ECE 301
Fall Semester, 2005
HW #8
wlg
Practice: No turn-in
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(1) You are given the ideal transformer of Figure 1. (a) Find I1. Ans I1 = 3.07∠39.81o A.
(b) Find Vo. Ans Vo = 3.07∠39.81 V.
2Ω
-j2 Ω
-j2 Ω
2Ω
1:2
+
I1
•
+
V1
12∠0 V
_
_
•+
I2
V2
2Ω
_
+
Vo
_
ideal
Figure 1: Circuit for problem 1.
(2) Find Io and Zab in the linear transformer of Figure 2. Ans: Io = 2.2∠-4.88 A; Zab = 1.5085∠17.9o Ω
4Ω
a
k = 0.5
1Ω
3Ω
•
Io
+
0.5 F
12cos2t V
_
•
1H
2Ω
b
•
Figure 2: Circuit for problem 2.
linear
transformer
•
1H
2H
(3) Determine the input impedance looking into terminals a-b of the linear transformer circuit
shown in Figure 3. Ans: Zab = 0.1989 – j9.7 Ω
j12 Ω
-j2 Ω
j5 Ω
a
•
•
Z
j20 Ω
-j6 Ω
j30 Ω
4Ω
b
linear
transformer
Figure 3: Circuit for problem 3.
(4) (a) Find I1 and I2 in the ideal transformer of Figure 4. Ans:I1 = 1.07∠5.88o A, I2 = 0.536∠185.9o A
(b) Switch one of the dots in the circuit of Figure 4. Find I1 and I2 again. Ans:I1 = 0.576∠-17.1o A,
I2 = 0.288∠-17.1 A.
j16 Ω
+
10 Ω
12 Ω
1:2
I1
•
16∠60o V
_
-j8 Ω
I2
+
10∠30o V
•
_
ideal
transformer
Figure 4: Circuit for problem 4.
(5) A transformer is used to match an amplifier with an 8 Ω speaker load as shown in Figure 5.
The Thevenin equivalent of the amplifier is VTh = 10 V, ZTh = 128 Ω.
(a) Find the required turns ratio for the maximum energy power transfer to the speaker.
Ans: n = 0.25
(b) Determine the primary and secondary currents. I1 = 39.06 mA, I2 = 4xI1
(c) Calculate the primary and secondary voltages. V1= 5 V, V2 = 1.25 V
1:n
Amplifier
•
•
speaker
8Ω
Circuit
ideal
Figure 5: Diagram for problem 5.