1、4.4 Circuit Equivalence The circuit shown in Fig. 1 can be regarded as a circuit which consists of two loops where the loop currents i1 and i2 are circulated independently. s1v s2v01R2R 3R1i 2i Figure 1: A typical circuit for loop analysis. From Fig. 1, both i1 and i2 flow through R2, so the current
2、 of R2 is i1+i2. According to KVL, we can obtain ( )( )s1 1 2s2 3 2111222v R Rv R Riiii ii= + += + + (1) i1 and i2 can be solved from (1). Then any voltage and current in the circuit we care can be got. This method for circuit analysis is called loop current method. Reorganizing the equation (1), we
3、 can get standard loop current equations: ( )( )1 2 2 s12 2 322 s1 21R R R vR ii viRRi + + =+ + = (2) There are two steps when we analyze circuit by using loop current method. Step 1: Choose the loops. Step 2: Set up the KVL equation for each loop. So how do we choose the loops? Usually we choose me
4、shes in a circuit as the loops, as shown in Fig. 1. Lets give another more complex example, as shown in Fig. 2. s1v s2v1R 2R3R1i 2i3i 4R6R5R Figure 2: A complex circuit for loop analysis. We can write the KVL equations for three meshes: ( ) ( )( ) ( )( ) ( )2s 1 1 2 33 4 4 s 26 4 21 1 1 33 3 332212 12000iiiiiiv R R RR R R viiiR iiRiiiiR + + + = + + + =+ + = (3) Reorganize (1) into standard loop current equations, then the loop currents i1, i2 and i3 can be solved.
