ECE 391: Suggested Homework Problems

Transcription

1 ECE 391: Suggested Homework Problems Cascaded Lines 1. Two lossless transmission lines are connected in tandem through a series resistance as shown in figure 1. vr(t) 10 Zo=60 36 amlitude v,1=10cm/ns v,2=20cm/ns 5km 5km Figure 1: Problem 1 (a) Determine the60 delay time of each line; (b) determine the reflection and transmission coefficients (ρ 11, ρ 22, ρ 12, ρ 21 ) at the junction between the two lines; (c)draw a lattice matching diagram and secify Zo=60 the voltage and current of each wave comonent u to 1 t = 80usec; (d) lotamlitude the voltage across the 10Ω series resistor as a function of time for 0 t 80usec; v,1=20cm/ns v,2=15cm/ns (e) determine the steady-state voltage across the 36Ω load resistor. 20m amlitude t f1 =? t f2 =? 25 Line 1 Line 2

2 10 Zo=60 36 amlitude v,1=10cm/ns v,2=20cm/ns 2. Two lossless transmission lines are connected in tandem as shown in figure 2. Initially, assume that the end of line 1 is directly connected to the inut of line 2. (a) Determine the voltage at the junction 5km of the two lines for 0 t5km 310ns; (b) Design a matching such that no reflected waves aear at the 1Ω terminating resistor. Determine the steady-state voltage across the terminating resistor as well. 60 Zo=60 matching 1 amlitude v,1=20cm/ns v,2=15cm/ns 20m amlitude Figure 2: Problem 2 25 t f1 =? t f2 =? Line 1 Line 2

3 matching Zo=60 1 amlitude v,1=20cm/ns v,2=15cm/ns 3. Two lossless transmission lines with different characteristic imedances are connected through a consisting of three resistors. The delay times of the lines are unknown. Line two is terminated in an unknown resistance 20m. amlitude t f1 =? t f2 =? 25 Line 1 Line 2 Figure 3: Problem 3 t time t = 0, a 12V battery is connected to the inut of line 1 through an unknown resistor R g. The voltages at the inut of line 1 (- ), and line 2, (- ) are observed on an oscilloscoe as seen in figure 4 below. V v(b1) v(a1) V time ns Figure 4: Problem 3

4 5km 5km (a) Determine the flight times t f1, and t f2. (b) Determine the60 generator resistance R g. (c) Determine the reflection coefficient ρ 11 at the junction between the two lines. (d) Determine the transmission coefficient ρ 21 at the junctions between the two lines. matching (e) Determine the reflection coefficient Zo=60 ρ 22 and the transmission coefficient ρ 12 at the junction 1 between the two lines. amlitude (f) Determine the unknown terminating v,1=20cm/ns resistance. v,2=15cm/ns (g) Determine the steady-state voltages (i.e. for t ) at the inut of the first line (- ) and at the inut to the second line (- ). 20m 4. Two transmission lines with different characteristic imedances 25 are to be connected as shown. a) You have one variable resistor (0 R 200) with two terminals available. Determine the value of R and how you would connect t o the lines order to have a reflectionless system. R f1 =? t f2 =? t (b) ssume now that the value Line of 1 at the end of the second line Line is changed 2 such that reflections are generated amlitude at the end of theline. n additional resistor will be required at the boundary between the lines to maintain a relectionless system. Determine the connection and values of a two resistor connection that will maintain a reflectionless system. Figure 5: Problem 4 TITLE FILE: PGE

5 5. For the cascaded line given below, find: (a) ρ S (b) ρ L (c) ρ 11 (d) ρ 21 (e) ρ 12 (f) ρ 22 (g) Plot the voltage at and for t = 0 to t = 12ns on the grah below. Td=2ns 41.6 Td=2ns 1u( ) t (volts) R 1 L V, V t (ns) Figure 6: Problem 5 TITLE FILE: PGE OF REVISION: DRWN Y:

6 6. Two lossless transmission lines are connected through a matching at their junction. Draw the voltages at the inut terminal (a1) of and the outut terminal of (b2). matching vin a1 a2 25 b1 b2 2u(t) volts 225 td = 4ns td = 2ns 1 a1 a2 b1 2 b2 (a) Incident wave at inut to : (b) ρ S (c) ρ L (d) ρ 11 2u(t) (e) volts ρ 21 (f) ρ 22 (g) ρ 12 Rs td=5ns 0 Zr z 25 Lt 125nH (h) On the grah below, draw the voltages at the inut terminal (a1) of and the voltages at the outut terminal (b2) of. Fill in the X and Y axis values. v(z=0,t) t/nsec (i) [4] Determine the steady-state voltages (t = ) at the inut to the first line (a1 and a1 ) and the outut of the second line (b2 and b2 ).