Let the given n/w have l no. of message place a dot inside each mesh and no. the as {1,2,3,4,5 etc.} place and extra dot out side the n/w and denoted by zero.
- The dot place inside original n/w . The dot place external to the n/w represanted the refferance node of the dual n/w.
- The consist and the dual n/w draw "l"no. of nodes spretaly and no. them {1,2,3,4,5 etc.} also draw the refrence node and denote it by zero.
- In the original network draw all posible line from dot to dot by crossing each element only one time.
- Each line b/w two dot crossing an element in orignal n/w can be reprasented as the branch in the dual n/w by drawing a branch b/w two crossponding nodes with dual of element crossed for ex-
"It an inductence is crossed in the original n/w by drowing a line b/w dots then draw with capacitence b/w the node in the dual network."
Qus:-Draw the dual n/w of the?