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IN ORDER TO ANALYZE A CIRCUIT WHICH HAS ne ELEMENTS, 2-ne EQUATIONS WITH 2-ne UNKNOWNS NEEDS TO BE SOLVED.
COULD IT BE POSSIBLE TO SOLVE (ANALYZE) A CIRCUIT WITH LESS THAN 2ne NUMBER OF EQUATIONS ?
YES BUT UNKNOWNS SHOULD ALSO BE REDUCED AS MANY AS EQUATIONS.
THERE ARE TWO SOLUTIONS:
MESH-CURRENT METHOD
NODE-VOLTAGE METHOD
ASSUME THAT FOR EACH MESH THERE IS A CURRENT
SUCH THAT EACH ELEMENT'S CURRENT CAN BE WRITTEN IN TERMS OF MESH CURRENTS.
IF AN ELEMENT IS IN TWO MESHES (ELEMENT "B" IN THE FIGURE),
ELEMENT B'S CURRENT IS THE SUM OF THE MESH CURRENTS
IF AN ELEMENTS IS IN ONE MESH ONLY (ELEMENT "A" IN THE FIGURE)
AND ELEMENT CURRENT REFERENCE AND MESH CURRENT DIRECTION IS THE SAME
STEP 1
Write independent KVL equations:
number of KVL equations: (ne-nd+1)
Unknowns: ne elements voltages.
STEP 3
Substitute elements currents for mesh currents
Unique solution
In step 2,
if an element voltage cannot be substituted for its current
then
Supplementary equation is written by
the definition relation of the new introduced voltage unknown which could be Vıs ,Vcccs or Vvccs.
In this definition relation all the variables should be transferred to mesh currents.
STEP 2
Using elements definition relations, substitute elements voltages for elements currents;
Once the linear equations are solved, all the mesh currents and new introduced unknowns (if any) are found.
This solution is unique since number of equations is equal to number of unknowns.
It is possible directly write the third step mesh current equations! write a rule for that.
What happens if an independent source is not DC but AC, such as VB=10sin(2t+60)?
What can yo say about elements currents and voltages depend on what?
NODE-VOLTAGE: THE VOLTAGE MEASURED BETWEEN A NODE AND REFERENCE NODE (GROUND) IS CALLED THAT NODE-VOLTAGE.
ASSUME THAT FOR EACH NODE THERE SHOULD BE A VOLTAGE (NODE-VOLTAGE) SUCH THAT
RULE:
ELEMENT'S VOLTAGE (Va) =
=[Element's (+) related terminal node-voltage, (vd1)] -[Element's (-) related terminal node-voltage(vd2)]
STEP 1
Write the independent KCL equations
In step 2,
if an element current cannot be substituted for its voltage
then keep this element current as a new unknown ( these could be currents of independent/dependent voltage sources i.e Ivs ,Icccs, Ivccs).
Supplementary equation is written by
the definition relation of the new introduced current unknown which could be Ivs ,Icccs, Ivccs.
In this definition relation all the variables should be transferred to node-voltages.
STEP 2
Substitute elements current for element voltages by using elements definition relations
STEP 3
Write elements voltages in terms of node-voltages (as explained two frame back)
Once the node-voltages found
Vd2=29.8V, Vd3=19.2V, Vd4=16.9V
It is possible directly write the third step node-voltage current equations! write a rule for that.
What happens if independent source not DC but AC, such as 10sin(2t+60)?
What can yo say about elements' currents and voltages depend on what?
A simple analysis of resistive circuits can be done
Mesh current method:
Level 1:
Level 2:
Node-voltage method:
Level 1:
Level 2:
Which method is chosen when?why?