1. Level 2 Electromagnetism Laboratory Experiment
Ernestas Lucinskas
22nd January 2013
Transmission
lines
Transmission Lines [TL] /01/2013

2. Transmission Lines [TL] 22/01/2013
Summary
Objectives
Preface Theory:
What are Transition Lines?
Reflections and Standing Waves
Measuring the speed of light
Setup of the Equipment
Summary of the results
Analysis
Finale
Transmission Lines [TL] /01/2013

3. Transmission Lines [TL] 22/01/2013
Objectives:
Inspect the effect on pulses caused by closing the line with different electronic components, leaving an open or closed circuit.
Find and explain the effect caused by interference of the outcoming and reflection signal.
Estimate the speed of light and EM waves within the line.
Transmission Lines [TL] /01/2013

4. What are Transmission lines?
It is any structure which is designed to carry electricity or an electrical signal over large distances with minimum losses and distortion.
A uniform transmission line will have constant inductance per unit length [L] and capacitance per unit length [C].
The motion of EM waves within the line can be described by Traveling wave equation.
Waves can travel back and forward along the line.
Transmission Lines [TL] /01/2013

5. Reflections and Standing Waves
The forward traveling wave can be produced by connecting a signal or pulse generator to one end of the line and the backward traveling wave will be the reflection incident wave at the termination point (discontinuity) of the line.
The reflection coefficient [ρ] can be expressed
as the ratio of the reflected and incident voltage
[eq.2] and assuming that x=0 at the termination
point the amount of reflection comes to be directly
proportional to the
difference of
impedance .
Transmission Lines [TL] /01/2013

6. Measuring the Speed of Light
Two different methods to measure the Speed of Light [c]:
Measuring the time [τ] between the incident and reflected pulse.
And since the speed of light is defined by [c].
The final expression after substitution is [cf].
Estimating the phase displacement [k] (Impedance mismatch theory)
𝑐= 1 𝜀 0 𝜇 0
= 2𝜋𝑓 𝑘
𝑘= 𝜔 𝑐
𝑐= 𝜔 𝑘
Transmission Lines [TL] /01/2013

7. Transmission Lines [TL] 22/01/2013
Setup of the Equipment
Pulse generator (Lyons Instruments PG 73N)
Signal generator (UoS Appliance no. SW39)
Digital Oscilloscope (Tektronix TDS-1002B)
Coaxial Transmission Lines (22.85m / 20m)
Capacitor (1 000 pf)
Resistor (50Ω)
Coil (2.2 μH) 4 2 1 4
Transmission Lines [TL] /01/2013

8. Transmission Lines [TL] 22/01/2013
Summary of the Results
After connecting all the components together the scale of the oscilloscope was set to be 0.5V/0.25μs (unit measure in graphs).
The pulse is set to be 60ns long and delayed by 900ns.
The amplitude of the signal observed in all cases is 1V.
The sketches of the oscilloscope display when the line is terminated by the following options:
Open Circuit ( ρ = +1)
Short Circuit ( ρ = -1 )
Resistance ( ρ = 0 )
Capacitor ( ρ = +1)
Coil ( ρ = -1 )
Transmission Lines [TL] /01/2013

9. Transmission Lines [TL] 22/01/2013
Summary of the Results
The peak to peak voltage has been measured on the tapping points along the coaxial cable attached to the wooden board.
It was estimated that phase shift of the wave [k] is roughly equal ¼.
Speed of light values were estimated with 2 different methods:
𝑐 0 = 2𝑙 μ ε 0 𝑡 =294,925,453 ±3.4%𝑚/𝑠
Measuring the time between
pulse and reflection
𝑐= 𝜔 𝑘 = 2𝜋𝑓 𝑘 =299,079,620±2.5% 𝑚/𝑠
Phase shift
Transmission Lines [TL] /01/2013

10. Transmission Lines [TL] 22/01/2013
Analysis
The reflections of the pulses came as predicted in theory for open and short circuit termination. No reflection was observed while terminating the line with the load matching impedance (50Ω Resistor). Coil and capacitor case showed to have an extra peak in the middle that was caused due to the reflection of the electronic component itself and was delayed by ~1 μs. Errors are small in this part as it is easy to zoom in the display of the oscilloscope to get accurate readings.
Transmission Lines [TL] /01/2013

11. Transmission Lines [TL] 22/01/2013
Analysis
The Peak to Peak Voltage graph on different tapping points looks quite sharp and scattered, but it is still possible to estimate the phase shift.
On the tapping we measure the combined wave. Superposition principle can explain the significant increase and decrease of the amplitude.
The signal strength is decreasing with time due to decrease in resistance.
Transmission Lines [TL] /01/2013

12. Finale Successful Experiment
We observed nice phase changes of reflections.
Nice relationship of Pk-Pk Voltage across the line
Small errors in estimation of the Speed of Light
Finale
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13. Transmission Lines [TL] 22/01/2013
Acknowledgments
Special thanks to:
Samuel Beeke
Lab Technicians
Demonstrators
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14. Transmission Lines [TL] 22/01/2013
Questions?
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