Basic Circuit Theory Chpter12 Problems 1 Find the four Y parameters of the network shown in Fig. 12-19. + + -- L R1 ? V sI ? 2 ? I1 ? I 2 ? V S R Two port + + - - - + ?20 ?5 ?50 ?10 1 ? V TV ? 2 ? V ?40 Fig. 12-20 For prob.2. Fig. 12-19 For prob.1. 2 Let R = 1k , y =3 mS, y 12 = - 1 mS, y = 24 mS, y =0.5 mS, and R = 4 k? for the circuit shown in Fig. 12-20. Determine numerical values for: (a) voltage gain G V = / ; (b) current gain / and / ; (c) power gain G =P /P ; (d) input impedance Z = / ; (e) output impedance Z = / with = 0 and R = S ? 11 21 22 L 2 ? V 1 ? V ? 2 I ? 1 I ? 2 I ? S I P L S in 1 ? V ? 1 I out 2 ? V ? 2 I ? S I L ∞; (f) reverse voltage gain G = / with = 0 and R = VR 1 ? V 2 ? V ? S I L ∞. 3 (a) Find all the Y parameters for a two-port characterized by the equations: 6v 1 - 3i = 0 and 5v 2 = 12i 1 + 2i - 3v 1 . (b) Find new values for the Y parameters after a 5 2 2 ? resistor is added in series with one conductor of the output port. 4 For the amplifier circuit of Fig. 12-21, find the four Y parameters and the ratio of output power to that supplied by the ideal voltage source. DaLian Maritime University 1 1 - - + + + - ?10 1 ? V 10 xI ? ?100 ?30 2 ? V ?10 ?200 xI ? °0/ V L R A°0/ [Z] ?500 1 Fig. 12-22 For prob.5. Fig. 12-21 For prob.4. 5 The block in Fig. 12-22 is described by the following open-circuit impedance parameters: z 11 =100 , z 12 = - 500? , z = 1000? 21 ? , z =10k 22 ? . (a) If R = 5 k L ? , what is the rms voltage across it. (b) What value of R would result in maximum power delivered to R ? (c) What are the values of the Y parameters for the block? L L 6 Find the four hybrid parameters for each network shown in Fig. 12-23. ?k1 L R 1 ? V + sV ? 2 ? V ? + ? + ? [H] ++ - - 1 ? V 2 ? V ?10 h 11 =30Ω h 12 =0.02S h 21 =4 h 22 =0.02S Fig. 12-24 For prob.7. Fig. 12-23 For prob.6. Basic Circuit Theory Chpter12 Problems 7 The two-port shown in Fig. 12-24 has these hybrid parameter values: h 11 =1000? , h 12 = 0.0015, h = 100, h =100 21 22 μ S. Let =10 mV. (a) Find if R =10 kSV ? o 0∠ 2 ? V L ? . (b) Find the value of R , which result in maximum power being delivered to R . (c) What are z parameters for this two-port? L L 8 In the circuit shown in Fig. 12-25 the transmission parameters for each of two-port are given, find transmission parameters T for entire network. 9 Find the y 11 and y 22 for the two-port shown in Fig. 12-26. 10 Find the four Y parameters for the network of Fig. 12-27. + + -- ?20 ?2?5 ?10 1 ? V ?3 2 ? V ? ? 0 3 ?2 1 4 2 ? 3 3 ? ? ? ? ? ? ? ? Fig. 12-25 For prob.8. Fig. 12-26 For prob.9. DaLian Maritime University - ++ - ?25 ?100 1 ? V 2 2 ? V 1 ? I 1 ? I + - + - + - ? ? ? ? ][Y ?5 ?2 1 ? V 2 ? V V1 1 ? I 2 ? I Fig. 12-27 For prob.10. Fig. 12-28 For prob.11. 2 Basic Circuit Theory Chpter12 Problems Reference Answers to Selected Problems 1: (a) y 11 =125, y 12 =-62.5, y =-62.5, y =93.8 mS. 21 22 2: (a) G V =-3.2; (b) 0.299; (c) 0.222; (d) G =256; (e) Z =28.6 P in ? ; (f)Z =153.9 ; (g) G VR =0.25. out ? 3: (a) y =0.6, y =0.333, y =-2.1, y =0.5S; (b) y =1.6, y =0.0952, y =-0.6, y =0.1429S. 11 12 21 22 11 12 21 22 4: y 11 =25.3, y 12 =-1.21, y =-242.2, y =-31.3 mS; G =23.84. 21 22 P 5: (a) 186.1V; (b) 10.83 k ; (c) y =6.67, y =0.333 y =-0.667, y =0.0667 mS. ? 11 12 21 22 6: h 11 =7.5? , h =-0.05, h =1, h =0.04S. 12 21 22 7: (a) –4V; (b) 40 k ; (c) z =-500, z 12 =15, z =-10 , z =10 4 ? 11 21 6 22 ? . 8: T= . ? ? ? ? ? ? 126 108 9: 141.8 and –76.6 mS. 10 Y= (S). ? ? ? ? ? ? ? ? 03.004.0 04.004.0 DaLian Maritime University 3