KCL and KVL independent equations - Solutions - Huaqiang Electronic Network

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The so-called general method of circuit analysis refers to the general method of solving any circuit, especially the current and voltage of each branch in a complex circuit. For a circuit with 6 branches of n nodes, there are 6 branch voltages and 6 branch currents to be solved, that is, there are 26 variables to be sought. This requires 26 separate circuit equations with six branch currents and six branch voltages as variables. Taking the branch current as a variable, the KCL can be used to list (nl) independent node current equations for n nodes, and it is an arbitrary (nl) node current equation. The so-called independent node equation means that no equation can be linearly represented for other equations. When the KCL current equation is listed for the nodes in turn, the new equation must contain at least one new branch current. However, the (nl) independent node current equation cannot solve for 6 branch currents. Therefore, this (nl) independent node current equation is incomplete. Using the six branch voltages as variables, the KVL is used to list the b-(nl) independent KVL voltage equations for the closed loop in the circuit. These voltage equations each contain at least one new branch voltage to ensure the independence of the equation. However, b-(nl) independent voltage equations cannot solve for six branch voltage variables. Therefore, b-(nl) independent voltage equations are incomplete. The above equations are listed as independent variables by branch current and branch voltage.
(nl)+[b-(nl)]=6 means that there are 6 independent circuit equations, and 26 circuit variables cannot be solved. In order to solve 26 independent variables, for the circuit with given circuit structure and component parameters, the branch current and branch voltage can be used as variables to list the branch VAR equations of the relationship between the six branches and the branch current. The branch VAR equations are independent circuit equations. Therefore, (nl) independent node current equations, b-(nl) independent loop voltage equations, and 6 branch volt-ampere relationship equations have 26 independent circuit equations. From these 26 independent circuit equations, 26 pending branch currents and branch voltage variables can be solved. This method of analysis is called the 26 method.

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