ECE 301 Fall Semester, 2005 HW #8 wlg Practice: No turn-in Name __________________ Print (last, first) (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.