Lab 1: Pulse Propagation and Dispersion

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ab 1: Pulse Propagation and Dispersion NAME NAME NAME Introduction: In this experiment you will observe reflection and transmission of incident pulses as they propagate down a coaxial transmission

1 ab 1: Pulse Propagation and Dispersion NAME NAME NAME Introduction: In this experiment you will observe reflection and transmission of incident pulses as they propagate down a coaxial transmission line You will observe the effects of matched and mismatched termination impedances on the amplitude and sign of the reflected pulses By measuring the time between the arrival of the incident and reflected pulses, you will calculate the length of the line By varying the pulse width you will observe the superposition of the incident and reflected pulses Control Settings: Scope Pulse Generator ertical Scale: 10 /div Frequency: 50 khz Horizontal Scale: 02 µs/div Pulse Width: 02 µs Amplitude: 4 Procedure: 1

2 1 Connect the pulse generator to both the oscilloscope and the transmission line eave the end of the transmission line open Use the control settings as a reference to display the incident and the reflected pulses on the oscilloscope (This should be set up for you but you should move the trace horizontally so that the initial pulse lines up with a vertical axis trace on the oscilloscope) Carefully measure the time delay between the incident and the reflected pulses You will use this information to calculate the length of the line The time delay between the incident pulse and the first reflected pulse: 2 τ = s ook up the cable characteristics on line You will see the type of cable stamped on the cable The website should give Z o, the characteristic impedance and, the inductance per unit length From these calculate C and thus calculate v ph, the phase speed on the line Z o = Ohms = Henries/m C = Farads/m Thus the phase velocity of the pulses is υ ph = The length of the line: m Using the expression in the book for C for a coaxial line, taking the magnetic permeability as the vacuum value 7 µ 0 4π 10 H / = m calculate the ratio of the outer conductor radius to the inner conductor radius and the relative dielectric coefficient of the insulator between the inner and outer conductors ε r = (Outer radius) /(Inner radius) = 2

3 2 Using the control settings as a guide, display the incident and reflected pulses on the scope Terminate the line with the various terminations provided Below note the type of termination used and carefully draw the incident and reflected (if any) pulses Please label oltage/div and Second/Div on your graph as you set up on the oscilloscope Termination: Short Theoretical reflection coefficient at the load is: Measured reflection coefficient at the load is: What causes the discrepancy between the measured and the calculated reflection coefficient? Termination: 50 Ω Did you see a reflected pulse? Why? Termination: 10 Ω 3

4 Theoretical reflection coefficient is: = Measured reflection coefficient is: = Why does the reflected pulse look different from the incident pulse? Termination: 100 Ω Measured reflection coefficient is: Theoretical reflection coefficient is: Termination: Open With an open termination on the line vary the width of the incident pulse and observe the effect of this change on the waveform displayed on the scope Draw the waveform below and explain briefly what has happened 4

et a transmission line having characteristic impedance Z 0 [Ω], attenuation constant α [m -1 ] and length l [m] be terminated in a load resistor R [Ω] et inc [] be the amplitude (magnitude) of the

5 et a transmission line having characteristic impedance Z 0 [Ω], attenuation constant α [m -1 ] and length l [m] be terminated in a load resistor R [Ω] et inc [] be the amplitude (magnitude) of the incident pulse at the generator, and ref [] be the amplitude (magnitude) of the reflected pulse at the generator The reflection coefficient at the load is R Z 0 Γ = R + Z 0 Therefore, the reflection coefficient magnitude of the load measured at the generator is: η = ref inc = Γ e 2αl From your measured η in the cases of short, 10 Ω, and 100 Ω loads, use the above equation to calculate the attenuation constant α = m -1 5

Pulse Transmission and Cable Properties ================================

PHYS 4211 Fall 2005 Last edit: October 2, 2006 T.E. Coan Pulse Transmission and Cable Properties ================================ GOAL To understand how voltage and current pulses are transmitted along