TITLE ECE 391: Suggested Homework Problems Reflections 1. Multiple digital devices wish to communicate over a shared 5Ω transmission line. Only one driver will be enabled at any time and any receiver may be listening. Each bidirectional driver/receiver pair on the line has an output impedance of (Zout < 2) and an input impedance of (Zin > 2KΩ). The input receivers logic one input threshold is V dd 2 and should not see voltages above Vdd. Determine what terminations if any are necessary at locations,,c and D, to create a reflection-free network. Show a circuit diagram for your design. Zo=5 Zo=5 Zo=5 C D rc Zo=1 Td=2.5ns Vsrc 2 PULSE source parameters: 3.3v amplitude, 1ns delay to first edge with 1pS tr and tf, 2ns pulse width, 5ns cycle time Figure 1: Problem 1 2. For the transmission line circuit shown in figure 2: R L 4 v,i 3V.5 15V 1 2 Vs rc 75 Vs(t)=2V U(t) Zo=5 Td=25ps open circuit 5 Zo=75, V T Figure 2: Problem 2 v Zo=75, Vp=.66c (a) draw a lattice diagram from 15 t = ns through t = 1.75ns. (b) simulate the circuit in R (t)=3v ngspice U(t) for 1.7ns showing the steps at the initial T rising edge at the driver end, and at the receiver end of the transmission line. 5V r =2m 6 FILE:
rc 75 open circuit Vs 3. Consider the transmission line circuit shown in figure 3 with V g (t) = 3u(t)(V ), R g = 15, Vs(t)=2V U(t) Z = 75, length r = 2m, and velocity factor v p =.66c. 15 (t)=3v U(t) Zo=75, Vp=.66c R T v 5V r =2m 6 Figure 3: Problem 3 (a) Draw a lattice diagram and plot the voltage and current waveforms at =, =.75 r, and = r for t 43nsec for the cases (i) R T =, (ii)r T = 15, and (iii) R T = 125. (b) Simulate the circuits in ngspice and compare with your results. (c) What are the final values of voltage and current (i.e., for t ) for the three terminations? 4. n uncharged, lossless coaxial transmission line with ɛ r = 4 is short-circuited at its far end ( = r ). t time t =, the near end of the cable ( = ) is connected through a series resistance R g to an ideal source of V g volts. finite portion of the voltage observed at the input (near end) of the line is shown below. shorter portion of the corresponding current is also shown. R L 4 v,i.5 3V 15V 1 2 3 t (usec) = = r n circuit R T Zo=75, Vp=2m/usFigure 4: Problem 4 damage Find the numerical values of: 5 (a) velocity of propagation, v p Rt (b) the length of the line, r 5 (c) the T-line characteristic impedance, Z (d) the reflection coefficient atd the generator and termination sides (Z g and Z t ) (e) the series v resistance at the source R g (f) the source voltage, V. (e) Draw a lattice diagram and complete the voltage and current waveforms up to time t = 25µsec. Specify the explicit 5V numerical values of voltage and current. 6 t (usec)
(f) Simulate the circuit in ngspice and compare your voltage and current waveforms obtained earlier with the Spice simulation results. (g) What are the final values of voltage and current (i.e., for t ) at the near end and far end?
5. For the following circuit: Vsrc rc 2 Zo=1 PULSE source parameters: 3.3v amplitude, 1ns delay to first edge with 1pS tr and tf, 2ns pulse width, 5ns cycle time Td=2.5ns R L 4 v,i 3V.5 15V 1 2 FigureZo=5 5: Schematic rc Td=25ps (a) Draw the lattice diagram75that shows the voltage at points open and circuit for 1ns. On your Vs lattice diagram, show the magnitudes of the reflections for both current and voltage and the5 total voltages at both and Vs(t)=2V. U(t) (b) Using your lattice diagram, draw a voltage versus time graph of the voltage waveforms at and. (c) Confirm the correctness of your waveforms in part b by running an ngspice simulation. v (d) Repeat all the above with R L = 2Ω. Zo=75, Vp=.66c 15 R (t)=3v U(t) T 5V Zo=75, V T r =2m 6
=1 1pS tr and tf, Td=2.5ns v,i 6. lossless R 3V L transmission line cable (Z = 5, vp = 2m/sec) is suspected to be damaged at an unknown 4 distance d from the.5input. The cable is terminated in a matched resistance R T = 5Ω. 15V In order to find the location of the damaged cable, a step voltage is applied at the input at time t =, and the voltage waveform is observed at the input of the cable. The step-voltage generator is matched to the transmission line (R G = 5). 1 2 3 t (usec) = = =5 Td=25ps open circuit 5 Zo=75, Vp=2m/us damage Rt 5 =75, Vp=.66c R T v 5V d r =2m 6 t (usec) Figure 6: Schematic and Waveform (a) What are the voltage and current amplitudes of the first outgoing wave? (b) Determine the generator voltage. (c) Determine distance d at which the cable is damaged. (d) Determine the voltage of the returning wave (reflected at the damaged location). (e) What is the reflection coefficient at the location of the damaged cable? (f) How would you model (equivalent circuit model) the damaged section of the cable? TITLE FILE: PGE OF REVISION: DRWN Y:
7. n engineer started the lattice diagram shown below but was distracted and never finished his work. Given the information below, find: (a) ρ L (b) R L (c) Z o (d) t d (e) R s (f) V s RS Zo=?, t d=? Vs RL t=ns 2.25V.3 t=1ns.7425v t=2ns.3713v t=3ns t=4ns Figure 7: Unfinished Lattice Diagram
8. For each waveform below at point, circle the correct circuit parameters. Dotted lines extending from a waveform indicate the waveform will continue its present behavior. Figure 8: Reflections at
9. Consider the circuit and spice waveform for Lossy point Coaxial Cable below. The generator launches the rising edge at 5ns. Find: Zo=75 (a) The flight time delay t f of the transmission line. HighPowered 75 (b) R S R Transmitter L (c) R 2 L = Zo=75 ntenna V1 1V t f =? R L Vsrc 2V rms Vsrc 1V @1Mh TITLE FILE: PGE
1. Consider the circuit below. is a lossless transmission line with Z o = 5Ω t d = 5ns. 1u(t) volt 25 Zo=5 td=5ns Rt 8 Zr (a) 1 (b) (a) Determine ρ s and ρ l. (b) Fill in the numerical voltage and current values for the first three wave components and add the time and length scales in the lattice diagram shown below. Include units as appropriate. a1 = a2 Zo=75 /meters 75 mystery 1u(t) volts termination 2nS 1 matching network vin 5 a1 a2 25 b1 T2 b2 time/nsec Zo=5 Zo=75 2u(t) volts 225 td 1 = 4ns td 2 = 2ns a1 a2 b1 b2 (c) Sketch the voltage at the beginning and end of the line ( = ) and ( = Z r ) for t 15ns. Include voltages and time on the axes. Indicate voltage levels that do not fall on the axis marks. v(=,zr) 2u(t) volts 75 Zo=75 td=5ns Rt 25 t/nsec Zr Lt 125nH