Problems

1. In Fig. 4, Zi is a 0.05-microfarad capacitor, and Z₂ is a 0.12-henry inductor. Calculate the values to be used for midseries and midshunt terminations such as shown in Figs. 5(a) and 5(b).

2. Calculate the values for the equivalent T section and the equivalent π section of a network such as Fig. 4 in which Z₁ = 0.15 henry, and Z₂ = 0.5 microfarad.

3. In Fig. 9(a), Z_A = 100 ohms resistance, Z_R = 50 ohms resistance, and Z_c = 100 ohms resistance; Z_D = 0.05 microfarad, Z_E = 0.05 microfarad, and Z_F = 0.01 microfarad; Z₇ = 450 ohms resistance and 0.002 henry inductance, E_g = 58 volts open circuit at 1000 cycles, and Z_L = 275 ohms resistance. Calculate the magnitude and phase angle of the current through Z_L, the angle to be measured with respect to the generator voltage.

4. A transformer has the following characteristics L_p = 0.159 henry, R_P = 193 ohms, M = 0.1585 henry, secondary same as primary. For a frequency of 1000 cycles determine the equivalent unbalanced T and π networks. What is the coefficient of coupling? The turns ratio? The mutual impedance?

5. A generator has an internal impedance of 600 ohms resistance and an open-circuit voltage of 26.4 volts at 1000 cycles. It is connected to a load resistance of 768 ohms. Calculate the current through the load resistor using Thévenin's theorem and Norton's theorem.

6. Find the reflection loss for the circuit of Problem 5.

7. Design a pad to insert 7.5 decibels loss in a 600-ohm circuit.

8. Design a low-pass constant-A; filter for a 600-ohm circuit and a cutoff at 5000 cycles.

9. Design a high-pass constant-k filter for a 600-ohm circuit and a cutoff at 100 cycles.

10. Design a composite filter for a 600-ohm circuit, for a cutoff frequency of 5000 cycles, and an a = 1.2.