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100 | cuapter s Summary » Nodal analysis for an N-node circuit » Select one node in the N-node circuit as the reference node. Assume that the node voltage is zero and measure all node voltages with respect to this node. > Ifonly independent current sources are present in the fiet- work, write the KCL equations at the N ~ 1 nonreference nodes. If dependent current sources are present, write the KCL equations as is done for networks with only indepen- dent current sources; then write the controlling equations, for the dependent sources. } Ifvoltage sources are present in the network, they may be connected (1) between the reference node and a nonrefer- ence node or (2) between two nonreference nodes. In the former case, if the voltage source is an independent source, then the voltage at one of the nonreference nodes is known. If the source is dependent, it is treated as an independent source when writing the KCL equations, but an additional constraint equation is necessary. In the latter case, if the source is independent, the voltage between the two nodes is constrained by the value of the voltage source and an equation describing this con- siraint represents one of the N — | linearly independent equations required to determine the N-node voltages. The surface of the network described by the constraint equa- tion (i.e., the source and two connecting nodes) is called a supernode. One of the remaining N — | linearly indepen- dent equations is obtained by applying KCL at this su- pemode. If the voltage source is dependent, it is treated as an independent source when writing the KCL equations, but an additional constraint equation is necessary. Problems SECTION 3.1 BTV HCH NODAL AND LOOP ANALYSIS TECHNIQUES Loop analysis for an N-loop circuit One loop current is assigned to each independent loop in a circuit that contains N independent loops. If only independent voltage sources are present in the net- work, write the N linearly independent KVL equations, one for each loop. If dependent voitage sources are present, write the KVL equations as is done for circuits with only independent voltage sources: then write the controlling equations for the dependent sources. If current sources’are present in the network, either of two. techniques can be used. In the first case, one loop current is selected to pass through one of the current sources. This is done for each current source in the network. The remaining loop currents (N — the number of current sources) are de- termined by open-circuiting the current sources in the net- work and using this modified network to select them. Once all these currents are defined in the original network, the N-loop equations can be written. The second approach is similar to the first with the exception that if two mesh cur- rents pass through a particular current source, a supermesh is formed around this source. The two required equations for the meshes containing this source are the constraint equations for the two mesh currents that pass through the source and the supermesh equation. If dependent current sources are present, the controlling equations for these sources are also necessary. Ideal op-amp model For an ideal op-amp, i, = i, = Oand v, = v_. Both nodal and loop analysis are useful in solving circuits containing operational amplifiers. 3.1 Find /,, in the circuit in Fig. P3.1 using nodal analysis. 12kaS 4) 3kO Jy Figure P3.1 3.2 Find /, in the circuit in Fig. P3.2 using nodal analysis. 3k Cd) 5k 10mA Figure P3.2 
