1 ECE 3144 Lecture 32 Dr. Rose Q. Hu Electrical and Computer Engineering Department Mississippi State University

2 Reminder from Lecture 31 Impedance Z: –The two-terminal input impedance Z, is defined as the ratio of the phasor voltage V to the phasor current I => Z=V/I –If Z 1, Z 2, …., Z n are connected in series, the equivalent impedance Z s is Z s = Z 1 +Z 2 +…+Z n –If Z 1, Z 2, …, Z n are connected in parallel, the equivalent impedance Z p is given by Admittance Y: –Admittance Y of a circuit element is defined as the ratio of phasor current to phasor voltage. => Y=I/V –If Y 1, Y 2, …, Y n are connected in series, the equivalent admittance Y s is –If Y 1, Y 2, …, Y n are connected in parallel, the equivalent admittance Y p is Phasor diagram Y p = Y 1 +Y 2 +…+Y n

3 Solution techniques for ac steady state analysis For relatively simple circuits, use Ohm’s law: V = IZ KCL and KVL –Current divider and voltage divider For more complicated circuits with multiple sources, –Nodal and loop analysis –Superposition and source transformation –Thevenin/Norton Theorem –Matlab –Pspice

4 Voltage divider: multiple Z in series + -

5 Current divider: multiple Z in parallel.. Where Y i = 1/Z i

6 Nodal analysis and loop analysis Nodal analysis –Select one node in the N-node circuit as the reference node. –Write the KCL equations at the nonreference nodes the same way as what was done in the dc resistive networks. –Solve the phasor voltage for each node. Loop analysis –One loop phasor current is assigned to each independent loop in a circuit that contains N independent loops. –Write KVL equations for each loop the same way as what was done in the dc resistive networks. – Solve the phasor current for each loop.

7 Superposition and source transformation Superposition: –In a network containing multiple independent sources, each source is applied independently with the remaining sources turned off. –To turn off a voltage source, replace it with a short circuit; and to turn off a current source, replace it with an open circuit. –The results are then added algebraically to obtained the solution. Source transformation –A voltage source in series with an impedance can be transformed into a current source in parallel with the impedance, and vice versa. –Repeated application systematically reduces the number of circuit elements.

8 Thevenin/Norton Theorem Thevenin theorem –Remove the load and find the phasor voltage Voc across the open terminals. –Determine the Thevenin equivalent impedance Z TH at the open terminals. –The load is now connected to the Thevenin equivalent circuit, consisting of Voc in series with Z TH. Norton theorem –Remove the load and find the phasor current Isc across the short-circuited terminals. –Determine the Norton equivalent impedance Z N at the open terminals. –The load is now connected to the Norton equivalent circuit, consisting of Isc in parallel with Z N.

9 Homework for lecture 32 Problems 7.38, 7.47, 7.53, 7.57, 7.61, 7.68, 7.72(no Matlab result is required) Due April 8