The two-port in Figure 2.10 consists of three two-ports placed in series. The

Chapter 2, Problem 45

(choose chapter or problem)

The two-port in Figure 2.10 consists of three two-ports placed in series. The transmission matrices are indicated. (a) What is the transmission matrix of the composite two-port? (b) If the input voltage is five volts and the current is two amps, determine the output voltage and current. 2ps 1 2 1 2 + [-n + olts V2 ! ::: ,;;;: ,;;;: f Sv 1 2 1 2 Figure 2.10 (d) If A 2 = A then A' = A for all positive integer values ofr. (e) If X1 is a solution of AX = B1 and X2 is a solution of AX= B2then X1 + X2is a solution ofAX = B1 + B2 Two-Ports 44. Determine the transmission matrices of the two-ports in Figure 2.9. Hints: (a) V 1 = V 2 since terminals are connected directly. Current through resistance R is I 1 - I 2 Drop in voltage across R is V 1 (b) Current through R1 is /1 - 12 Drop in voltage across R 1 is V 1 Current through R2 is I 2 Drop in voltage across R2is V1 - V2. (c) Current through R1 is Ji. Drop in voltage across R1 is V 1 - V 2 Current through R2isI1 - I 2 Drop in voltage across R2 is V 2 45. The two-port in Figure 2.10 consists of three two-ports placed in series. The transmission matrices are indicated. (a) What is the transmission matrix of the composite two-port? (b) If the input voltage is five volts and the current is two amps, determine the output voltage and current. (c) 1 2 1 1 1 2 V2 V1 Rl R2 V2 1 2 1 1 1 2 _ 13 13 14 - D J f [ 3 -1] + 3 -1 1 v ...;; f ...; ::: ! 4 13 13 14