Download 6 Coax Cable in t and f domains

Electromagnetic Waves – ECEN 3410 – Prof. Wagner
Homework #5b - Circuit analysis of Transmission Lines and Coax cable mini-lab
1-5 Due Wednesday April 5, 2017. 6 due April 12, 2017.
1. 12.26 a) Resistive line impedances on Smith chart
2. 12.28 Quarter wave matching on Smith chart
3. 12.33 TDR of buried cable
4. 12.38 Pulse response of open circuited line
5. 12.47 line terminated in R k C
6 Coax Cable in t and f domains
Equipment and parts (available in the circuits lab):
• function generator
• a 2-channel oscilloscope
– with a 50-ohm and a high-impedance input
• a 10-m long 50-ohm coaxial cable;
• 2 shorter coaxial cables; 2 Tee connectors,
• 2 low-inductance potentiometers and an ohmmeter.
6.1 Measuring cable length
One of the most important techniques for measuring transmission line circuits is time domain
reflectometry (TDR), or cable radar. Usually, one would buy an instrument designed for this purpose,
but we will put one together using the parts above. Connect the output of the signal generator to
channel 1 of the scope. You will need to trigger the scope externally with the signal generator trigger
out. Make sure the input impedance of channel 1 is set to a high value, so as not to disturb the
measurement of waves at an intermediate point on the line.
1. Now use a Tee connector at channel 1 and connect a long (roughly 10m) piece of coaxial cable
from channel 1 to channel 2 of the scope, as in the figure. Set the function generator to a
1-MHz square wave with 1-V amplitude. Set the input impedance of channel 2 of the scope to
50 ohms. Sketch the scope display. If the relative permittivity of the dielectric in the line is
r = 2.5, calculate the length of the cable from the measured time delay between the pulse at
the generator end and the pulse at the load. (Instead, you could use a very short, e.g., 20-ns,
pulse if your signal generator has this capability.)
2. Now set the input impedance of channel 2 of the scope to a high value (i. e., remove the 50Ω
load). Sketch what the scope display looks like now. How has it changed, and why does it have
this new appearance?
3. The input impedance of the scope is typically 1MΩ in parallel with a 20 pF capacitor (read off
the exact values from your scope input). This capacitance is connected in parallel at the end
of the cable. What does it do to our length measurement?
6.2 Measuring resistive and reactive loads
1. Set the signal generator to pulse mode. We want the pulse length to be long, so that any
reflected pulses die out before the next pulse is generated. For example, you can set the pulse
to be 5µs long with a 50% duty cycle and 1V amplitude. Set the horizontal scale on the scope
so that you observe one cycle and you can see the rising edge of the pulse well. Set the input
impedance of channel 2 to its high value. Ex plain the amplitudes and delays of the pulses
observed on both channels.
2. Now connect a Tee to channel 2 and connect a low-inductance pot resistor in parallel with the
scope input using a Tee connector. Change the value of the pot resistance until you get no
reflection. Measure the value of the resistance with an ohmmeter. What does this tell you?
3. Set the pot resistance to some value larger than 50 ohms (e.g., 75) and then to a value smaller
than 50 ohms (e.g., 25). Calculate the values of th e resistance from measurements of the
reflected pulse amplitude. How close are the TDR and ohmmeter resistance measurements?
Also try a wire shorting the center and outer conductor to make a short and sketch the result.
4. Finally connect a capacitor at the end of the long cable. Sketch the waveform observed on
channel 1 for two capacitor values. Calculate the value of the capacitance and show your work.
6.3 Measuring cables in the frequency domain
For this part of the project, set the function generator to give a sinusoidal output at a 30-MHz
frequency and 0.5V amplitude. Unless otherwis e noted, terminate channel 1 with a high impedance,
and channel 2 with 50 ohms. This is done to provide a matched load at the end of the transmission
line (channel 2) while measuring an intermediate position (channel 1) without disturbance to the
waves on the line. First disconnect the long cable from channel 1, and temporarily connect a 50 ohm
resistor load there. Sketch the waveform you see on channel 1 and record carefully the position (in
time) of the peak of the sine wave (for ex ample, set it to be in the middle of the screen). We need
this information, as well as external triggering, in order to be able to track phases throughout the
lab.
1. Now attach the long piece of cable back to channel 1, resetting channel 1 to a high impedance.
What does the waveform on channel 1 look like compared to the one in the previous question?
Explain. Sketch the voltage observed on channel 2 and compare it to that on channel 1. You
should see two differences; the amplitude and the phase. Measure the change in phase noting
what portion of the cycle it has changed from channel 1. How many wavelengths is the cable
long (remember the relative dielectric constant of the cable filling is 2.5)? Based on that, what
phase change should you get knowing that a one-wavelength long cable produces 360 degrees
of phase change?
2. Inspect the amplitude on channel 2. How large is it? Explain. Remembering that voltage in a
cable varies like exp(−αz), calculate the attenuation coefficient α knowing the length z of your
cable. Does the approximate expression for α hold in this case?
3. The voltage (and current) along the cable are a result of forward and backward (reflected)
waves, which add destructively and constructively along the cable. It would be nice if we could
measure the voltage all along the cable, but we cannot do that. However, we can do something
that is nearly equivalent: we can change the frequency, so that the cable looks like it is changing
the number of wavelengths long. Terminate the long piece of cable in an open circuit. At what
frequency is the cable one wavelength long? Set the signal generator frequency to 1/20 of this
frequency. Compare the waveforms observed on channels 1 and 2 and explain. Now set the
frequency so that the cable is λ/4 long. Sketch the waveform on channel 1 and explain. Repeat
for frequencies where the cable is λ/2, λ/3, λ/4 and 1 λ long and explain your result each time.
4. If your signal generator can sweep over this frequency range, set it up to slowly sweep and
observe and describe the resulting phase and amplitude.