Transcript ECE 3144 Lecture 4

ECE 3144 Lecture 32
Dr. Rose Q. Hu
Electrical and Computer Engineering Department
Mississippi State University
1
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 Z1, Z2, …., Zn are connected in series, the equivalent impedance Zs is
Zs = Z1+Z2+…+Zn
– If Z1, Z2, …, Zn are connected in parallel, the equivalent impedance Zp is
given by 1
1
1
1
Zp

Z1

Z2
 ... 
Zn
• Admittance Y:
– Admittance Y of a circuit element is defined as the ratio of phasor current to
phasor voltage. => Y=I/V
– If Y1, Y2, …, Yn are connected in series, the equivalent admittance Ys is
1
1
1
1


 ... 
Ys
Y1
Y2
Yn
– If Y1, Y2, …, Yn are connected in parallel, the equivalent admittance Yp is
Yp = Y1+Y2+…+Yn
• Phasor diagram
2
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
3
Voltage divider: multiple Z in series
+
-
n
Zs   Z j
j 1
Zi
Vi 
Vs
Z j
Vs
I
Zs
n
j 1
4
Current divider: multiple Z in parallel
....
n 1
1
 
Z p i1 Zi
Ij
Y j Is
N
 Yj
j 1
V  IsZ p
Where Yi = 1/Zi
5
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.
6
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.
7
Thevenin/Norton Theorem
• Thevenin theorem
– Remove the load and find the phasor voltage Voc across the open
terminals.
– Determine the Thevenin equivalent impedance ZTH at the open
terminals.
– The load is now connected to the Thevenin equivalent circuit,
consisting of Voc in series with ZTH.
• Norton theorem
– Remove the load and find the phasor current Isc across the
short-circuited terminals.
– Determine the Norton equivalent impedance ZN at the open
terminals.
– The load is now connected to the Norton equivalent circuit,
consisting of Isc in parallel with ZN.
8
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
9